OPTIMISING THE MECHANICAL PROPERTIES AND MICROSTRUCTURE OF ARMOURED TEMPERED CONDITION

OPTIMISING THE MECHANICAL PROPERTIES AND MICROSTRUCTURE OF ARMOURED TEMPERED CONDITION
University of Pretoria etd, Kasonde M (2006)
OPTIMISING THE MECHANICAL PROPERTIES
AND MICROSTRUCTURE OF ARMOURED
STEEL PLATE IN THE QUENCHED AND
TEMPERED CONDITION
by
MAWEJA KASONDE
Submitted in partial fulfilment of the requirements for the degree
MASTER OF ENGINEERING
( Metallurgical Engineering )
in the Department of Materials Science and Metallurgical Engineering,
Faculty of Engineering, Built Environment and Information Technology,
University of Pretoria
December 2005
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University of Pretoria etd, Kasonde M (2006)
To my lovely wife Aimée,
Our daughters and son Gentille, Candide and Artig
And Nelie
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ACKNOWLEDGEMENTS
The thesis we are honoured to write today is the blossom of various contribution and
influence from divers people and institutions. We are greatly indebted to Many for the
learning and training received, idea and discussion shared, question and answer
exchanged, hypothesis and verification implemented, financial and spiritual support.
We wish to thank to the Department of Materials Science and Metallurgical
Engineering of the University of Pretoria for organising useful advanced courses at
postgraduate level and for the logistic and financial supports offered during our studies.
We are grateful to Professor Waldo STUMPF for the illuminating supervision of this
work and for his suggestion of the characterisation of the martensite in armour steels
using the atomic force microscopy ( AFM ) and the sake of the direct relationship
between microstructure and ballistic performance. This approach methodology has
contributed for many in the contraction of project duration and the quality of the
results.
″ To measure is to know ″ . More than 350 hours of course, training, work,
measurement, analysis and discussion were necessary with the help of the personnel of
the Industrial Metals and Minerals Research Institute ( IMMRI ). We are thankful
towards François VERDOORN for the training in dilatometry analysis, his particular
intervention during the execution of the project by providing the technical notes and
specifications for ballistic materials, the raw materials and samples of armour plates
(local and imported), for the organisation of the ballistic testing at Vanderbijlpark and
for the discussion during the stressing ballistic testing. Carel COETZEE and Alison
TULING for the training, analysis and valuable discussions of the electron microscopy
results, which constitute an important part of the proof of the hypothesis advanced in
this study.
The presentation and discussion of the mechanical properties as done in this project was
inspired by many consideration suggested by Professor Gerrit van ROOYEN. The
proposition of the Ballistic Parameter is one example of ideas that were elaborated after
discussing with him.
Amount of analysis, measurements and calculus presented in this work were realised
with the help of Doctors Sabine VERRYN of the Department of Geology and Nic
vander BERG of the Department of Physics.
Thanks also extend to Willem BRITZ and Ian FERREIRA for organising and realising
the ballistic testing at the Vanderbijlpark tunnel and for their encouragement during the
distressing test. I needed that.
To Daudet TSHIKELE, W. LEE, A. SHIKONGO, Vinod C and J. MUKADI for
friendship
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University of Pretoria etd, Kasonde M (2006)
OPTIMISING THE MECHANICAL PROPERTIES AND
MICROSTRUCTURE OF ARMOURED STEEL PLATE
IN THE QUENCHED AND TEMPERED CONDITION
MAWEJA KASONDE
Supervisor: Professor Waldo STUMPF
Department of Materials Science and Metallurgical Engineering
Master of Engineering (Metallurgical Engineering)
ABSTRACT
The effect of the chemical composition, austenitisation temperature and tempering
temperature and time on the mechanical properties and on the ballistic performance of
martensitic steel armour plates was studied.
It was established in this study that the mechanical properties and the ballistic
performance of martensitic steels can be optimised by controlling the chemical
composition and the heat treatment parameters. However, it was observed that for a
given chemical composition of the steel the heat treatment parameters to be applied to
advanced ballistic performance armour plates were different from those required for
higher mechanical properties. Such a contradiction rendered the relationship between
mechanical properties and ballistic performance questionable. Systematic analysis of
the microstructure and the fracture mechanism of some martensitic armour plate steels
was carried out to explain the improved ballistic performance of steels whose
mechanical properties were below that specificied for military and security
applications. It was inferred from phase analysis and its quantification by X-ray
diffraction, characterisation of the martensite using scanning electron microscopy,
transmission electron microscopy and atomic force microscopy that the retained
austenite located in the plate interfaces and on grain boundaries of the martensite was
the main constituent resisting localised yielding during ballistic impact on thin steel
plates.
A part of the kinetic energy is transformed into adiabatic heat where a reaustenitisation
of the plate martensite and the formation of new lath martensite was observed. Another
part is used to elastically and plastically deform the ballistic impact affected region
around the incidence point. Dislocation pile-ups at twinned plate interfaces suggest that
the twin interfaces act as barriers to dislocation movement upon high velocity impact
loading. The diameter of the affected regions, that determines the volume of the
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material deforming plastically upon impact, was found to vary as a function of the
volume fraction of retained austenite in the martensitic steel. Upon impact, retained
austenite transforms to martensite by Transformation Induced Plasticity, the “ TRIP ”
effect. High volume fractions of retained austenite in the martensitic steel were found to
yield low values of the ratio yield strength to ultimate tensile strength (YS/UTS) and a
high resistance against localised yielding and, therefore, against ballistic perforation.
A Ballistic Parameter was proposed for the prediction of ballistic performance using the
volume fraction of retained austenite and the thickness of the armour plate as variables.
Based on the martensite structure and the results of the ballistic testing of 13 armour
plate steels a design methodology comprising new specifications was proposed for the
manufacture of armour plates whose thicknesses may be thinner than 6mm.
KEYWORDS: Martensite, retained austenite, ratio yield strength to ultimate tensile
strength (YS/UTS), ballistic performance, ballistic parameter, reaustenitisation,
martensite start temperature.
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University of Pretoria etd, Kasonde M (2006)
University of Pretoria etd, Kasonde M (2006)
Chapter 1: Introduction
CHAPTER 1. INTRODUCTION
1.1. Industrial objective
The main objective in developing the new armoured steel plate to supersede the currently
used steel A and steel B plates, is the manufacture of lighter armoured vehicles by
decreasing the required thickness of the steel plates. The new plate should be able to
withstand a 5.56 mm R4 round whereas the steel A and steel B plates manufactured
currently, need a 8.5 to 20 mm thickness or higher for this ballistic requirement. According
to ISCOR [1], the properties listed in Table 1.1 would need to be achieved to meet this
objective.
Table 1.1 Specifications for the new armoured steel plate [1]
Property
Brinell hardness
Charpy V-notch transverse impact
energy on full size specimens [2]
Yield strength Rp at 0.2%
Ultimate tensile strength
Elongation of a 50 mm gauge length
Specification
570-640 BHN
12 Joules (minimum) at -40
0
C
1500 MPa (minimum)
2000 MPa (minimum)
7% (minimum)
The process parameters for the new armoured steel plate should be as close as possible to
the existing ones for the current steels A and B produced by Mittal Steel South Africa. The
processing parameters during hot rolling are more or less fixed, although the post-rolling
heat treatment temperatures and times can be slightly adjusted. After preliminary
austenitisation of the current steel B, followed by water quenching and a low-temperature
tempering, it appears that the harder new armour plate will almost certainly require a
change in composition for its higher hardness requirement (Carbon content) and
hardenability (Carbon and alloying elements), as well as for its toughness requirement.
To move from the current steel B to the new armour plate, will require an improvement of
ballistic properties through optimising the plate’s resistance to impact or shock loading and
its resistance to spalling as well as meeting the resistance against localised yielding and
ballistic perforation. Minimum hardness and strength requirements of the alloy should also
be realised. The design of the steel alloy and its heat treatment should allow an efficient
way for the development and manufacture of the armoured steel plate (steel making, rolling
and heat treatment parameters). The assessment of the ballistic performance will be
provided after ballistic testing according to the military and civil specifications for South
Africa as determined by ARMSCOR. These standardised specifications for ballistic tests in
South Africa are presented in Table 1.2. Each test consists of at least five firings of rounds
under the prescribed conditions.
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Chapter 1: Introduction
Table 1.2: Specification for the assessment of armour plate materials in South Africa [1]
Obliquity
Muzzle velocity
Distance
Assessment
0
0
930 m/s (minimum)
30 m maximum
1. No light path going through the thickness of the plate in the
impact region (i.e. no visible through-penetration)
2. No spalling at the rear face of the plate after ballistic testing
1.2. Project aim and methodology
The research project was undertaken with the aim of developing an improved
understanding of the relationship between ballistic properties of martensitic armour plate
steels and their structures and mechanical properties. By this means design criteria have
been proposed that meet the industrial objective outlined in Section 1.1. In the course of the
project, benchmarking was carried out using the scientific and industrial background on
armour steels currently produced or used in South Africa and throughout the world.
Microstructural investigations were used to explain the high or the low ballistic
performance of these steels before designing the candidates for the advanced performance
RB600. Mechanical testing, fracture analysis, measurement of martensite start temperatures
by dilatometry, phase analysis by X-ray diffraction, characterisation of the martensite and
surface relief analysis and ballistic tests were conducted to explain the differences in
performances and to optimise the ballistic as well as the mechanical properties of the new
martensitic armour steels through the control of the chemical composition and the heat
treatment parameters.
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Chapter 1: Introduction
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Chapter 2: Literature Review
CHAPTER 2. LITERATURE REVIEW
2.1 Industrial background
Mittal Steel South Africa already manufactures both the steels A and B at its
Vanderbijlpark plant that require armour resistance. These steels are used typically in
combat vehicles, security vehicles, bulletproof jackets and security doors. The
specifications for the chemical compositions of the current armour steels A and B are listed
in Table (2.1). From this table, it appears that the compositions for the two products differ
mainly in their Nickel and Chromium contents. The ratio of their Nickel to Chromium
content are respectively 2 and 0.7 for the respective steels A and B. Steels A and B are
fully killed fine-grained steels, which are also calcium treated and vacuum degassed to
achieve low sulphur levels and inclusion content. These armour plate steels are quenched
and tempered to achieve an ultra high strength with a fine microstructure.
Table (2.1). Specifications for the chemical compositions of the currently produced
armour steels A and B
Steel A: specification
Steel A: actual
composition
Steel B: specification
Steel B: actual
composition
%C
0.290.31
0.317
%Mn
0.800.90
0.855
%P
0.00.01
0.008
%S
0.00.003
0.002
%Si
0.150.25
0.176
%Cu
0.00.03
0.026
%Ni
2.83.0
2.8
%Cr
0.81.0
0.79
%Mo
0.450.55
0.45
0.300.32
0.253
0.550.65
0.606
0.00.015
0.007
0.00.005
0.002
0.300.45
0.327
0.00.03
0.012
1.41.5
1.41
1.51.6
1.54
0.550.60
0.58
2.1.1. The heat treatment cycle of steel A.
The Brinell hardness range for steel A is:
Table (2.2). Brinell hardness range of steel A armour plate [1]
Thickness [mm]
Brinell hardness
3.5 to 8
460 to 540 BHN
10 to 25
380 to 440 BHN
The typical heat treatment cycle of steel A consists of [1]:
Table (2.3): Typical heat treatment of steel A
Plate Thickness
[mm]
6
8
Austenitisation
temperature [0C]
900
870
Austenitisation time
[minutes]
20
24
Tempering
temperature [0C]
280
400
Tempering time
[minutes]
38
46
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The 3.5 to 4.5mm steel A plates are heated and then quenched in a water-cooled press.
Plates from 6 mm to 25 mm thick are heat-treated in a roller quenching plant that subjects
the entire plate to a rapid high volume water quench after solution treatment.
The high cooling rate ensures maximum use of the alloying elements to give the required
properties throughout the plate thickness [3]. After quenching, plates are tempered in a
tempering furnace where the temperature is selected so that the desired degree of hardness
for the specific plate thickness is obtained. The 3.5 to 4.5mm steel A plates are not
tempered after quenching but are used in the as-quenched condition[1].
2.1.2. The heat treatment cycle of the steel B
The thermomechanical treatment for steel B consists of:
1. Hot rolling in the austenite region (above Ac3) to the final thickness;
2. Stack the plates on top of each other for a slow cool to remove possible Hydrogen
cracking;
3. Send the cold plates to the Roller Quenching plant;
4. Solution treatment at 910°C;
5. Water quenching in the Roller Quenching plant (for the 3.5 to 4.5 mm plates); and
6. Low temperature tempering.
The steel B Brinell hardness’ range is given in Table (2.4).
Table (2.4): Brinell hardness range of steel B Plates
Thickness [mm]
Brinell hardness
6 to 12
477-532 BHN
15 to 25
450-512 BHN
The results after ballistic testing must conform to the ARMSCOR-ARMOUR PLATE
SPECIFICATION FOR RSA, specification No. SK112.
•
Storage: all material, with exception of the 3.5 to 4.5 mm plates, are shot blasted
after heat treatment to remove surface scale. The material must preferably be stored
under roof to prevent corrosion.
•
Fabrication [1] :
1. The hardness, high strength and toughness, as well as the weldability are
the main considerations for fabrication of steels A and B;
2. Due to the high hardness of the materials, bending is not recommended.
However, if any form of bending is to be done, it is advised that it be done
transverse to the rolling direction and at room temperature of ± 25 0 C. Cut
edges should be smoothly ground before bending.
3. Hot rolling: local or general heating must be performed before the final heat
treatment, as this could have an effect on the properties of the material. The
exposed face of the armour plate on the vehicle can have a higher hardness
than the opposite face facing into the vehicle. The latter must have a higher
strength.
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Chapter 2: Literature Review
4. Machining can be performed using high-speed tool steel tips and reducing
the speed to 50% of speeds used for normal carbon steels.
5. Flame cutting is not recommended for plate thickness less than 15 mm. For
these thicknesses plasma or laser cutting is recommended.
6. Preheating and welding: Preheating usually plays an important role in the
application of armour steel plates. Accordingly, a welding specification
SK108 has been developed for the correct welding procedures for steels A
and B [1] . Preheating of plates is recommended to minimize the adverse
effect of welding and flame cutting on the microstructure of the heataffected-zone (HAZ) by reducing the cooling rate in the HAZ. Rapid
cooling after welding and flame cutting result in a hard and brittle
martensitic microstructure, which is susceptible to hydrogen cracking. The
recommended maximum preheating temperature is 120 0 C [1].
Direct-quenching and tempering after hot rolling is now a viable technology in the
production of high strength steel plate, and it is widely practiced, especially in Japan.
In conventional reheat-quenching and tempering, microstructures and properties are
determined by the chemical composition and the tempering conditions. Direct-quenching is
an alternative route to reheat-quenching as practised at the Vanderbijlpark plant of Mittal
Steel (South Africa)[4].
2.2 Scientific background
2.2.1. Ballistic material
Each class of armour plate is heat treated to provide maximum resistance to ballistic
perforation. The microstructure must be homogeneous throughout the section thickness and
without inclusions that would act as crack initiators.
The external surface can present a higher hardness for resistance against penetration and
compressive impact, whereas the internal surface could have a higher tensile strength [2].
Cast armour has always been more resistant ballistically than rolled armour due mainly to
the fundamental difference in mechanical and metallurgical properties between rolled and
cast steel [2]. However production of armour plate is not feasible in cast forms.
It is possible to design a casting with smoother contours and higher obliquities than a flat
plate, although normally heavier than a corresponding structure fabricated from rolled plate
and in many cases with equal or even improved ballistic protection. Cast homogeneous
steel armour is still used on Army Combat Vehicles under MIL-S-11356 to produce such
components as hulls, turrets, cupolas, hatch covers, etc.
A large amount of empirical data obtained from a variety of tests confirmed that the armour
strength or hardness of the steel is a very important parameter in resisting ballistic
penetration. According to this design philosophy the candidate armour material should
exceed the hardness of the projectile [2]. This can be achieved primarily by thermal or
thermomechanical processing.
The assessment criterion of ballistic resistance is that of “no visible light to pass through
the impacted plate after the test” as illustrated by Figure 2.1 and quoted from [2].
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Chapter 2: Literature Review
(a) FRONT
(b) REAR
Figure.2.1 (a) and (b), Multiple ballistic impact capability of armour plate made from an
unidirectionally solidified ingot at a hardness in excess of 55 HRC. Light spots show the
difference in sizes between the openings in the front and the rear faces of the impacted plate.
The following figure shows the increase in the ballistic performance versus hardness as a
function of technological developments.
Figure.2.2. Relationship between armour hardness and ballistic performance [2]
There are several additional factors to consider in the choice of alloy for armour plate but
the major consideration would be that it should be effective in the field, and it should be
light, which in turn gives a variety of advantageous secondary effects.
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Chapter 2: Literature Review
Above all the armour plate must also be cost-effective. Other considerations are that the
armour plate should be amenable to modern fabrication and construction techniques and be
readily weldable and capable of being produced in a variety of shapes. Bulk is an important
factor because if the armour is bulky even though its area density is low, it will be difficult
to provide sufficient room under the armour to meet volume requirements for the crew,
gun, ammunition, fuel and power train, etc. For many years various alloy steels have
measured up to this requirement very well. Armour application for these steels is well
understood and can be made with optimisation of various properties by changing the
proportion and presence of the alloying elements.
Although steel is a dense material with a larger area density (i.e. mass per unit area)
comparatively to other armour materials, it does offer very good levels of protection
against KE (Kinetic Energy) and HESH (Highly Explosive Squash Head) attacks, but its
performance against HEAT (Highly Explosive Anti Tank) attack is considerably reduced
[2]. Most alloy steels contain some or all of the elements Manganese, Chrome, Nickel,
Molybdenum and Vanadium to give the correct blend of high strength and resistance to
fracture or toughness.
The major problem with all armour is that if the energy from the projectile is not to be
transferred from the armour to the supporting structure then a way has to be found to
dissipate the energy before this happens or the secondary effect may be equally fatal.
Experience indicates that homogeneous steel armour (i.e. not a layered combination made
from layers of different steels) should be made as hard as possible for defeating small arms
and armour piercing (AP) ammunition. However, as homogeneous steel becomes harder it
also becomes more brittle and as the material becomes more brittle, its ballistic limit
cannot be measured due to severe fracture of the armour. Thus, limits on homogeneous
armour hardness have to be established to prevent shatter of the armour due to
embrittlement, but not necessarily because of strength limitations on the ballistic limit. This
important fact has formed the basic guideline for improved steel armour development
programs. That is, to increase the steel armour’s ballistic limits by increasing its hardness
without increasing the tendency towards brittle failure. An armour hardness of at least 58 to
62 Rockwell C would be required to induce shattering of the projectile upon impact [2].
Various definitions for complete and partial penetration are illustrated in Figure 2.3.
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Chapter 2: Literature Review
Figure 2.3. Definitions of perforation and partial penetration for defining the ballistic limit
The ballistic superiority of steels of higher metallurgical quality has been demonstrated
often. The development of unidirectionally solidified wrought steel armour showed that
cast steels with superior ductility could be produced by unidirectional solidification, which
produces a cast structure in which columnar grains extend from the chill surface completely
through the casting. The resulting solidified steel ingots have been found to be virtually
free of gross porosity and with a much finer segregation pattern, factors that contribute to
higher ductility [2].
The homogenisation heat treatment, which consists of holding the casting at 1316°C for 64
hours, would virtually eliminate alloy segregation. Steels of armour composition have been
produced by this process and have been homogenised, rolled, and heat-treated to hardness
levels ranging from 50 to 60 HRC.
The important requirement of structural tank armour is that it should maintain structural
integrity at sub-zero temperatures when impacted by overmatching artillery rounds. Test
plates are inspected after proof testing for their ability to withstand fracture, spalling, and
cracking. The long-standing empirical materials specification, which applies to structural
tank armour and its ability to maintain integrity at low temperatures, requires that the
material must have a minimum of 27.12 J (20 ft-lbs) transverse Charpy V-notch impact
energy at a temperature of -40 0 C [1, 2].
2.2.2 Stress waves in solids
The response of materials and structures to intense impact loading is quite complex. For
loading conditions that result in stresses below the yield point, materials behave elastically
and Hooke’s law is applicable for metals. However the mathematical solutions for various
loading conditions in this regime are obtained for semi-infinite bodies. Practical impact
problems involve strikers and targets with finite boundaries, which exert considerable
influence on their behaviour. As the intensity of the applied load is increased, the material
is deformed into the plastic range. The behaviour in this range involves large deformations
together with localised heating, and often failure of the colliding solids through a variety of
mechanisms. With still further increases in loading intensity, pressures are generated that
exceed the strength of colliding solids by several orders of magnitude which, in effect, then
start behaving hydrodynamically [5]. Failure modes in impacted plates may be classified as
one of the six illustrated in Figure 2.4.
For low intensity excitations, both the geometry of the entire structure as well as the nature
of the material from which it is made, play a major role in resisting any external forces. As
loading increases, the response tends to become highly localized and is more affected by
the constitution of the material in the vicinity of the impact region than the geometry of the
structure. The description of the phenomena in terms of elastic, plastic, and shock waves
becomes appropriate.
When either a dilatational or distortional wave impinges on a boundary of the solid, waves
of both tensile and compressive types are generated. Of particular interest in impact
situations is the normal impingement of a strong compressive pulse on a free surface. The
pulse is reflected from any discontinuity or a free surface as a tensile wave and if its
magnitude is greater than the tensile fracture strength of the material, fractures will occur.
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Chapter 2: Literature Review
Figure 2.4. Failure modes in impacted plates [2]
Simple analyses predict reasonably well the location of the fracture plane and the size and
speed of the ejected material for high strength solids. If after fracture, the magnitude of the
stress pulse still exceeds the material’s tensile strength, multiple fractures can occur [5].
The reflection of the input compressive pulse and the subsequent formation of a tensile
wave are illustrated in Figure 2.5. The evolution of the phenomenon is depicted as different
time function of the compressive wavelength λ and the celerity of the light C.
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Chapter 2: Literature Review
Figure 2.5: Illustration of the propagation and reflection at a free surface of the shock-induced
compressive wave and its subsequent conversion into a tensile wave [2]
A high dynamic tensile strength is then required to avoid multiple fractures and spallation
during ballistic testing. This observation will be compared later to the experimental results
of the ballistic performances in this study on 13 armoured steels. As the intensity of the
applied load increases, the material is driven beyond its elastic limit and becomes plastic.
Two waves now propagate in the solid, an elastic wave (or precursor) followed by a much
slower but more intense plastic wave. The principle is illustrated considering an elasticlinear hardening behaviour for a material whose Young’s modulus is E, the yield strength is
E
σy and the specific mass is ρ. The elastic wave front propagates at the speed C 0 =
ρ
whereas the slow plastic wave follows at a velocity C1 =
E1
ρ
where the two values of E
differ because of elastic linear hardening. Figure 2.6 illustrates the delay of the plastic wave
front on the elastic wave in the space-stress reference. The same principle may be
illustrated in velocity-strain space as in Figure 2.7.
Figure 2.6: Stress-strain relationship and wave-profile for elastic-linear hardened material
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Figure 2.7: Strain distribution in a rod produced by a its constant velocity impact at end. ξ=x/t.
If the characteristics of the medium are such that the velocity of propagation of large
disturbances is greater than the propagation velocity of smaller ones, the stress pulse
develops a steeper and steeper front on passing through the medium, and the width of this
front is ultimately determined by the molecular constitution of the medium. The shock
wave (or steep pressure pulse) thus formed, differs from the high pressures generated by
conventional methods in that it relies on the inertial response of the material to rapid
acceleration rather than on static constraints. If the intensity of the loading is so great or its
duration so short that the material no longer possesses rigidity, it will behave as though it
had the properties of a fluid. Transverse (shear) waves cannot exist then within the body
and only a longitudinal wave will be propagated with a velocity c given by:
c2 =
K
ρ
(Eq 2.2.2-1)
where K is the bulk elastic modulus and ρ the density. The bulk modulus K may be found
from Young’s elastic modulus E and Poisson’s ratio ν:
K=
E
3(1 − 2ν )
(Eq 2.2.2-2)
In this shock wave regime, extremely high pressures are generated which can lead to
changes in the density of materials with changes as large as 30% in steels [5]. The stress
response is governed by dilation of the steel, since pressures are typically in the hundreds
of kilobars while material strengths are only of the order of a few kilobars. This
circumstance led to the development of hydrodynamic theories in which the material
strength was neglected and the metal assumed to behave as a perfect fluid with resistance
only to dilation. Lee [5] suggests that hydrodynamic theories need to be modified to
account for strength effects and finite deformations. Finite strains and strength effects can
play a dominant role in determining the stress-wave profile. For fracture problems, this
profile is crucial for determining the location and the type of failure.
2.2.3. Material behaviour at high strain rates
The behaviour of materials at high rates of strain has been studied with considerable
interest since World War II when dynamic plasticity and plastic-wave propagation first
received attention. The most general form of a material-constitutive equation should cover
the prediction of material behaviour under the total range of strain rates that may be
encountered. However, this can be difficult even for an uniaxial stress and, therefore, the
majority of constitutive equations generally cover only a narrow range of strain rates. This
is consistent with the physics of the problem since different mechanisms govern the
deformation behaviour of materials within different strain-rate regimes.
Five classes of strain rates are identified due to dynamic loadings in metallic structures.
The duration of impact, the state of stress and strain as well as the thermal effect
accompanying each class, are shown in Table 2.5. From this table it appears that at very
high strain rates and the associated short time scale involved, thermodynamic
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Chapter 2: Literature Review
considerations become important. The nominally isothermal conditions then translate to
adiabatic conditions.
Table (2.5): Classes of strain rates [5]
Strain rate [s
−1
Characteristic
time [s]
]
−8
−2
10 to
10-6
10
6
10 to 10
10 to
2
10
0
10
0
−2
2
10 to 10
10
−4
to 10
4
−6
10
10
6
−8
4
10
Creep
Quasi-static
Intermediate
strain rate
Bar impact
High-velocity
plate impact
Mechanical
resonance in
machines and
specimen
Elastic-plastic
wave
propagation
Shock wave
propagation
Isothermal
Inertia forces neglected
Adiabatic
Inertia forces important
Plane stress
Plane strain
Increasing stress levels
2.2.4. Ballistic performance
The development of metallic armour involves a large number of tedious ballistic
experiments, since any change in alloy composition or heat treatment parameters
significantly alters the ballistic performance. Although considerable knowledge exists on
how the alloy compositions and heat treatment parameters affect the mechanical properties,
a quantitative understanding of the correlation between the mechanical properties and the
ballistic performance is still lacking [6]. Most of the earlier models on ballistic
performance focused on the target and the projectile geometry and penetration parameters
such as striking velocity and the striking angle. Contrarily most of the actual models are
based on the mechanical properties of the projectile and the target, with the latter related to
the metallurgical processes. Srivathsa et al [6] suggest that the kinetic energy of the
projectile is absorbed in the following three modes:
1. the elastic deformation of the material;
2. the plastic deformation of the material; and
3. the kinetic energy imparted to the target material.
The total energy absorbed in each of the above cases is the product of the energy absorbed
per unit volume and the participating volume. In previous work [7] the same authors
suggested a model for the calculation of the energy Ψ per unit area-density (ρd) absorbed
by the three modes as follows:
2
2 2
⎡ α
⎤
⎛
⎞
⎛
⎞
(
)
Ψ
+
1
1
1
1
1
1
k
k
γ
4
I
e
⎜
⎟
⎜
⎟
⎥ (Eq 2.2.4-1)
= πt 2ν r ⎢
+
+
+
+
+
+
α
1
1
II
2
k j ⎜⎝ k p ⎟⎠ 2k p 2 2 ⎜⎝ k p ⎟⎠ ⎥
ρd
⎢ 2(1 + kb )2
2k j
⎣
⎦
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Chapter 2: Literature Review
where α I and α II are the fractional widths of the constrained (I) and unconstrained (II)
regions, respectively. The non-dimensional parameters k e , k p , k j , k b and k f can be
computed as described below:
kγ =
1 −ν
,
(1 − 2ν )(1 + ν )
ke =
Vr
kγ
ρ
E
,
ρVr 2
,
kj =
σy
k b = Vr
ρ
k p = Vr
Ep
V
α I = 1 − α II = 1 − 1
V0
ρ
K
where K =
where E p =
where ν I =
E
,
3(1 − 2ν )
σ u (1 + ε γ ) − σ y
,
εr
− kγ
ρE + kγ 2 Eρ + 10.4 ρσ y
2ρ
,
where ρ is the density, E the elastic modulus, σ y the yield strength, σ u the tensile
strength, ν is Poisson’s ratio, ε r the reduction in area or the fractional elongation and V0
the striking velocity, VF is a material and thickness independent representative of the
average velocity, defined as:
V
Vr = 0
1.85
In this model the terms inside the square bracket in the equation 2.2.4-1 correspond to the
mechanical properties as well as the striking velocity of interest. Srivathsa et al [6] express
the Ballistic Performance Index (BPI) as:
2
2 2
⎡ α
⎛
⎞
⎛
⎞ ⎤
(
)
+
1
k
k
1
1
1
1
1
γ
I
e
Φ=⎢
+ α II
+ ⎜1 + ⎟ +
+ ⎜1 + ⎟ ⎥
2
k j ⎜⎝ k p ⎟⎠ 2k p 2 2 ⎜⎝ k p ⎟⎠ ⎥
⎢ 2(1 + kb )2
2k j
⎣
⎦
In the BPI the first two terms represent the elastic components, the third and the fourth
terms represent the plastic components and the last term corresponds to the kinetic energy
component and Φ is a dimensionless parameter. The strain-hardening rate H is computed
as:
H=
σ u (1 + ε r ) − σ y
εr
(2.1)
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The strain-hardening rate affects the plastic wave velocity in the material, which essentially
determines the extent of plastic deformation in the region of impact.
The authors have applied this model to the following materials:
Table (2.6): Materials tested and their properties [6]
Material
Mild steel
Aluminium
Steel-A
Ti-6Al-4V
Al-2024
Steel-B
Density
[kg/m3]
7800
2720
7800
4550
2770
7800
Yield strength [MPa]
325
130
1068
990
345
1610
Tensile strength
[MPa]
691
217
1210
1050
565
1860
They observed that from the ballistic performance:
-
Maraging steel is only 1.4 times better than mild steel despite its higher
strength. This has been confirmed experimentally [8];
The BPIs of Steel-S and Steel-B are 1.55 and 2.33, which agreed with the
experimental results;
The Aluminium alloy Al-2024 is nearly 2.2 times better than mild steel.
Also, the performance of Ti-6Al-4V is 1.9 times better than that of mild
steel.
It can be seen that merely increasing the strength of the material does not necessarily lead
to significantly improved performance. This observation is highly significant and will be
returned to later in this study on new experimental steels for advanced ballistic
performance.
2.2.5. Fracture prediction under high-velocity localised impact
It is well known that the dynamic strength of hard metal sheets and their fracture strength
are not identical to those determined for static loading or for low strain rates. Several
fracture criteria have been postulated throughout the years. In the present study two of them
are presented.
In 2004, Lee and Wierzbicki [9] have postulated that fracture initiates at the critical point
of the structure when the accumulated equivalent plastic strain ε with a suitable weighting
function, reaches a critical value of:
εf
⎛σ m
⎞
, ε , T ⎟dε = DC
⎠
0
where ε f , the upper limit of the integral, is the equivalent strain to fracture; f is a
∫ f ⎜⎝ σ
weighting function dependent on the stress triaxiality and is defined as the ratio of the
hydrostatic mean stress σ m to the von Mises equivalent stress σ , ε the strain rate, and T
the absolute temperature; DC is a critical damage value of the specific material. The
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Chapter 2: Literature Review
authors [9] observed three regimes for the fracture mechanisms depending on the stress
triaxiality value:
• for a stress triaxiality larger than 1/3 the fracture is controlled by the mechanism of
void nucleation, growth and coalescence;
• under negative stress triaxiality the so-called shear decohesion becomes the
fracture mechanism; and
• the third regime is a combination of the other two.
It should be pointed out that their study strictly only applies to the prediction of the onset of
fracture of uncracked bodies. They further assumed that ductile crack propagation is
essentially a process of continuous reinitiation ahead of the crack, so that the same microstructural events occur in front of the crack tip of previously existing crack, as in the region
of a flawless body in which the crack initiates [10]. They have also considered the possible
dependence of the fracture criterion on the strain rate and temperature. However Borvik et
al. [11-12-13], and Hopperstad et al. [14] have recently shown that the effect of strain rate
and temperature on the fracture strain are much smaller than that of any stress triaxiality for
Weldox 460E steel.
2.2.6. Shock induced transitions and transformations
The effect of target strength on the perforation of steel plates using different projectile nose
shapes, has recently been investigated by Dey and co-workers [15]. They confirm as
modelled by Zukas [5], that when a blunt projectile hits the target, the material in front of
the projectile accelerates, while the rest of the target is relatively stationary as shown in
Figure 2.5.
Figure 2.5. Three-stage perforation model showing the increase in the effective mass of the
bullet as it progresses through the plate
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Chapter 2: Literature Review
Hence, the deformation localises in narrow shear bands under adiabatic conditions where
the shear strain, shear strain rate and temperature may locally be very high. According to
Bai and Dodd [16], these shear bands may either consist of only deformed material or
transformed material, depending on the temperature that was reached in this localised area.
Deformation bands are regarded as zones of intense plastic shear only, whereas
transformation bands are zones of intense shear in which a phase transformation has
occurred. When the localised temperature reaches about 720 0 C , the steel will undergo a
phase transformation. In impact problems involving steel targets, temperatures of this order
are produced in micro- or milliseconds, before the band is subsequently quenched by heat
flow into the surrounding material.
The common thread is that the spalling-strength of the steel is sufficient as an objective
characteristic tensile strength of the material at the microsecond scale of dynamic loading.
In reality, a preliminary compression of the material takes place during the passing of the
compressive pulse front. If this dynamic compression achieves a critical value, irresistible
structural changes within the solid occur before the tensile stresses are generated within the
spalling zone of the target. Thus dynamic failure during spallation depends on the plastic
instability of the material under compression at the wave front of the loading pulse [17].
The plastic instability can be considered as a strain-rate dependent structural phase
transition by means of which the shock wave itself establishes the microstructural features
on a mesoscopic scale. Micro-deformation models based on the solution of a non-linear
sine-Helmholtz equation, predict a non-stable behaviour of the crystal lattice that is
subjected to shear deformation in the non-linear elastic region of loading. This instability
leads to the nucleation of large-scale structures such as meso-rotations, shear bands and
their combinations. At higher strain gradients a bifurcation transition takes place, which
results in the nucleation of structures on a mesoscopic scale commonly seen in
microstructural investigations [17]. In accordance with a generally accepted classification
(Panin et al., 1982) the microstructural size defining a mesoscopic scale ranges from about
7 to 10 μm .
The transition to a new regime of dynamic deformation can be considered as a structural
phase transformation initiated by shock loading. Mescheryakov et al [17] have determined
the instability threshold to be at 307 m/s. According to their observation on a set of steels,
fracture occurs by a cleavage mechanism at impact velocities less than 307 m/s. However,
at impact velocities higher than the instability threshold, blocks of grains and brittle
fragmentation become the mechanism of fracture.
2.2.7 Role of material properties
The penetration depth upon impact loading is known to be determined on the basis of a
modified Bernoulli equation (Hohler and Stilp, 1990):
Y+
1
1
ρ imp (ν − u )2 = ρ t u 2 + R ,
2
2
(Eq 2.2.7-1)
where v is the impactor velocity, u is the particle velocity in the material of the target, Y
and R are empirical constants defining the dynamic strength for the material of the
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Chapter 2: Literature Review
penetrator and target respectively. It is claimed that the physical meaning of parameters Y
and R remains to unclear (Hohler and Stilp, 1990).
The value of R takes into account any deviation in behaviour of the material of the target
from the hydrodynamic model of penetration.
Micromechanisms of dynamic deformation responsible for the physical nature and value of
R are the subject of investigations on microplasticity. The parameter R is often identified
with dynamic hardness H D which is related to the dynamic yielding limit, YD , by the
following dependence (Tate, 1967; Lasarev et al., 1993):
H D = (3 − 3.5)YD
(2.2.7-2)
The dynamic yielding again is determined by the Hugoniot elastic limit, σ HEL :
YD =
1 − 2ν
σ HEL
1 −ν
(2.2.7-3)
where ν is Poisson’s ratio. The main conclusion [17] following from the analysis of
peculiarities of high-velocity penetration and also from the analysis of experimental data, is
that the strength-component of the resistance of solids to penetration (as a complementary
factor for the inertial forces) is determined by the resistance to plastic deformation. This
means that if the character of the plastic deformation changes, for example, because of a
change of the structural mechanism of deformation, the strength-component of the
resistance to penetration changes as well.
Rosenberg et al [18] have investigated the strong dependence of the penetration on a rod’s
aspect ratio, the so-called “ L/D effect ”, by rewriting the modified Bernoulli equation as:
1
1
ρ imp (ν − u )2 = ρ t u 2 + Rt
2
2
(2.2.7-4)
They have observed that the term Rt is reasonably independent of the impact velocity as
well as the densities of the rod and target, but is strongly dependent on the target strength.
Rt may reach critical values as high as 5.5GPa, whereas YD may reach only 2GPa.
2.2.8. Prediction of the martensite start temperature Ms and the Driving Force ΔGγ→M
for the martensitic transformation
Much work has been done to assess the various factors that determine the type or
morphology of martensite that forms upon quenching steels from the austenite region. The
influence of temperature, composition, magnetic character of the austenite, quench rate,
stacking fault energy, shear strength of the austenite and driving force for the martensite
formation have been investigated by various authors.
The free energy change accompanying the martensitic transformation may be expressed as:
ΔG γ →m = ΔG γ →α + ΔG α →m + ΔG ∗
(2.2.8-1)
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ΔG γ →m is the driving force required for the transformation from austenite to martensite,
ΔG γ →α is the sum of the chemical and structural free energy change from the austenite to
the ferrite at equilibrium, ΔG α →m is the structural free energy change from ferrite to
martensite, ΔG ∗ is Zener’s ordering energy from which Zener’s ordering parameter Z has
been evaluated by Fisher [19] as:
ΔG ∗ = − 2.12 × 10 5 X C2 Z 2 + 2.77 X C Tφ J.mol-1
(2.2)
Z = Zener’s ordering parameter:
φ = 2(1 − Z ) ln(1 − Z ) + (1 + 2 Z ) ln(1 + 2 Z )
(2.3)
The maximum values of Z and φ are 1 and 3.295.
ΔG α →m has been evaluated with the assistance of the result for Fe-C [20] as:
ΔG α →m = 2.1σ + 900 J.mol-1
(2.4)
in which σ is the yield strength of austenite at the Ms temperature. It may be approximated
for Fe-Mn-C systems by [20]:
σ = 127.4 + 3920 X C + 490 X Mn + 0.265(800 − M S ) MN.m-2 [20]. (2.5)
Morozov et al [21] studied the transformation in Fe with 0.01% C from low to very high
cooling rates. They found four arrest temperatures corresponding to four plateaux and
denoted them I, II, III and IV. They identified plateau III with the formation of martensite
by slip (lath martensite) and plateau IV with the formation of martensite by twinning (plate
martensite). Plateau I is mainly due to the formation of incoherent equiaxed α and plateau
II is mainly caused by the transformation of austenite to acicular ferrite (AF) or
Widmanstätten ferrite. Depending on the cooling rate there are then two Ms temperatures
and not one. The plateaux of transformation are illustrated in Figure 2.6 for the Fe-Ni-C
system. The two Ms lines intercept at low Ms temperatures [21].
Figure 2.6. Plateaux of transformation and intersection of Ms lines for the Fe-Ni-C system [21]
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University of Pretoria etd, Kasonde M (2006)
Chapter 2: Literature Review
Table (2.7) presents the intersection temperatures for the two Ms lines as reported by
different researchers in varying the cooling rate up to 5x105 K/s in Fe – C alloys containing
from 0.01% C up to 0.89% C and for some Fe-X systems.
Table (2.7): Temperature [°C] of intersection of the two Ms lines
Fe-C
Fe-Ni
Fe-Mn
Fe-Cr
Mizrayev
et al
[16c]
342
392
Mizrayev
et al
[16c]
284
Shteynberg
et al [16d]
Mizrayev
et al [16e]
Mizrayev et
al [16f]
Zhao and
Jin [16g]
Zhao
Wilson
252
250
0
346
244
0
232
300
300
Wilson
200
323
The Lacher, Fowler and Guggenheim (LFG) model for the calculation of ΔG γ →α in
multiple component systems, which was first proposed by Aaronson et al. [22] by
incorporation it with Zener’s work [23], may be expressed as:
ΔGγ →α = RT(5 −16X C ) ln(1 − 2 X C ) − 4RT(1 − X C ) ln(1 − X C ) + 7RTXC ln(3 − 4 X C ) −
4RTXC ln 2 − 6RT(1 − 3X C ) ln(δ γ + 1 − 3X C ) + 6RT(1 − X C ) ln(δ γ + 1 − X C ) − 8RTXC ln(δα + 3 − 5X C )
⎡⎛ −
⎤
− ⎞ ⎛
− ⎞
⎜
α
γ ⎟ ⎜
xs(α )
xs(γ ) ⎟ ⎥
⎢
+ X C ⎜ Δ HC − Δ HC ⎟ − ⎜ Δ SC − Δ SC ⎟T + (1 + X C )
⎢⎜
⎟ ⎥
⎟ ⎜
⎠ ⎦⎥
⎠ ⎝
⎣⎢⎝
⎡
i
) + ΔGFeγ →γ
× ⎢141∑ X i (ΔTNm
i
⎣
⎧
i ⎫⎤
× ⎨T −100∑ X i ΔTmag
⎬⎥
i
⎩
⎭⎦
(2.6)
where
[
= [(1 − X
δ α = 9(1 − X C )2 − 4 X C (3 − 4 X C )J α
δγ
)2 − 4 X C (1 − 2 X C )J γ ]
]
12
12
C
J α ,γ = 1 − exp(− ω α ,γ / RT )
ω α = -25,310 J.mol
ω γ = 1380 J.mol-1
(2.7)
(2.8)
(2.9)
-1
−
Δ H Cα = 109,680 J.mol-1
−
Δ H Cγ = 38,460 J.mol-1
ΔS
−
xs (α )
C
= 39.90 J.mol-1.K-1
−
Δ S Cxs (γ ) = 10.65 J.mol-1.K-1
T refers to the Ms temperature in absolute degrees and is the term to be evaluated; X C and
X i are the mole fractions of Carbon and the ith substitutional alloying element; ΔTmag and
ΔTNm are the magnetic and non-magnetic components respectively affecting the ΔG γ →α of
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Chapter 2: Literature Review
pure iron, or the displacement in Ms temperature of pure iron by 1 at.% of alloying element.
From the Aaronson, Domian and Pound (ADP) model [21] ΔTmag =-35.5 K and
ΔTNm =-37.5 K.
Wang et al [24] have developed an advanced set of equations in which combined binary
effects between sets of alloying elements were taken into account for the estimation of the
Ms temperatures. The nominal concentration of binary terms was defined as the square root
of the products of the mass percentages of two chemical constituents.
wi − j = wi w j leading to the general equation: Ms= k 0 + ∑ k ij wi w j
( )
Ms 0 C = 540 − 584.9 wC − 23.1wSi − 117.7 wMn − 42.5wCr − 49 wMo − 62.5wC − Si
+ 178.3wC − Mn − 10.0 wC −Cr + 52.5wC − Mo + 117.2 wSi − Mn + 50.9wSi −Cr − 142.2wSi − Mo
(2.10)
− 129.2 wMn −Cr − 9.7 wMn − Mo + 69.9 wCr − Mo
This equation may be applied to typical steel compositions in the range of 0.2 to 0.5%C,
0.5 to 2%Si, 0.5 to 2.0%Mn, 0.5 to 2.0%Cr and 0.1 to 0.7%Mo.
Note that with binary interaction effects, some positive changes in the Ms temperature are
to be expected as opposed to the generally negative effects with single element
considerations. Other formulae proposed for the Ms estimation in ferrous steels are
summarised in the following table:
Table (2.8). Different formulae for the estimation of MS temperatures in steels
Reference
[27]
[28]
[29]
MS [K], all compositions in wt.%
772 − 316.7C − 33.3Mn − 11.1Si − 27.8Cr − 16.7 Ni − 11.1Mo − 11.1W
811 − 361C − 38.9 Mn − 38.9Cr − 19 Ni − 27.8Mo
2
785 − 453C − 15Cr − 16.9 Ni − 217(C ) − 71.5(C )(Mn ) − 67.6(C )(Cr )
All these attempts that were made at modelling the compositional dependency of Ms using
linear regression or similar methods, are classified as non-adaptative [30] because the
‘shape’ of the function is predetermined by the authors rather than adapted to the data.
Neural networks, as opposed to traditional linear or polynomial regression methods, do not
impose a shape of the function on the data. In contrast, neural network methods that are
currently under development are adaptive functions.
From these empirical formulae it appears that Nitrogen decreases the Ms temperature more
largely than Carbon. This is attributed to its stronger stabilisation of the austenitic matrix
due to a larger solid solution strengthening effect. The same observation [30] may be
arrived at on the effects of Manganese and Molybdenum due to a difference in solid
solution strengthening. Hayzelden et al [31] have investigated the effect of the austenite
grain size and the dislocation density on the Ms temperature. In an Fe - 0.38%C - 26.13%Ni
alloy and in the absence of a change in dislocation density, Ms was found to be determined
by the grain size of the austenite. For a given grain size, the Ms is raised by an increase in
dislocation density. In this case the microhardness of the austenite is unaffected by a
reduction in grain size but is raised by an increase in dislocation density within the grains.
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The depression in MS in the fine-grained alloy could not be explained by the Hall – Petch
strengthening of the austenite and was believed to result from the segregation of active
martensite nuclei into a few small grains, a suppression of the autocatalytic stimulation of
martensite plates between adjacent grains and a possible reduction in the number of
potential martensite nuclei.
From their study on the heterogeneous nucleation of martensite within the vicinity of grain
boundaries using an SEM-EBSD method, Ueda et al [32], observed that only some grain
boundaries with a specific character could activate martensitic transformations effectively.
These include 90°<211> symmetric tilt boundaries that acted as a favourable site for
martensite formation while 90 0 <211> twist boundaries did not. In the vicinity of grain
boundaries, some martensite variants with the habit plane almost parallel to the grain
boundary were preferentially formed from amongst 24 possible habit plane variants. The
equivalent variants were adjoined at the tilt boundary to maintain the compatibility of the
transformation strains across the boundary, resulting in an increase in the martensite-start
temperature. These authors have defined this type of nucleation as “cooperative nucleation
(CN)”. They have estimated the difference in Ms temperatures for different tilt angles in the
vicinity of the grain boundaries as 50K. A grain boundary may reduce the strain energy for
the nucleation of martensite. In particular, the symmetric tilt boundary 180 0 <211>
demonstrated the highest Ms temperature. It suppresses the growth of embryos into
martensite (the self-accommodation of a group of variants), since the compatibility
requirements are maintained at the boundary and result in higher Ms temperatures and more
effective CN.
Many researchers have succeeded in explaining various phenomena or crystallographic
features of phase transformations using Eshelby’s inclusion theory [33]. According to this
theory, the elastic strain energy due to martensitic transformation may be calculated from
the shape strain matrix as follows: The shape strain matrix must be first converted to the
T
symmetric matrix ε ij , which is given by
ε ij T =
S ij + S ji
− δ ij ,
(2.11)
2
where δ ij is the Kronecker delta [33]. δ ij =1 for i = j and δ ij = 0 for i≠j. The strain energy
U0, generated by the shape change of ε ij in an elastic medium, is given by:
ε ij
U 0 = ∫ σ ij dε ij
(2.12)
0
Since Hooke’s law is applicable in an elastically isotropic matrix, the elastic strain energy
can be expressed in terms of the strain components as follows:
U0 =
(
)
(
νG M
(ε xx + ε yy + ε zz )2 + GM ε xx 2 + ε yy 2 + ε zz 2 + 2GM γ xy 2 + ε yz 2 + ε xz 2
1 − 2ν
)
(2.13)
where G M is the shear modulus and ν is Poisson’s ratio. When a martensite plate
nucleates independently in a single crystal, the strain energy U0 is calculated to be about
1500 J/mol.[34].
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Borgenstam and Hillert [35] presented a very good summary on the thermodynamic theory
of the martensitic transformation in Fe-X systems. The following paragraph is based on
their work and on the general observation by Nishiyama [36]. Johansson [37] was the first
to publish in 1937 a thermodynamic analysis of the α and γ phases in the Fe-C system.
He discussed the martensitic transformation, presuming that martensite cannot form at that
temperature where α and γ have the same Gibbs free energy, but it requires further
undercooling for the necessary driving force. He proposed that this extra driving force
results from the Carbon atoms within martensite being “frozen” into the positions inherited
from the parent γ , and he believed that those positions would give a higher free energy as
well as a lower entropy than in α with its random distribution of the Carbon atoms. Zener
[38] instead assumed that martensite, which is tetragonal at higher Carbon contents because
of the non-random positions of the Carbon atoms, would have a lower free energy because
of the Carbon atoms collaborating and thus minimising the strain energy caused by the
presence of these atoms in interstitial sites of insufficient size. He even proposed that there
is a temperature-composition region where the tetragonal martensite with the non-random
distribution of Carbon atoms would have a lower Gibbs free energy than α with a random
distribution. He developed a simple theory of ordering and by minimizing the Gibbs free
energy, it was possible to predict the degree of order at equilibrium. When evaluating the
driving force for the martensitic transformation he assumed that martensite would have
those equilibrium ordered properties. Fisher [19] made a more thorough analysis of the
Gibbs energy of the ordered α phase by evaluating the driving force for martensite
formation and determined values for the Zener’s ordering driving force ΔG * and ordering
parameter Z as presented earlier in this paragraph. Many evaluations of the driving force
for martensite formation have been published over the years with most of them taking
Zener ordering into account.
It should be emphasized that the idea of Carbon atoms inheriting their positions from the
parent γ is based on the assumption that the rate of transformation is so high that there is
not enough time for Carbon atoms to redistribute by diffusion during the actual
transformation. It seems that this could apply to the edgewise growth of plate martensite
but possibly not to the growth of lath martensite. If this is so, then the equilibrium degree of
order should be used for lath martensite. Furthermore, at very high growth rates there is not
even time for the reaction heat to diffuse away and the temperature will be higher at the
γ / α interface than in the rest of the system [39].
After these results [19, 35, 36, 37, 39] the driving force for the formation of plate
martensite may have a constant value of about 2100 J/mol. For lath martensite it may vary
linearly with the formation temperature, possibly from 500 J/mol at 800 0 C to 2100 at
250 0 C .
Another uncertainty in the description of the Gibbs free energy of the α phase is the effect
of Carbon on the ferromagnetic transition in the α phase. The analysis of the properties of
the α phase made by most researchers is made with the assumption that the magnetic
properties are not affected by Carbon. Earlier, Nishiyama [36] had already voiced his
reservation on the validity of the thermodynamic theories of the martensitic transformation.
He stated that in the current thermodynamic theories on the growth of a martensite nucleus,
the interfacial and internal chemical energies are considered to be dominant, as in the case
of crystallization in a liquid. In addition because of the solid medium, the strain energy of
the transformation is also taken into account. These theories, however, assume thermal
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equilibrium and ignore the microstructural and crystallographic characteristics of the
martensitic transformation. He, therefore, felt that such theories are not reasonable and it
would be better to rather construct a thermodynamic theory that takes microscopic
structures into consideration.
2.2.9. Kinetics of the martensitic transformation
The nucleation of martensite during cooling is believed to take place at structural
imperfections in the parent phase. These pre-existing embryos (defects) are stimulated to
grow into martensite crystals at different degrees of undercooling below the Ms temperature
as they have different energy barriers to activation. Growth can, however, be very fast.
Each nucleation event directly leads to the formation of a typical volume of the new phase.
Thus, the volume fraction of martensite varies only with the degree of undercooling, which
expresses the athermal character of the transformation. Koistinen and Marburger [40] have
postulated that the evolution of martensite formation in a sample that is initially fully
austenitic, may be described by:
f = 1− e
C1 ( Ms −T )
(2.14)
where f is the volume fraction of martensite in the sample at temperature T below Ms,
and C1 is a constant. This volume fraction is defined as the volume of martensite divided
by the volume of austenite that exists in the sample prior to the formation of martensite.
Magee [41] derived the following empirical equation from first principles, assuming that in
a temperature interval dT , the incremental number dN of new martensite crystals (plates
or laths) that form per unit volume of austenite is proportional to the increase in driving
'
force ΔG γ →α due to the temperature decrease dT:
(
d ΔG γ →α
dN
= −C 2
dT
dT
'
)
( ΔG γ →α < 0 )
'
(2.15)
where C 2 is a positive constant expressing the proportionality between the increase in
driving force and the consequent increase in density of activated nucleation sites. The
change in the volume fraction of martensite corresponding to the temperature decrease
dT is then given by:
dN
df
= Ω(1 − f )
dT
dT
(2.16)
where (1 − f ) is the volume fraction of austenite available for further transformation and
Ω is the average volume of martensite per newly formed crystal. Combining these two
equations, yields:
(
d ΔG γ →α
df
= −Ω(1 − f )C 2
dT
dT
'
)
(2.17)
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University of Pretoria etd, Kasonde M (2006)
Chapter 2: Literature Review
(
)
d ΔG γ →α
Assuming that Ω , C 2 , and
are constant over the extent of the transformation
dT
and integrating from Ms ( f = 0) to T gives:
'
(
)
d ΔG γ →α
(Ms − T ) (2.18)
ln (1 − f ) = ΩC 2
dT
This equation is equivalent to equation (2.14) with the positive parameter C1 expressed by:
'
(
d ΔG γ →α
C1 = −ΩC 2
dT
'
)
(2.19)
Thus ln (1 − f ) is expected to vary linearly with T when the nucleation and growth of the
martensite crystal in a sample obey the characteristics as proposed by Magee. The
assumption that Ω is a constant is in contradiction with the Fisher model [42], which
assumes that Ω decreases strongly as the transformation progresses. Van Bohemen et al
[43] have fitted their experimental data to the Koistinen and Marburger equation for the
following steels:
Table (2.9). Chemical composition of steels used in Van Bohemen’s study [43]
Steel
C60
C70
C80
C
0.6
0.7
0.8
Si
0.39
0.37
0.41
Mn
0.50
0.68
0.61
P
0.020
0.027
0.012
S
0.04
0.04
0.05
Cr
0.23
0.29
0.28
Cu
0.21
0.22
0.23
Ni
0.07
0.16
0.15
They have found the following values for the fitting parameters of the kinetic equation:
Table (2.10). Fitting parameters for the kinetics of the martensitic transformation
Steel
C60
C70
C80
Ms
( C)
0
282
248
211
C1 (K −1 )
dΔG γ →α dT (J mol 0 C )
ΩC 2 (mol kJ )
f A (− )
0.067
0.055
0.046
7.2
7.0
6.9
9.3
7.9
6.7
0.90
0.95
1.00
'
2.2.10. Crystallography and morphology of martensite, general considerations and
definition of martensite
In optical microscopy one may distinguish between two kinds of martensite: lath and plate
types. Lath martensite is usually formed at low alloy contents (or at high Ms) and plate
martensite at high alloy contents (or low Ms) and a mixture of the two types occurs in
between. At higher magnifications with transmission electron microscopy it appears that
lath martensite is a highly dislocated structure and it probably has formed through slip. The
midrib of plate martensite is heavily twinned and it probably has formed by a twinning
mechanism. The outer part of a martensite plate is often dislocation-rich and without twins
and sometimes it resembles lath martensite in optical microscopy.
A martensitic transformation is a phase transformation that occurs by cooperative atomic
movements.
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That a given structure is produced by a martensitic transformation can be confirmed by the
presence of the diffusionless character, the surface relief, and the presence of many lattice
defects. Such characteristics are, therefore, criteria for the definition of martensite [36].
Martensite may have many other characteristics, which though suggesting the presence of
martensite, are not necessarily proof in themselves that a martensitic transformation has
occurred. For example, high hardness was believed a necessary property of martensite at
the time when the word “martensite” was first adopted but it is no longer regarded as a
good criterion. Equally, the rapidity of the transformation does not necessarily lead to
martensite. Though in most steels the time of formation of an α ' crystal is of the order of
10 −7 seconds, the growth is so slow that the process in some alloys may be followed under
an optical microscope [36]. The existence of a habit plane and orientation relationship with
the parent phase is a necessary consequence of the coherency of a martensitic
transformation; although in turn it is not a sufficient criterion, because coherent precipitates
that are definitely not classified as martensite also have such characteristics.
A number of types of martensite have been observed in nonferrous alloys. In Carbon and
low alloy steels with Ms temperatures well above room temperature, the complete
suppression of Carbon diffusion during quenching is virtually impossible to attain. In the
lowest Carbon steels with high Ms temperatures the Carbon mobility is sufficient to even
cause epsilon carbide (Fe2.4C) precipitation in the martensite during quenching to room
temperature, a process referred to as autotempering [60]. A more common manifestation of
Carbon diffusion in martensite during quenching is its segregation to dislocations and lath
boundaries. Speich [51] has presented indirect evidence based on electrical resistivity
measurements, for the segregation of Carbon atoms in Iron – Carbon martensite. He
reasoned that the lower slope in the change in resistivity curve for martensitic structures
containing less than 0.2% C, corresponds to complete segregation of the Carbon to
dislocations, leaving the ferrite free of the scattering centres due to carbon trapped in
octahedral interstitial sites. The higher slope in the change in the resistivity curve in
martensitic microstructures in steels containing more than 0.2% C was attributed to the
scattering by carbon atoms randomly distributed in octahedral sites of the martensite. The
measurement of increasing tetragonality of Fe – C martensite crystals with increasing
Carbon concentration by X – ray diffraction [61] certainly verifies that a significant
fraction of Carbon atoms are retained in octahedral sites in untempered higher Carbon
steels. Direct evidence for Carbon atom segregation to dislocations during quenching and
room temperature aging of martensite has been obtained by Smith and his colleagues [62]
with field ion / atom – probe microscopy. They confirmed Speich’s conclusion that almost
90% of the Carbon atoms in a 0.18%C martensite are segregated to dislocations. Mader and
Krauss [63] showed that packet martensite consists of dislocated laths ( α ' ) which form in
steels when the Ms transition temperature is above 350 0 C . This temperature is strongly
dependent on the steel’s composition, especially its Carbon content. McMahon and Thomas
[64] showed that the dislocated structures at martensitic lath boundaries ( α ' ) were in fact
thin microlayers of retained austenite. The identification of such thin layers of retained
austenite requires diffraction analysis through electron microscopy. This interlath austenite
was revealed by the authors through high resolution lattice imaging electron microscopy
from which it was suggested that there was considerable Carbon enrichment at the α ' / γ
interfaces, i.e. also suggesting Carbon movement. Heat treatments of α ' / γ phase mixtures
in the range 300 to 500 0 C result in the austenite decomposing to interlath carbides. The
structure becomes similar to lower bainite, causing embrittlement in directions transverse
with respect to prior austenite.
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University of Pretoria etd, Kasonde M (2006)
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Liu and Dunne [65] investigated the nature of the terminating interfaces of the twin
volumes in Cu-14%Al-3.4%Ni twinned martensite, using Atomic Force Microscopy.
Although twin relief was generally evident in the random sections they have examined,
well-defined interfacial facets corresponding to the terminating twin volumes were not
observed. Instead, side-plates extending beyond the habit plane were common, being
associated with the smaller of the twin volumes. They noted that the twin plane is close to
the habit plane and its extension ahead of the general interface with its own twinned
substructure, is probably related to the plate growth mechanism. From the observed
difference in side-plate extensions between thermal and stress-induced plates they suggest
that growth occurs by the motion of only one interface in providing strain accommodation
of the applied stress, whereas for thermal martensite the growth is constrained by the
surrounding matrix and the stresses imposed by transformation shear and a volumetric
change. Moreover fine twins on a system other than the primary twinning system were
also observed for the thermal martensite in their investigation.
2.2.10.1. Habit plane
Christian [44] noticed that the habit plane is usually one of three types:
- planar, irrational and semi-coherent, separating a single-crystal parent from a slipped
and/or faulted single-crystal product;
- planar, irrational and separating a single-crystal parent from a twinned product; or
- curved and thus macrospically displaced from the “true” habit plane, because of
interfacial steps.
The martensite interface is observed to be glissile, at least for the forward transformation,
and it is implied that either:
- planar sections migrate as a unit, consisting of twin-parent volumes or surface
dislocations; or
- steps consecutively sweep across the whole interface.
Christian [45] concluded that the invariant plane strain condition might only be met for
“unconstrained” single interface transformations. In polycrystalline austenite, local
constraints such as coherency strains could induce the operation of a more complex lattice
invariant shear, giving significant habit plane variations. Kennon and Dunne [46] explored
'
the suggestion by Christian , in the case of γ 1 (2 H ) plates in a cubed-shaped single crystal
Cu-Al-Ni alloy. After accurate tilt and habit plane trace measurements with an estimated
experimental error in the habit plane normal of less than ± 10 , they concluded that even in
the case of unconstrained transformation, a real variability in the habit plane normal could
occur. A close examination of the interface of γ 1' martensite by the authors indicated that
variations in transformation twin width are not uncommon, resulting in changes in the local
average interface plane. The habit plane can curve to accommodate minor localised
constraints and any atomic matching across the interfacial twin facet must be high. This
observation has been confirmed recently in the case of a {225} martensite transformation
in Fe-Cr-C alloy by Lin et al. [47].
26
University of Pretoria etd, Kasonde M (2006)
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Tadaki and Shimizu [48] suggested that the temperature dependence of the lattice
parameters of the austenite and the difference between that of austenite and martensite must
mean that the crystallography of the transformation will change with the actual temperature
of formation of the martensite during the quenching. A continuous spectrum of habit planes
is, therefore, possibly to be expected over the transformation temperature range as a
function of order and temperature. Dunne and Kennon [49] concluded from the systematic
type of habit plane variation, that there is clearly a scatter which is not accounted for by the
theory and which is a characteristic feature of the martensitic transformation. Moreover,
habit plane “flexibility” is likely to be a characteristic feature of martensite plates.
Given the plane and direction of the lattice invariant shear, the lattice correspondence
between the parent and martensite and the pure strain, the crystallographic theory predicts
the habit plane on the basis that it is exactly invariant. However, Dunne and Kennon [49],
noticed that the invariance may only be local because of localised plastic and/or elastic
constraints, leading to macroscopic habit plane measurements which may differ
significantly from the predicted plane. Local changes in the invariant shear will occur with
strains created by the plate itself or by prior transformation. Accommodating slip or
faulting can occur in the parent phase or in the martensite, influencing the form of the
moving interface. On the basis of their analysis of habit plane scatter, Dunne and Kennon
[49] concluded that the response to the question: “how regular is the habit plane?” must be:
“not very”. Moreover the variability should be regarded as a characteristic feature of the
transformation rather than an anomaly. As the literature shows, good correspondence
between measured and predicted habit planes is usually restricted to precisely controlled
conditions in which limited transformation occurs in a coarse grained or a single crystal
parent phase. In other circumstances and particularly for transformations involving a large
volume change, considerable habit plane variability should be expected.
Morito et al [50], have examined the morphology and crystallography of lath martensite in
Fe-C alloys with different Carbon contents such as 0.0026, 0.18, 0.38 and 0.61 mass %C by
means of optical microscopy, by SEM and by TEM. Their main findings were: as the
carbon content increased from 0.0026% to 0.61%, the block and packet size of the
martensite units decreased; the orientation relationship between austenite and martensite
was close to the Kurdjumov-Sachs relationship and some laths seemed to have nearly the
Nishiyama relationship; twenty-four variants in the K-S relationship were suggested as
presented in Table (2.11).
In low Carbon alloys (typically 0.0026%C – 0.38%C), martensite packets consisted of
well-developed parallel blocks with three blocks (with different orientations) in each
packet. Each block consisted of laths of two specific K-S variant groups (called a “subblock”) which were misoriented by small angles of about 10°; and in high Carbon alloys
(>0.61% C), packets consisted of fine blocks whose width were a few microns. Blocks
consisted of laths with a single variant and six blocks with different orientations existed in
a packet.
In martensitic Fe-C alloys and low-alloy Carbon steels with above-room temperature Ms
temperatures, Krauss [51] observed that it was impossible to prevent Carbon diffusion
during quenching, and strengthening of martensite becomes dependent on static and
dynamic strain aging due to Carbon atom interaction with dislocation substructures. The
substructure of the martensitic matrix appears to be the dominant strengthening component
in these steels.
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University of Pretoria etd, Kasonde M (2006)
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Table (2.11). Variants in K-S relationship [50]
Variant N 0
V1
V2
V3
V4
V5
V6
V7
V8
V9
V10
V11
V12
V13
V14
V15
V16
V17
V18
V19
V20
V21
V22
V23
V24
Plane parallel
(111) γ
//(011) α ′
(1-11) γ
//(011) α ′
(-111) γ
//(011) α ′
(11-1) γ
//(011) α ′
Direction parallel
[γ ] //[α ′]
Rotation from variant 1
Axis (indexed by martensite)
Angle [deg.]
[-1 0 1] // [ -1 –1 –1 ]
[-1 0 1] // [ -1 1 -1]
[ 0 1 –1 ] // [ -1 –1 -1 ]
[ 0 1 –1 ] // [ -1 1 –1 ]
[ 1 –1 0 ] // [ -1 –1 1 ]
[ 1 –1 0 ] // [ -1 1 -1 ]
[ 1 0 –1 ] // [ -1 –1 1 ]
[ 1 0 –1 ] // [ -1 1 –1 ]
[0.5774 – 0.5774 0.5774]
[0.0000 – 0.7071 – 0.7071]
[0.0000 0.7071 0.7071]
[0.0000 0.7071 0.7071]
[0.0000 – 0.7071 – 0.7071]
[ -0.5774 – 0.5774 0.5774]
[0.5774 – 0.5774 0.5774]
60.00
60.00
10.53
60.00
49.47
49.47
10.53
[ -1 –1 0 ] // [ -1 –1 1 ]
[ -1 –1 0 ] // [ -1 1 -1 ]
[ 0 1 1 ] // [ -1 –1 1 ]
[ 0 1 1 ] // [ -1 1 -1 ]
[ 0 –1 1 ] // [ -1 –1 1 ]
[ 0 –1 1 ] // [ -1 1 -1 ]
[ -0.1862 0.7666 0.6145]
[ -0.4904 –0.4625 0.7387
[ 0.3543 –0.9329 –0.0650
[ 0.3568 –0.7136 0.6029]
[ 0.9329 0.3543 0.0650]
[ -0.7387 0.4625 –0.4904]
50.51
50.51
14.88
57.21
14.88
50.51
[ -1 0 –1 ] // [ -1 –1 1 ]
[ -1 0 –1 ] // [ -1 1 -1 ]
[ 1 1 0 ] // [ -1 –1 1 ]
[ 1 1 0 ] // [ -1 1 -1 ]
[ -1 1 0 ] // [ -1 –1 1 ]
[ -1 1 0 ] // [ -1 1 -1 ]
[ -0.2461 –0.6278 –0.7384]
[0.6589 0.6589 0.3628]
[ -0.6589 0.3628 –0.6589]
[ -0.3022 –0.6255 –0.7193]
[-0.6145 0.1862 –0.7666]
[ -0.3568 –0.6029 –0.7136]
57.21
20.61
51.73
47.11
50.51
57.21
[ 0 –1 –1 ] // [-1 –1 1 ]
[ 0 –1 –1 ] // [--1 1 -1]
[ 1 0 1 ] // [ -1 –1 1 ]
[ 1 0 1 ] // [ -1 1 -1 ]
[ 0.9551 0.0000 –0.2962]
[ -0.7193 0.3022 –0.6255]
[ -0.7384 –0.2461 0.6278]
[ 0.9121 0.4100 0.0000]
20.61
47.11
57.21
21.06
Lath martensite forms in low and medium-Carbon steels and consists of parallel arrays or
stacks of board- or lath-shaped crystals. In these steels most of the crystals in a parallel
group have the same crystal orientation and the parallel groups are referred to as blocks
[52]. As Carbon concentration increases, the parallel or almost parallel crystals in a group,
termed packets, may have different orientations and variants of {557}A habit planes around
a given {111}A plane [53-54]. Plate martensite crystals form in non-parallel arrays and are
characterized by irrational habit planes, including {3 10 15}A,{2 2 5}A and {259}A [55].
The low Ms temperatures, in high Fe-C alloys and steels, cause the lath martensite crystals
to form at temperatures where the lattice invariant deformation is accomplished by
twinning and limited dislocation motion occurs.
The morphology of the martensite affects the deformation and strengthening of the
microstructure in a number of ways. In lath martensites, the block and packet structures,
because of the largely common crystallographic orientation of the parallel laths within the
blocks and packets, become the effective grain structures, which control deformation.
Similarly, because of common {1 0 0}m cleavage planes in the parallel laths in blocks and
packets of martensite, the size of cleavage facets which produce brittle transgranular
fracture is directly related to the packet size [56-57]. Also the morphology of the retained
austenite within lath and plate martensites determines whether the austenite will
mechanically transform by stress- or strain-induced mechanisms [58]. The non-parallel
formation of plate-shaped martensite crystals often results in intraplate microcracking due
to the impingement of the plates during quenching [54].
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2.2.10.2 Theory of the martensitic transformation
A number of crystallographic and thermodynamic theories have been proposed to explain
the transformation mechanisms in martensite formation. In the current thermodynamic
theories on the growth of the martensite nucleus, the interfacial and internal chemical
energies are considered to be dominant, as in the case of the crystallization in a liquid. In
addition in solids, the strain energy of the transformation is also taken into account.
Thermodynamic theories assume thermal equilibrium and ignore the microstructural and
crystallographic characteristics of the martensitic transformation [36]. The Bowles and
Mackenzie model [in 36], one of the phenomenological theories, predicts the
crystallographic features such as the habit plane, the strain and the orientation relationships
between parent austenite and product martensite. Kelly [59] recently demonstrated that,
when applied in a rigorous fashion, the Infinitesimal Deformation (ID) approach is exactly
equivalent to the Phenomenological Theory of the Martensitic Transformation (PTMT).
The disadvantages of the PTMT are its computational cost and its complexity that makes it
less understandable than the physical concepts of the minimization of the strain energy
following the well-known Eshelby analysis used in the ID approach.
2.2.11. The Bowles – Mackenzie model [in 36]
2.2.11.1. Lattice parameters and tetragonality of the martensite.
Lattice parameters of martensite and retained austenite can be measured by X-ray
diffraction with good accuracy. Cheng et al. [66] noticed a significant redistribution of
Carbon atoms and a disappearance of the tetragonality of a 5.1at.%C martensitic steel at
room temperature during aging times of less than 50 hours. Carbon atoms segregated to
lattice imperfections and also transfer from a/b-type octahedral interstices to c-type
interstices, thereby decreasing the c m parameter at room temperature.
Lyssak and co-workers [67] found that the tetragonality of the martensite is abnormally
small for Mn steels. Moreover, there are several alloy systems in which the tetragonality of
martensite containing Carbon does not obey the well-known experimental equation:
c a = 1 + 0.046 p
where p is the mass percentage of carbon in the steel.
Kajiwara and Kikuchi [68] made a very extensive and systematic study on the martensite
tetragonality in Fe-Ni-C alloys, and found that the tetragonality is quite dependent on the
mode of the lattice invariant deformation in the martensite. Uehara et al. [68] have
investigated the tetragonality of martensite in high Carbon- Iron alloys containing some
Aluminium. From their study it appears that the tetragonality is enhanced by Aluminium
and Nickel additions that stop Carbon atoms from moving out of octahedral sites to
tetrahedral sites during quenching (auto-tempering). They have measured the tetragonality
in martensite containing 2 mass %C and up to 6 mass %Ni using XRD equipment fitted
with a cooling unit. Their measurements were done at temperatures as low as 90K.
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2.2.11.2. The principal strain.
After measuring the lattice parameters of the parent austenite and the product martensite,
the Bowles and Mackenzie (BM) model for predicting the transformation characteristics
may be applied as follows:
The principal strains in the Bain distortion denoted by η i (eta), are represented by:
η1 = 2 a M a γ
η 2 = 2 a M aγ = η1
η3 = cM a γ
(2.20a)
along x-1
(2.20b)
along x-2
(2.20c)
along x-3
A unit sphere representing the austenite crystal
x1
2
x2
2
2
+
x3
2
2
2
transforms to an
2
= 1 due to the Bain distortion.
η1 η 2 η 3 2
The cones of unextended lines are found from the equation:
ellipsoid
+
2
x1 + x 2 + x3 = 1
⎛
⎞
⎛ 1
⎞
⎛
⎞
⎜ 2 − 1⎟ x1 2 + ⎜ 12 − 1⎟ x 2 2 + ⎜ 12 − 1⎟ x3 2 = 0 .
⎜η
⎟
⎜η
⎟
⎜η
⎟
⎝ 1
⎠
⎝ 2
⎠
⎝ 3
⎠
(2.21)
The semi-apex angle Φ ' of the cone is obtained from the value of
x2
x3
when x1 = 0:
1
⎛x
tan Φ ' = ⎜⎜ 2
⎝ x3
( )
⎛1 −η 2 ⎞ 2 ⎛ η ⎞
⎞
⎟⎟
= ⎜⎜ 2 3 ⎟⎟ ⎜⎜ 1 ⎟⎟ .
⎠ x =01 ⎝ η1 − 1 ⎠ ⎝ η 3 ⎠
(2.22)
Φ ' gives the positions of the unextended lines after transformation. The initial cone of the
unextended lines can be determined by considering a hypothetical inverse transformation,
such as α ' to γ transformation, i.e. a unit sphere representing the martensite crystal
transforms to an ellipsoid representing the austenite.
η1 2 x1 2 + η 2 2 x 2 2 + η 3 2 x3 2 = 1
the semi-axes of which are
(η
2
1
1
,
1
1
η1 η 2 η 3
. Therefore, it is seen that the equation:
)
)
(
,
(2.23)
(
)
− 1 x1 + η 2 − 1 x 2 + η 3 − 1 x3 = 0
2
2
2
2
2
(2.24)
represents the locus of all vectors that are unchanged in magnitude due to the hypothetical
inverse transformation. The locus is nothing else but the initial cone of the unextended
lines. The semiapex angle Φ of the initial cone is calculated from:
1
⎛x ⎞
tan (Φ ) = ⎜⎜ 2 ⎟⎟
⎝ x3 ⎠ x =01
⎛ 1 −η32 ⎞ 2
⎟
= ⎜⎜ 2
⎟
−
η
1
⎝ 1
⎠
(2.25)
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2.2.11.3. Calculation of invariant lines and normal
A plane normal is defined as a vector whose direction is parallel to the normal of the plane
and whose magnitude is proportional to the inverse of the interplanar distance. This vector
is simply a reciprocal lattice vector. Then a unit sphere (formed by the plane normal) in the
austenite lattice transforms to an ellipsoid, whose semi-axes are:
1 1
1
,
,
.
η1 η 2 η 3
The intersection of the ellipsoid with the unit sphere forms a circle, and a cone passing
through the circle gives the final position of the plane normal which is unchanged in
magnitude. Such a normal is termed an unextended normal.
An unextended normal and an unextended line that are also unchanged in direction are
termed an invariant normal and an invariant line, respectively.
Consider x-1 or x-2 is a unit vector parallel to the invariant line. The Bain distortion allows
xi also to transform through the equivalence:
(2.26)
xi = Bxi .
−
Because xi is unchanged in length, xi' xi = 1 holds. In addition, p 2' xi = 0 because the shear
'
plane p 2 of the complementary shear must involve three equations for xi .
(
'
)
2 .(101)
Assuming: p 2 = 1
(2.27)
one obtains the following three equations for xi :
(
2
2
)
equivalent to P1 = R BPB −1 B = RBP (2.28a)
x1 + x 2 + x3 = 1
2
η1 x1 + η 2 x 2 + η 3 x3 = 1 equivalent to P1 = I + d1 p1 '
2
2
2
2
2
2
(2.28b)
x1 + x3 = 0
From these equations, two solutions for xi are obtained: xi1 and xi 2 .
Let a unit normal ni (n1 , n2 , n3 ) be the invariant normal. The Bain distortion then causes ni
'
'
to transform to n i ' = ni B −1 . As the n i ' is unchanged in length, n i n i = ni B −2 ni . In
'
'
'
addition, ni d 2 = 0 because the plane with normal ni does contain the shear direction d 2 .
'
'
[
]
'
Assuming that d 2 is parallel to 1 0 1 , one obtains the following three equations for ni :
n1 + n2 + n3 = 1
2
n1
2
η1 2
+
2
2
2
n3
n2
η22
+
2
η32
=1
(2.29)
− n1 + n3 = 0
'
'
From these equations two solutions for ni are derived, viz. ni1 and ni 2
'
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University of Pretoria etd, Kasonde M (2006)
Chapter 2: Literature Review
'
Four combinations of xi and ni are possible. From these four, one combination will be
taken for numerical calculations.
2.2.11.4. The Bain distortion
The Bain distortion is represented by the matrix B :
⎡η1 0 0 ⎤
B = ⎢⎢ 0 η 2 0 ⎥⎥
⎢⎣ 0 0 η 3 ⎥⎦
(2.30)
xi = Bxi
Now p 2 transforms to p 2 B −1 due to the Bain distortion. Considering the normalized p 2 ,
'
'
'
one finds
(
p 2 = p 2 B −1 / p 2 B − 2 p 2
'
'
'
)
1/ 2
'
(2.31)
'
x i is seen to lie in the plane with normal p 2 , because p 2 . x i =0
2.2.11.5 Calculation of the invariant line strain S
The invariant line strain S can be calculated if the rotation matrix is known, with which
'
both x i and n i ' rotate back to the initial positions, xi and ni . Such a rotation matrix can
−1
be obtained in principle by solving two equations, R0 x i = xi and n i R0 = ni , and using
the properties of an orthogonal matrix. But in practice, solving these equations is not
necessarily easy. A more convenient method is used to obtain the invariant line strain as
follows:
'
'
The first step is to obtain a rotation matrix that transforms x i to xi and the second is to
'
obtain a rotation matrix that leaves xi unchanged and transforms n i ' to ni . The former
matrix can be expressed as the product of a rotation matrix R1 , whose elements in the first
′
column coincide with the components of xi , by another rotation matrix R2 , whose
elements in the first row coincide with the components of x i . Though the other elements of
′
the rotation matrices, R1 and R2 , are arbitrary, their three-component vectors must satisfy
the orthogonal conditions. As component vectors satisfying these conditions, p 2 and p 2
will be chosen for R1 and R2 respectively. Then one obtains:
R1 = ( xi , p 2 , u ) ,
where
(
u = xi x p 2
)
R2 = x i , p 2 , v ,
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where v = xi x p 2
R1 × R2 is a rotation matrix that makes xi rotate back to xi . In other words, the matrix
'
−
defined by S ( 0 ) = R1 × R × B has x1 as an invariant line. In order to obtain a rotation
'
2
matrix that makes the n1 transform to n1 ' and x1 remain unchanged, it is convenient to
convert the basis to a new i basis ( i1 i2 i3 ) defined by three orthogonal vectors x1 , p 2 and
u.
In the i basis S ( 0 ) = R1 × R2' × B can be rewritten as (iS ( 0 ) i ) = R2' × B × R1 .
Then, the invariant line strain S referred to the i basis (iSi ) is obtained by adding a rotation
of β around x1 ; that is,
[1
0 0, 0 cos β
cos β ]× R2' BR1 = (iSi )
− sin β , 0 sin β
0
⎡1
⎢0 cos β
⎢
⎢⎣0 sin β
⎤
'
− sin β ⎥⎥ R2 BR1 ≡ (iSi )
cos β ⎥⎦
0
(2.32)
The value of β must be chosen so that ni remains unchanged after it is operated on by
'
(iSi ) . When
'
ni is referred to the I basis, that is,
n1i = n1 R1
'
iS 0 i = R2 BR1
'
(n ; i ) = n R
'
'
i
i
(2.33)
1
The following equation must hold:
(n ; i )(iSi ) = (n ; i )
'
'
i
i
(2.34)
From these equations β can be determined. That is substituting equations (2.32) and (2.33)
into (2.34).
0
⎡1
⎢
Q = ⎢0 cos β
⎢⎣0 sin β
0
⎡1
⎢
(iSi ) = QR2 BR1 = ⎢0 cos β
⎢⎣0 sin β
'*
⎤
− sin β ⎥⎥
cos β ⎥⎦
0
⎡η1 0 0 ⎤
⎤
'* ⎢
⎥
− sin β ⎥ R2 ⎢ 0 η 2 0 ⎥⎥ R1
⎢⎣ 0 0 η 3 ⎥⎦
cos β ⎥⎦
0
(2.35)
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The shape strain matrix is then given by:
S = R1 (iSi )R1
'
(2.36)
2.2.11.6. Calculation of the total shape change P1 and the complementary shear P2
The invariant plane normal p1 in the shape deformation is parallel to p 2 S −1 − p 2 . The
'
'
'
'
'
normalised vector is p1 and D is parallel to p1 . The Displacement Vector d 1 of the shape
deformation is equal to:
(Sd 2 − d 2 ) / ( p1 ' d 2 ) .
(2.37)
'
where y is an arbitrary vector lying in the plane with normal p1 .
Then, choosing y to be the cross product [1 0 0] x p1 :
(
d 2 = y − yS −1
) ( p y ')
'
2
(2.38)
Thus, d 1 is not a unit vector. From the normalisation factor for this vector, the magnitude
of the shape deformation can be obtained:
m1 = norm(d1 )
(2.39)
From the normalisation factor for d 2 , the magnitude m 2 and the shear angle α of the
complementary shear can be obtained through:
λ1 = η1
λ3 = 1
λ 2 = η1 .η 3
[(
)(
s = λ1 − 1 1 − λ 2
m2 = s / (λ1λ 2 )
α = a tan (m2 2)
2
2
)]
1/ 2
(2.40)
2.2.11.7. Calculation of the orientation relationship
2.2.11.7.1 Kurdjumov – Sachs
The total shape change P1 associated with the transformation is equal to SP . Since P is not
accompanied by any change of crystal orientation, the orientation relationship is
determined only by S . According to the Bain correspondence, (1 1 1) f and 1 0 1 f in
[
]
[
]
the austenite lattice correspond to (0 1 1)b and 1 1 1 b , respectively in the martensite
lattice. The (1 1 1) f plane should be transformed by S to J = [1 1 1]. The (1 1 1) f
(
)
plane should be transformed by S to 1 3 (1 1 1)S −1 . The unit normal of the
transformed (1 1 1) f plane is u1 . u1 should be a unit vector parallel to the normal of the
(0
1 1)b plane.
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Therefore, the scalar product of the normal of the (0 1 1)b plane and that of the
original (1 1 1) f plane is the cosine of the angle between (1 1 1) f and (0 1 1)b . Next,
[1
]
[
]
0 1 f is transformed by S to S 1 0 1 f . By normalizing this, we obtain a unit vector
[
]
[
]
parallel to 1 1 1 b . From the scalar product of this unit vector with that of 1 0 1 f , the
[
]
[
]
angle between 1 0 1 f and 1 1 1 b is obtained. The non-parallelism indicates that the
K-S relation does not hold exactly.
2.2.11.7.2. Nishiyama Wasserman
[
Use similar calculations regarding the 1 1 2
[0
]
]
f
direction and the corresponding
1 1 b direction.
2.3. Tempered martensite and its mechanical properties
Generally mechanical properties of a material are determinable (at least in principle), if its
microstructure is known in detail. The crystal structure and the chemical composition of the
phases in the microstructure are important factors for the mechanical, physical, and
chemical properties. Volume fraction, shape, arrangement, and orientation of
microstructural constituents are less important for the chemical properties, where
constituents can be compared (e.g. in their corrosion resistance). In some cases, such as
intercrystalline corrosion or high temperature corrosion, the phase boundaries and the
chemical composition of the surrounding matrix must be taken into account. Volume
fraction, shape, arrangement, and phase orientation in a microstructure have a greater
influence, however, on the physical and mechanical properties. In the different
microstructures, the strengthening mechanisms in steels – strengthening by solid solution,
dislocations, second phase particles and grain size – are superimposed. Additional effects
arise from the arrangement of second phases.
2.3.1 Effect of Carbon additions
In steels, the Carbon content of the alloy will have a significant effect on the hardness of
martensite. At too high a value of Carbon, retained austenite will appear and the macrohardness of the alloy will decrease once more. It appears that the hardness of martensite is a
linear function of the square root of the Carbon content. These results are a summary of a
large number of investigations [72,73] that also include low alloy steels where the tensile
strength of a martensitic steel obeys the following equation:
σ M = σ M0 + K M C M
where σ M0 and K M are constants and C M is the mass percent of Carbon in the steel. This
relationship is, of course, only valid if the alloy contains 100% martensite. If this is not the
case, then a weighting factor needs to be introduced. Such a relationship is of particular use
in martensitic/austenitic dual phase steels.
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2.3.2 Effect of Sulphur and Manganese content
There is abundant [74], evidence that reducing the inclusion volume fraction by lowering
Sulphur levels to the minimum possible, will improve the upper shelf fracture energy and
the impact toughness of the steel. In some cases such data have been interpreted in terms of
sulphide spacing and shape and their impact has been primarily the motivation in the
production of cleaner steels with very low Sulphur levels. Today, Ultra High Strength
steels can be produced with Sulphur levels of the order of 0.003wt %S, or even lower. The
Rice and Johnson model [in 74] suggests that the upper shelf fracture toughness of ultra
high strength steels should scale as the square root of the sulphide spacing.
Implicit in the second approach to the design of ultra high strength steels is the assumption
that appropriate modifications to the microstructure by changes in composition, heat
treatment or both, can be found which will improve the toughness of the steel. Empirical
knowledge has been gained which suggests that the microstructural features that influence
the toughness, include prior austenite grain size, martensite packet size, the amount,
morphology and mechanical stability of retained austenite, the size, spacing, shape and
coherency of particles precipitated upon tempering, as well as the relative amounts of
dislocated and plate-shaped martensite. The proposed model of Garrison [in 74] suggests
that at the point of fracture initiation the crack tip opening displacement will scale as the
product of two terms – one being the sulphide spacing and the other a measure of localised
ductility lacking in the Rice and Johnson model. The data to date suggest that it is through
this measure of localised ductility that the microstructure influences the toughness of the
steel. This implies that two distinct alloy design methodologies are possible, one to
maximise the sulphide spacing and the other to maximise the localised ductility through
control of the microstructure.
The critical crack tip opening displacement, δ IC , can be related to the fracture toughness,
through the equations:
J
δ IC = d n IC
(2..41)
σ0
K
J IC = IC
E′
2
(2.42)
E
for plane strain conditions
1 −ν 2
where E is Young’s modulus, σ 0 is the average of the yield strength and ultimate tensile
strength, ν is Poisson’s ratio, and d n is a function of the yield strain, K IC is the fracture
toughness, J IC is the area specific energy for crack propagation, and whether plane stress
or plane strain conditions are assumed. The plane strain fracture toughness should scale E ′
as:
E ′ = E for plane stress conditions and E ′ =
(
)
1/ 2
K IC
⎧ X ( R / R )σ E ⎫
≈⎨ 0 V l 0 ⎬
dn
⎩
⎭
(2.43)
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This approach predicts the same dependence on X 0 , the primary particle spacing, as the
Rice and Johnson model, but ( RV / Rl ) introduces a measure of the ductility lacking in that
model. Rl is the radius of primary particles assumed to be spherical sulphide and RV is the
void radius. This model has been applied to several ultra high strength steels for which the
primary particles are spherical sulphides. The average three-dimensional nearest neighbour
distance between sulphides, X 0 , is been calculated from [74]:
X0
= 0.89 f
R0
−1 / 3
(2.44)
where f is the sulphide volume fraction and R0 the average sulphide radius.
From formulas (2.41) to (2.44) there appears to be an excellent correlation between δ IC
and the quantity X 0 ( RV / Rl )
R0
. However, the factors which determine ( RV / Rl )
really known. According to the model, ( RV / Rl )
R0
R0
are not
will continue to increase in accordance
with the stress-strain history until the voids nucleated at sulphides coalesce through
processes of void sheet coalescence, strain localisation or both. There is clear evidence that
the microstructure can influence ( RV / Rl ) R0 . However, a number of other factors could
also influence this parameter. Presumably these include the yield strength and work
hardening capacity as both influence flow localisation. In addition, while manganese
sulphides are believed to be weakly bound to the matrix, it is possible that the nucleation
strains as well as spatial and size distributions of the sulphides could influence ( RV / Rl ) R0 .
The influence of microstructure on ( RV / Rl )
R0
is most clearly illustrated by considering the
X0
= 0.89 f −1 / 3 , X 0 can be
R0
increased by increasing R0 , the average sulphide radius, or by reducing the sulphide
effect of tempering on the toughness. From the equation
volume fraction f , which in effect reduces the sulphur content. While X 0 can be increased
by reducing f , the fracture toughness will scale as f
−1 / 6
if R0 remains unchanged.
However, if R0 is increased without changing f , the fracture toughness will scale as R0
1/ 2
.
The strong dependence of fracture toughness on R0 suggests that by increasing the average
sulphide size – that is, by replacing a dispersion of fine closely spaced sulphides by larger
more widely spaced sulphides – significant improvements in toughness can be realised.
Even if Sulphur levels are reduced to very low levels ( ≅ 0.001wt % S), it should be possible
to achieve further improvements in toughness by increasing X 0 through R0 . At a sulphide
spacing of about 10 μm , low alloy quenched and tempered steels can achieve a fracture
toughness of 115 MPa(m)1/2 at a yield strength of about 1700 MPa [74]. Significant further
improvements in toughness of such steels will require sulphide spacing of the order of 20 –
30 μm . The only way sufficiently large sulphide spacing can be obtained is by reducing
sulphide volume fractions to the minimum level possible and then increasing the average
size.
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Therefore, the application of this methodology for improving toughness reduces to the
problem of maximising, for a given sulphide volume fraction, the average size.
The methods utilised in achieving this goal will depend on the nature of the sulphides
present in the steel. If sulphides are Manganese sulphides then it is suggested that
maximum sulphide size, and hence spacing, can be achieved by integrated application of
three strategies. The first is the control of sulphide shape and size in the as – cast condition
with the goal being equiaxed sulphides of the largest possible size. The second is to utilise
forging techniques, which minimize elongation of the sulphides in the as-cast structures.
The third is to coarsen the sulphide distribution after forging [74].
On solidification, three primary sulphide morphologies are observed [74]. Type I sulphides
are spherical and are favoured by high Oxygen and low Carbon levels. Type II sulphides
are often dendritic, rosette-like or fan-like in form, and are favoured by low Oxygen levels.
Type III sulphides are faceted equiaxed particles and are favoured by low Oxygen levels in
combination with high Carbon levels, Silicon additions and Aluminium additions. There is
also an influence of Sulphur content on sulphide type, with type III sulphides favoured as
the Sulphur content is reduced. Cooling rate on solidification can influence the sulphide
type. Type II sulphides are favoured over both type I and type III sulphides as the cooling
rate is increased. It is agreed [74] that type II sulphides form as a result of the eutectic
reaction L → Fe + MnS . Type III sulphides, because of their faceted form, are believed to
precipitate as a solid in the interdendritic liquid. However, Type III sulphides seem to be
more uniformly distributed than type II sulphides [74]. This could be attributed to their
precipitation in the liquid at higher temperatures than Type II sulphides and their
entrapment by growing dendrites. The most useful compositions should be those, which
promote Type III sulphides.
There have been numerous studies [74] of the effects of temperature and extent of
deformation during hot rolling on the shape and morphology of manganese sulphides.
During hot rolling the rod-like type II sulphides become aligned parallel to the rolling
direction and type I and type III sulphides become elongated plates, lengthening primarily
parallel to the rolling direction. The extent of this elongation is minimised by rolling at the
highest possible temperatures. In general it has been found that type III sulphides are more
plastic than type I sulphides and elongate during rolling to a greater extent [74]. This has
been attributed to the higher Oxygen content of type I sulphides. However, upset and cross
forging could alter this simple description. Rolling would orient the rod-like Type II
sulphides parallel to the rolling direction and elongate Type III sulphides in the direction of
rolling. However, upset and cross forging could break up the Type II sulphides and
possibly preserve the equiaxed nature of the Type III sulphides. In that case, after upset and
cross forging, the sulphides precipitated as Type II and Type III, would now consist of
small broken fragments and larger equiaxed particles respectively.
2.3.3. Effect of alloying elements
Tanino and co-workers [26] have shown that Mo moderately increases the yield strength of
martensitic steels, probably due to its large atomic size, whereas the addition of Mn results
in a slight decrease in yield strength. Schramm et al. [2] reported that both Mn and Mo
increase the stacking fault energy of the austenite matrix, although Mn is generally
considered to stabilize the γ- phase by lowering the stacking fault energy of the austenite.
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Carbon is considered to increase the stacking fault energy of the austenite matrix [73]. The
strengthening of the austenite matrix will require a larger driving force for its
decomposition to martensite, giving rise to a decrease in Ms temperature. Silicon has an
incredibly small solubility in cementite. Therefore, increasing the Silicon concentration of a
steel to a value greater that about 1.5 wt%Si ensures the absence of cementite in upper
bainite [75]. Interlath cementite in bainite is responsible for initiating fracture in highstrength steels. Its absence is, therefore, expected to make the microstructure more resistant
to cleavage failure and void formation.
The ductile films of austenite, which usually are intimately dispersed between the plates of
martensite, have a blunting effect on crack propagation. They further add to the toughness
by increasing the energy of fracture as the austenite is induced to transform to martensite
under the influence of the stress field of a propagating crack. This is the TRIP effect, or
transformation induced plasticity effect.
2.3.4. Ageing of Iron – Carbon martensite at room temperature
The details of Carbon partitioning during or after displacive or martensitic transformation
are still somewhat controversial. In martensite, the displacive transformation is usually
believed to occur without diffusion of Carbon or interstitials [41], and thus the body –
centred martensite phase can be substantially saturated with Carbon. Subsequent Carbon
partitioning between martensite and retained austenite is not considered because the
temperature is too low for substantial amounts of diffusion to occur after quenching, and
because Carbon supersaturation is usually eliminated by competing processes, e.g. carbide
precipitation during tempering [59]. There is, however, evidence that Carbon partitioning
from martensite to retained austenite does occur to thin interlath films during cooling [26]
or by isothermal holding in a Si-containing steel after transformation [76].
Carbon partitioning is one means of stabilizing austenite against further transformation at
lower temperatures, and is likely to be especially important in these steels containing
alloying additions (e.g. Silicon) that suppress formation of Iron carbides [77].
2.3.5. Low temperature tempering of Martensite
Generally, quenching and tempering are well-established means to produce strengthening
in steel, which can be achieved mainly due to the precipitation of a fine dispersion of alloy
carbides during tempering at elevated temperatures [72]. Known for forming the highest
level of strength in steel, the martensite structure is rarely used in an untempered condition
because a large number of internal stresses associated with the transformation cause the
material to be lacking in ductility [2,78]. However, low-temperature tempering is sufficient
to reduce these stresses considerably without changing the basic features of the martensite
structure. Therefore, from the commercial point of view, the study of martensitic steels has
to include that of steels tempered in the range of 200-250 0 C . However, apart from the
effect of tempering temperature, the strength of the martensitic structure is dominated by
the Carbon content and volume fraction of martensite and, therefore, is affected indirectly
by the Ms and the Mf temperatures [75].
The mechanical behaviour of a quenched-and-tempered steel depends strongly on its
microstructure. Thus, the study of the effects of the microstructure and dislocation
substructure of a steel on its strength, ductility and fracture characteristics is of great
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importance from the viewpoint of both theory and practice. The so-called “first stage” of
tempering (T1) is associated with the appearance of a metastable and coherent ε transition
carbide, which precipitates uniformly throughout the martensite phase. Although the
precipitation of the transition carbide proceeds within a few minutes in the temperature
range of 100 to 200 o C , precipitation of ε carbides has been detected at temperatures as
low as room temperature after several months of aging [78]. Tempering well into the T1
temperature range leads to a dispersion of coarse particles in a matrix of low-Carbon
martensite. Above 200 o C the transition carbide is replaced by the more stable Fe3C and at
higher temperatures by the M3C carbide if substitutional carbide forming alloying elements
are present in the steel. This implies diffusion of substitutional alloying elements at the
higher temperatures. If the steel is tempered below 200 o C the transformation to cementite
would necessitate several months to become effective [78]. The precipitation of cementite
marks the third stage of tempering.
2.3.5.1. Structure and Morphology of the Stage 1 Carbide
In his early X-ray investigation, Jack [in 72] found that the Stage 1 carbide in high-Carbon
martensite possessed hexagonal symmetry and he called this phase epsilon carbide ( ε
carbide). Jack’s proposed orientation relationship between ε carbide and low-carbon
martensite:
(0001) ε // (011) α
and
−
( 10 11 ) ε // (101) α
was confirmed by Wells [in 72] more than 20 years ago and has also been found in
numerous other selected-area electron-diffraction studies. Unable to identify the positions
of the Carbon atoms in the ε structure, Jack suggested that the ε carbide might exhibit a
range of compositions from Fe2C to Fe3C. Later calculations based on dilatometry results
[78, 79] placed the composition at Fe2.4C. The APFIM results of Chang [in 78] on an Fe15%Ni-1%C martensite tempered at 130 0 C , indicate a composition of about 20 to 25
at%C. This is close to the M3C stochiometry, but considerably less than the 33 at% C
required for an M2C carbide. Detailed electron-diffraction investigations of Fe-C and FeNi-C martensites by Hirotsu et al. [in 72] indicated that Carbon atoms may be ordered in
the transition carbide, reducing the symmetry from hexagonal to orthorhombic. They
referred to the ordered phase as eta carbide ( η carbide) to distinguish it from Jack’s
hexagonal carbide. Taylor [in 72] has suggested that the η carbide can be regarded as a
derivative of the ε carbide structure, and that it may be more appropriate to refer to the
ordered carbide as “ ε ' ”, thereby recognizing its structural similarity to Jack’s ε carbide.
A variety of morphologies have been reported for the Stage 1 carbide. Early TEM
investigations of Fe-Ni-C martensitic steels [in 72] reported a plate-like carbide with a
{100} α habit plane. Later work on Fe-Mn-C [in 72] alloys concluded that the carbides were
rodlike in shape along 100 α . Other studies of Fe-Ni-C and Fe-Si-C alloys found the
carbide particles to be rodlike, but with the long axis nearly parallel to
211 α . To
complicate this issue further, several studies employing dark-field electron microscopy [72]
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indicated that what appeared to be rodlike carbides were actually composed of arrays of
much smaller particles. The disparity among these observations suggests that alloy
composition might exert an important influence on the actual carbide morphology.
2.3.5.2 Nucleation and Growth of the Stage 1 Carbide
For many years, Stage 1 carbide precipitation was regarded as a homogeneous process
occurring by classical nucleation and growth in a single-phase matrix. However, results on
martensite ageing [72] show that a decomposition process precedes the precipitation of T1
carbides, opening up the possibility that structural features of aged martensite influence the
mechanism of subsequent Stage 1 carbide nucleation. Nakamura et al. [in 72] have
suggested that stage 1 carbides emerge directly from the modulated structure associated
with the prior A stage of tempering below room temperature. Nakamura et al., based on
their high-resolution TEM imaging results on an Fe-1.5%C alloy, concluded that the Ironatom displacements produced by interstitial Carbon atoms favour nucleation in the highCarbon product of the modulated structure. Although the actual mechanism by which Stage
1 carbide nucleation occurs is not yet firmly established, the above results indicate that the
nucleation of T1 carbides is heterogeneous, at least in martensites that undergo spinodal
decomposition prior to T1 carbide precipitation such as in high Chromium Fe-Cr steels.
Macroscopically, precipitation appears to be homogeneous, because the decomposition of
virgin martensite occurs uniformly throughout the martensitic phase providing a fine,
uniform distribution of sites for subsequent carbide nucleation. New insights into the nature
of the growth of the Stage 1 carbide may come from recent results on Fe-Ni-C martensite
[72]. What appeared to be stacking faults within platelike carbide particles were observed.
These faults appear to represent shearing on the basal plane of the carbide lattice.
In considering the lattice correspondence between ε carbide and the bcc or bct parent
phase, Taylor [in 72] demonstrated that the carbide habit plane is macroscopically invariant
if a simple shear on the basal plane (representing an internal accommodation deformation
mechanism) accompanies the orthorhombic lattice distortion that relates the two structures.
Hence, the observed platelike shape of the particles would minimize the strain energy
associated with precipitation.
Taylor [in 72] points out that the carbide habit plane and morphology may be composition
dependent, inasmuch as the lattice constants (and hence the crystallographic relationship
between parent and product phases) are generally a function of alloy composition. This
may partly explain the varied carbide morphologies that have been reported. The concept
of an invariant-plane strain (IPS) transformation proposed by Taylor has, of course, been
widely applied to the diffusionless martensitic reaction in steels. Although the precipitation
of T1 carbides is clearly not diffusionless, observations of surface relief produced by Stage
1 tempering on the surfaces of prepolished metallographic specimens [72, 71], indicate that
this precipitation has a displacive component. In fact, the net shape strain produced by the
bcc → ε ' -carbide transformation may be responsible for the stress relaxation observed
during Stage 1 tempering [72], although other processes such as twinning and detwinning
in the martensite phase may also operate. Evidence is accumulating that the IPS mechanism
may be at play in reactions that are both displacive and diffusive in nature [72], at least
when a lattice correspondence between the parent and product phases can be defined.
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2.3.5.3. Kinetics of Stage 1 precipitation
The kinetics of Stage 1 carbide precipitation have been measured in a number of
investigations [72]. However, overlap between the A stage (spinodal decomposition of the
martensite) and the T1 stage generally complicates the interpretation of the data.
Consequently, the rate-controlling mechanism(s) are still not well understood. In general,
apparent activation energies in the range of 100 to 150 kJ/mol have been reported [72, 74].
These values are well above the activation energy for Carbon-atom diffusion in bodycentred Iron. It has been suggested that carbide precipitation involves the short-circuit
diffusion of metal atoms along dislocations, with an activation energy of about 140 kJ/mol.
Such diffusion was invoked for the accommodation of growing particles through plastic
deformation of the martensitic matrix [77]. However, the proposed IPS transformation
suggests that accommodation occurs within the carbide particle, and hence growth would
require an intrinsic metal-atom diffusion. Further investigation is required before the
factors controlling carbide growth will be completely understood.
2.4. Mechanical properties of tempered martensitic steels
For an alloy steel with the chemical composition;
Elements
Wt.(%)
C
0.39
Si
0.24
Mn
0.61
Ni
1.46
Cr
0.67
Mo
0.17
P
0.021
S
0.006
Woei-Shyan et al. [78] have found the following main results on the tempering of the
martensite:
Effect of tempering temperature and time
Vickers hardness 62.5 kg
650
600
550
Tempering time 2 h
Tempering time 48 h
500
450
400
350
0
100
200
300
400
500
600
Tempering temperature [Celsius]
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Chapter 2: Literature Review
Ultimate tensile strength
Ultimate tensile strength [MPa]
1900
1800
1700
1600
1500
Tempering time 2 h
1400
Tempering time 48 h
1300
1200
1100
1000
900
0
50
100
150
200
250
300
350
400
450
500
550
Tempering temperature [Celsius]
Figure 2.7. Variation of hardness and ultimate tensile strength with the tempering temperature [°C] of a low
carbon steel [78]
In the as-quenched condition, the material has the highest level of strength and hardness but
its ductility is the lowest, because of the presence of untempered martensite. A large
amount of distortion occurs during the formation of the platelets of martensite, which leads
to a rapid increase in strength and hardness. The thermal instability of interlath austenite
after tempering often leads to the formation of carbide films, which is a fairly general cause
of tempered martensite embrittlement [78]. Woei-Shyan et al correlated a loss in toughness
after tempering at 300 0 C with the retained interlath austenite and the formation of interlath
carbide films that are decomposed from the lath boundary retained austenite.
The study of retained austenite films associated with martensite in low alloy steels has
assumed new significance, primarily due to its apparent effect on the mechanical properties
of quenched and tempered high-strength steels [51]. Retained austenite has been found
even in low-alloy steels with high Ms temperatures after fast cooling to -196 0 C [80]. Since
such refrigeration fails to give a significant decrease in the amount of retained austenite,
chemical or thermal stabilization has been ruled out as the possible reasons for the
anomalous stability of the retained austenite films [76]. Azevedo and da Silva [in 74] using
Mössbauer spectroscopy, and Bhadeshia [77] using X-ray diffraction, observed no
evidence for the chemical stabilization by Carbon enrichment of the austenite. While no
such enrichment is expected on the basis of the displacive nature of the martensite
transformation, partitioning of Carbon is feasible either during the quench (i.e. after
formation of some martensite) or during subsequent tempering [75]. Hence, although no
direct evidence is available, the stability of the retained austenite has been attributed to
mechanical stabilisation [76].
The propensity for austenite retention has been rationalised in terms of the local intermartensite crystallography, and it was found that twin-related martensite variants do not
favour the retention of austenite. Inter-martensite retained austenite films were most
profuse when the adjacent martensite variants were in the same crystallographic
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Chapter 2: Literature Review
orientation [81]. A mechanical stabilisation effect hindered and often prevented
transformation to martensite.
Speer and co-workers [95] have recently proposed a thermodynamic model to describe the
endpoint of Carbon partitioning between quenched martensite and retained austenite in the
absence of carbide formation. This model assumes a stationary α / γ interface, and requires
a uniform chemical potential for Carbon (but not for Iron) in the two phases, leading to a
metastable equilibrium condition identified as “constrained para-equilibrium” or CPE. In
their calculations the authors have shown that the metastable ortho-equilibrium condition
between ferrite and austenite cannot be achieved. Consequently they developed a CPE
model to predict the endpoint of Carbon partitioning in the presence of a stationary α / γ
interface. They have predicted that the austenite inherits most of the Carbon in the steel at
constrained para-equilibrium conditions, and the retained austenite can be highly enriched
with Carbon in some instances. Applications of CPE partitioning may be considered in
steels where carbide formation is suppressed (e.g. with Si, Al, P, or even Ni additions) [75].
They propose the potential for a new “quenching and partitioning” process, or Q&P, where
the resulting martensite/austenite mixtures may be substituted for more conventional
carbide-free bainitic microstructures such as high-strength TRIP sheet steels or even
austempered ductile cast iron.
2.5. The variations of microstructure with tempering temperature and hold time
Woei-Shyan Lee et al. [78] have used TEM investigations to determine the nature of the
structural changes and the dislocation distribution after various tempering processes. Since
the Ms of their steel was well above room temperature, this has led to autotempering
behaviour in the as-quenched structure. Thus, in the case of quenched martensite there are
some brief periods in which Carbon atoms can redistribute themselves. Because the stress
fields in the lath martensite are situated around individual dislocations and cell walls,
certain interstitial lattice sites near to these places, such as defects, provide lower energy
positions for Carbon than the normal sites. Such migration can be detected by
metallography or by a smaller contribution of Carbon to electrical resistivity or to internal
friction, if comparing the Carbon situated in an interstitial site near to a dislocation with
that in a “normal” one [82]. Autotempered precipitates were not present in any of the
twinned plates but were only resolved in the dislocated laths and untwinned plates formed
at lower temperatures, i.e. near to Mf. Tempering involves many different basic processes,
such as the precipitation of carbides, the decomposition of retained austenite, and the
recovery and recrystallization of the martensite substructure. In the case of Woei-Shyan et
al. [78], epsilon carbide ( Fe2.4C, hcp) was the carbide precipitated when the material was
tempered at 2000C for 2 h. This result confirms fully that of Jack [in 72], but differs from
that of Hirotsu et al.[in 72], who found that for martensitic high-Carbon steel, the carbide
precipitated during the first stage of tempering is eta-carbide or neta-Fe2C. The material’s
microstructure at this temperature is shown in Figure 2.8.1, in which tangles of highdensity dislocations and smaller dislocation cells are the two main characteristics in the
dislocation structures. Also, epsilon carbide precipitates can be found at the interfaces
between the lath martensite.
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Chapter 2: Literature Review
(a)
(b)
Figure 2.8.1. (a) Optical micrograph and (b) TEM thin foil of an Fe − 0.2%C specimen quenched in oil
0
(850 C /30minutes) [72].
(c)
(d)
0
Figure 2.8.1. (c) TEM micrograph of an Fe − 0.2%C specimen tempered for 2h at 200 C and (d)
tempered 48h at 200
0
C [72].
(d)
Figure 2.8.1 (e) TEM micrograph of an Fe − 0.2%C specimen quenched in oil (850
0
C /30min) and
0
tempered for 2h at 300 C [72].
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Chapter 2: Literature Review
For the case of material tempered at 200°C for 48 h, the observation by transmission
electron microscopy shows that some laths have grown larger. Two operating mechanisms
should be involved in lath growth. One is the movement of lath boundaries and the other is
the elimination of lath boundaries due to the movement and annihilation of dislocations at
the boundaries. In this tempered condition, a high density of dislocations with precipitated
carbides on them, are present in most of the laths. These carbides immobilise the
dislocations and these cannot form dislocation arrays with a low energy as with small-angle
grain boundaries. During tempering of this steel at 300°C for 2h, the nucleation sites of the
carbides at low temperatures are frequently martensite lath boundaries and at higher
temperatures, ferrite grain boundaries. Pietikainen [85], found similar results than WoeiShyan and Tzay-Tian Su [78] using a steel with the chemical composition;
Element
Content
C
0.43
Si
0.28
Mn
0.70
P
0.012
S
0.025
Cr
1.054
Ni
0.201
Mo
0.179
V
0.007
Cu
0.130
Al
0.017
Pietikainen [85] austenitised the Charpy specimens (without notches) and the tensile
specimens at 855 0 C for 30 minutes. The specimens were tempered for 1 hr and for 1s in
salt baths and the grain size of the austenite was about ASTM No 7. The main results from
their study are presented in Figure 2.9. Pietikainen observed that on the fracture surface of
the specimens tempered at 200 0 C , about 20% of the intergranular fracture face occurred
along former austenite grain boundaries. This kind of fracture was near the hinge area of
the Charpy specimen. At a tempering temperature of 100 0 C this type of fracture was rare,
as also in the case of a tempering temperature of 280 0 C [85]. No tempered martensite
embrittlement during the short tempering time is evident in the figure but with some
embrittlement appearing after the 1 hour tempering times.
a)
b)
Figure 2.9. a) Charpy impact energy U-notch au and V-notch av , b) Vickers hardness as functions of the
tempering temperature [85]
Nakashima and Libsch [86], reported that the Fe3C particles already become spherical after
short tempering times. They were successful in eliminating the TMB in that way.
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Chapter 2: Literature Review
It seems that this result supports the models in which the plateau with the TMB-valley is
connected with the plate-like Fe3C and not necessarily with the presence of impurities such
as As, P, Sb and Sn on austenite grain boundaries. Mechanical instability was considered to
be the reason for the tempered martensite embrittlement. Zia-Ebrahimi and Krauss [87]
also concluded that TMB was affected by the microstructure and not necessarily by
impurities. They also proposed that the localisation of plastic deformation was the reason
for the presence of TMB.
2.6. Diffraction patterns of iron carbides
Bimal et al. [88], have investigated the stability of retained austenite in a low Carbon steel
subjected to a low temperature ageing treatment. The diffraction patterns of different iron
carbides were analysed to characterise the iron carbides precipitated as a function of the
tempering temperature. In their study ε -carbide was found to occur in the austenite phase
as a result of enrichment by interstitials during isothermal holding.
Decomposition of the austenitic phase commenced at 200 0 C . At 300 0 C dislocations were
rearranged into parallel arrays. Interfacial dislocations were formed due to the mismatch
between the parent austenite and the ferrite product. The ε -carbide gave way to the
formation of ε ′(η ) -carbide when the tempering temperature was near and above 400 0 C
and the ε ′(η ) -carbide particles formed on dislocations. Tempering at 500 0 C led to the
formation of stable cementite. From their study it seems that the shape of the ε -carbides
may be a function of the tempering time, although they did not analyse this aspect. The thin
foil micrographs and the Selected Area Diffraction Patterns established after their
experiments, are illustrated in the following figures 2.10.1 through to 2.10.6.
In their low Carbon steel martensite was seen to undergo degeneration from a planar
arrangement of dislocations at 200 0 C , as shown in Figure 2.10.1 (d). The tiny particles
that decorated these line defects were identified as ε − carbide by the associated [012] α
direction on the SADP. The orientation relationship from the schematic diagram were
found as follows:
[2110] ε //[012] α
(0110) ε //(200) α
(0001) ε //(042) α
The early stages in the decomposition of the blocky austenite and the degeneration of the
martensite at 200 0 C were also studied.
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Chapter 2: Literature Review
Figure 2.10.1. Transmission electron micrographs of an Fe-0.43%C: a) Bright field electron micrograph
revealing blocky nature of retained austenite and the presence of stacking faults as indicated by the arrow. b)
Selected area diffraction pattern (SADP) from the same area. c) Schematic representation of the [113] γ
SADP of Fig. (b) indicating positions of ε − carbide reflections in austenite matrix. d) Bright field image of
the same sample showing generation of partials preceding the transformation (region A) and twinning in
martensite (region B ). After Bimal et al. [88].
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Chapter 2: Literature Review
0
Figure 2.10.2. Bright field electron micrographs from an Fe − 0.43%C sample tempered at 200 C . (a) Early
stages in the decomposition of blocky austenite. (b) Film type of austenite in the martensitic regions remain
unaffected by tempering. (c) Early stages of degeneration of martensite. After Bimal et al. [88].
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Chapter 2: Literature Review
0
Figure 2.10.3. Transmission electron image from a sample tempered at 300 C . (a) Planar arrays of closely
spaced dislocations in ferritic region. Note also the precipitation of fine carbides along dislocations. (b) SADP
from the same region. (c) Schematic representation of [012] α SADP of Fig. (b) indicating positions of
ε − carbide reflections in ferritic matrix. After Bimal et al. [88].
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Chapter 2: Literature Review
Figure 2.10.4. (a) Bright field electron micrographs showing a three pronged pin-wheel-shaped morphology
of ε − carbide precipitate in ferritic matrix. (b) SADP from the same region as in (a). (c) Schematic
representation of [012] α of Fig. (b) depicting presence of two domain variants of ε − carbide. After Bimal et
al. [88].
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Chapter 2: Literature Review
0
Figure 2.10.5. Transmission electron micrographs from steel sample tempered at 400 C . (a) Bright field
showing interfacial structure; (b) precipitation of ε ′ ( η ) – carbide along the interfacial dislocation network;
(c) SADP from the same region, note the splitting in the
[211] α indicating locations for
{200}α and {211}α
ε ′ ( η ) – carbide and magnetite reflections.
spots; (d) indexed pattern for
After Bimal et al. [88].
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Chapter 2: Literature Review
0
Figure 2.10.6. Transmission electron micrographs from steel sample tempered at 500 C . (a) parallel arrays
of dislocations in the degenerated martensitic region. (b) Formation of coarse cementite particle in he same
specimen. 9c) SADP from the same region as Fig. b. (d) Schematic representation of [133] α SADP of Fig. c
showing presence of two variants of cementite precipitates. [88].
Thomson and Miller [89] have investigated the partitioning of substitutional solute
elements during the tempering of martensite in Cr and Mo containing steels. They observed
no partitioning of Cr, Mo and Mn between cementite and martensite after tempering at
350 0 C for 40 hours. The enrichment of Cr, Mo and Mn in the cementite during prolonged
ageing at 450 0 C for 187 hours, before the onset of softening, was the same in both the low
and high Carbon alloys, with the interface concentration of solute elements rising slowly
towards the equilibrium values. Their results provide further support for the theory that
cementite precipitates from supersaturated ferrite via a para-equilibrium displacive
transformation mechanism. After prolonged ageing at these higher temperatures, significant
enrichment of the cementite with respect to the substitutional alloying elements occurs,
with a corresponding depletion in the matrix surrounding the carbide. This enrichment at
the cementite/matrix interface was not observed to reach the high levels predicted by
equilibrium thermodynamics, as they were found experimentally to be the same in
cementite in both a low Carbon and a high Carbon alloy with significantly different
equilibrium levels of solute elements. This led the authors to conclude that diffusion of the
substitutional solutes through the matrix and within the cementite is the rate-controlling
step during the early stages of the enrichment process.
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The interface concentrations gradually rise from those dictated by para-equilibrium towards
the equilibrium concentrations [89].
Interlath austenite was revealed by high resolution lattice imaging electron microscopy
from which it was suggested that there was considerable Carbon enrichment at the α ' / γ
interfaces. Confirmation of this enriched/stabilised interlath austenite was obtained by the
powerful atomic resolution method of field atom probe spectroscopy. Heat treatments of
α ' / γ in the range 300 to 500 0 C resulted in austenite decomposing to interlath carbides.
The structure became similar to lower bainite, causing embrittlement transgranularly with
respect to the prior austenite.[89]
2.7. Tensile properties
Martensite tempered at temperatures between 150 and 200 0 C is in the temperature range
that defines the first stage of tempering. In this temperature range, fine transition carbides,
of the order of 2 – 4 nm in size, precipitate within the martensite crystals [90-91]. Many of
the Carbon atoms are tied up in the carbide particles and are, therefore, not available for
dynamic strain ageing. Also, the higher the Carbon content of the martensite is, the higher
the density and closer the spacing of the transition carbides and the transition carbide
clusters [92-93]. Reduced lengths of Carbon-free dislocation segments between the
transition carbides would require higher stresses for plastic flow according to the work
hardening theory of Kuhlmann-Wilsdorf [in 51]. The theory states that the flow stress τ at
any given plastic strain, is given by the equation:
−
τ = τ 0 + GM b / l
−
where τ 0 is the friction stress, l is the instantaneous average of the active dislocation link
lengths, and the other terms have their customary meaning.
2.8. Multiple regression as sequential simple regression
Multiple regression analysis is a useful tool to link a large volume of experimental data
with an empirical predictive capability. For example in martensitic alloys, a dependent
variable such as the Ms temperature can be linked with an arbitrary number of independent
variables such as the weight percentages of the alloying elements. The multiple regression
approach consists of regressing a dependent variable y (here the Ms temperature)
simultaneously with the independent variables U0 = 1 and x (here the weight percentage of
an alloying element) .
The error function is given by:
e= y – aU0 – bx
The two regression coefficients a and b are found by the solution of the simultaneous
equations:
a + b∑x=
∑y
a ∑ N + b ∑ x = ∑ xy
2
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Solving these simultaneous equations by the most efficient method possible, namely either
the Gauss method or its equivalent in the form of the Crout method or the m-reduced array
method then, in fact, results in the simple regression approach [94]. This consists of three
separate simple regressions, each of them not requiring the solution of simultaneous
equations. The first is the simple regression of x on U0 which yields the net variable
x = x - x as the error.
The second is the simple regression of y on U0 which yields the net variable
y= Y - y as the error.
The third simple regression depends upon the results of the first two, and hence the simple
regressions must be carried out in a definite sequence in order to build up the multiple
regression [94]. Thus multiple regression may be regarded as a sequential simple
regression.
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University of Pretoria etd, Kasonde M (2006)
Chapter 3. Experimental Techniques
CHAPTER 3. EXPERIMENTAL TECHNIQUES
In this part of the work the variables and the techniques used for analysis are presented and
rationalised. The choice of the variables and techniques of analysis is based on the
hypothesis made in the paragraph 3.1 of this work and on the scientific and industrial
backgrounds presented Chapter 2.
3.1. Hypothesis
3.1.1. How to improve the Hardenability and the Hardness
To obtain a Brinell hardness of at least equal to 600 BHN after tempering, as specified by
ARMSCOR and Mittal Steel South Africa, one should consider a Carbon content of the
alloy above 0.38%C, which is greater than the specified 0.35%C maximum in the current
steels A, B, C and D armour plates. The largest effect on the hardenability of the armour
plate should arise from the Manganese content of the steel [3]. A compromise should be
considered between the hardenability and the final grain size by considering the fact that
the large austenite grain size improves the hardenability, but is detrimental to the impact
toughness of the final microstructure. Both the homogenisation temperature and time are
important parameters as this determines the dissolution of alloying elements in the
austenite from pre-existing carbides. The martensite will present the highest hardness in the
as-quenched steel. [3]
3.1.2. How to improve the Toughness of the martensite.
The pure martensitic microstructure will be hard and brittle. To achieve the ballistic
requirements, i.e. resistance against spalling, a low- temperature tempering treatment is
specified. High-temperature tempering above 4000C is unacceptable for a high ballistic
performance as the softening of the steel is accompanied by a high decrease in the
hardness, which should be at about 600 BHN as specified. The final ballistic properties will
be strongly dependent on both the tempering temperature and time, as well as on the
chemical composition of the steel.
3.1.3. How to improve the resistance to Shock and to Spalling
The largest change in DBTT results from changes to the amount of Carbon and Manganese
in the alloy. The transition temperature for V- notch Charpy specimens is raised by about
+4 0 C for each 0.1%C and is lowered by about –12 0 C for each 0.1%Mn [74]. Increasing
the Carbon content also has a pronounced detrimental effect on the upper shelf impact
energy and reduces the weldability of the alloy if that should be considered in
manufacturing the armoured vehicle structure. The Mn/C ratio should, therefore, be at least
3:1 for satisfactory notch toughness [2].
3.1.4. How to improve the Tensile Strength
An important development that has resulted in high-strength low-alloy steels with good
impact properties is the addition of small amounts of V [73] by causing V4C3 precipitates to
form during tempering. The dispersion strengthening by this carbide raises the yield
strength while at the same time retards grain growth and improves the impact resistance.
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Chapter 3. Experimental Techniques
3.2. Alloy design
The elements likely to be found in armour steels as well as their potential effects on the
microstructure and mechanical properties, are presented in Table (3.1)
Table (3.1). Alloying elements likely to be found in the armour plate steels and their
effects on the microstructure and mechanical properties.
Element
C
Mn
Mo
Ni
Cr
Cu
Si
P
S
N
Effect
High C content increases the volume
fraction of retained austenite after
quenching to martensite.
Increases the micro-hardness of the
martensite
Improves the hardenability of the steel.
Weak carbide former.
Only the metastable Mo2C provides
secondary peak hardening by tempering at
about 500 0 C. Mo2C forms by separate
nucleation on dislocations.
M3 C
Mo2C
M6C
At 700°C, Mo2C dissolves and transforms to
M6C. [72, 77] (this will also happen at lower
temperatures, such as 600 and 650ºC)
Proposed specification
0.38% - 0.45%
0.50% - 2.0 %
Not applicable in
this case
0.6% maximum
Solid solution hardening.
Increases the precipitate/matrix misfit by
modifying the lattice spacing of the matrix.
Grain refiner, decreases the DBTT. Has a 2% - 4.0%
strong effect on decreasing the AC1 .
Cr is effective in retarding the softening 1.5 %
from Fe3C in tempering by forming M3C.
M7C3 has little strengthening effect.
Increases the matrix precipitation of Cu, 0.3%
apparently due to a heterogeneous
nucleation mechanism on vacancy-Cu atom
combinations [74].
Reduces the lattice spacing of the ferritic
matrix and increases the precipitate/matrix
misfit.
1.2% maximum
Delays the decomposition of the martensite
and the precipitation of the transition
carbides upon tempering.
Increases the corrosion resistance.
Segregates to grain boundaries
Unwanted in this case and
must be reduced to lower
than 0.005%P
Segregates to grain boundaries
Unwanted.
Increases the hardenability, decreases the
Unwanted
Ms temperature and forms coarse
carbonitrides
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Chapter 3. Experimental Techniques
To move from the current steels A, B, C and D to the high performance steel armour plates
by changes only to the heat treatment parameters, e.g. the solution treatment temperature,
the temperature of the last pass in the rolling mill, the cooling rate after rolling, the
tempering temperature and time, could be considered as the first approach to the objective.
Changes to the chemical composition of an improved alloy would be considered later if the
changes to the thermomechanical parameters are not sufficient for achieving the required
properties. It is likely, however, that the harder and tougher armour plate will require a
change in composition for achieving its hardness, hardenability as well as its toughness.
3.3. The Heat treatment design
The Grossman hardenability of the current steels A and B alloy is about 33 mm. This is
sufficient for producing a fully martensitic microstructure through the entire thickness of a
6 mm thick plate. Nevertheless, the true mass fraction of martensite formed at the centre of
the plate will be strongly dependent on the cooling rate and the initial temperature before
quenching. The final hardness, toughness and strength will depend on all of the parameters
considered at each step of the thermomechanical treatment.
The Carbon equivalent is not a highly accurate parameter for predicting the weldability but
it nevertheless allows a first qualitative assessment. For good weldability, the Carbon
Equivalent (CE) should be less than 0.6%. Above CE = 0.6%, there is a risk of forming
martensite and weld-cracking may occur [2]. For armoured steels, it will certainly be
difficult to simultaneously obtain good mechanical properties together with good
weldability, because the Carbon content cannot be decreased to lower values without
compromising the hardness. The high CE, however, does not mean that welding is
impossible. Specific pre- and post-treatment of the steel should be adopted to avoid any
damage after welding.
The ballistic performance of these alloys will depend on the ability to form a homogeneous
martensitic microstructure throughout the cross section of the plate. The Cr-containing
carbide M3C and the additions of Cr to a ferritic low Carbon steel will delay the onset of
overageing or softening considerably [73]. The hardening precipitates should be formed
within the matrix or on dislocations, and not on grain boundaries. For this, the driving force
for precipitation must be high enough and the precipitates as fine as possible for an
effective pinning of dislocations and grain boundaries.
From the above considerations the heat treatment cycle for the armoured steels may
comprise:
•
•
•
•
•
Solution treatment for homogenisation at 1050 - 1100 0 C for 1 hr;
Hot rolling with the temperature during the last pass in the rolling mill between Ac3
+ 50 to +100 0 C according to the chemical composition. Using the lowest possible
finishing temperature for hot rolling of plates is also beneficial for grain refinement
but it can be detrimental to the shape and the surface finish of the plate and of the
Manganese sulphide particles [72];
The degree of the hot work will be between 20% and 30% strain per pass;
Air-cooling to room temperature;
Austenitisation at 800 0 C to 950 0 C for 1 hour;
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•
•
•
Water-quenching to room temperature;
Tempering (for stress relief and precipitation) at 150 0 C to 300 0 C for less than
1hour. The particular tempered structure should produce the best combination of
strength, resistance to spalling and to localised yielding;
Air-cooling
3.4. Experimental Variables
To optimise the mechanical properties of the armoured steel plates the following variables
have been considered:
1. The chemical composition is considered to be the primary independent variable of
the system. It has a determining influence on the martensite start temperature, the
volume fraction of retained austenite, the type as well as the thermodynamics,
kinetics and the nucleation sites of precipitation during tempering. These factors
may determine the mechanical behaviour of the armoured steel plates. Four
armoured steels, namely Steel A, Steel B, Steel C and Steel D were used for the
preliminary investigation of the effect of the chemical composition on the
microstructure, mechanical and ballistic performances. Thereafter nineteen
laboratory cast steels with carefully chosen chemical compositions have been tested
in two steps. First, steels E through to I, and later after their ballistic testing, Steels J
through to W have been tested. The chemical compositions of these twenty-three
armoured plate steels are presented in tables (3.2) and (4.3.32).
2. The martensite start temperatures of the steels are strongly dependent on their
chemical compositions, but are also functions of the austenitisation temperature and
time, which determine the degree of carbide dissolution, the grain size and the grain
boundary surface area per unit volume. Moreover the martensite start temperature
of the steel determines the morphology of the martensite, either plate or lath
martensite, and the volume fraction of retained austenite, which influence the
mechanical properties as well as the ballistic performance of the plates. The
martensite start temperatures of the twenty-three armoured steels have been
measured and an empirical relationship with the chemical composition is proposed
for these steels using a multilinear regression method. The surface relief after the
martensitic transformation was measured by Atomic Force Microscopy (AFM) and
the results are compared between the alloys with low Ms and those with high Ms
temperatures. The defect structures in the martensite/retained austenite
microstructures are also compared between the different alloys.
3. The austenitisation temperature and time determine the grain size, the degree of
carbide dissolution into the matrix and, therefore, the martensite start temperature of
the alloys. Four austenitisation temperatures ranging from 800 0 C to 950 0 C were
selected for this purpose. The minimum temperature of 800 0 C is based on the
measurement of the austenite finish temperature, which was found to be between
739 0 C and 768 0 C for the twenty-three steels. A minimum austenitisation
temperature of ( A f + 50 0 C ) has been considered which is approximately 800 0 C .
The maximum of 950 0 C has been chosen to avoid the disadvantages of coarse
austenite grains.
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4. The Reheat-quench versus Direct-quench (i.e. directly quenched from hot rolling)
effect on the ballistic performance has also been investigated. Plates from five
alloys were reheated at 900 0 C before being water quenched. Plates from eight
other alloys were directly water quenched after the final hot rolling pass in the
laboratory hot rolling mill. The effect of a second reheating of the armoured steel
plates for 15 minutes at 850 0 C after the first ballistic testing have also been
investigated on plates from five alloys.
5. The location and shape of the retained austenite in the inter-lath or inter-martensite
plate spaces may influence the plastic behaviour of the armoured steel plates. Its
effects on the ratio between the yield strength and the ultimate tensile strength of
seven alloys have been measured and the effects on the diameter of the deformed
regions after the ballistic testing were analysed on eight alloys.
6. The tempering temperature and time may strongly affect the existence and
properties of the martensitic armoured steels. The effect of low-temperature
tempering treatments on the carbide precipitation behaviour and on the mechanical
properties and ballistic performance of the alloys have been analysed. The hardness,
the tensile properties, the Charpy V impact energy at -40 0 C , the precipitation
following different tempering conditions, were also compared for the different
alloys. The crack formation and the spalling of the plate due to high velocity
impacts during the ballistic testing were compared for the different tempering
conditions.
7. The lattice parameters of the martensite and the austenite, and their orientation
relationships were measured and compared to the predicted values calculated
through the phenomenological theory of the martensitic transformation. An
approach based on the Bowles and Mackenzie model of the phenomenological
theory of the martensite transformation for the calculation of the transformation
characteristics and their relationships with the ballistic performances, was
examined. A MATLAB script of the BM model is presented for the calculations.
The lattice parameters are functions of the chemical composition of the steel and the
temperature of the quenching medium. Therefore, they should be considered as
dependent variables and their dependencies on the first variables always considered
during the analysis.
8. The plate thicknesses through hot rolling have been varied between 4.7 mm and 6.2
mm and the effect of this was compared in terms of radius of the affected region
due to the high velocity impact with the fired rounds, the subsequent work
hardening and the resistance to cracking and spalling.
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Table (3.2): Chemical composition (wt%) of armour steels currently produced or used in RSA and elsewhere in the World
C
Steel A
Mn
P
S
Si
Cu
Ni
Cr
Mo
V
Nb
Ti
N
0.37
0.52
0.005
0.002
0.754
0.855
3.8
0.318
0.367
0.003
0.001
0.003
Steel B
0.317
0.855
0.008
0.002
0.176
0.26
2.8
0.79
0.45
0.005
0.001
0.003
0.009
Steel C
0.37
0.684
0.003
0.002
0.241
0.005
1.9
0.48
0.32
0.004
0.001
0.003
0.009
Steel D
0.385
0.55
0.004
0.002
0.768
0.1
1.79
0.14
0.36
0.001
NIL
0.007
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3.5. Plate manufacturing
In addition to the four alloys already available at the start of the investigation, nineteen
further chemical compositions were designed for the armoured steel plates to be tested. The
main raw material, about 5 kilograms of steel B for each melt, supplied by Mittal Steel
South Africa, was melted in an alumina crucible of a vacuum induction furnace under
argon with an appropriate addition of high grade ferromanganese to adjust the chemical
composition to the target. The melted material was degassed. The alloys were cast into a 45
mm x 70 mm x 230 mm mild steel mould. The final compositions of the cast ingots were
verified by spectrometer analysis. The top and bottom of the slabs were cut off to remove
the casting defects and the final lengths of the slabs were about 190 mm. The ingots were
processed by hot rolling with a 20% strain per pass maximum. The first passes in the
rolling mill were with the rolling direction parallel to the 70 mm long side to be elongated
up to about 200 mm. The sheet was reheated to 950°C for 20 minutes and hot rolled this
time with the rolling direction parallel to the 230 mm long side. This second reduction is
referred to as the rolling direction in the next Sections of this work.
The slabs were solution treated for one hour at 1100°C before hot rolling. The temperature
of the slab at the last pass in the rolling mill was between 900 0 C and 950 0 C with a 20%
thickness reduction per pass. After reduction to the desired thickness the plates were aircooled. The final thickness of the plate was considered as a variable in the study of the
ballistic performance. The smallest selected thickness was 4.7mm and the highest was
6.2mm. The plate’s sizes for ballistic testing after hot rolling were 200 mm to 250 mm
wide and 500 to 550 mm in length. Two or three plates were obtained from each of the
nineteen chemical compositions. One plate from each alloy was used for the determination
of the mechanical properties and a second for the ballistic testing.
3.6. Mechanical testing
The shock between the fired round and the armoured plate is a high strain rate deformation
process. The localised temperature within the shock waves of the impacted region may rise
by some hundreds of degrees Celsius [18] due to the conversion of a part of the kinetic
energy of the fired round into heat. Another fraction of the kinetic energy is adsorbed by
the mechanical strain around the impact region and a third fraction is dissipated through the
supports of the structure holding the plate.
The interaction between the plate and the fired round is complex, however, and the
following mechanical properties have been suggested for predicting the ballistic
performance of steel armoured plates [1,2,6,8,12,15,18]:
ƒ
ƒ
ƒ
ƒ
the hardness of the steel at room temperature;
the tensile strength at room temperature;
the elongation during tensile testing at room temperature; and
the Charpy impact energy at – 40 0 C .
These mechanical properties were measured for seven steels selected from amongst the
twenty-three steels considered in the study. The hardness measurement, the dilatometer
analysis and X-Ray diffraction results were considered as a basis for the selection of the
seven steels.
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The hardness of the plates after hot rolling and air-cooling was higher than 500 Vickers.
They were then annealed and furnace cooled before the manufacture of the specimens for
tensile and Charpy V impact testing.
The samples were then austenitised for 20 minutes at 800 0 C , 850 0 C , 900 0 C and 950 0 C
respectively in an Argon atmosphere to prevent oxidation of the steels. The furnace used
was LINDBERG MK-1018 with maximum temperature of 1200 0 C . After austenitisation,
the samples were water quenched to 20 0 C to form the martensite microstructure.
Tempering treatments at 150 0 C , 180 0 C , 200 0 C , 250 0 C , 300 0 C , 350 0 C and 400 0 C
for times from 15 to 60 minutes, were applied to the alloys.
3.6.1. Hardness measurement
Hitherto the hardness was considered as the main mechanical property for armour plate
steels. South African specifications suggest the Brinell hardness to be higher than 600 BHN
[1] whereas the American specifications [2] suggest the Rockwell C number to be at least
between 55 and 60 Rc for armoured plate. The Australian specifications for military and
security applications recommend a Brinell hardness between 478 and 578 BHN. [2]
Four techniques have been used for the measurement of the hardness of the steels in the
quenched and tempered conditions, and comparisons have been done with the
specifications.
Small samples of the hot rolled plates were cut to 15 mm length and 10 mm width. The
thickness varied between 4.7 mm and 6.2 mm depending on the thickness of the plate.
Samples were austenitised, quenched and tempered as defined previously and the hardness
measured. The samples were finely mounted in resin and mechanically polished before the
measurement of the hardness.
The Brinell hardnesses were measured in a hydraulic Otto-Wolpe –Werke machine with a
2.5 mm diameter ball at a constant load of 62.5 kg.
Figure 3.1.The tubular furnace
LINDBERG MK-1018 for austenitisation
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The Vickers microhardnesses were measured in a microhardness tester of Future-Tech
Corporation of Japan with a load of 300g.
Figure 3.2. Microhardness Tester FM F11-1
Striking direction
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Chapter 3. Experimental Techniques
Figure 3.3. (a) Cross sections wire-cut through the ballistic impact-affected regions of steels P and Q. (b)
Illustration of the iso-depth lines along which microhardness was measured through the cross sections which
were wire cut after ballistic impact.
3.6.2. The tensile strength and elongation
The front surface of the armour plate is subjected to a high rate compressive strain when
impacted by a projectile. The rear surface may fail under a high rate tensile stress. Earlier,
mention has been made of the localised temperature that rises in the impact region due to
shock wave propagation. However, the specifications have been established for ballistic
performances using the uniaxial tensile test at room temperature. South African
specifications specify the yield strength to be a minimum of 1300 MPa, the tensile strength
a minimum of 1700 MPa and the elongation to be more than 7% for good ballistic
performance.
The tensile specimens were cut parallel to the rolling direction from the hot-rolled and aircooled plate for the selected steels. For others, because of a high hardness, an annealing
treatment was applied to the plates before the wire cutting of the tensile specimens. The
flat tensile specimens had a rectangular cross section calculated according to Barba’s law
[101] for comparison with the standard specimens.
As
A1
=
Ls
L1
where As and A1 are the cross section areas of the standard and the tested specimens
respectively and Ls and L1 their respective gauge lengths. The dimensions of the flat
tensile specimens are then:
Table (3.3). Dimensions of the tensile specimens
Total length [mm]
Gauge length [mm]
100
33
Accord radius
[mm]
5
Width
[mm]
6 ± 0.2
Thickness
[mm]
6 ± 0.2
The tensile specimens were wire-cut before the heat treatment to avoid the laborious
machining of the hard martensite formed after quenching and were austenitised under
Argon, quenched and tempered as stated before. The yield strength, the ultimate tensile
strength and the elongation were determined using an INSTRON 8500 hydraulic tensile
testing machine.
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Figure 3.4. Universal testing machine INSTRON 8500
The Yield strength and the Ultimate tensile strength were correlated through the first
constraint equation with the optimum of the hardness and the ballistic performances of the
armour steel plates. Fractured specimens were analysed under a scanning electron
microscope to establish the mechanisms of fracture and the possible role of inclusions.
3.6.3. The Charpy V-notch impact energy
As in the case of the tensile properties, specifications exist for the impact energy of
armoured plate steels. Those specifications utilise the results from a Charpy V-notch test
that is relatively a slow strain rate phenomenon compared to the high velocity impact
during ballistic testing. The more conservative specifications [2] for armour steels
recommend a minimum of 27 Joules impact energy at -40 0 C on full size Charpy V-notch
specimens, which has its axis transverse to the rolling direction. The less conservative
specifications [1] fix the minimum at 13 Joules impact energy at -40 0 C on full size Charpy
V specimens with its length normal to the rolling direction. The Impact energy also
provides an indication of the resistance of the steels to brittle fracture and to spalling. The
resistance to spalling during the impact is a safety criterion and is also a good indication of
the ability of the armour steels to absorb the kinetic energy of the bullets. The Charpy-V
impact energy of the sub-sized specimens was, therefore, considered as the second
constraint on the hardness and the ballistic performance. The relationship between the
impact energy and the heat treatment parameters was used to construct the second
constraint equation on the optimum level of hardness on ballistic performance.
Because of the plate thicknesses being less than 10 mm, sub-standard Charpy sized
specimens had to be used. These were wire-cut with the following dimensions: 55 x 10 x 5
mm. The notch was 2 mm deep with an angle of 45 0 , and the radius of the fillet at the tip
was 0.25 mm.
The Charpy V-notch impact energy of the sub-sized specimens quenched and tempered,
were measured at -40 0 C to construct the second constraint equation on the ballistic
performances. Specimens were cooled and kept for 10 minutes at -60 0 C in a mixture of
ethanol and dry ice. They were then heated to -50 0 C by adding controlled amounts of
ethanol to the mixture, and were then removed from the cold liquid and tested. The time
between the removal from the cold liquid and the impact of the pendulum was estimated to
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Chapter 3. Experimental Techniques
be between four and six seconds. Testing was done on a Charpy impact testing machine
from Mohr and Federhaff AG, Germany.
Figure 3.5. The Pendulum Impact Testing Machine
3.6.4. Fracture analysis
The fracture surfaces after tensile and impact testing were analysed in a scanning electron
microscope to determine the mode of cleavage and the possible role of inclusions in the
fracture mechanism. Freshly fractured surfaces were protected against contamination and
analysed in the secondary electron mode on a JEOL JSM-6300. Fracture surfaces (if
present), cross sections through the impact region, cracks, micro-cracks and grain
boundaries in the impact region after ballistic testing were also analysed in both the
backscattered and secondary electron modes in the same SEM equipment.
Figure 3.6. Scanning Electron Microscope JEOL JSM-6300, Model P90E.
3.6.5. Microstructure analysis
The microstructure of the steels is the result of a complex combination of the effects of the
chemical composition, the mechanical processing and the heat treatment. The properties
that determine the ballistic performance of the armour steel plates, may be attributes of the
microstructure. The structure and morphology of the martensite laths or plates, the location
and volume fraction of retained austenite, its orientation relationships with the martensite
and the precipitation of the cementite have been analysed and their effects on the ballistic
performances were established. The combination of the scanning electron microscopy, the
transmission electron microscopy, the atomic force microscopy and the X-ray diffraction
was necessary to fully characterising the microstructures of these armour steels.
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Chapter 3. Experimental Techniques
3.6.5.1. Phase analysis and Lattice parameters measurements
X-ray diffraction was used to determine the phases present in the steels and their lattice
parameters. The analysis was done on two different groups of samples.
The first group was solution treated for 20 minutes at 900 0 C in a tubular furnace under an
argon atmosphere, water quenched to 20 0 C and then electro polished in a solution of 5%
volume perchloric acid and 95% volume of glacial acetic acid before the X-ray diffraction
analysis. The second group of 1 mm thick discs of the same steels, was finely polished and
then solution treated for 10 minutes at 900 0 C , under a 10 −4 torr vacuum in a Theta
dilatometer, then quenched to room temperature in Helium gas. The equipment used was
from X’Pert PRO PANalytical
Figure 3.7. X-ray diffraction analyser X’Pert PRO PANalytical
3.6.5.2. Morphology of the martensite
The defect structure of the martensitic structure together with the surface relief and the
diffusionless character, are proof of the existence of the martensitic transformation. The
Bright Field and Dark Field Images from the TEM were analysed to determine the
morphology of the plate or lath martensite, and the phases present such as the retained
austenite and the cementite. Carbon replicas and thin foils of fifteen armour steels were
analysed.
The thin foils were prepared from the 3 mm diameter discs wire-cut as shown in Figure 3.4
in the as-quenched or in the quenched and tempered plates before and after ballistic impact.
The discs had an initial 0.6 mm thickness. They were mechanically polished to less than
200 micrometers in thickness before eletropolishing in a solution of 6vol% of perchloric
acid and 0.5vol% chromium oxide in glacial acetic acid. The thin foils and the carbon
replicas were analysed in a PHILIPS CM 200 TEM equipped with STEM, EDS and an
electron beam source of 160 kV.
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Chapter 3. Experimental Techniques
Figure 3.8. Transmission Electron Microscope PHILIPS CM 200
3.6.6. Transformation surface relief
The surface relief after the martensitic transformation was measured on a nanometre scale
using the Atomic Force Microscope Topometrix TMX 2000 “Discoverer”. The samples for
the atomic force microscopy were prepared from 1 mm thick specimens of the selected
steels. They were finely polished on a one micron diamond paste before electropolishing in
a solution of 5vol% perchloric acid and 95vol% glacial acetic acid at 0ºC. The polished
samples were then austenitised for 10 minutes at 900 0 C under high vacuum in the Theta
dilatometer and quenched to room temperature in a flow of Helium gas. The quenched
samples were then cleaned in an ultrasonic cell with pure acetone to remove any
contamination or dust from the surface.
The very small features such as the size of the twins, the twinning angles and the relative
orientation between the plate axis and the twins were measured for these steels. The Fast
Fourier Transform implemented by the discrete Fourier transform algorithm was used to
analyse the periodicity of the surface relief. The calculations were performed using
MATLAB 7.0 software.
Figure 3.9. Atomic Force Microscope: Topometrix TMX 2000 “Discoverer”
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Chapter 3. Experimental Techniques
3.7. Martensite start temperatures
The characteristic transformation temperatures during cooling of all twenty-three steels
were measured by a dilatometer. The Martensite start temperatures were correlated with the
chemical compositions and with the solution treatment temperatures of all 23 steels and an
empirical relationship is proposed for estimating the Ms temperature of these armour steels.
The Ms temperature was used later as an indirect variable for estimating the volume
fraction of retained austenite in the martensitic steel and the orientation relationship
between the retained austenite and the martensite. The dependence of the ballistic
performances of these armour plate steels on the Ms temperature were also analysed. The
autotempering phenomenon was also detected for some of these steels through the
dilatometer curves.
The sample preparation for the dilatometer analysis is described in paragraph 3.6.5.1. The
equipment used was a THETA 734 Single Silica Push Rod LVDT dilatometer.
Figure 3.10. Dilatometer THETA 734
3.8. Ballistic testing
3.8.1. Specifications for the test
Thirteen armoured steels were tested in a ballistic testing tunnel at Mittal Steel South
Africa (Vanderbijlpark) where the temperature and the humidity are controlled as specified,
to standardise testing conditions. The testing distance was 30 metres and the obliquity
angle was zero degrees. One plate was tested from a distance of only 10 meters. The
prescribed velocity range for the R4’s 5.56 mm rounds is 940 ± 10 m/s. An optical testing
system assesses the success or failure of the plate by remaining opaque to a light beam.
3.8.2. Analysis after ballistic testing
After ballistic testing optical and scanning electron microscopy analyses were done on the
front and rear surfaces of the plates. The impact region was sectioned by wire cutting and a
cross section was analysed through optical and scanning electron microscopy for crack
analysis. Hardness profiles along three iso-depth lines, respectively at 1.5, 2.5 and 4.5 mm
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Chapter 3. Experimental Techniques
below the front surface of the impact region, were determined. Finally thin foils from the
centre and the periphery of the impact region were analysed by TEM and their
microstructures compared to the initial martensite before ballistic testing.
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Contents
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Contents
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Chapter 4: Results and Discussion
CHAPTER 4. RESULTS AND DISCUSSION
4.1. Preliminary results on the steels A and B currently in production in South Africa
as well as two imported steels C and D.
4.1.1.Objective
Steel A and B armour plates are currently produced by Mittal Steel (South Africa) and were
considered as the reference steels for the development of the advanced armour plate steels
for two reasons:
- the materials are known, they meet the ballistic requirements and have already been
tested both in ballistic tunnel tests and in combat; and
- Steels C and D are imported and are also used occasionally in South Africa for ballistic
protection as substitutes for the Steels A and B.
These four armour steels, therefore, served as benchmark steels for the development of the
new advanced performance armour steel RB600. A good understanding of the differences
in ballistic performance of these four steels constitutes the basis for the desired
improvement. Moreover, the industrial implementation of the metallurgical processes for
the manufacture of the new RB600 armour steel, may be economically justified if the
processing parameters remain close to those currently applied for the manufacture of steels
A and B as armour plate.
4.1.2. Methodology
The specifications for armour steel plate in South Africa are actually formulated in terms of
mechanical properties, i.e. hardness, yield strength, tensile strength, elongation of a 50 mm
gauge length and assessed by ballistic tests. Amongst these specifications the hardness of
the steel is considered to be the main indicator of ballistic performance. This design
approach has been considered as an hypothesis in the first step for the characterisation of
these steels. The attempt to maximise the hardness of these four armour steels has been
established through water quenching of austenitised samples. More investigations based on
the chemical compositions, dilatometric analyses, carbon extraction replicas and thin foil
transmission electron microscopy have revealed some significant microstructural
differences between steels A, B, C and D armour plates.
4.1.3. Results
4.1.3.1. Dilatometric analysis
a) Principle of the determination of the Ac1 and Ac3 temperatures
The 2 mm thick samples were slowly heated from room temperature to 900°C at a constant
rate of 2°C per minute. The cooling down to room temperature was also done at the same
rate. The useful part of the heating curve was then isolated for accurate reading of the Ac
temperatures as schematically presented in the following figure:
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Chapter 4: Results and Discussion
1.42
1.41
Dilatation [mm]
1.40
1.39
Ac1
1.38
1.37
1.36
1.35
Ac3
1.34
1.33
500
600
700
800
900
Temperature [degrees Celsius]
Figure 4.1.1. Illustration of reading off of the Ac temperatures on the heating curve of steel E
b) Principle of the determination of the Ms temperature
The Ms temperatures are read off from faster cooling rate curves. The 2 mm thick samples
were heated up to 800°C, 850°C, 900°C or 950°C at a constant rate of 2°C per minute,
soaked for 5 minutes and then quenched in a flow of Helium at a cooling rate higher than
200°C per second to form martensite. A typical dilatation curve is presented in figure 4.1.2.
The determination of the martensite finish temperature by this technique is not accurate
because it is difficult to determine the exact point of contact between the cooling curve and
the straight-line tangent. Here the tangent is considered to be parallel to the first part of the
heating curve. The measured transformation temperatures, for steel A to D are presented in
table (4.1.1)
Table (4.1.1). Transformation temperatures measured by dilatometric analysis
Steel A
Steel B
Steel C
Steel D
Ac1 [°C]
Ac3 [°C]
Ms [°C]
698
704
702
694
758
764
742
748
285
253
241
243
From these results the minimum austenitisation temperature was determined by adding
50°C (at least) to the Ac3 temperatures, leading to about 800°C as a minimum.
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Chapter 4: Results and Discussion
1.50
1.45
Dilatation [mm]
1.40
Mf
1.35
1.30
1.25
Ms
1.20
0
200
400
600
Temperature [degree Celsius]
800
1000
Figure 4.1.2. Determination of the Ms and Mf temperatures
4.1.3.2 . Quenching and tempering of Steel B
The average hardness of 8.5 mm thick steel A and that for 30 mm thick steel B armour
plates after quenching and tempering, were found to be 520 VHN and 390 VHN
respectively. The hardness profiles of both steels A and B produced lower hardnesses than
the specified range of 640 VHN to 750 VHN, or a minimum of 600 BHN as specified for
the RB600 armour steel to be developed.
Samples of Steel B were austenitised at 800°C, 850°C, 900°C and 950°C for 20 minutes,
quenched into brine and then tempered at low temperatures varying between 170°C and
250°C. This ideal quench was used to determine the maximum hardness achievable for this
steel. The initial material was received in 30 mm thick plates with a hardness of 378 VHN
to 400 VHN. The highest hardness value obtained after the above ideal quench was 543
VHN, i.e. well below the specified minimum.
These results are plotted in Figure 4.1.3. At low tempering temperatures of between 170°C
and 200°C, the effect of the tempering treatment on the hardness is more pronounced
within the first hour. The hardness is very sensitive to the tempering temperature for a
given tempering time.
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Chapter 4: Results and Discussion
Table (4.1.2). Hardness values of Steel B after austenitisation at 850°C, water-quenched
and low-temperature tempering
Vickers hardness after tempering at
these temperatures
Tempering time
[hr]
170°C
200°C
250°C
0
543
543
543
0.5
540
500
481
1
520
502
481
4
502
508
473
11
511
484
436
24
499
481
449
560
Tempered at 170 degree Celcius
Tempered at 200 degree Celcius
Tempered at 250 degree Celcius
Vickers hardness (30kg)
540
520
500
480
460
440
420
0
5
10
15
20
25
30
Tempering time [hr]
Figure 4.1.3. Vickers hardness of Steel B after austenitisation at 850°C for 20 minutes, water-quenching and
tempering
An increase in the austenitisation temperature to 900°C or to 950°C does not alter this
general behaviour, but rather determines the highest hardness achievable as shown in
Figure 4.1.4. After austenitisation at 900°C and water-quenching, the Vickers hardness of
steel B is slightly higher than the one obtained after austenitisation at 850°C, but the
corresponding decrease in hardness during tempering is faster as shown in Table (4.1.3).
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Chapter 4: Results and Discussion
The austenitisation treatment at 950°C for 20 minutes produced a lower hardness in the asquenched condition. The maximum Vickers hardness obtained for Steel B, was only 454
VHN in this case. That is almost equal to the hardness in the as-received condition.
Table (4.1.3). Vickers hardness of Steel B after austenitisation at 900°C, water-quenching
and tempering
VHN hardness after tempering
at these temperatures
Time [hr]
170°C
200°C
250°C
0
557
557
557
0.5
527
508
429
1
517
465
429
4
481
467
462
11
454
454
459
24
454
454
462
580
Tempered at 170 degree Celcius
Tempered at 200 degree Celcius
Tempered at 250 degree Celcius
Vickers hardness (30kg)
560
540
520
500
480
460
440
420
0
5
10
15
20
25
30
Tempering time [hr]
Figure 4.1.4. Vickers hardness number of steel B austenitised at 900°C for 20 minutes, water-quenched and
tempered.
Carbon extraction replica transmission electron microscopy of the as-received steel B,
revealed a significant volume fraction of coarse carbides formed on ferrite grain
boundaries. The semi-quantitative analysis of the carbide particles by X-ray diffraction
showed that these coarse particles contain Iron, Chromium, Manganese and Vanadium,
whereas the finer particles contain mainly Titanium and Vanadium with less Chromium,
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Manganese and Iron. The coarse carbide particles formed consistently during the tempering
of the 30 mm thick plates of steel B at 590°C. The Titanium particles were inherited from
the steel making process and would necessitate a very high solution temperature (and for a
long time) to dissolve before quenching. This will cause grain growth with its detrimental
effect on the subsequent toughness of the armour plate. Therefore, from a direct
comparison of the locally produced steel B with the imported steel C, it appears that the
Titanium and Vanadium should be reduced to the lowest level in these steels, and the
tempering temperature should be low to prevent diffusion of the alloying elements and the
subsequent formation of the corresponding carbide. To avoid excessive grain growth,
however, in a Ti-free steel, the austenitisation times should be kept as short as possible.
(a)
(b)
Figure 4.1.5. (a), (b) Carbon extraction replica transmission electron microscopy of a 30 mm steel B armour
plate austenitised at 910°C , water quenched and tempered at 590°C for 38 minutes (label scale length = 10
microns)
4.1.3.3. Dilatometric analysis, quenching and tempering of steel C
From the experience at Mittal Steel (South Africa), the imported steel C has superior
ballistic properties than the locally produced steel B. The hypothesis of the existence of a
relationship between the microstructure and the ballistic performance of an armour steel,
suggests that the difference in ballistic performance between these two steels may be
established from their differences in microstructures.
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Chapter 4: Results and Discussion
The mechanical properties and microstructure of steel C have, therefore, been used as the
minimum requirement for the new RB600 armour steel. The specifications for the steel C
are given in Table (4.1.3).
Table (4.1.4). Specifications for steel C
BHN
YS0.2%
[MPa]
UTS
[MPa]
Charpy impact energy
at-400C[ Joule]
Minimum elongation
[%] on a 50 mm gauge
length
Steel C
(specification)
570 – 640
1500
2000
12
5
Steel C (actual)
573 – 632
1400
2000
18
6
The transformation temperatures of steel C were determined by dilatometry and are
reported in Table (4.1.1). A typical slow heating curve of steel C is shown in Figure
4.1.6(a), and the fast cooling curve for the determination of its MS is shown in Figure
4.1.6(b).
0.33
0.31
702 0 C
Dilatation [mm]
0.29
0.27
742 0 C
0.25
0.23
0.21
500
600
700
800
900
1000
Temperature [Degree Celsius]
Figure 4.1.6(a): Slow heating curve of Steel C showing it’s Ac transformation temperatures
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
Determination of the Ms temperature
0.14
0.12
Dilatation [mm]
0.10
0.08
0.06
0.04
241°C
0.02
0.00
0
100
200
300
400
500
Temperature [degree Celsius]
Figure 4.1.6(b) Fast cooling curve of steel C and reading off of the Ms temperature.
4.1.3.3.1. Hardness of steel C
The measurements of the Vickers hardness along four traverse lines crossing the 6.7 mm
thick plate of steel C, are given in Table (4.1.5).
Table (4.1.5). Hardness profile of the 6.7 mm armour steel C plate
Depth from the
surface [mm]
0.5
1.5
2.5
3.5
4.5
5.5
Average
Std dev%
VHN 30[kg/mm2]
Cross-line
Cross-line 1
2
652
648
680
661
631
635
614
622
635
626
648
626
643
636
3
2
Cross-line
3
618
657
644
644
652
622
640
2
Cross-line
4
639
666
637
627
638
632
640
2
Steel C produced a Vickers hardness of 640 VHN with a standard deviation of 3%. Steel C
is, therefore, harder than steel B. It also appears that steel C has a more consistent hardness
through its cross section, which suggests the presence of a harder homogeneous
microstructure. Nevertheless the hardness profile shows a relative maximum at about 1.5
mm below the outer surface and a relative minimum at a depth of about 3.5 mm on each of
the four cross - lines.
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This hardness profile indicates a relatively harder microstructure near the outer surface than
near the inner surface, probably due to a difference in cooling rate on either side during the
quench. The outer surface would, therefore, present a higher resistance to penetration in a
ballistic test while the inner surface would be more resistant to spallation. Within the first
0.4mm depth from the outer surface, the Vickers micro hardness drops below 446 HV,
probably due to some decarburisation during austenitisation. Near the other surface the
micro hardness remains above 600 HV. This surface will, therefore, be better as the outer
surface of the protective structure.
670
Vickers hardness (30kg)
660
650
640
630
620
0
1
2
3
4
5
6
D is t a n c e f r o m t h e s u r f a c e [ m m ]
Figure 4.1.7. Transverse average hardness profile of Steel C
To explain the transverse hardness profile, two hypotheses were made. The first hypothesis
is a possible segregation and a non-uniform distribution of alloying elements along the four
hardness cross-lines. A cross-line semi-quantitative analysis with the scanning electron
microscope did not reveal any major or measurable segregation of the main alloying
elements, as may be seen in Figure 4.1.8, where the approximated weight percentages of
the alloying elements determined by X-ray diffraction may be read off from the y-axis.
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Chapter 4: Results and Discussion
3
2.5
Nickel
(wt%)
2
1.5
Manganese
1
0.5
Chromium
0
0 0.5 1 1.5 2 2.5 3
3.5 4 4.5 5 5.5 6
Silicon
Distance from the inner surface [mm]
Figure.4.1.8. Alloying element distribution along a cross-line of Steel
The second hypothesis that was tested, is a possible fine precipitation of some carbides on
grain boundaries during cooling after hot-rolling or during the tempering treatment. Such a
precipitation can lead to some degree of depletion in Carbon within some areas. The
assessment of this hypothesis is presented in the next section in Figure 4.1.10, by means of
carbon extraction replica transmission electron microscopy.
.
4.1.3.3.2. Microstructure of steel C
The microstructure of steel C consists of a fine-grained martensite as shown Figure 4.1.9,
by scanning electron microscopy. The resolution of optical microscopy was not enough to
resolve this fine microstructure and, therefore, backscatter scanning electron microscopy
was used for this purpose. Through the use of this SEM technique, it was not possible to
confirm the presence of bainite in the martensitic microstructure. The grain size of steel C,
as measured by SEM, varies between 8 and 10 micrometers. The grain boundaries and the
precipitates were unresolvable because of their small sizes of less than 2 micrometers.
(a)
(b)
Figure. 4.1.9. Microstructure of the 6.7 mm thick Steel C plate. Scanning electron micrographs at (a) 2.5 mm
and (b) 3.5 mm depth into the plate.
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Chapter 4: Results and Discussion
The microstructure of this steel is a fine and homogeneous martensite throughout the cross
section of the 6.7 mm plate. This fine microstructure may partially explain the higher
hardness, combined with the higher toughness of steel C compared to steel B since it is
well known that the microstructure predetermines the mechanical properties as assumed in
the table below.
Table (4.1.6). Relationships in microstructure – mechanical properties
Properties
High hardness, high strength
Martensite
Fine
microstructure
Homogeneity
Controlling parameters
Carbon and Manganese contents,
austenitisation temperature and time,
quench rate
highly defected substructure, Nickel content,
austenitisation temperature,
retained austenite, fine
cooling rate
precipitates
Sulphur, Copper and Silicon
No stress raisers, high
contents, austenitisation temperature,
impact energy
cooling rate, tempering parameters
Figure 4.1.10 reveals no coarse carbide particles through carbon extraction replica
transmission electron microscopy of sections taken at different depths below the outer
surface. Contrary to steel B, the grain boundaries of steel C are without any carbides. Its
matrix has finely dispersed particles of Titanium carbides and Titanium nitrides and these
contain less Chromium and Manganese as in Steel B. There was also no measurable
coarsening of the fine Titanium carbide and nitride particles during the tempering
treatment, as was observed in steel B. A lower-temperature tempering for a shorter time of
steel C may be the reason of the observed no coarsening of those particles.
Figure 4.1.10 (a)
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Chapter 4: Results and Discussion
Figure 4.1.10 (b)
Figure 4.1.10 (c)
Figure 4.1.10 (d)
Figure 4.1.10. Carbon extraction replica transmission electron micrographs and dark field images showing
very fine carbides and nitrides within the matrix
(a): TEM carbon extraction replica at a depth of 0.5 to 1.5 mm from the surface;
(b) and (c): TEM extraction carbon replicas at a depth of 1.5 to 2.5 mm from the surface showing precipitatefree grain boundaries and small Titanium carbides and nitrides within the matrix.
(d): TEM extraction carbon replica at a depth of 3.5 to 4.5 mm from the surface revealing more fine particles
than at depths of 1.5 mm and at 2.5 mm from the surface. (label scale length = 10 microns)
Thin foil transmission electron microscopy of Steel C in the as-received condition and an
optical micrograph of a sample after a high-temperature tempering at 600°C for 30
seconds, are presented in figures 4.1.11 (a), 4.1.11 (b) and 4.1.12.
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Chapter 4: Results and Discussion
Interlath carbides
(a)
(b)
Carbides within
martensite laths
Figure 4.1.11. Thin foil transmission electron microscopy of Steel C in the as-received condition.
Figure 4.1.11 (a) and (b) show fine elongated carbides within the martensite laths of Steel
C and slightly round carbide particles on and near the lath interfaces. The optical
micrograph of the sample tempered at 600°C presents a microstructure composed of ferrite
and coarse carbide particles, with a lower hardness.
Figure 4.1.12. Optical micrograph of the Steel C after tempering 30 seconds at 600°C (magnification x1000).
Tempering of Steel C at 600°C for 30 seconds already softened the material to a hardness
well below the specification. The hardness values of Steel C corresponding to the
microstructures in figure 4.1.11 and figure 4.1.12 are compared in table 4.1.7.
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Chapter 4: Results and Discussion
Table (4.1.7). Vickers hardness of Steel C as-received and after tempering at 600°C.
As-received
Figure No.
4.1.10 (a) and 4.1.10
(b)
850°C for 20 minutes
652
900°C for 20 minutes
0
Tempered at 600 C for 30
seconds
Vickers hardness
640
661
4.1.11
446
The hardness values of Steel C after austenitisation at 850°C and 900°C followed by waterquenching to room temperature, are slightly higher than in the as-received condition, as
shown in Table 4.1.7. The difference in Vickers hardness between the austenitised and then
water quenched sample, and the as-received Steel C armour plate, is about 20 VHN units,
confirming the presence of a low-temperature tempering applied to this steel, contrary to
the high-temperature-tempering applied to Steel B. After tempering at 600°C for 30
seconds, the martensitic microstructure is completely transformed into a structure
consisting of ferrite and carbides have also formed, as shown in figure 4.1.11. This
structure had a hardness of only 446 VHN, far below the specified range for Steel C which
is 660 to 720 VHN or 580 BHN to 640 BHN.
Simulation of water quenching of a 6 mm and a 8 mm plate of Steel C, was performed in
the THETA dilatometer using a flow of Helium as coolant.
This was done to assess the efficiency of the industrial quenching process. After this
simulation the Vickers hardness varied between 661 VHN and 671 VHN, which is in the
same range of the Vickers hardness obtained after water quenching and higher by 30 units
than the hardness of the as-received 6.7 mm Steel C armour plate. This again confirms the
effectiveness of a low-temperature tempering treatment for a short time as was apparently
applied in the case of Steel C armour plate. Figure 4.1.13 presents the three simulation
curves superimposed on six experimental cooling curves of water quenching in the Mittal
plant of steel bars and plates. The legend attached to the curves may be read as: 13B8P WQ
designates the cooling curve for a 13 mm bar or a 8 mm plate, water-quenched to room
temperature.
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Chapter 4: Results and Discussion
13B8P WQ
1000
31B20P WQ
900
25mm
8mm
Temperature [degree Celsius]
800
700
5B WQ
20mm
5mm
39B25P WQ
Simulation
6mm
600
60B WQ
500
1s-450_1s25
0.5s-450_1s25
10B6P WQ
400
300
200
100
0
0.01
0.1
1
10
100
1000
Time [s]
Figure 4.1.13. Three simulation curves of the water quenching of Steel C plates superimposed on 6
experimental cooling curves of industrial water quenching of plate steels in the Mittal plant.
The simulation samples were austenitised at 900°C for 10 minutes before being quenched
in a flow of Helium according to the three simulation curves in °C versus time (in seconds)
above.
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Chapter 4: Results and Discussion
4.2. Proposed design for an advanced RB600 armour plate
From these experiments it appears that the highest achievable hardness with steel B under
the specified conditions, is 557 VHN. This hardness is reached through austenitisation at
900°C for 20 minutes and a water-quench to room temperature. The relatively low Carbon
content of 0.3%C is the main barrier to the improvement in hardness of Steel B to values
up to 640 VHN or 600 BHN after quenching, as required by the specification. Extraction
carbon replica transmission electron microscopy has revealed that the high-temperature
tempering at 590°C for more than 38 minutes (as was applied to Steel B armour plates) led
to the precipitation of coarse carbides and to undesirable heterogeneities in the
microstructure that alter the ballistic performance negatively. The coarse carbide particles
are potential stress-raisers and reduce the nominal stress for effective resistance to impact
loading. A low-temperature tempering should be considered to avoid this effect. Moreover,
preliminary experiments have also shown that the hardness decreases by 10% to 25% of its
initial value in the as-quenched condition when a low-temperature tempering between
170°C and 250°C is applied to both steel B and C armour plates.
A good armour martensitic steel should, therefore, have a fine and homogeneous
microstructure consisting of a low temperature tempered martensite. Furthermore, such
material must be clean with neither inclusions nor carbide precipitates on grain boundaries.
The following hypotheses have, therefore, been formulated for the development of an
advanced armour plate steel with a superior ballistic performance:
1. to slightly increase the hardness and the strength of the martensitic steel through a
moderate increase of the Carbon content to between 0.38%C and 0.43%C;
2. to prevent quench-cracking in the plates by adding Manganese in the range of 0.8 % to 2
%Mn;
3. to prevent or to delay the precipitation of cementite or any M3C precipitates by adding
Silicon and Chromium within the range of 0.4 % to 1.5 %;
4. to austenitise between 80°C 0 and 950°C for less than 60 minutes to prevent austenite
grain growth;
5. to temper the armour plate below 250°C for less than 60 minutes for the necessary
reduction of quench residual stresses for an increase of the toughness of the martensitic
microstructure;
6. the Sulphur content should ideally be kept below 0.005%S to prevent the formation of
Manganese sulphide particles that may act as stress raisers; and
7. the Titanium and Niobium contents should ideally be kept lower than 0.005%.
These seven hypotheses formed the basis for designing the first five high-performance
armour steels. In practice, however, slight deviations from some of these “ideal” limits
were found in some of the experimental alloys. These slight deviations appeared, however,
not to be critical to the main hypotheses by which the alloy’s compositions were selected.
The optimisation of their mechanical properties, microstructures and their ballistic
performances are presented in the next paragraph.
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Chapter 4: Results and Discussion
4.3. Optimisation of the mechanical properties.
4.3.1. The optimisation problem
Until now, the hardness of armour plate was considered to be the decisive criterion in
predicting the ballistic performance of the steel as it is supposed to indicate the ability of
the target to withstand the impact of the projectile. Other design specifications for ballistic
steels are based on the true strength to fracture and the resistance to spallation upon high
velocity and hypervelocity impact that induces a high strain rate in the target. It appears
that one possible approach in designing an advanced performance armour steel, defined
here as RB600, would consist of a constrained optimisation problem of the hardness, the
objective function, with two constraint functions, i.e. the tensile strength and the impact
energy. Another design philosophy would specify an optimum constrained minimum of the
objective function defined by the ratio YS/UTS of the candidate armour steel with two
constraint functions, namely the Charpy impact energy at -40°C and the tensile strength at
room temperature which is an indication of the true fracture strength of these steel.
It may be shown that the ratio YS/UTS is proportional to (n ) , where n is the Hollomon
n
⎛ e × 0.2 ⎞
=⎜
⎟ . The Hollomon work
UTS ⎝ n ⎠
hardening exponent n, defines the ability of the material to resist instability in strain as
YS (0.2 )
, therefore, may
found in the localisation of plastic deformation. The function
UTS
define the objective function that must be minimised to meet the ballistic requirements,
because this ratio decreases when n increases as n < 1.
work hardening exponent, by the relationship
YS (0.2 )
n
It was noted in Chapter 2 that adiabatic conditions prevail in the impacted region during
ballistic testing and the localised temperature may exceed 700°C, which is far above the
testing temperature at which the mechanical properties are commonly measured for
ballistic materials. At 700°C, phase transformations may occur that modify the
microstructure and the mechanical properties of the armour steels. It is, therefore, necessary
to finally assess the ballistic performance of the armour steels by ballistic testing to assure
conformation with the requirement for military and security standards. The analysis of the
localised microstructures of the armour steels before and after ballistic testing will,
therefore, become a vital tool for understanding the relationship between the
microstructures, the mechanical properties and the ballistic performance. The following
methodology was, therefore, followed in the design of the advanced RB600 armour plate
steel:
- design the first five alloys and their heat treatment based on the industrial and
metallurgical understanding of the current armour steels B and C;
- solve the constrained optimisation problem of the mechanical properties in terms of four
independent variables; viz. the austenitisation temperature, the tempering temperature, the
tempering time and the chemical composition and one dependent variable, the martensite
start temperature;
- predict the ballistic performance of the armour steels using three different criteria based
on the hardness, the Ballistic Performance Index (BPI) [6], (quoted in paragraph 2.2.4), and
the ratio YS/UTS;
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- perform the ballistic testing according to the ARMSCOR specification for military
applications and assess the validity of the specification;
- analyse the microstructures and other features of the martensitic steels;
- understand and explain the metallurgical reasons for the high as well as the low
performances; and
- redesign a range of new alloys and their heat treatment parameters and repeat steps 3 to 6
of the above methodology scheme.
4.3.2 The chemical composition
Based on the hypothesis formulated in section 2.8 and the conclusion after the orientation
tests in section 4.2, five steels, namely, steels E, F, G, H and I whose chemical
compositions are given in Table (4.3.1), were vacuum melted in 5 kg casts each, hot rolled,
heat treated and tested mechanically as well as ballistically. The tensile tests were
performed at room temperature whereas the Charpy-V impact energy of the sub-sized
specimens (due to limitations on the plate thicknesses) was measured at -40°C. The hot
rolled plates were austenitised for 20 minutes at different temperatures and tempered for
different times up to two hours, also at different temperatures, as described in section 4.3.3.
Table (4.3.1): Chemical compositions (wt%) of the first five high performance armour steels
C
Mn
P
S
Si
Cu
Ni
Cr
Mo
V
Nb
Ti
N
Steel E
Steel F
0.39
1.22
0.008
0.003
0.21
0.10
2.99
1.49
0.5
0.006
0.002
0.003
0.0049
0.39
0.65
0.017
0.009
0.8
0.23
2.8
0.22
0.24
0.003
0.006
0.01
0.0051
Steel G
0.37
0.40
0.016
0.011
0.43
0.33
2.3
0.24
0.3
0.006
0.006
0.009
Steel H
0.37
1.15
0.015
0.011
1.06
0.14
3.8
0.52
0.43
0.008
0.008
0.007
Steel I
0.34
0.39
0.019
0.012
0.40
0.32
2.43
0.27
0.37
0.009
0.009
0.008
0.0036
The martensite start temperatures of these steels were measured by dilatometry as
described previously and are given in Table (4.3.2). The volume fractions of retained
austenite in the respective alloys were determined by quantitative X-ray diffraction.
Table (4.3.2): Measured MS temperatures [°C] and volume fractions of retained austenite after quenching
of steels E through to steel I
Ms temperature [°C]
Volume fraction of the
retained austenite [%]
Steel E
196
5
Designation of the Steel
Steel F
Steel G
Steel H
255
271
210
0.6
0.5
4
Steel I
309
0.5
4.3.3. The heat treatment cycle
Tensile specimens and sub-sized Charpy specimens, whose dimensions are presented in
paragraphs 3.6.2 and 3.6.3 respectively, were austenitised at temperatures ranging between
800°C and 950°C for 20 minutes, before being water-quenched to room temperature and
tempered at relatively low temperatures between 150°C and 400°C for various times
between 0 and 120 minutes. The low-temperature tempering treatment was motivated by
the constraint on the hardness requirement which, as specified by ARMSCOR and Mittal
Steel South Africa for the high performance armour steels, should be as high as 600 HBN
or 640 VHN, and also by the abrupt drop of hardness to values lower than 450 VHN
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Chapter 4: Results and Discussion
observed on steels B and C when tempered above 200°C. However, to capture the effects
of this softening behaviour, the effect of the tempering temperature on the mechanical
properties was, therefore, studied over quite a large range, i.e. from room temperature to
400°C. Moreover, the effect of the heat treatment parameters on the ratio YS/UTS was
analysed.
4.3.4. Variation of the mechanical properties
The variation of the yield strength to ultimate tensile strength ratio YS/UTS, the ultimate
tensile strength and the Charpy impact energy of steels E through to I as a function of the
austenitisation temperature and the tempering temperature, are first presented. This will be
followed by a comparative analysis taking into account the differences in the martensite
start temperatures of the candidate advanced performance armour steels. The optimisation
problem is stated for each steel in terms of the objective function that needs to be
minimised and two constraints. The three equations were determined for each of the five
steels E through to I by surface fitting using EXCEL 2000 software. The three-dimensional
plots of the surfaces and the projections of the isolines for the two-dimensional mapping of
the optimum regions were performed using MATLAB 7.0.
From the experimental data it was observed that third degree polynomials could fit the
results within the experimental ranges of the austenitisation temperature and the tempering
temperature, with good accuracy. This led to the general mathematical expression of the
surfaces representing the properties as follows:
¾
The austenitisation and tempering temperatures require normalisation to allow the
computation and to provide the minimum rounding errors. It was found to be better to work
with values within the same numerical range, i.e. –1 to +2 rather than using two different
ranges for the austenitisation temperatures and the tempering temperatures. The normalised
tempering temperature Ttn is defined, here, as follows:
(T − Ttm )
(4.1)
Ttn = t
(Ttm − 25)
where Tt is the actual tempering temperature in degrees Celsius, Ttm is a mean tempering
25 + 300
temperature from Ttm =
=162.5°C. Exactly how this normalised temperature is
2
defined is not too important for the purposes of this study as the same trends will be found
using a different normalisation definition.
¾
The normalised austenitisation temperature Tan is defined, here, as follows:
Tan =
Ta − Tam
Tam − 850
(4.2)
where Ta is the actual austenitisation temperature in degrees Celsius and Tam is the mean
800 + 950
austenitisation temperature from Tam =
=875°C.
2
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Chapter 4: Results and Discussion
¾
The particular mechanical property (MP) is then fitted by the surface fitting
equation:
MP(Tan , Ttn ) = a (Tan ) × Ttn + b(Tan ) × Ttn + c(Tan ) × Ttn + d
3
2
(4.3)
where the fitting parameters a, b, c and d are polynomials in Tan and are of the general
form:
p = A × Tan + B × Tan + C × Tan + D
3
2
(4.4)
where A, B, C and D are constant real parameters.
¾
Combining equations (4.3) and (4.4) gives a sixth order non-linear equation in the
normalised temperatures Tan and Ttn :
(
)
(
)
MP(Tan , Ttn ) = A1 × Tan + B1 × Tan + C1 × Tan + D × t tn + A2 × Tan + B2 × Tan + C 2 × Tan + D2 × t tn +
(A
3
3
2
)
(
3
3
2
× Tan + B3 × Tan + C 3 × Tan + D × t tn + A4 × Tan + B4 × Tan + C 4 × Tan + D4
3
2
3
2
)
2
(4.5)
Equation 4.5 is the mathematical presentation of the particular mechanical property to be
considered in the optimisation problem. The optimisation techniques currently used apply
to the optimisation of quadratic non-linear problems. It then becomes necessary in the
present case to graphically solve the problem using two-dimensional projections of
contours of equal height (i.e. iso-lines) to visualise the optimum regions in the normalised
( Tan , Ttn ) planes.
4.3.4.1 Mechanical properties of Steel E
a) Fitting function for the UTS
The results from the measurements of the ultimate tensile strength of steel E are presented
in Table (4.3.3).
Table (4.3.3). Ultimate tensile strength of steel E (MPa)
Ultimate tensile strength in MPa as a
function of the austenitisation
temperature [°C]
Normalised
tempering
Tempering
temperature[°C] temperature Ttn
-1
25°C
-0.09091
150°C
0.272727
200°C
0.636364
250°C
1
300°C
1.363636
350°C
1.727273
400°C
800°C
1202
1956
1935
1874
1800
1553
1532
850°C
1456
1767
1846
1609
1320
1265
1202
900°C
1400
1580
1472
1326
1308
1173
1076
950°C
1436
1524
1535
1484
1317
1115
995
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Chapter 4: Results and Discussion
The surface fitting is done in two steps and the first one gives the estimate of the
parameters required in Equation (4.3) at different austenitisation temperatures. The results
of these calculations and the correlation coefficient R2 for steel E are tabled below:
Table (4.3.4): The fitting parameters and the correlation coefficients in equation (4.3) for
the ultimate tensile strength of steel E
Fitting parameters in equation
(4.3)
Normalised
Austenitisation austenitisation
temperature temperature
a
158.3
184.05
79.271
12.683
-1
-0.33333
0.333333
1
800°C
850°C
900°C
950°C
Correlation
coefficient
b
c
d
-488.26 112.67 1961.2
0.984
-410.62 -209.35 1832.6
0.939
-201.67 -148.29 1537.3
0.965
-177.44 -67.755 1553
0.978
It appears that the parameters a, b, c and d are some function of the austenitisation
temperature. The second step of the surface fitting process consists of determining the
variation of each of these parameters in Table (4.3.4) with the normalised austenitisation
temperature. The results of the calculations are tabled as follows:
Table (4.3.5): The fitting parameters and the correlation factors in equation (4.4) for the ultimate tensile
strength of steel E.
a
b
c
d
Parameters in equation (4.4)
Correlation
coefficients
A
B
C
D
94.905 -51.94 -167.71 137.43
1
-177.77 -30.043 333.18 -302.81
1
-204.53 226.44 114.32 -203.98
1
268.71 81.169 -472.81 1675.9
1
The variation of the ultimate tensile strength of steel E with the normalised austenitisation
and tempering temperatures may then be represented mathematically by the function:
(
)
(
)
UTS = 94.905Tsn − 51.94Tan −167.71Tan + 137.43 ×Ttn + −177.77Tan − 30.043Tan + 333.18Tan − 302.81 ×Ttn
(
3
2
)
3
(
3
2
)
2
+ − 204.53T + 226.44T +114.32Tan − 203.98 ×Ttn + 268.71T + 81.169T − 472.81Tan +1875.9
3
an
2
an
3
an
2
an
(4.6)
b) Fitting function for the ratio YS/UTS
The determination of the function expressing the variable YS/UTS for steel E, also as a
function of the austenitisation and tempering temperatures, is done by the same two-step
process above that was used for the surface fitting of the ultimate tensile strength.
The results on the YS/UTS ratios from the tensile tests at room temperature on steel E are
given in the Table (4.3.6). The calculated surface fitting parameters to be considered in
Equations (4.3) and (4.4) for the YS/UTS ratio are shown in Tables (4.3.7) and (4.3.8).
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
Table (4.3.6): The YS/UTS ratio of steel E at room temperature, as a function of the austenitisation and
tempering temperatures
YS/UTS ratio as a function of
the austenitisation
temperature
Tempering
temperature
25°C
150°C
200°C
250°C
300°C
350°C
400°C
Normalised
tempering
temperature
-1
-0.09091
0.272727
0.636364
1
1.363636
1.727273
800°C
0.47
0.50
0.53
0.57
0.61
0.64
0.66
850°C 900°C 950°C
0.46
0.44 0.42
0.47
0.44 0.43
0.49
0.45 0.46
0.51
0.49 0.51
0.53
0.53 0.55
0.55
0.57 0.59
0.57
0.61 0.64
Table (4.3.7) The fitting parameters and the correlation coefficients in equation (4.3) for the ratio YS/UTS of steel E
Parameters in equation
(4.3)
Normalised
Correlation
Austenitisation austenitisation
coefficient
temperature temperature
a
b
c
-1
0.0159 0.0632 0.5167
0.98
800°C
-0.33333
0.0098 0.0336 0.4816
0.997
850°C
0.333333
0.033 0.043 0.4444
0.993
900°C
950°C
1
0.0291 0.0635 0.4464
0.991
Table (4.3.8) : The fitting parameters and the correlation factors in equation (4.4) for the ratio YS/UTS of
the steel E.
a
b
c
Parameters in equation (4.4)
Correlation
coefficients
A
B
C
D
-0.0317 0.0012 0.0383 0.0213
1
-0.0157 0.0282 0.0158 0.0352
1
0.0232 0.0209 -0.0584 0.4607
1
The variation of the YS/UTS ratio with the austenitisation and the tempering temperatures
is then described by the function introducing the normalised temperatures Tan and Ttn
expressed in Equation (4.7):
(
)
(
)
YS
3
2
2
3
2
= − 0.0317Tan + 0.0012Tan + 0.0383Tan + 0.0213 × Ttn + − 0.0157Tan + 0.0282Tan + 0.0158Tan + 0.0352 × Ttn
TS
3
2
+ 0.0232Tan + 0.0209Tan − 0.0584Tan + 0.4607
(
)
(4.7)
c) Fitting function for the Charpy impact energy
Equation (4.7) is the objective function that needs to be minimised for steel E. Equation
(4.6) is the first constraint on the system while the second constraint is taken from the
Charpy impact energy of the sub-sized specimens tested at -40°C.
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
The fitting surface is obtained from the experimental values of the Charpy impact energy
presented in Table (4.3.9). The fitting parameters for Equations (4.3) and (4.4) obtained by
regression analysis, are given in Tables (4.3.10) and (4.3.11) respectively.
Table (4.3.9): Charpy impact energy (in Joules) of steel E (of the sub-sized specimens) tested at -40°C, as a
function of both the austenitisation and the tempering temperatures
Charpy impact energy (J) as a
function of the austenitisation
temperature
Normalised
Tempering tempering
temperature temperature 800°C
-1
6.9
25°C
-0.09091
7.9
150°C
0.272727
8.9
200°C
0.636364
10.8
250°C
1
12.8
300°C
1.363636
13.8
350°C
1.727273
13.8
400°C
850°C
5.9
6.9
7.9
8.9
9.8
11.8
12.8
900°C
4.9
5.9
7.9
7.9
8.9
9.8
11.8
950°C
4.9
4.9
6.9
6.9
7.9
7.888
10.8
Table (4.3.10: Fitting parameters of the Charpy impact energy of steel E, in Equation (4.3)
Fitting parameters in (4.3)
Normalised
Austenitisation austenitisation
temperature temperature
800°C
-1
850°C
900°C
950°C
-0.33333
0.333333
1
Correlation
a
b
c
d coefficients
0.995
1.3036 1.8385 4.1496 7.946
0.1717 0.925 2.2822 7.1079
0.995
0.2342 0.2435 1.7912 6.648
0.97
0.293 0.4097 1.0982 5.808
0.906
Table (4.3.11): Fitting parameters of the Charpy impact energy of steel E, in Equation (4.4)
Fitting parameters in (4.4)
A
B
a 0.2131 -0.6036
b 0.3463 0.6073
c -0.8878 0.6606
d -0.4265 -0.0011
C
0.5825
-1.0607
-0.6379
-0.6425
Correlation
coefficients
D
0.0983
0.5168
1.9633
6.8781
1
1
1
1
The mathematical expression that fits the experimental Charpy impact energy may be
written as:
(
) (
)
(
)
CIE − 400 C = 0.2131Tan − 0.6036Tan + 0.5825Tan + 0.0983 × Ttn + 0.3463Tan + 0.6073Tan −1.0607Tan + 0.5168 × Ttn
(
3
2
)
(
3
3
2
)
2
+ − 0.8878Tan + 0.6606Tan − 0.6379Tan + 1.9633 × Tan + − 0.4262Tan − 0.0011Tan − 0.6425Tan + 6.8781
3
2
3
2
(4.8)
Equation (4.8) is the second constraint of the system to be optimised.
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
Overall fitting
The optimisation problem may be written in classical form as follows:
YS / UTS ≤ r0
UTS ≥ Σ 0
(4.9)
CIE (-40°C) ≥ IE0
where r0 is the boundary in the YS/UTS ratio yet to be determined after ballistic testing,
Σ 0 is the current limit in UTS specified by ARMSCOR and is equal to 1700 MPa. The
validity of this limit will be re-assessed later after the ballistic testing. CIE 0 is the
minimum Charpy impact energy that indicates the resistance against spallation when the
armour steel is impacted by a high velocity projectile at sub-zero temperatures. The
ARMSCOR specification fixes this minimum at 13 Joules for full size Charpy specimen
tested at -40°C. The optimisation problem represented in Equation (4.9) is shown
graphically in Figure (4.3.1). From Tables (4.3.3), (4.3.6) and (4.3.9), it appears that a
three-dimensional plot of the three functions that compose the system within the same axes,
will require a scaling factor for visualisation of the problem. This is due to the fact that the
absolute values of the YS/UTS ratio are very small compared to the ultimate tensile
strength. A scaling factor of 2000 is, therefore, applied to the YS/UTS ratio and one of 100
to the Charpy impact energy function CIE (-40°C) before plotting. The effect of the scaling
factors is only a translation of the fitting surfaces from lower to high values, but will still
display the trends as before. The objective function YS/UTS is represented by the surface
in between the ultimate tensile strength surface on top and the Charpy impact energy
surface on the bottom. The feasible region as well as the optimum region are visualised by
the use of the contours of equal values of the properties.
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
Steel E
UTS
2000
1500
1000
500
YS/UT
0
2
CIE
1
1
0.5
0
0
-0.5
-1
Normalised tempering T
-1
Normalised austenitisation T
Figure 4.3.1(a): Three-dimensional representation of the YS/UTS objective function (surface in the middle),
the UTS (upper surface) and the Charpy impact energy (lower surface)
0.
9
62
49
0.
0
1.5
0.5384
3
0.49629
3
84
53
0.622 71
0.58057
8 43
0.53
0.
58
05
7
Normalised tempering temperature
0.5
2
0.58
0 57
1.5
1
UTS of steel E
0.66
4 86
0.496 29
4
54 1
0. 4
0.4
54 1
4
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperature
0.5
0.8
1
Figure 4.3.1(b): Contours of constant YS/UTS
ratio for steel E
11 41
.2082
13 07
.2238
14 7
16
3.2
39.
395
255
1
18
05.
14 7
270
3.2
16
7
395
39
.25
51
0
-0.5 18 05.2
707
-0.5
-1
-1
1
13
07
.2
23
8
-1
-1
1141.2082
238
13 07.2
5
39
.2
73
14
18
05
.27
07
YS/UTS of steel E
0. 6
22 7
1
95
.23
73
14
0.6
22
71
0 57
0.58
Normalised tempering temperature
2
1473.2395
551
9. 2
16 39.2551
16 3
1473.2395
14 73.2395
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Normalised austenitisation temperature
1
Figure 4.3.1(c): Contours of constant tensile
strength (in MPa) of steel E
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
Charpy impact energy of steel E
2
7
12 .689
Normalised tempering temperature
1.5
1
0.5
97
.68
12
02
.35
11
97
12 .68
02
11 .35
5 02
11 .3
08
10 .01
1
10 .0
29
8.671
1 08
10 .0
1 29
8.67
0
1
31 8
7. 3
7. 331 81
7. 331 81
5. 992 34
-0.5
5.
-1
-1
1 29
8.67
08
-0.8
-0.6
4
23
99
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperature
0.8
1
Figure 4.3.1(d): Contours of constant Charpy impact energy (in Joules) at -40°C for Steel E
From Figure 4.3.1(b), it appears that the optimum region for the YS/UTS ratio corresponds
to the region of medium to high normalised austenitisation temperatures which lie between
the normalised values of –0.6 to 1, or actually between 830°C and 950°C; together with
low values of the normalised tempering temperatures, lying between the normalised values
of –1 and 0.4, or actually lower than 217°C.
From Figure 4.3.1(c), it appears that a tensile strength larger than 1700 MPa is obtained for
steel E when the normalised austenitisation temperature is lower than –0.1 or lower than
actually 867°C and the normalised tempering temperature lies between the normalised
values of –0.5 and 1, or actually between 95°C and 300°C. If the tempering temperature is
lower than 95°C, the tensile strength would become difficult to determine because of the
brittle behaviour of steel E in this condition. From Figure 4.3.1(d) a Charpy impact energy
at -40°C that is higher than the specified 13 Joules, is obtained for the normalised
temperatures between –1 and 0.2 or lower than the actual 890°C and the normalised
tempering temperature is above 0.9 or actually 286°C. The summary of this discussion is
presented in Table (4.3.12).
Table (4.3.12). Heat treatment conditions predicted to be favourable to the ballistic properties for steel E.
Property
Low YS/TS
High UTS
CIE(-40°C)
Favourable conditions
Austenitisation
Tempering temperature
temperature
830°C to 950°C
< 217°C
< 867°C
< 890°C
95°C to 300°C
> 286°C
The optimum heat treatment region for steel E may be fixed in a first approach, at an
austenitisation temperature between 830ºC and 900ºC. It is more difficult to find a
compromise concerning the tempering temperature between the YS/UTS ratio and the
Charpy impact energy at -40°C, as can be seen from the third column in Table (4.3.12).
Predominance has been given to the ratio YS/UTS according to the design methodology
chosen in Section 4.3.1; and the optimum tempering temperature is, therefore, fixed at
below 200°C for steel E.
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
The hardness of steel E varies with both the austenitisation temperature and the tempering
temperature. The results on the Vickers hardness of this steel are given in Table (4.3.13).
The regression analysis and the surface fitting were developed following the same scheme
as proposed earlier in this Chapter. It is to be noted that the hardness of steel E decreases
very fast to values as low as 450 VHN when the tempering temperature is above 200°C.
That would be very low compared to the value of 650VHN specified by ARMSCOR and
Mittal Steel South Africa for their advanced performance armour steels.
Table (4.3.13): Variation of the Vickers hardness of Steel E with the austenitisation temperature and the
tempering temperature.
Vickers hardness as a function of the
austenitisation temperature [0C]
850°C
900°C
950°C
800°C
Tempering
temperature °C
25°C
150°C
200°C
250°C
300°C
560
550
490
460
440
590
545
450
422
415
630
550
450
430
420
620
610
545
520
500
The fitting parameters for the corresponding Equations (4.3) and (4.4) are contained in
Tables (4.3.14) and (4.3.15) respectively.
Table (4.3.14): Fitting parameters for the Vickers hardness of Steel E, in Equation (4.3)
Fitting parameters for (4.3)
Normalised
Austenitisation austenitisation
temperature temperature
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
75.755
44.411
29
79.519
b
-33.953
-14.824
8.5389
-32.044
c
-135.13
-116.57
-113.52
-138.65
d
534.8
532.79
537.12
593.22
Correlation
coefficients
0.992
0.998
0.997
0.985
Table (4.3.15): Fitting parameters for the Vickers hardness of steel E, in Equation (4.4)
a
b
c
d
Fitting parameters for (4.4)
Correlation
coefficients
A
B
C
D
28.123
46.048
-26.241
31.589
1
-38.351
-33.588
39.306
0.5894
1
0
-24.576
-1.1265
-112.31
0.983
0
32.687
26.939
531.32
0.96
The variation of the Vickers hardness with the austenitisation temperature and with the
tempering temperature is then written in terms of the normalised temperatures as follows:
(
)
(
)
HV = 28.123Tan + 46.048Tan − 26.241Tan + 31.589 × Ttn + − 38.351Tan − 33.588Tan + 39.306Tan + 0.5894
3
(
)
(
3
3
× Ttn + − 24.576Tan − 1.1265Tan − 112.31 × Ttn + 32.687Tan + 26.939Tan + 531.32
2
2
2
2
)
(4.10)
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
The surface representing the Vickers hardness is presented in Figure 4.3.2(a), together with
the plane for a hardness of 650VHN as specified by ARMSCOR and Mittal Steel South
Africa. The plane for 550VHN is also shown in the same figure.
Vickers hardness of steel E
650
600
550
500
450
400
1.5
1
1
0.5
0.5
0
0
-0.5
-0.5
-1
-1
Normalised austenitisation
Normalised tempering temperature
Figure 4.3.2(a): Variation of the Vickers hardness of steel E with the normalised austenitisation and
tempering temperatures. The surface corresponding to the specified 650 VHN is shown together with one for
550 VHN.
Lines of constant Vickers hardness for Steel E
467.3208
1.5
49
7.1
64
9
46 7.3208
Normalised tempering temperature t
208
46 7.3
1
08
46 7.3 2
0.5 467.3208
9
49 7.1 64
497.1649
0
.1
49 7
527.0089
52 7.0089
55 6.8 53
55 6.8 53
52 7.0
-1
-1
-0.8
-0.6
089
.8
55 6
.6
58 6
53
971
-0.5
.6
58 6
649
.5
61 6
412
971
2
41
6.5
61
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperature T
0.8
1
Figure 4.3.2(b): Lines of constant hardness corresponding to Figure 4.3.2.a.
The hardness of steel E in the quenched condition, is relatively constant when the
austenitisation temperature is increased between 800°C and 900°C. Above this
austenitisation temperature range, for instance at 950°C, however, the maximum hardness
that was attained increased. This increase in hardness is mainly due to two factors; firstly
the solid solution hardening of the parent austenite due to the increased dissolution of some
carbides when the austenitisation temperature was increased and secondly, to a subsequent
decrease in the MS temperature leading to a harder untempered martensite with a greater
amount of Carbon in solution.
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Chapter 4: Results and Discussion
At 950°C grain growth of the austenite may also become significant. The decrease in the
martensite start temperature may, however, lead to an increase in the volume fraction of
retained austenite and impose a limit on the increase in the average hardness of the steel.
The grain size of steel E after austenitisation for 20 minutes, as determined by the line
intercept method using the line scanning function of the scanning electron microscope,
increased from 7.0 ± 0.8 μm when the austenitisation temperature was 850°C, to
10 ± 0.8 μm when the austenitisation temperature was 950°C.
It is to be noted in Table (4.3.12) that the higher tensile strength was achieved when the
austenitisation temperature was below 867°C and it dropped again above this
austenitisation temperature. This effect may also be related to grain growth and the increase
in the volume fraction of the retained austenite. Therefore, it appears that both the tensile
strength and the hardness increase with an increase in the austenitisation temperature, but
the upper limit in the tensile strength occurs earlier than for the hardness. This apparent
“disjunction” between the maximum hardness and UTS at a low austenitisation temperature
for the former and at a high austenitisation temperature for the latter, may be related to the
presence of retained austenite after a high austenitisation temperature which affects the
different mechanical processes of hardness and tensile testing differently (due to different
strain rates). A secondary effect may also arise from an increase in grain size at high
austenitisation temperatures although this effect is probably relatively small due to a small
increase in grain size from 7 to 10 μm.
The rate of decrease in hardness of steel E upon low-temperature tempering, appears to be
slower when the austenitisation temperature is lower within the range from 800°C to
900°C. This trend indicates that at higher austenitisation temperatures the amount of
Carbon dissolved into the parent austenite is high, which leads to a higher activity of
Carbon in the martensite upon tempering. The sudden change of slope of the hardness
curves in Figure 4.3.2(a) suggests the existence of two different mechanisms by which the
martensite is softened within the considered tempering temperature range. The first
softening mechanism is active below 150°C and the second mechanism, leading to a sharp
drop in hardness, becomes active upon tempering between 200°C and 250°C. Tempering
this armour steel between 200°C and 250°C leads to the coarsening of the metastable
transition ε -carbides or η -carbides previously formed below 150°C and to their
transformation into cementite.
The elongation upon tensile testing at room temperature increases when the tempering
temperature is increased and it decreases when the austenitisation temperature is increased.
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Chapter 4: Results and Discussion
Table (4.3.16): Elongation of the 33 mm gauge length of steel E that was austenitised at 850°C and at 900°C
respectively, water-quenched and tempered for 60 minutes.
Tempering temperature
Water quenched
150°C
Tensile
elongation (%)
after
austenitisation
at these
temperatures
850°C 900°C
0.3
0.3
4.5
3.5
200°C
7
4.5
250°C
8.5
5.8
300°C
8.5
6.5
4.3.4.2. Mechanical properties of steel F
The optimisation problem for the candidate armour Steel F was established in the same
manner than was done for steel E. The fitting parameters and final equations are given in
Appendix A2 and only the graphical presentation is given here.
The optimum region for the predicted ballistic performance of this steel is discussed later in
comparison with the optimum region for its mechanical properties.
Table (4.3.17): The yield strength to the tensile strength ratio of steel F.
YS/UTS ratios as a function of
the austenitisation
temperature
Normalised
Tempering
tempering
temperature temperature
-1
25°C
-0.09
150°C
0.27
200°C
0.64
250°C
1
300°C
1.36
350°C
1.73
400°C
800°C 850°C 900°C
0.51
0.49
0.46
0.53
0.51
0.47
0.53
0.53
0.51
0.57
0.54
0.53
0.61
0.59
0.57
0.66
0.65
0.60
0.71
0.67
0.61
950°C
0.44
0.47
0.49
0.51
0.55
0.59
0.60
The first constraint equation is derived from the measured tensile strength of steel F at
room temperature and these are presented in Table (4.3.18). The corresponding fitting
parameters are presented in Tables A2.1(c) and A2.1(d) of Appendix A2, which leads to
the mathematical expression of the fitting surface A2.Eq1(b).
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Chapter 4: Results and Discussion
Table (4.3.18): Room temperature tensile strength in MPa of steel F.
Ultimate tensile strength (MPa) as
a function of the austenitisation
temperature
Normalised
Tempering
tempering
temperature temperature
-1
25°C
-0.09
150°C
0.27
200°C
0.64
250°C
1
300°C
1.36
350°C
1.73
400°C
800°C
1624
2154
2131
2064
1982
1710
1687
850°C 900°C
1934
2246
2277
2375
2364
2280
2103
2054
1784
1882
1724
1623
1654
1516
950°C
1901
1998
2010
1954
1770
1548
1415
The second constraint is derived from the Charpy impact energy of the sub-sized specimens
of steel F measured at –40°C. The results in Joules are contained in Table (4.3.19) and the
fitting parameters in Tables A2.1(e) and A2.1(f) from which the regression equation may
be derived.
Table (4.3.19): The Charpy impact energy at –40°C of the sub-sized specimen of steel F
Charpy impact energy (Joules)
as a function of the
austenitisation temperature
Normalised
Tempering
tempering
temperature temperature
-1
25°C
-0.09
150°C
0.27
200°C
0.64
250°C
1
300°C
1.36
350°C
1.73
400°C
800°C 850°C 900°C 950°C
9.0
7.7
6.4
6.4
10.3
9.0
7.7
6.4
11.5
10.3
10.3
9.0
14.1
11.5
10.3
9.0
16.7
12.8
11.5
10.3
17.9
15.4
12.8
10.3
17.9
16.7
15.4
14.1
The optimisation problem for steel F is written in terms of the objective function A2.1(a)
and the constraint equations A2.1(b) and A2.1(c) given in Appendix 2. The fitting surfaces
for steel F are graphically represented in Figure 4.3.4(a). The same scaling factors as were
applied to steel E were also applied here. The optimum regions for the mechanical
properties are visualised in two-dimensional plots of the iso-lines in the plane ( Tan , Ttn ).
102
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Chapter 4: Results and Discussion
Steel F
UTS
2500
2000
1500
1000
YS/UTS
500
0
2
1
CIE
1
0.5
0
0
-0.5
-1
Normalised tempering T
-1
Normalised austenitisation T
Figure 4.3.4(a): Three-dimensional representation of the optimisation problem for steel F showing the
surface of the ultimate tensile strength at room temperature (upper surface), the Charpy impact energy at –
40ºC (lower surface) and the objective function of the YS/UTS ratio in the middle.
YS/UTS of steel F
UTS of steel F
1.5
88
0.543
8
0.5438
0.5
8
0. 5438
15
0.510
0.510
15
6 43
0.47
0 15
0.51
43
76
0.4
-0.5
-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperatutre
0.8
1
Figure 4.3.4(b): Iso-lines of the objective function
YS/UTS of steel F
17 85. 4268
1916.5766
0.5
-0.5
-1
-1
19 16.576
6
20 47.7265
2178.8763
.8763
21 78
262
23 10.0
0
1785.4268
1916.5766
2047.7265
.0262
23 10
0
1
23 1
0.02
62
21
78
.87
63
21 7
23 10.0
262
8.87
19 1 20 4
63
7
6. 5
766 .7265
2178.8763
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperatutre
20
47
.7
26
5
20 4
7.72
65
76
0.57
0.5776
16 54. 277
17 85.426
8
21
78
.87
63
0. 61133
16 54.2
77
0.5776
Normalised tempering temperature
1
1 33
0.61
3
.876
21 78
Normalised tempering temperature
0.645 05
23
10
.0
26
2
1.5
0.8
1
Figure 4.3.4(c): Iso-lines of the ultimate tensile
strength of steel F
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
Charpy impact energy of steel F
12 .3
4
64
.43
10
12
25
8.5
10
.43
64
0.5
-0.8
64
.43
10
8.
52
51
2
8.5
25 1
2
6.61
3 88
8.5
25 1
2
-1
-1
10
.43
64
6. 613 88
0
-0.5
76
.34
12
76
8.52
5 12
16 .1
14
7 01
.25
12
88
.34
76
1
12 .3476
8
38
61
6.
Normalised tempering temperature
1.5
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperatutre
0.8
1
Figure 4.3.4(d): Iso-lines of the Charpy impact energy of the sub-sized specimens of steel F measured at 40°C
Figure 4.3.4(b) shows that the lower YS/UTS ratio for steel F is achieved with low
normalised tempering temperatures between –1 and 0, or actually lower than 163°C. This
limit is lower than the 200°C found in the case of steel E. Steels E and F have the same
Carbon content of 0.39%C but have two different martensite start temperatures, which are
196°C and 255°C respectively. This difference is due to the differences in their Manganese
and Chromium contents. The morphology of the martensite in these two steels is compared
in section 4.4.3 through thin foil transmission electron microscopy. The tensile strength of
steel F is very high compared to steel E and is also high compared to the limit specified by
ARMSCOR and Mittal Steel. The tensile strength of steel F was found to be higher than
1700 MPa throughout the entire range of austenitisation and tempering temperatures used
here, as shown in Figure 4.3.4(c). Steel F also has tensile elongations larger than 11% when
tempered at 200°C. This steel also has the highest hardness in the as-quenched condition
and also after tempering below 200°C. The Vickers hardnesses are above 720 VHN or 640
BHN. Finally it also has a higher YS/UTS ratio than steel E. More details on the
comparison between these two armour steels will be given in section 4.4 after the ballistic
testing and in Section (4.5) after transmission electron microscopy and atomic force
microscopy.
4.3.4.3. Mechanical properties of steel G
Steel G has a lower Manganese and Chromium contents than both steels E and F. The
martensite start temperature of steel G was measured as 271°C. The volume fraction of
retained austenite in this steel was lower than the detection limit of the X-ray diffraction
technique used in this study. The optimisation problem for steel G follows the same scheme
than for steels E and F. The objective function YS/UTS ratio is derived from the results of
the tensile tests at room temperature and is presented in Table (4.3.20). The similar
regression analysis produced the fitting parameters in Tables A2.2(a) and A2.2(b) in
Appendix 2 after which the mathematical expression of the objective function may be
found.
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Chapter 4: Results and Discussion
Table (4.3.20): The yield strength to ultimate tensile strength ratio of steel G
YS/UTS ratio as function of the
austenitisation temperature
Tempering
temperature
25°C
150°C
200°C
250°C
300°C
350°C
400°C
Normalised
tempering
temperature
-1
-0.09
0.27
0.64
1
1.36
1.73
800°C 850°C 900°C 950°C
0.66
0.61
0.49
0.46
0.67
0.68
0.51
0.49
0.68
0.67
0.53
0.53
0.72
0.77
0.57
0.57
0.76
0.71
0.61
0.61
0.79
0.74
0.66
0.66
0.83
0.76
0.69
0.64
The first constraint on the system is the tensile strength and its variation with the
austenitisation and tempering temperatures is presented in Table (4.3.21). The surface
fitting parameters are again calculated in two steps. The first analysis produced the
parameters for Equation (4.3) and the second produced the parameters for Equation (4.4).
These parameters are presented in Tables A2.2(c) and A2.2(d) in Appendix 2. As may be
observed, the parameters in Table A2.2(c) are some function of the austenitisation
temperature. Hence they are fitted to third degree polynomials to obtain the final
parameters A, B, C and D in Table A2.2(d).
Table (4.3.21). Measured tensile strength in MPa for steel G.
Ultimate tensile strength in
MPa as a function of the
austenitisation temperature
Normalised
Tempering tempering
temperature temperature
-1
25°C
-0.09
150°C
0.27
200°C
0.63
250°C
1
300°C
1.36
350°C
1.72
400°C
800°C
1324
2252
2061
1872
1643
1597
1335
850°C 900°C 950°C
1934 2120 1901
2171 2193 2089
2020 1932 1926
1790 1833 1750
1631 1753 1565
1594 1584 1488
1326 1340 1298
The second constraint is defined by the Charpy impact energy at -40°C. The measured
impact energy values in Joules, are tabulated as follows:
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
Table (4.3.22): Charpy impact energy in Joules measured at –40°C on sub-sized specimens of steel G
Charpy impact energy (in
Joules) as a function of the
austenitisation temperature
Normalised
Tempering tempering
temperature temperature
-1
25°C
-0.09
150°C
0.27
200°C
0.64
250°C
1
300°C
1.36
350°C
1.73
400°C
800°C
9.9
17.7
18.7
18.7
17.7
17.7
17.7
850°C 900°C 950°C
8.9
9.9
9.9
14.8
16.8 13.8
15.8
16.8 15.3
16.8
17.7 15.8
16.8
17.7 16.3
17.3
18.2 16.8
16.3
17.7 15.8
From the results in Table (4.3.22), the fitting parameters for the Equations (4.3) and (4.4)
are calculated and tabulated in Tables A2.2(e) and A2.2(f) respectively, in Appendix 2. The
fitting parameters in Table A2.2(e) are again some function of the austenitisation
temperature. The second regression analysis becomes necessary and gives the fitting
parameters in Table A2.2(f). The second constraint of the system is written after the
parameters in Table A2.2(f) and is mathematically presented in Equation A2.Eq2(c) in
Appendix 2.The optimisation problem is then written in the classical form using the
objective function to be minimised given by Equation A2.Eq2(a) and the two inequality
constraints given by the Equations A2.Eq2(b) and A2.Eq2(c) in Appendix 2, as described
in Equation (4.9). The three-dimensional representation of the system is shown in Figure
4.3.5(a). The same scaling factors applied in the two previous cases are also applied here
for the same reasons. The corresponding two-dimensional representations in the ( Tan , Ttn )
planes are shown in Figures 4.3.5(b) through to 4.3.5(d).
Steel G
UTS
2200
2000
YS/UTS
1800
1600
1400
1200
1
CIE
1000
800
1.5
0.5
0
1
-0.5
0.5
0
-0.5
-1
-1
Normalised a
Normalised tempering T
Figure 4.3.5(a): Three-dimensional representation of the objective function and the constraints in the case of
steel G.
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Chapter 4: Results and Discussion
YS/UTS of steel G
UTS of steel G
1
5
92
61
0.
0.
68
18
6
0.
74
44
6
1.5
6
70
80
0.
6
70
80
0.
14 49.0246
Normalised tempering temperature
0. 5
56
65
0.6
19
25
0.6
81
86
6
44
74
0.
0.5
0.4
94
05
-1
-1
-0.6
0.556 65
25
0.619
0.68
1 86
-0.8
0.49
4 05
0
-0.5
692
15 70.8
1570.8692
0.55665
6
0.6818
Normalised tempering temperature
1.5
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperatutre
0.8
1692. 7138
1814.5584
0.5
1936.4031
20 58
.2477
-0.5
Figure 4.3.5(b): The yield strength to ultimate tensile
strength ratio of the Steel G
temperature
16 92
.7138
1814.5584
18 1
4.55
84
1936.4031
19 36
.4031
2058.2477
0
20 58.247
7
20 5
8.24
77
19 3
18 1 6.403
1
4.5
584
-1
-1
1
8
16 92.713
1
15 70
.8692
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperatutre
7
247
58.
20
0.8
1
Figure 4.3.5(c): Iso-lines of the ultimate tensile
strength in MPa of steel G measured at room
Charpy impact energy of steel G
17 .2
4
22
22
4
17 .2
1
22
.24
17
-0.5
-1
-1
15 .8
4
14 .43 79
79
7
.43
14 3 .03 5
1
6
3
3
11 .6
10 .2314
-0.8
17 .2
4 22
15.84
-0.6
13 .0
3
15
.8
4
14
.43
79
0
17 .2
4 22
0.5
15
.8
4
Normalised tempering temperature
1.5
57
11 .63
36
14 .43
79
13.0357
11.63 36
10 2314
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Normalised austenitisation temperatutre
10 .2314
1
Figure 4.3.5(d): Iso-lines of the Charpy impact energy of the sub-sized specimens of steel G measured at 40°C
Some similarity of steel G to steel F may be noticed. The YS/UTS ratios are higher than in
the case of steel E. The tensile strength is also higher than the specified 1700 MPa
throughout the entire range of the austenitisation and tempering temperatures. The Charpy
impact energy at –40°C is also higher than the specified 13 Joules throughout the entire
range of the heat treatment parameters. Some resemblances are then expected between the
microstructures of steel G and steel F that differ from steel E. Their martensite start
temperatures are both above 250°C and no retained austenite was detected by X-ray
diffraction. The ultimate tensile strength of steel G is slightly lower than for steel F but
remains higher than 1700 MPa when the normalised tempering temperature does not
exceed the normalised value of 1 or actually 300°C.
4.3.4.4. Mechanical properties of steel H
Steel H has the same Carbon content than steel G but has a lower martensite start
temperature of 210°C, which is below 250°C. X-ray diffraction detected 4% volume
fraction of retained austenite in the quenched specimens. The YS/UTS ratio of this steel as
a function of the austenitisation and tempering temperatures is given in Table 4.3.23. The
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
regression analysis allowed the determination of the fitting parameters presented in Tables
A2.3(a) and A2.3(b) in Appendix 2.
Table (4.3.23): The yield strength to ultimate tensile strength ratio of steel H
YS/UTS ratio of steel H as a
function of the austenitisation
temperature
Normalised
Tempering tempering
temperature temperature
-1
25°C
-0.09
150°C
0.27
200°C
0.64
250°C
1
300°C
1.36
350°C
1.73
400°C
800°C 850°C 900°C 950°C
0.46
0.44
0.44
0.43
0.47
0.46
0.46
0.44
0.50
0.47
0.47
0.45
0.55
0.53
0.49
0.46
0.59
0.57
0.53
0.49
0.57
0.61
0.55
0.51
0.66
0.61
0.57
0.53
The function describing the variation of the YS/UTS ratio is noted as Equation A2.Eq3(a)
in the same appendix. The constraint equation on the ultimate tensile strength is derived
from the experimental measurements in Table (4.3.24) from which the fitting surface is
determined. The surface fitting parameters are given Tables A2.3(c) and A2.3(d).
Table (4.3.24): The ultimate tensile strength in MPa of steel H.
The ultimate tensile
strength (in MPa) of steel
H as function of the
austenitisation
temperature
Normalised
Tempering tempering
temperature temperature 800°C 850°C
-1
1415 1543
25°C
-0.09
1905 1806
150°C
0.27
2020 1942
200°C
0.64
1902 1909
250°C
1
1929 1724
300°C
1.36
1713 1704
350°C
1.73
1603 1615
400°C
900°C 950°C
1118 822
2146 1816
2146 1862
1955 1830
1894 1770
1698 1566
1678 1521
The mathematical expression of the tensile strength in MPa is written using the parameters
in Table A2.3(d) and has the form given in Equation A2.Eq3(b) in Appendix 2. The second
constraint is defined by the Charpy impact energy measured at -40°C and is derived from
the experimental results reported in Table (4.3.25).
The surface fitting parameters obtained by regression analysis are contained in Tables
A2.3(e) and A2.3(f) (Appendix 2). The equation for the Charpy impact energy surface is
written in terms of the normalised temperature as Equation A2.Eq3(c). The second
constraint equation is written in terms of the normalised temperatures using the parameters
determined in Table A2.3(f) (Appendix 2) and is noted as Equation A2.Eq3(c).
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Chapter 4: Results and Discussion
Table (4.3.25): The Charpy impact energy in Joules of the sub-sized specimens of steel H measured at -40°C
Charpy impact energy (in
Joules) of steel H as function of
the austenitisation temperature
Normalised
Tempering tempering
temperature temperature
-1
25°C
-0.09
150°C
0.27
200°C
0.64
250°C
1
300°C
1.36
350°C
1.73
400°C
800°C 850°C 900°C 950°C
7.5
8
6
6.5
19
14.5
18
12
19
15
17
14
19
13.5
17
14
15
10
12
11
13
8
8
8
10
7.5
8
7
The optimisation problem for the properties of steel H is stated in the classical form
described in Equation (4.9) using the objective function of Equation A2.Eq3(a) and the
constraint functions of Equations A2.Eq3(b) and A2.Eq3(c). The three-dimensional
representation of the system is shown in Figure 4.3.6(a).
Steel H
2500
UTS
2000
1500
1000
500
CIE
YS/UTS
0
-1
0
1
Normalised austenitisation T
-1
-0.5
0
0.5
1
1.5
Normalised tempering T
Figure 4.3.6(a): Three-dimensional representation of the optimisation problem for steel H showing the
ultimate tensile strength surface(upper surface), the Charpy impact energy surface in the middle and the
YS/UTS ratio in the bottom (bottom surface).
The same scaling factors than in the previous figures have been applied here. The
corresponding iso-lines in the planes ( Tan , Ttn ) are shown in Figures 4.3.6(b) through to
4.3.6(d).
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Chapter 4: Results and Discussion
YS/UTS of steel H
0.5683
0 74
0.54
0.54074
8
0.5131
62
85
0.4
8
13 1
0.5
5 62
0.48
0.48562
0
1642. 3873
6
58 0
0.4
0.458 06
-0.5
1
0.5
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperatutre
0.8
19
05
.21
59
16 4
59
2.3
5.21
873
19 0
13 7
11 16.730
9.55
1
1642.3873
87
85 3.9
1
591.07288
1379.5587
0149 1 16.7301
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Normalised austenitisation temperatutre
1642.3873
1379.5587
-0.5
-1
-1
1
Figure 4.3.6(b): Iso-lines of the YS/UTS
ratio in the plane ( Tan , Ttn )
19
05.
215
9
0
6
80
45
0.
-1
-1
159
19 05.2
1905.2159
0.5
1.5
18
13
0.5
1905.2159
1
UTS of steel H
74
40
0. 5
68 3
0.5
59
.21
05
19
Normalised tempering temperature
6
0.5958
Normalised tempering temperature
1.5
1
Figure 4.3.6(c): Iso-lines of the ultimate
tensile strength (in MPa) of steel H in the plane
( Tan , Ttn )
Charpy impact energy of steel H
1.5
15 .46 74
13 .47
76
15
.4
67
4
7 76
13 .4
-0.8
15
.46
74
17 .4
5
72
15 .46 74
74
.46
15
13 .4
7 76
11.4877
72
.45
17
-0.5
-1
-1
76
13 .47
17.4572
0
11 .4
8 77
77
11 .48
6
77
.4
13
0.5
9.49788
9. 497 88
17 .4
5 72
1
76
74
.47
.46
13
15
Normalised tempering temperature
9.4
97
88
15 .4674
77
.48
13.4776
11
88
7
11.4877
9
9.4
9.49788
9.49788
7.50804
7 508 04
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Normalised austenitisation temperatutre
13 .477
6
11.4877
Figure 4.3.6(d): Iso-lines of the Charpy impact energy (in Joules) at –40°C of steel H
Steel H has intermediate values of the YS/UTS ratio, lying between steel E on one side and
steels F and G on the other side. Like steel E it presents a brittle behaviour in the
untempered condition, where it is difficult to measure the ultimate tensile strength. The
tensile strength of this steel has also intermediate values between the two groups of steels
previously identified. It remains close and above the specified 1700 MPa after tempering at
350°C for the entire range of the austenitisation temperature. The Vickers hardness of steel
H also remains above 550 VHN after tempering at 300°C for one hour. The resistance to
tempering of this steel is due to its high Silicon content. It is well known that Silicon delays
the transformation of the transition ε - carbide to cementite during tempering.
4.3.4.5. Mechanical properties of steel I
The martensite start temperature of steel I measured by dilatometry was found to be 309°C,
which is higher than the martensite temperatures of the other four steels. The volume
fraction of retained austenite in the quenched condition was lower than the detection limit
of the X-ray diffraction technique used for the analysis. The results of the measurement of
the YS/UTS ratio of this steel are shown in Table (4.3.26). It may be observed that steel I
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University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
presents the highest values of the YS/UTS ratio of all of the five steels considered up to
here.
The YS/UTS ratio of steel I in the quenched condition is in the same range than that of
steels E and H after low-temperature tempering. The relatively high values of this ratio for
steel I may be caused by auto-tempering during the quenching of this steel, in view of its
relatively high Ms temperature.
Table (4.3.26): The YS/UTS ratio of steel I
YS/UTS ratio as a function of
the austenitisation
temperature
Normalised
Tempering tempering
temperature temperature
-1
25°C
-0.09
150°C
0.27
200°C
0.64
250°C
1
300°C
1.36
350°C
1.73
400°C
800°C 850°C 900°C
0.66
0.62
0.6
0.70
0.71
0.61
0.74
0.74
0.63
0.78
0.74
0.63
0.80
0.78
0.64
0.83
0.77
0.66
0.83
0.81
0.71
950°C
0.62
0.61
0.63
0.62
0.64
0.64
0.66
The objective function describing the YS/UTS ratio is written in terms of the normalised
temperature using the fitting parameters in Table A2.4(b) in Appendix 2 and is noted as
Equation A2.Eq4(a). The constraints on the system are derived from the results of the
tensile tests and the Charpy impact tests. Table (4.3.27) contains the results of the ultimate
tensile strength measurements. The fitting parameters for the ultimate tensile strength
surface of this steel are presented in Tables A2.4(c) and A2.4(d) of Appendix 2.
Table (4.3.27): The ultimate tensile strength (in MPa) of steel I
Ultimate tensile strength (in
MPa) as a function of the
austenitisation temperature
Normalised
Tempering tempering
temperature temperature
-1
25°C
-0.09
150°C
0.27
200°C
0.64
250°C
1
300°C
1.36
350°C
1.73
400°C
800°C 850°C 900°C
2100 1954 1948
2040 1920 1900
1842 1751 1763
1714 1675 1623
1515 1446 1485
1447 1453 1434
1312 1261 1284
950°C
1543
1755
1649
1588
1452
1327
1187
The mathematical equation describing the tensile strength of steel I is then derived from the
parameters in Table A2.4(d) (Appendix 2) and noted as Equation A2.Eq4(b). The second
constraint is derived from the measured vales of the Charpy impact energy at -40°C using
the experimental values in Table 4.3.28.
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Table (4.3.28): Charpy impact energy of the sub-sized specimens of steel I at -40°C
Charpy impact energy as a
function of the austenitisation
temperature
Normalised
Tempering tempering
temperature temperature 800°C 850°C 900°C 950°C
-1
16
17
17
17
Ally 25°C
-0.09
18
19
19
19
150°C
0.27
19
19
20
20
200°C
0.64
18
19
20
19
250°C
1
18
19
19
20
300°C
1.36
19
19
19
21
350°C
1.73
18
20
20
21
400°C
The equation representing the Charpy impact energy of the sub-sized specimens of steel I
measured at -40°C, is finally derived from the parameters contained in Table A2.4(f) and
noted as Equation A2.Eq4(c). The optimisation problem is stated in classical form by
substituting the objective function in Equation A2.Eq4(a) and the constraint functions in
Equations A2.Eq4(b) and A2.Eq4(c) in the system defined in Equation (4.9). The threedimensional representation of this system, using the previous chosen scaling factors, is
presented in Figure 4.3.7(a).
Steel I
CIE
2200
2000
1800
1600
1400
1200
UTS
1000
YS/UTS
800
1.5
1
1
0.5
0.5
0
Normalised tempering T
-0.5
-0.5
-1
0
-1
Normalised austenitisation
Figure 4.3.7(a): Three-dimensional representation of the optimisation system for steel I.
From Figure 4.3.7(a), it may be observed that the surface representing the Charpy impact
energy of steel I is at high levels and it remains high throughout the entire range of heat
treatment parameters considered.
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However the ultimate tensile strength surface drops to levels lower than 1700 MPa when
the tempering temperature is higher than 200°C. The corresponding iso-lines are shown in
Figures 4.3.7(b) through to 4.3.7(d).
YS/UTS of steel I
UTS of steel I
0.7
07
-1
-1
-0.8
-0.6
13 91.8
648
1515.3209
1515.3209
15 15.320
9
16 38. 777
1638.777
16 38.7
77
17 62.2
33
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperatutre
0.8
-0.8
Figure 4.3.7(b): Iso-lines of the yield strength to
ultimate tensile strength ratio of steel I
-0.6
17 62
.233
1885.6891
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperatutre
17 62
.233
-0.5
-1
-1
1
1762.233
18 85
.6891
0
0.5
16
55
2
35
64
0.
0.5
80
03
-0.5
0.5
1391.8648
91
.68
85
18
07
0.7
1
1391. 8648
20 09.1452
Normalised tempering temperature
0.
51
65
5
0. 6
43
52
0.77
0 49
0
0.5
80
03
0.7
07
0.5
3
00
58
0.
0.6
43
52
0.
83
39
7
0.
77
04
9
1
1.5
97
33
0.8
Normalised tempering temperature
1.5
0.8
1
Figure 4.3.7(c): Iso-lines of the tensile strength
of steel I.
Charpy impact energy of steel I
1.5
19
.74
75
19 .08
8
1
0.5
2
18 .4
85
Normalised tempering temperature
18 .42 85
19
.08
8
0
19 .08 8
17
.76
89
-0.5
18 .4
2
17 .1
0 94
-1
-1
85
18.4285
17.7689
16 .4
4
99
-0.8
-0.6
19.088
17.1094
18.4285
17.7689
17.1094
-0.4
-0.2
0
0.2
0.4
0.6
Normalised austenitisation temperatutre
0.8
1
Figure 4.3.7(d): Iso-lines of the Charpy impact energy of steel I measured at -40°C
4.3.5. General observations on the mechanical properties of steels E through to I.
From the results of the measurements presented in Section 4.3.4, it appears that the five
armour steels considered may be classified following their martensite start temperatures.
Three groups of armour steels may be defined. The first group of armour steels, comprising
steel E and steel H, have relatively low martensite start temperatures, lower than 210°C.
The second group comprises steels F and G which has martensite start temperatures near to
250°C. The third group comprises steel I which has martensite start temperatures near to
300°C. The YS/UTS ratios of these steels are plotted for graphical comparison in Figure
4.3.8.
Table (4.3.29). Groups of armour steels classified according to the martensite start temperatures for the
austenitisation temperatures comprised in the range from 800°C to 950°C.
Group
1
2
3
Armour
steel
E
H
F
G
I
Martensite start
temperature
196°C
210°C
255°C
271°C
309°C
YS/UTS
< 0.6
0.65 to 0.75
> 0.70
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Chapter 4: Results and Discussion
Tensile strength to Ultimate tensile strength ratio
1
I
0.9
YS/TS
0.8
G
0.7
0.6
0.5
E
H
0.4
2
1
0
-1
Normalised T(tempering)
-0.5
0
0.5
1
Normalised T(austenitisation )
Figure 4.3.8: Showing the comparison of the levels of the yield strength to ultimate tensile strength ratio
surfaces of the steels E through to I. Steel I and steel G on top, steel E, steel F and steel H on the bottom. The
plane of YS/UTS=0.5 is also shown.
From this figure it may be observed that high martensite start temperatures lead to high
values of the YS/UTS ratio in the quenched as well as in the tempered conditions for these
five armour steels. The YS/UTS ratio increases with an increase in the tempering
temperature. The high values of this ratio in the cases of high martensite temperatures, is
probably a consequence of auto-tempering during quenching. However, this ratio decreases
with an increase in the austenitisation temperature which leads to grain growth and an
increase in the volume fraction of retained austenite because of the lower martensite start
temperature. The volume fraction of retained austenite in the armour steels becomes the
main factor determining the YS/UTS ratio. This ratio is lower in the conditions
corresponding to a higher volume fraction of retained austenite in these armour steels. This
is the case for the two armour steels E and H in the first class.
The tensile strength of steel E (group 1) and steel F (group 2) are compared in Figure 4.3.9,
where the plane of 1700 MPa is also shown. The gap in the tensile strength between these
two groups of armour steels is large. It was noted earlier that the steels A (Ms =285°C ), B
(MS = 253°C), C (MS =241°C ) and D (MS =265°C ) are currently in production by Mittal
Steel and others and are already utilised in military and security applications. The
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Chapter 4: Results and Discussion
specifications for these ballistic purposes are stated in terms of the yield strength that
should be higher than 1500 MPa and the tensile strength, that should be higher than
1700 MPa. These two strength limits will lead to values of the YS/UTS ratio close to 0.88
and will lead to the occurrence of localised yielding during impact. Experience within the
industry has found that steel C has a better ballistic performance than the other three for
plate thickness between 8.5 mm up to 30 mm. In the current assessment methodology, steel
A, steel B and steel D may, therefore, be classified into the second class, whereas steel C
belongs to the transition between the first class and the group 2 of armour steels as
previously defined from their martensite start temperatures.
Ultimate tensile strength of steels E and F
2600
2400
2200
TS [MPa]
2000
1800
1600
1400
1200
1000
800
2
1
Normalised tempering temperature
0
-1
-1
-0.5
0
0.5
1
Normalised T(austenitisation)
Figure 4.3.9: Comparison of the ultimate tensile strength between steel E (group 1) in the lower surface, steel
F (group 2) in the upper surface and the specified plane of 1700 MPa.
The armour steels in group 3 (high martensite start temperatures) have an intermediate
tensile strength between those in the first and in the second groups. The same observation
is valid for their hardnesses. Hence the second group of armour steels is currently produced
for military applications based on the design philosophy that would link the ballistic
performance to the hardness and the tensile strength of these steels. Earlier in Chapter 2
mention was made of a new approach in the definition of the Ballistic Performance Index
where the hardness of the armour steel is no longer an important determinant. Rather the
tensile strength is considered to be important as it compares well to the true fracture
strength during high-velocity impact. In the present study the YS/UTS ratio is also
considered in predicting the ballistic performance of the armour steels and comparison is
made between the three modes of predicting the ballistic performances using (i) the
hardness of the plates, (ii) their ballistic performance index BPI, or (iii) their YS/UTS ratio.
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Chapter 4: Results and Discussion
Ultimate tensile strength
2500
TS [MPa]
2000
1500
1000
500
2
1
0.5
1.5
1
0.5
Normalised tempering temperature
0
0
-0.5
-0.5
-1
-1
Normalised T(austen)
Figure 4.3.20: Comparison between the tensile strength of steels E, F and I showing the intermediate level of
the strength of steel I (group 3) between that of steel F (group 2) in the upper surface and steel E (group 1) in
the lower surface. The plane of 1700 MPa is also shown.
The Charpy impact energy at -40°C of steels E, F, G and I are compared in Figure 4.3.21,
where it may be observed that steel I (group 3) has the highest impact energy (upper
surface) throughout the entire range of the austenitisation and tempering temperatures,
whereas steel E and steel H (group 1) have the lowest impact energy (lower surfaces)
throughout the entire range of the austenitisation and tempering temperatures considered in
this study. Steel F (group 2) has a fairly intermediate level of Charpy impact energy. It also
appears from Figure 4.21 that the Charpy impact energy of the sub-sized specimens of the
armour steels measured at –40°C, increases when the martensite start temperature of the
armour steel is higher.
The fracture surfaces after the tensile tests at room temperature and the Charpy impact tests
at -40°C of these three classes of armour steels, as classified according to their martensite
temperatures, are compared in Section 4.3.6. The effect of Silicon, Chromium and
Manganese contents in their resistance to low-temperature tempering, are also analysed.
The effect of the shape and the size of the Manganese sulphide particles on the fracture
mode of these armour steels is particularly examined.
4.3.6. Fracture analysis after the Charpy impact and the tensile tests.
4.3.6.1. Group 1 armour steels
The fractured surfaces of the Charpy specimens of steels E (0.003%S, 1.22%Mn) and H
(0.011%S, 1.15%Mn) whose martensite start temperatures are respectively 196°C and
210°C, were analysed by secondary electron scanning electron microscopy. Two areas
were considered in each fractured surface, firstly, where only the shear lips were analysed
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for the sake of the mechanism by which the fracture was initialised, and secondly, the
unstable propagation of the crack that occurred throughout the cross-section of the
specimen.
Charpy Impact energy
25
CIE [Joules]
20
15
10
5
1
0
2
0.5
0
1
-0.5
0
-1
Normalised tempering temperature
-1
Normalised T(austen)
Figure 4.3.21. Comparison between the Charpy impact energy of the sub-sized specimens of steel E (lower
surface), steel H (second lower surface), steel G (second upper surface) and steel I (upper surface). The plane
of the specified 13 Joules is also shown.
The first area was generally near the standard notch of the Charpy specimen while the
second area was situated within the fracture face at a position below the notch and very
near to the area of contact with the striking edge of the pendulum. The Charpy impact
energy of the sub-sized specimens, measured at -40°C, allowed the selection of the three
tempering temperatures for steel H, as shown in Figure 4.3.22. The Charpy impact energy
of these two steels remains lower than the specified 13 Joules in the untempered condition
and also when tempered at temperatures lower than 200°C. It exceeds 13 Joules, however,
when the steels E and H are tempered at temperatures between 200 and 300°C and
decreases again when the tempering temperature is higher than 300°C. The untempered
Charpy specimens and those tempered at 200°C and at 300°C for 20 minutes and for 60
minutes, were selected for observation in the scanning electron microscope.
From Figure 4.3.22 it appears that the armour plates in the group 1 (low martensite start
temperatures) fractured by a brittle inter-granular mechanism in the untempered condition
during the test at -40°C. The former austenite grain size is the operating grain size during
the fracture. This behaviour is more noticeable in the shear lips formed near to the notch in
the specimens ( Figure 4.3.22(a-1)) than in the shear lips near the impact point
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( Figure 4.3.22(a-2)) where fracture rather occurs by a compound mechanism involving an
inter-granular and a trans-granular mechanism. The specimens tempered at 200°C again
show a more brittle behaviour near to the notch ( Figure 4.3.22(b-1)) than near to the
impact point ( Figure 4.3.22(b-)2). Tempering at 200°C slightly improved the toughness of
these armour steels and increased their Charpy impact energy to 12 Joules. Dimples were
formed in areas near the faces close to the impact area away from the notch. At the same
time the effect of Manganese sulphide particles becomes observable (craters on the bottom
of Figure 4.3.22(b-2)). Tempering at 250°C led to values of the impact energy between 13
Joules and 18 Joules for steels E and H. The fracture of these Charpy specimens became
ductile with small dimples formed near the notch (Figure 4.3.22(c-1)) as well as near the
impact area away from notch. The size of the plastically deformed regions around the
Manganese sulphide particles became larger as may be observed in the Figure 4.3.22(c-2).
The decrease in the Charpy impact energy of the specimens upon tempering above 300°C
is partially attributed to the detrimental effect of the Manganese sulphide particles in a
relatively soft martensite when the tempering temperature exceeds 200°C.
The brittle inter-granular fracture near the notch of the Charpy specimens may be explained
by the stress concentration effect of the notch that introduces local stresses higher than the
nominal stress far from the notch during the impact test.
Tempering produces carbides and removes the Carbon from solid solution in the martensite
and it is this that lowers the hardness and increases the toughness. However the
detrimental effect of the Manganese sulphide particles plays a role in the fracture
mechanism of these steels and imposes a limit to their increase in toughness with fracture
cavities of up to 7 μm that were formed. The shape of the Manganese sulphide particles has
a strong effect on the stress concentration effect during impact and tensile loading as will
be shown later in this paragraph. The shape is important but of equal importance here is the
very low adhesion between the ferrite matrix and MnS particles. Specifically, upon
tempering above 250°C the softening of the martensite promotes the decohesion around the
elongated Manganese sulphide particles. Cavities of diameters larger than 16 μm were
formed upon unstable shearing of the areas around the Manganese sulphide particles as
illustrated in Figure 4.3.22(c-2). The Charpy impact energy of these armour steels becomes
once again lower upon tempering at 400°C.
Backscattered scanning electron microscopy of the untempered and the specimen tempered
at 400°C for 60 minutes, show the advanced decomposition of the martensite into ferrite
and cementite in between the plates previously formed upon quenching. A high
magnification is necessary to observe this advanced decomposition of the martensite as
shown in Figures 4.3.23(a-1) to 4.3.23(b-2). At a low magnification of about 1700X the
shape of the martensite plates seems unaltered upon tempering at 400°C (Figure 4.3.23(b1)) compared to the untempered condition (Figure 4.3.23(a-1)). But a higher magnification
of about 20000X reveals the decomposition of the martensite whereas in the untempered
condition backscattered electron microscopy does not reveal the presence of any cementite
(Figure4.3.23(a-2)).
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Chapter 4: Results and Discussion
18
16
14
12
800
850
900
950
10
8
6
4
2
0
0
100
200
300
400
Tempering temperature [degree Celsius]
a-1
a-2
b-1
b-2
c-1
c-2
Figure 4.3.22. Secondary electron scanning electron micrographs of the fractured Charpy specimens of steel
H after testing at -40°C, showing the evolution of the operating mode during the fracture as a function of the
tempering temperature and the effect of the notch.
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Chapter 4: Results and Discussion
0
Fig. 4.3.22(a-1) and (a-2): SEM fractograph of steel H austenitised at 850 C , quenched in water showing a
brittle inter-granular fracture near the notch (Figure a-1), and a quasi cleavage fracture near the incidence site
of the specimen in direct contact with the striking edge of the pendulum.
Fig. 4.3.22(b-1) and (b-2): SEM fractograph of steel H austenitised at 850
0
C , quenched in water and
0
tempered at 200 C , showing brittle fracture near to the notch and a more ductile fracture near the impact
area away from the notch. Cavities were formed around the MnS particles.
Fig. 4.3.22(c-1) and (c-2): SEM fractograph of steel H austenitised at 850
0
C , quenched in water and
0
tempered at 300 C , showing ductile fracture near the notch as well as near the impact area away from the
notch. Small equi-axed dimples and large cavities had formed around the MnS particles.
Figure 4.3.23(a-1): SEM of untempered and
polished sample of the steel H at
1700 magnification
Figure 4.3.23(a-2): SEM of untempered
and polished sample of steel H at 20000 magnification
Figure 4.3.23(b-1): SEM of polished sample
of steel H tempered at 400°C
( × 1700 magnification)
Figure 4.3.23(b-2): SEM of polished
sample of steel H tempered at 400°C
( × 20000 magnification)
The presence of the cementite and the Manganese sulphide is, therefore, prejudicial to the
resistance against impact loading despite the presence of the soft ferrite. The shear lips of
the tensile specimens have also been examined in secondary electron scanning electron
microscopy. The brittle behaviour of the armour steels in the untempered condition makes
it very difficult for the determination of the tensile properties. Figure 4.3.24 shows the
fracture surface under tensile stress of steel H in the quenched and untempered condition. It
confirms that the brittle behaviour in the case of a low strain rate axial loading is less
severe than one under impact loading as was illustrated in the Figures 4.3.22(a-1) and
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4.3.22(a-2). The fracture surface of the untempered tensile specimens presents features of
brittle fracture by decohesion of the grains as can be seen in Figure 4.3.24. Cavities of 2.5
μm are formed around the spherical inclusions of Manganese sulphide. The elongated
plate-like inclusions of Manganese sulphide increases the size of the cavities to more than
12 μm that are formed during the tensile test and are shown in Figure 4.3.25 . This
phenomenon may by explained by the occurrence of localised high stresses around the
inclusions of the Manganese sulphide plates and consequently it leads to a decrease of the
nominal ultimate tensile strength of the armour steel upon tempering. The other reason for
this decrease of the ultimate strength is the decomposition of the martensite itself and the
formation of coarse cementite.
Figure 4.3.24: Secondary electron scanning microscopy of the shear lips of steel H in the quenched and
untempered condition, showing spherical inclusions of MnS after tensile test.
Figure 4.3.25: An elongated plate-like inclusion of Manganese sulphide, observed after the tensile test of
steel H tempered at 150
0
C , showing large cavities around the inclusions of the MnS.
4.3.6.2 Group 2 armour steels
The sub-sized Charpy specimens of steel F (0.009%S, 0.65%Mn) whose martensite start
temperature is 255°C, have shown the same brittle behaviour in the untempered condition
as was the case with the steels E and H but with a slightly higher impact energy. Besides
the mentioned reasons of the brittle behaviour in the untempered condition, other inclusions
such as the Calcium-Aluminium compounds inherited from the casting process also act as
stress raisers and, therefore, act as crack initiators in the hard untempered martensite during
the tensile test. The initiation of such cracks is illustrated in Figure 4.3.26. For steel F also
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the effect of the Manganese sulphide inclusions becomes observable and large cavities
were formed around this type of inclusion that weakens the armour steel when the tensile or
the Charpy specimens are tempered at temperatures above 200°C, as illustrated in Figure
4.3.27.
Figure 4.3.26: Crack initiation near an inclusion of a Calcium-Aluminium-Oxygen compound in the tensile
specimen of steel F.
The comparison between the fracture appearances of the shear lips in the untempered and
the tempered conditions in steel F also showed a transition from brittle to ductile fracture
when the specimens were tempered at 200°C.
Fig. 27(a)
Fig. 27(b)
Fig 4.3.27. Secondary electron scanning microscopy of Steel F after tensile testing at room temperature (a)
austenitised at 900
0
C and water quenched, (b) austenitised at 900 0 C , water quenched and tempered at
0
200 C , showing dimples that indicate ductile fracture during the tensile test.
The mechanical properties of steel F in the above mentioned conditions are shown in Table
(4.3.30).
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Table (4.3.30): Mechanical properties of the steel F austenitised at 900°C for 1 hr, in the quenched condition
and after tempering at 200°C.
Austenitised and
quenched
Austenitised,
quenched and
tempered at
200ºC
UTS
[MPa]
Elongation
Af%
Impact energy at
2246
4
7
2280
9
12
0
-40 C [J]
The ultimate tensile strength and the elongation of steel F (MS = 255°C), containing 0.6%
volume fraction of retained austenite is very high compared to that of steels E (MS =
196°C, 5% retained austenite) and H (MS = 210°C, 4% retained austenite) in the same
conditions. The impact energy of steels F and H are comparable. It has been mentioned
previously that the tensile properties were very difficult to determine in the untempered
condition in the case of steels E and H because of their brittle behaviour. The intermediate
martensite start temperature of the Group 2 armour steels led to the highest ultimate tensile
strength and hardness but it did not improve the impact energy compared to the armour
steels of Group 1.
4.3.6.3. Group 3 armour steels
The fracture of steel I (0.012%S, 0.39%Mn) whose martensite start temperature was
309°C, was ductile with formation of dimples within the grains under tensile stress, as
shown in Figure 4.3.28. The auto-tempering of the martensite laths increases the
elongation to fracture to 11% of this armour steel. The same goes for the impact energy that
supersedes 16 Joules in all the conditions. On the other hand, the ultimate tensile strength
decreases from 2000 MPa to values below 1300 MPa due to the auto-tempering and the
tempering effects.
2200
UTS [MPa]
2000
1800
800
850
1600
900
950
1400
1200
1000
0
50
100 150 200 250 300 350 400
Tempering temperature [degree Celcius]
Figure 4.3.28: Typical surface fracture
appearance of steel I under tensile
stress austenitised 30 min at 850°C and
tempered at 150°C for 1 hr
Figure 4.3.29: Ultimate tensile strength of steel F.
austenitised for 30 min at the given temperatures and
tempered for 1 hr.
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4.3.6.4 General observations
The surface appearance of the fractured faces after the tensile and impact testing showed
significant differences between the specimens that produced higher and those that produced
lower mechanical properties, as observed in secondary electron scanning electron
microscopy. The surface appearances were analysed on the shear lips where the fracture
initiated before the unstable propagation of the cracks through the cross section.
The brittle fracture of steels E and H indicates that they cannot be used in the untempered
condition because of the risk of spallation if impacted by high velocity projectiles. The
tempering treatment at temperatures ranging between 150°C and 250°C has increased the
ability of the armour steels of Group 1 and 2 to undergo ductile plastic deformation at room
temperature and at sub-zero temperatures. The secondary electron scanning electron
microscopy also showed that the tempering treatment enhanced the negative effect of the
Manganese sulphide particles. Inclusions of Manganese sulphide were not observed in
steel E that contains only 0.003% Sulphur. The notch in Charpy testing enhanced the brittle
behaviour and inter-granular fracture of the untempered armour steels in Group 1. All
potential stress raisers should therefore be avoided in the manufacturing of armour plates.
Any inclusions have negative effects on both the strength and the resistance to impact
loading. Other workers [71] have observed the influence of the shape, the distribution and
the size of the Manganese sulphide particles on the strength of steels. In this study two
types of inclusions, namely Manganese sulphide and the Calcium-Aluminium-Oxygen
compounds have been identified in the fractured surfaces.
The tensile strength, the elongation and the resistance to impact loading may then be
improved by developing cleaner steels without Sulphur and inclusions or by lowering the
volume fraction of the Manganese sulphide. For improving the toughness of these steels, it
is then suggested that the control of Manganese sulphide shape and size in the as-cast
condition be introduced with the goal of equi-axed sulphide particles of the largest possible
size to increase their interspacing throughout the matrix. A small interspacing between the
Manganese sulphide inclusions will be negative as illustrated in Figure 4.3.30.
The most useful compositions should be those, which promote equi-axed sulphide particles
(Type III). Type III sulphides are faceted equi-axed particles and are favoured by low
oxygen levels in combination with high Carbon levels, and are promoted by Silicon and
Aluminium additions. There is also an effect of Sulphur content on sulphide type, with type
III sulphides favoured as the sulphur content is reduced.
The cooling rate upon solidification can also influence the sulphide type. Type II sulphides
(rosette-like or fan-like) are favoured over both Type I (spherical) and type III sulphides as
the cooling rate is increased.
The second type of inclusions seen in these fractured surfaces, are the coarse particles of a
Calcium-Aluminium-Oxygen compound inherited from the steel-making process.
Secondary electron scanning electron microscopy has shown that micro-cracks within the
hard martensitic armour steel, are initiated near and around these type of inclusions before
they propagate toward the surface of the tensile specimen. Therefore, they act as stress
raisers and participate in the reduction of the nominal tensile strength of the armour steels.
124
University of Pretoria etd, Kasonde M (2006)
Chapter 4: Results and Discussion
Figure 4.3.30: Effect of the small interspacing between inclusions of MnS in steel F
4.3.7. Martensite start temperatures of the armour steels.
Measurements of the martensite start temperatures of steels E through to W whose
chemical compositions are given in Tables 4.3.31 and 4.3.32, were done using dilatometry.
The measured values have been compared to values calculated using two different formulas
published in the literature. The scatter between the measured and the calculated values
using these two formulas have suggested the determination of another multi-linear
approximation for the prediction of the martensite start temperatures for these armour
steels.
The main hypothesis made for this estimate is the dependence of the MS temperature on the
chemical composition. The predicted values of the martensite start temperature were
calculated from the following formulas:
•
After Stevens and Haynes [73] based on 59 steels without considering any
interaction parameters between alloying elements themselves:
( )
M s 0 C = 539 − 423C − 30.4 Mn − 17.7 Ni − 12.1Cr − 7.5Mo − 7.5Si + 10Co (4.12)
•
After Wang et al [73] based on 157 steels and considering interaction parameters
between alloying elements using an Artificial Neural Network analysis (ANN):
M
( C ) = 540
0
s
− 584 W C − 23 . 1W Si − 117 . 7 W Mn − 42 . 5W Cr − 49 W Mo − 62 . 5W C − Si +
178 . 3W C − Mn − 10 . 0 C − Cr + 52 . 5W C − Mo + 117 . 2W Si − Mn + 50 . 9W Si − Cr − 142 . 2W Si − Mo −
(4.13)
129 . 2W Mn − Cr − 9 . 7W Mn − Mo + 69 . 9W Cr − Mo
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Chapter 4: Results and Discussion
Table (4.3.31): Chemical composition (wt%) of the steels tested for the development of advanced performance steel armour plates
Steel E
Steel F
Steel G
Steel H
Steel I
Steel J
Steel K
Steel L
Steel M
Steel N
Steel O
Steel P
Steel Q
Steel R
Steel S
Steel T
Steel U
Steel V
Steel W
C
0.39
0.39
0.37
0.37
0.34
0.30
0.3
0.30
0.43
0.42
0.42
0.43
0.40
0.39
0.39
0.39
0.40
0.40
0.43
Mn
1.22
0.65
0.40
1.15
0.39
0.48
0.65
0.97
1.21
0.63
0.44
1.87
1.81
1.56
1.57
1.59
1.57
2.08
2.11
P
0.008
0.017
0.016
0.015
0.019
0.018
0.016
0.018
0.018
0.016
0.018
0.019
0.012
0.011
0.011
0.012
0.012
0.01
0.01
S
0.003
0.009
0.011
0.011
0.012
0.012
0.017
0.013
0.012
0.014
0.013
0.011
0.005
0.005
0.005
0.006
0.005
0.008
0.007
Si
0.21
0.8
0.43
1.06
0.40
0.35
0.75
0.93
0.76
0.5
0.49
1.37
1.43
1.03
1.03
0.45
0.45
0.98
0.98
Cu
0.102
0.23
0.33
0.14
0.32
0.12
0.11
0.12
0.13
0.11
0.12
0.18
0.15
0.16
0.16
0.16
0.16
0.17
0.16
Ni
2.99
2.8
2.3
3.8
2.43
1.4
2.83
4.1
4.34
2.8
2.53
4.20
3.55
3.83
3.7
3.66
3.84
3.76
3.78
Cr
1.49
0.22
0.24
0.52
0.27
0.48
0.84
0.83
1.52
0.52
0.51
1.64
1.63
0.94
0.92
1.41
1.46
1.00
0.99
Mo
0.5
0.24
0.3
0.43
0.37
0.19
0.45
0.69
0.44
0.28
0.28
0.61
0.57
0.6
0.59
0.61
0.63
0.57
0.61
V
0.006
0.003
0.006
0.008
0.009
0.01
0.01
0.005
0.005
0.005
0.005
<0.005
<0.005
<0.005
<0.005
<0.005
<0.005
<0.005
<0.005
Nb
0.002
0.006
0.006
0.008
0.009
0.01
0.01
0.008
0.01
0.007
0.007
<0.005
<0.005
<0.005
<0.005
<0.005
<0.005
<0.005
<0.005
Ti
0.003
0.01
0.009
0.007
0.008
0.015
0.01
0.012
0.01
0.012
0.012
<0.005
<0.005
<0.005
<0.005
<0.005
<0.005
<0.005
<0.005
N
0.0049
0.0051
0.0036
0.0059
0.0049
Table (4.3.32): Martensite start temperatures [°C] of the steels A through to O measured by dilatometry.
Steel
MS [°C]
Steel
MS [°C]
Steel
MS [°C]
A
285
I
309
Q
178
B
253
J
305
R
170
C
241
K
318
S
182
D
243
L
252
T
184
E
196
M
175
U
170
F
255
N
241
V
145
G
271
O
218
W
130
H
210
P
115
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Chapter 4: Results and Discussion
Linear regression based on Ms measurements of these 23 armour steels without considering
any interaction parameters between alloying elements showed that it is difficult to fit all the
experimental data on the martensite start temperature with the chemical composition using
one equation. The formula proposed by Wang gives good approximations only when the
Ms of the armour steel is higher than 200°C. Above 0.40%C the differences from the
measured values of Ms become larger than 100°C. The following approach was then
suggested in this study for the estimation of the martensite start temperature of the steels
with chemical compositions in the range considered.
MS
( C ) = 548 − 590C − 35Mn − 18Ni − 14Cr − 9.5Mo − 12Si
0
(4.14)
Formula (4.14) proposed in this work for the estimate of the martensite start temperature of
the armour steels, is based on measured values within the range of chemical compositions
of interest for ballistic performance steels. The chemical compositions of these steels are
well within the specified ranges for the previous formulas (4.12) and (4.13), which makes
the comparison between them valid.
4.3.7.1 Determination of the relationship between the chemical composition and the
martensite start temperature proposed in formula (4.14)
After measuring the martensite start temperatures of the first 15 armour steels ( Steels A
through to O) their martensite start temperatures were fitted through multi-linear regression
of the martensite start temperatures to the chemical compositions. The validity of each
fitting was verified with the eight remaining steels. The three best fittings were considered
in the prediction of the martensite start temperatures of the steels P through to W and the
final equation was assessed through a comparison between the predicted and the measured
values.
Table (4.3.34) Measured martensite start temperatures of six armour steels
Name of the
steel
B
G
H
I
J
K
Martensite start
temperature [°C]
253
271
210
309
306
318
The most likely elements in these steels to affect the Ms temperature are Carbon,
Manganese, Silicon, Nickel, Chromium and Molybdenum. The hypothesis of the chemical
composition dependency of the martensite start temperature of the steels may be expressed,
without interaction parameters, as:
MS
[ C ] = 539 + a × W
0
C
+ b × WMn + c × W Si + d × W Ni + e × WCr + f × W Mo
(4.15)
where a, b, c, d, e and f are six regression parameter to be determined and WC , WMn , WSi ,
etc. are the mass percentages of the alloying elements in the armour steels. The
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Chapter 4: Results and Discussion
experimental values of the martensite start temperatures and the chemical compositions of
the six steels were introduced into Equation (4.15). Therefore, a system of six equations
with six unknowns, viz. the regression parameters, was developed. The corresponding
matrix representation for the martensite start temperatures measured after austenitisation at
900°C, therefore, was:
⎡− 286⎤
⎢ − 268⎥
⎥
⎢
⎢ − 329 ⎥
⎥=
⎢
⎢− 230⎥
⎢ − 233⎥
⎥
⎢
⎢⎣ − 221⎥⎦
⎡0.317 0.855 0.176 3.8 0.318 0.367
⎢ 0.37 0.40 0.43 2.8 0.24
0.3
⎢
⎢ 0.37 1.15 1.06 3.8 0.52 0.43
⎢
⎢ 0.34 0.39 0.40 2.43 0.27 0.37
⎢ 0 .3
0.48 0.35 1.4 0.48 0.19
⎢
⎢ 0.30 0.65 0.75 2.83 0.84 0.45
⎢ 0.30 0.97 0.93 4.1 0.83 0.69
⎣
⎤
⎥
⎥
⎥
⎥
⎥×
⎥
⎥
⎥
⎥
⎦
⎡a⎤
⎢b⎥
⎢ ⎥
⎢c⎥
⎢ ⎥
⎢d ⎥
⎢e⎥
⎢ ⎥
⎢⎣ f ⎥⎦
(4.16)
The solution of the above system using the method of the inverse matrix, gives the
regression factor vector:
[− 719
− 197 9.83 64 96 − 325] (4.17)
The components of the vector in Equation (4.17) are the coefficients to be averaged to
obtain the coefficients in Equation (4.14). One should expect a dependence of these
coefficients on the austenitisation temperature and time because of differing degrees of
dissolution of alloy carbides; hence the martensite start temperature itself should be a
tribute of the austenitisation parameters.
The graphical comparison between the measured and the predicted values using the three
formulas for the 23 steels are compared in Figure 4.3.31. From Figure 4.3.31 it appears that
the published Equation (4.12) leads to systematically higher estimates of the martensite
start temperatures than the measured values. For the armour steels whose martensite start
temperatures are between 200°C and 318°C, the formulas (4.13): published) and (4.14):
proposed) give comparable results close to the experimental values. But at martensite start
temperatures lower than 200°C the published formula (4.13) deviates from the
experimental values whereas the proposed formula (4.14) still gives good agreement
between measured and predicted values. However, at low martensite start temperatures the
formula (4.14) also results in larger differences between the experimental and the predicted
values. This suggests that the effects of the alloying elements on the martensite start
temperatures of these steels is not necessarily linear. Moreover, the predictive models of
the martensite start temperature should possibly be defined for either the low (plate
martensite) or the high martensite start temperatures (lath martensite).
A single model that uses the estimates of martensite transformation temperatures for both
plate and lath martensite may deviate at one end of the temperature scale. Secondly,
Nitrogen (that has not been included in this analysis) may also modify the magnitudes and
the signs of the regression coefficients in these formulas substantially. The standard
deviation is 52°C for the published formula (4.12), 34°C for the published formula (4.13)
and only 19°C for the proposed formula (4.14).
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Chapter 4: Results and Discussion
Table 4.3.34. Measured and estimated values of the martensite start temperatures of 23 armour steels
Martensite start temperature {°C]
(Eq 4.14 proposed in
Wang Stevens
Steel designation Measured
this study
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
285
253
218
255
266
241
287
315
241
243
196
255
271
210
309
306
318
259
175
241
218
115
178
170
251
247
185
221
254
189
271
308
264
225
131
203
215
100
131
155
261
268
117
271
289
212
298
315
259
213
110
237
247
35
58
128
318
318
261
294
321
263
331
363
323
288
216
280
291
191
217
235
182
184
170
145
130
158
158
148
132
112
129
84
78
78
73
238
236
228
216
215
Theories on the chemical composition dependency of the martensite start temperature of
steels, stipulates that the substitutional elements Mo, Mn, Ni, Cr and Si have different
effects on the proof stress of the austenite matrix due to differences in the misfit strain and
the chemical bond energies.
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Chapter 4: Results and Discussion
400
350
Estimated Ms
300
250
Stevens
200
Wang et al
Formula 4.14
150
100
50
0
100
150
200
250
300
350
Measured Ms
Figure 4.3.31: Comparison between the measured and the predicted martensite start temperatures for the 23
experimental alloy steels. The predictions were from the published empirical formulas (4.12), (4.13) and the
proposed empirical formula (4.14) for armour steels is also shown. The diagonal represents the measured
values
The strengthening of the austenite matrix will require a larger driving force for its
decomposition into martensite since the transformation front has to move through a
hardened matrix, giving rise to a decrease in the martensite start temperature. However,
Schramm and Reed [21] reported that both Mn and Mo increase the stacking fault energy
of the austenite matrix, although most substitutional elements are generally considered to
lower the stacking fault energy of the austenite matrix, allowing stacking faults to separate
further making cross slip of screw dislocations more difficult.
A least squares fitting applied to the above three formulas for the 23 armour steels of this
study, gives the following values that show a better agreement between the measured
martensite start temperatures and the predicted values using formula (4.14).
Table (4.3.35): Sum of squared differences between measured and calculated values of the Ms for the 23
steels (steel A through to W)
Sum of the squared differences
Formula
Formula
Formula
(4.12)
(4.13)
(4.14)
72651
70670
13578
Stevens (formula 4.12) reported that Cobalt increases the martensite temperature and
Aluminium may have the same effect. The monotonic decrease of the martensite start
temperature with the alloying element content should then be considered as a particular
case and not as a rule. The multiplying factors are strongly dependent on the chemical
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Chapter 4: Results and Discussion
composition ranges, the austenitisation temperature and the technique used for the
measurement. The acoustic technique, for example, detects the formation of the very first
plates of martensite and generally gives higher values of the martensite start temperature
whereas optical metallography is less sensitive and gives lower values of the Ms. In turn,
the multiplying factor in a predictive formula will also change.
4.3.7.2 Effect of the austenitisation temperature on the Ms temperature
The effect of the austenitisation temperature on the martensite start temperature was
analysed for seven armour steels selected from the twenty-three experimental steels. The
martensite start temperatures of the steels E, F,G, H, J, M and N are presented in Table
4.3.36 for four different austenitisation temperatures.
Table (4.3.36): Martensite temperatures of seven steels as a function of the austenitisation temperature
Martensite start temperature [°C]
Austenitisation
temperature Steel E Steel F Steel G Steel H Steel J Steel M Steel N
193
244
278
202
299
187
241
800°C
189
244
275
205
305
176
239
850°C
196
255
282
210
308
175
238
900°C
187
248
271
193
293
169
233
950°C
350
Ms [deg Celsius]
E
300
F
G
H
250
J
M
200
N
150
800
850
900
950
Austenitisation temperature [deg Celsius]
Figure 4.3.32: Effect of the austenitisation temperature on the Ms of seven armour steels
The martensite start temperatures of these armour steels appear to slightly decrease when
the austenitisation temperature is increased from 800°C to 950°C. The increase in the
austenitisation temperature has many consequences, i.e. greater dissolution of carbides,
solid solution hardening of the parent austenite and grain growth and all of these may
modify the thermodynamic as well as the kinetic characteristics of the transformation.
Greater dissolution of the carbides changes the chemical composition of the matrix and,
hence, the chemical driving force for the transformation to martensite. It also increases the
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Chapter 4: Results and Discussion
solid solution hardening of the parent austenite, which affects the movement of the
transformation front through the austenite.
4.3.7.3. Steel composition considerations
From the preceding paragraphs it may be concluded that the following chemical
composition factors are to be noted in designing an improved armour steel:
a. Carbon is the main element determining the hardness of the martensite. A hardness
higher than 500 VHN may be obtained when the Carbon content of the armour steel is
above 0.37 wt%C as established in Sections 4.1 and 4.2.
b. It appears that the Silicon content of the steel has a strong effect on the stability of the
martensite upon tempering as shown in Table (4.3.37) for five armour steels from this
study. Silicon delays the softening of the martensite during tempering to higher
temperature.
Table (4.3.37): Silicon content and the temperature of softening of the martensite in five experimental steels
Steel
Si
Cr
Ms
E
F
G
H
I
0.21
0.8
0.43
1.06
0.40
1.49
0.22
0.24
0.52
0.27
196°C
255°C
271°C
212°C
309°C
Temperature of start in decrease in
mechanical properties
200°C
250°C
150°C
300°C
200°C
Silicon increases the stability of the martensite by reducing the chemical activity of carbon
[75, 77, 80]. Silicon becomes effective in delaying the decomposition of the martensite in
the range between 0.5 wt% to 1.0 %C. The combined effect of Silicon and Chromium
presents a maximum effect at 1.5 wt%(Si+Cr). In these steels the martensite remains stable
in an “untempered” condition below 150°C. Further Silicon additions may increase this
temperature up to 300°C.
c. The fractographs of the shear lips from the Charpy and tensile tests have shown a
detrimental effect of elongated particles of MnS under impact as well as under tensile
stress. Sulphur should therefore be kept below 0.003 wt%S for these steels. The shape of
the MnS particles is strongly dependent on the Oxygen content of the solidifying steel. A
lower Oxygen content will favour the less detrimental equi-axed shape.
d. The samples austenitised at 900°C, quenched in water at room temperature and then
polished electrolytically in a 5% percholric acid and 95% glacial acetic acid solution were
analysed by XRD for a semi quantitative analysis of the retained austenite.
e. The ideal alloy should be Titanium-, Niobium- and Aluminium-free to avoid the risk of
cracking initiation near the coarse inclusions or precipitates.
For the steels with 0.37%C to 0.39%C and 0.5 %Si to 1.0%Si, the tempering heat treatment
should be kept below 200°C to achieve both hardness (500– 600 VHN) and tensile strength
between 1300 and 2200 MPa. Tempering above 250°C is not acceptable because of the
lower hardness that results. In these conditions the impact energy of the sub-sized
specimens at -40°C is in the range 10 to 18 Joules.
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Chapter 4: Results and Discussion
f. The martensite start temperature of the armour steels may be approximated with
acceptable accuracy using the formula (4.14)
4.4. Results of the ballistic testing (First series)
4.4.1. Ballistic report
The first series of ballistic testing was done on five plates of which two of steel E, one of
steel F, one of steel G and one of steel H and their results are reported in Table 4.4.37. The
second plate of steel E was tested from a firing distance of only ten meters which is
significantly less than the specified thirty meters. The plates that were considered to have
passed the ballistic test, had to resist penetration after at least five shots. The parameters
and effect of each shot was recorded. No light should be visible through the impacted
region for the shot as having been resisted and the test to be considered as having passed.
The 5.56 mm projectiles used for the ballistic testing are presented in Figure 4.4.33.
Ball
High
Pressure
Tracer
SS109
Figure 4.4.33: 5.56 mm rounds fired by a R4 during the ballistic test (first series)
The mechanical properties of the first series of five armour steel plates mentioned above,
are as follows:
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Chapter 4: Results and Discussion
Table (4.4.37): Properties of the plates austenitised at 900°C for 1 hr and tempered at 180°C for 1 hr before
the first series of ballistic testing
Steel E
Steel F
Steel G
Steel H
Thickness
[mm]
Vickers
Hardnes
s
YS
[MPa]
UTS
[MPa]
YS/UTS
Retained
austenite
[%]
Elongation
[%]
Impact
energy
at –40
[Joules]
Martensite
start
temperatu
re [°C]
6.2
6.2
578
610
880
1500
1780
2200
0.50
0.68
6
0.6
4
8
10
14
196°C
255°C
6.1
6.1
475
565
1500
1100
2000
1897
0.75
0.58
0.6
4
12
6
17
14
271°C
210°C
In the above table the Charpy impact energy was measured on the sub-sized specimens of
5 × 10 × 55 mm. The comparison of the ballistic performances of these plates is shown in the
next Section and the validity of the prediction models discussed.
Typical images of the plates after ballistic testing are presented in Figure 4.4.34. The visual
analysis of the rear face of the plate of steel E in Figure 4.4.34(b) does not show any sign of
deformation due to the ballistic impact. This observation led to decreasing the firing
distance to ten meters for the second plate of steel E. This observation was also
instrumental in redesigning the alloys in the next series for the advanced performance
armour plates.
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Chapter 4: Results and Discussion
Table 4.4.38: Ballistic report (first series)
Plate designation
Thickness
Name
[mm]
Steel E
Steel E
Measured
Hardness
projectile
Vickers velocity (m/s)
Firing Distance
(Meter)
Firing Angle
(°)
6.2
30
0
578
943
951
956
952
987
Passed well
Passed well
Passed well
Passed well
Passed well
6.2
10
0
578
-
Passed well
Passed well
Passed well
Clean Penetration
Clean Penetration
Ballistic performance
Steel F
6.2
30
0
610
954
942
957
944
952
Clean Penetration
Clean Penetration
Clean Penetration
Passed well
Passed well
Steel G
6.1
30
0
475
948
955
947
933
948
Clean Penetration
Clean Penetration
Clean Penetration
Clean Penetration
Clean Penetration
Steel H
6.1
30
0
535
1013
Passed well
Bulge + Crack + No light
penetration
Passed well
Passed well
Passed well
951
947
956
940
4.4.34(a): Front face of steel E
4.4.34(b): Rear face of steel E
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Chapter 4: Results and Discussion
4.4.34(c:). Front of Steel F plate after firing
Figure 4.4.34: (a) and (b) Front and rear faces of the plate of steel E showing good resistance to the ballistic
impact after being fired from 30 meters. 4.4.34(c) : Front face of the plate of steel F showing the clear
penetration holes and the elevated contours at the edges of the penetration due to the compressive stresses in
the incidence region.
4.4.2. Comparison with the ballistic performance specifications
In the following sub-sections, results of the first series of ballistic testing, reported in Table
4.4.38 are compared to the prediction using two different criteria, one reported in the
literature and one specified by ARMSCOR and Mittal Steel (South Africa); and a third
improved criterion from this study is proposed.
4.4.2.1. The Ballistic Performance Index (BPI).
The Ballistic Performance Index introduced by Srivathsa and Ramakrishnan [6,7] has been
defined in Sub-section 2.2.4. Although the knowledge of the relationship between the
mechanical properties and the ballistic performance of steels is still lacking, the BPI
constitutes an attempt to quantify and to be able to compare such performance for two
armour materials. The BPI does not consider the hardness as a determining factor for the
ballistic performance. This is totally different for the specification used by Mittal Steel
(South Africa) where the high hardness of the steel plate is the major criterion in predicting
the resistance to ballistic impact.
The BPI of the steels E, F, G and H calculated according to the above-mentioned model are
shown in Table 4.4.39. For this calculation a minimum muzzle velocity of 940 m/s is
considered. The Young’s modulus of the steels is assumed to equal 200 GPa and the
density equal to 7800 kg/m3.The reductions in area after tensile testing were respectively
6%, 11%, 20% and 8% for these four steels.
Table 4.4.39: The ballistic Performance Index of the steels E, F, G and H
BPI
Steel E
3.7
Steel F
3.9
Steel G
4.6
Steel H
4.5
It is concluded from this table that the BPIs of these four steels are very close but with a
tendency to higher values for the steels with higher strength, which is contradictory to the
experimental observation on these four steels.
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The formula for the BPI has the value of taking into account the effect of the reduction in
area on the ballistic performance. It shows the tendency for localised yielding in steels with
a large reduction in area that leads to poor ballistic performance. The formula of the BPI
also demonstrates the decrease in ballistic performance when the velocity of the fired round
increases. In the case of these four steels the BPI is multiplied by 3 to 4 when the velocity
of the round is reduced from 940 to 400 m/s. But the BPI still seems to predict a higher
performance for steels that have a higher strength which the authors themselves disproved
from their experience and is also contradictory to the ballistic results of this study in Table
(4.4.39).
The assessment of performance by ballistic testing remains indispensable and confirms the
current observation that a clear relationship between the mechanical properties and the
ballistic performance is still lacking. The Ballistic Performance Index should then possibly
be considered only as a qualitative indication of ballistic performance and may be used for
the comparative selection between different armour materials only when the BPIs are
different by more than a margin or a ratio yet to be determined.
4.4.2.2. The Mittal Steel (South Africa) specifications
From the current specifications for military applications of armour steels, Mittal Steel
(South Africa) has determined the specification limits for the advanced performance
armour steel to be developed in this study, as follows [1]:
ƒ
ƒ
ƒ
ƒ
ƒ
the hardness is the main factor determining the ballistic performance and
should be higher than 600 BHN, that is equivalent to 640 VHN;
the Charpy impact energy of the full size specimen at -40°C should be
higher than 13 Joules;
the yield strength of the steel should be higher than 1500 MPa;
the ultimate tensile strength should be higher than 2000 MPa; and
the minimum elongation of a 50 mm gauge is fixed at 6%.
According to this specification the prediction of the ballistic performance is favourable for
steel F only. However, the result from the ballistic testing is uncertain because the plate of
this steel resisted two shots well but three others penetrated the plate. On the other hand
steels E and H passed the ballistic test well despite the lower hardness and tensile
properties than specified. Steel G satisfied all the aspects of the specification except the
main one, i.e. the hardness, and it failed the ballistic test. One should conclude then that the
high yield strength, the high tensile strength, the high elongation and the high impact
energy of steel G did not play a decisive role in resisting high velocity impacts.
4.4.3. Differences in the microstructures between steels E, F, G, H and I
This paragraph aims to define a direct relationship between the microstructure and the
ballistic performance instead of to seek an indirect relationship via the mechanical
properties. The microstructures and the phases present in these four armour steels before
ballistic testing were analysed in thin foil transmission electron microscopy, in atomic force
microscopy and X-ray diffraction. The X-ray diffraction allowed the determination of the
volume fraction of the retained austenite as well as the lattice parameters of both the
martensite and the retained austenite. In this paragraph the differences in microstructures
and phases are considered and used to explain directly the observed differences in ballistic
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Chapter 4: Results and Discussion
performance of the above steels. Further characterisation of the martensite will be done in
Chapter 6.
The measured volume fraction of the retained austenite in these five steels and their
martensite start temperatures were found to be:
Table (4.4.40): % Retained austenite in steels E, F, G, H and I after water quenching from
900°C
Retained
austenite
[%volume]
Martensite start
temperature
Steel E
6
Steel F
0.6
Steel G
0.5
Steel H
2
Steel I
0.5
196
255
271
210
309
The detection limit for retained austenite of the X-ray equipment used is generally less than
2% volume fraction, below which the volume fraction may not be quantified accurately.
From Table (4.4.40) it may be seen that the 6 mm armour plates of the Group 1 alloys
contains detectable amounts of retained austenite and these steels have passed the ballistic
test while those with non-detectable retained austenite failed the test.
It may also be observed from Table (4.4.37) that steels E and H have values of the yield
strength to ultimate tensile strength ratio smaller than 0.6. The low value of the YS/UTS
ratio indicates a resistance against localised yielding; in other words, it indicates the ability
of the material to dissipate the impact energy transversally to the incidence direction of the
fired round in the plate . This property increases the volume of the material interacting with
the fired round, offering better resistance to perforation. The elongation during uniaxial
tensile testing also indicates the tendency for localised yielding of the steel when impacted.
It should be kept lower than 7%, which is contrary to the specification used by Mittal Steel
(South Africa).
The different types of morphologies of the martensite in these five steels are shown in the
following figures where they are arranged in order of increasing martensite start
temperature.
The untempered steels E and H contain twinned martensite and nodular particles of
retained austenite (RA), as shown in Figures 4.4.35(a) and (b). The size of the RA nodules
allow their detection by X-ray diffraction analysis. The twins run across the entire width of
the martensite plates. No traces of auto-tempering were observed throughout the thin foils
under 18000 to 43000 magnification. Steels F and G on the other hand contain lath
martensite with high dislocation densities within the laths. They also contain thin films of
retained austenite along the lath inter-faces, as shown in the dark field thin foil electron
micrograph in Figures 4.4.35(c) and (d). The volume fraction of retained austenite in these
two steels was estimated to be less then 0.6%. The bright field transmission electron
micrographs of the quenched specimens of steels F and G also contain areas with fine
carbides along the lath inter-faces. In these steels with intermediate martensite start
temperatures, auto-tempering due to the relatively rapid diffusion of the Carbon atoms and
the subsequent formation of fine cementite particles, could not be avoided during the
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Chapter 4: Results and Discussion
quenching. This observation was also mentioned earlier by Krauss [51] for steels of which
the martensite start temperatures are well above room temperature.
Figure 4.4.35(e) is a thin foil bright field image of steel I of which the martensite start
temperature is relatively high, i.e. 309°C. The martensite in this steel consisted of large
laths which were less dislocated, possibly due to enhanced annealing of the dislocations
and the large plastic accommodation across the reaction front during the martensitic
transformation at this high temperature. The laths are large and contain large areas with
fine cementite particles that are not confined to the lath interfaces as was the case in steels
F and G. This microstructure of steel I presented the lowest hardness, the highest impact
energy and the largest elongation among the five steels discussed here. The tensile
properties of steel I were also measurable in the quenched condition that was not the case
for steels E and H.
From the morphology, Ms temperatures, Silicon contents of these steels and the evidence
obtained in indexing some SADPs of these steels (see later in Section 6.4) as well as the
fact that these dark field micrographs were obtained from untempered steels and hence
could only possess very minor quantities of autotempered carbides in the high-Ms
temperature steels, it is concluded that the dark field micrographs in Figure 4.4.35 do
represent the retained austenite.
The surface relief of these five steels after quenching and analysed in simple contact atomic
force microscopy shows, likewise, as in transmission electron microscopy, a change in the
morphology from the sheared twinned martensite to the dislocated and the plastically
accommodated lath martensite as the martensite start temperature increased. The Figures
4.4.36(a) through to (d) present the surface relief evolution for these five steels, once more
arranged by increasing martensite start temperatures. These measurements to analyse the
characterisation of the twinned and the lath martensite with respect to their surface relief,
are presented in Chapter 6. Olson [58] reported that the morphology of the retained
austenite within laths or plates, determines whether the austenite will transform by a stressor strain-induced mechanism to martensite.
Twins
RA
Figure 4.4.35(a): Steel E, MS=196°C
RA
Figure 4.4.35(b): Steel H, MS=210°C
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Figure 4.4.35(c): Steel F, MS=255°C (label 500 nm)
Figure 4.4.35(d): Steel G, MS=271°C
Figure 4.4.35(e): Steel I, MS=309°C (label 500 nm)
Figure 4.4.35: Thin foil transmission electron micrographs (x 10000, label 500 nm) showing the morphology
of the martensite and retained austenite in steels E through to I after water quenching from 900°C.
Figure 4.4.36(a): Steel E, MS = 196°C, twinned martensite
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Figure 4.4.36(b): Steel H, MS = 210°C, sharp edges and regular N-shaped surface of twinned martensite
without sheared micro-twins
Figure 4.4.36(c): Steel F, MS = 255°C, lath martensite with rounded edges
Figure 4.4.36(d): Steel G, MS = 271°C, background of lath martensite that contains some twins
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Chapter 4: Results and Discussion
Figure 4.4.36(e): Steel I, MS = 309°C, lath martensite. Surface showing plastic strain accommodation
Figure 4.4.36: Atomic force microscopy of the surface relief of steels E to I.
Figure 4.4.36 demonstrates that atomic force microscopy is a useful complementary
technique that may be used in characterising the martensite. It does suffer from two
deficiencies however. (1) The relief of peaks of the martensite plates formed at high Ms
temperatures, may be blunted somewhat through rapid surface diffusion of atoms before
reaching room temperature where the relief measurements are actually carried out. (2) The
martensite formed at a free surface is only partially restrained whereas that formed within
the volume of the microstructure is fully hydrostatically restrained. This difference may
place some question marks on conclusions derived from surface relief measurements.
Surface relief measurements nevertheless constitute a complementary contribution to a
study of the internal details revealed by the thin foil transmission electron microscopy.
Indeed Figure 4.4.36(a) demonstrates the formation of martensite with micro-twins within
the plate martensite. This mechanism of formation is one of those predicted by the
crystallographic theory of the martensitic transformation. The amplitude of the plastic
strain accommodation during the martensitic transformation increases as the martensite
start temperature increases. The mechanism of formation of the martensite seems to be a
shear when the martensite start temperature is lower than 210°C as shown in Figure
4.36(b). For the martensite start temperatures of 255°C and 271°C, the twinned martensite
was formed as plate martensite with their shape no longer regular with sharp edges as was
the case in Figures 4.4.36(a) and 4.36(b). These irregular shapes may be related to a
significant rotation of the habit plane during the martensitic transformation, although the
possibility of surface diffusion may also have made some contribution. This observation on
the rotation of the habit plane is in good agreement with the earlier conclusions in the
literature by Mou and Aaronson [21] on a change in the mechanism of martensite
formation and the coexistence of both lath and plate martensite when the martensite start
temperature is about 250°C.
The data reported in Table (2.7) show that the two types of martensite may be formed
together in a wide range of martensite start temperatures ranging from 200°C to 390°C. In
this range of martensite start temperatures both the shear mechanism and the plastic
accommodation of the deformation strain by slip and rotation of the habit plane are
operative. This combined mechanism produces irregular N-shaped profiles that indicate
irregular habit planes and is in agreement with the conclusion by Kennon and Dunne [46,
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Chapter 4: Results and Discussion
49] about the flexibility of the habit plane that is likely to be a characteristic feature of the
plate martensite not accounted for by the crystallographic theories. Tadaki and Shimizu
[48] also suggested that the formation of a continuous spectrum of habit planes should be
expected based on their measurements of the variation of the lattice parameters of the
martensite and the retained austenite as a function of the actual temperature of formation.
The topology of the surface of steel I, in Figure 4.36(e), of which the martensite start
temperature was 309°C, can be interpreted that the plastic strain accommodation results
from the slip of dislocations.
4.4.4. Differences in microstructure between steels E, F, G, H in the tempered
condition before ballistic testing
Thin foil transmission electron micrographs of the tempered armour steels E , F, G and H
before ballistic testing, are compared in Figures 4.4.37(a) through to 4.4.37(d). The steel
plates were tempered at 180°C for one hour. Fine elongated strings of carbides were found
to have precipitated within steels E and H respectively, as shown in Figures 4.4.37(a) and
4.4.37(b). These two steels passed the ballistic testing well. On the other hand, coarse
carbides have precipitated within the laths and on the lath interfaces of steels F and G that
gave poor ballistic performances.
4.4.37(a)
4.4.37(b)
4.4.37(c)
4.4.37(d)
Figure 4.37: Thin foil transmission electron microscopy of the steels E (4.4.37(a)), steel F (4.4.37(b)), steel F
(4.4.37(c)) and steel H (4.4.37(d)) after tempering at 180°C (label scale = 500 nm).
A high ballistic performance requires a microstructure consisting of twinned martensite
with some retained austenite without coarse carbides. The precipitation of cementite may
be controlled by the chemical composition of the armour steel and by the tempering
temperature.
Steels E and H that gave good ballistic performances after tempering at 180°C for one
hour, were then tempered at a higher temperature of 350°C for 1 hour with a view to
determine the maximum tempering temperature that does not lead to the precipitation of the
coarse cementite which is detrimental to the resistance to high velocity impact during
ballistic testing. The thin foil micrographs in Figure 4.4.38 show large strings of cementite
that had formed along the plate interfaces of steel E, shown in Figure 4.4.38(a) while steel
H had formed noticeably less of these coarse strings of carbides during tempering at 350°C.
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Chapter 4: Results and Discussion
4.38(a): Steel E
4.38(b): Steel H
Figure 4.4.38: Bright field thin foil transmission electron micrographs (x18000) of
tempering at 350°C (label scale = 500 nm).
steels E and H after
The retardation in formation of cementite during tempering of steel H may be attributed to
its higher Silicon content of 1.06%, compared to the lower Silicon content of steel E of
0.21%Si. Silicon is well known for its effect on delaying the formation of cementite from
supersaturated metastable martensite.
Figure 4.39: Thin foil TEM DF of steel E tempered at 400°C showing the cementite precipitated within the
plates
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Chapter 4: Results and Discussion
Figure 4.4.40: Bright field thin foil transmission electron microscopy of steel H tempered at 300°C showing
the cementite
Figure 4.4.41: Bright field thin foil transmission electron microscopy of steel E tempered at 400°C showing
large strings of the cementite.
4.4.2.3. Proposition to redefine the specification of armour plate steels
Considering that neither the high hardness nor the higher levels of mechanical properties
(yield strength, ultimate tensile strength, impact energy, % elongation) appear to be
accurate criteria for predicting the ballistic performance of armour steels, an alternative
design methodology is proposed. Those new design criteria are based on the results of this
study of ballistic testing, the mechanical properties and the microstructure of the
martensite.
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This design approach is developed by also considering the volume fraction of retained
austenite, the ratio of yield strength to ultimate tensile strength and the martensite start
temperature of the five plate armour steels tested. The new proposal is derived from Tables
4.4.37 and 4.4.38 in which the steels E and H of the Group 1 armour steels, gave superior
ballistic results, whereas steel G of Group 3 gave poor ballistic results and steel F of Group
2 gave intermediate ballistic results.
The new specifications should, therefore, rather prescribe the following:
ƒ
ƒ
ƒ
ƒ
ƒ
ƒ
the volume fraction of retained austenite in the martensitic steel should be
between 2% and 7%;
the ratio of yield strength to ultimate tensile strength should be less than 0.6;
the martensite start temperature should ideally be comprised in the range
from 130°C to 220°C. The martensite start temperature may be determined
by dilatometric analysis or predicted (with an error of ± 30°C) using the
empirical Formula (4.14) derived from this study;
the chemical composition should be close to that of steels E and H, i.e.
0.39%C, 1.2%Mn, 0.8%Si, 1.5%Cr, 0.5%Mo, 2.5%Ni.
The austenitisation temperature between 850 and 950 for 30 minutes to one
hour
The tempering treatment at temperatures lower than 250 for 15 minutes to 1
hour
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Chapter 4: Results and Discussion
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Chapter 5: Improvement in the Ballistic Performance
CHAPTER 5. IMPROVEMENT IN THE BALLISTIC PERFORMANCE
5.1 Approach methodology
The results of the first series of ballistic tests and the recommendations formulated in Chapter 4
constitute the basis for the ballistic improvement in steels E and H and the development of the
chemical compositions for the further eight advanced performance armour steels P through to
W and their appropriate heat treatment. The thickness range of the plates to be tested was
reduced from 6 mm to between 4.5 and 5.2 mm in order to introduce a further safety factor in
the maximum protection of the cockpit and the passenger cell with 6 mm thick armour plate.
The volume fraction of the retained austenite in the plate martensite is considered to be the
main factor determining the ratio of the yield strength to ultimate tensile strength (YS/UTS) of
the armour steels and their resistance to localised yielding and perforation during a ballistic
impact.
The morphology of the martensite and the volume fraction of the retained austenite after water
quenching of the steels are inter alia functions of the martensite start temperature, which in
turn, is a function of the chemical composition and the austenitising conditions. The latter
effect provides effective dissolution of the carbides into the austenite matrix, which modifies
its chemical composition and thus its chemical driving force for the martensitic transformation.
Moreover the grain size of the parent austenite that grows with increasing austenitisation
temperature and time, determines the total volume of the grain boundaries where the
heterogeneous nucleation of the martensite can initiate. Consequently, the following reverse
procedure was adopted in determining the chemical composition of the further eight advanced
performance armour steels:
ƒ
The retained austenite (RA) located in the plate inter-faces was more effective in
reducing the ratio YS/UTS than the RA located in the lath inter-faces. The
optimum range of the volume fraction of retained austenite for an advanced
ballistic performance was estimated at between 2% to 7%;
ƒ
The martensite start temperature of the advanced armour steels should,
therefore, be lower then 210°C to enhance the formation of plate martensite over
lath martensite;
ƒ
Using the proposed formula in Equation (4.14), the chemical compositions
within the range specified in Section 4.4.2.3 to obtain eight suitable
compositions, was found with predicted martensite start temperatures ranging
from 100°C to 200°C within a ±30°C error. The chemical compositions of the
eight steels P through to W were thus determined through this procedure;
ƒ
The steels were produced in a vacuum melting furnace, Calcium treated and
degassed and cast into 5 kg ingots before being solution treated at 1050°C for
one hour, hot rolled to thicknesses of 4.5 ± 0.2 or to 5.2 ± 0.2 mm, directly
quenched into water at room temperature and lastly tempered at 180°C or at
250°C for 20 minutes;
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ƒ
Samples for thin foil transmission electron microscopy before the ballistic
testing and those for the determination of the martensite start temperature, were
cut from these plates;
ƒ
The ballistic testing was performed and samples are cut from the impact regions
for the X-ray diffraction analysis of the retained austenite, for the scanning
electron microscopy of the cracks and for the thin foil transmission electron
microscopy. The micro-hardness profiles across the impact region were also
determined;
ƒ
Differences between the microstructures before and after the ballistic impact are
explained;
ƒ
A revised specification, comprising the chemical composition range, the heat
treatment and the mechanical properties for the high performance 6 mm steel
armour plates is then formulated.
The chemical compositions of the steels P through to W, as determined by the above
procedure, are given in Table (4.3.32). The martensite start temperatures after austenitisation
determined by dilatometric analysis and those calculated, are included in Table (5.1). The
volume fraction of the retained austenite before the ballistic test, determined by X-ray
diffraction is also included in the same table.
Table (5.1): Martensite start temperatures and volume fraction of retained austenite in the
tempered steels P through to W before ballistic testing
Designation of
the armour steel
P
Q
R
S
T
U
V
W
Martensite start temperatures
°C
Measured
Calculated using the
formula (4.27)
115
63
178
63
170
141
182
141
184
172
170
164
145
150
130
140
Volume fraction of
retained austenite
%
Vickers hardness
6
4
3
3
0.6
2
5.3
6
580
615
610
510
578
510
595
565
VHN (30kg)
The volume fraction of retained austenite was determined within a 0.5% standard deviation.
5.2. Ballistic report
Plates of these eight armour steels were tested in the same ballistic conditions than those of the
earlier steels E, F, G and H. The results of this second series of ballistic testing are reported in
Table (5.2).
The steel T was the only that did not pass the ballistic test despite its higher hardness and
thickness. Typical photographs of the front and of the rear faces of the plates that passed the
test well from this second series of ballistic testing are shown in Figure 5.1.
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Table (5.2): Ballistic report of the steels P through to W
Plate
Steel P
Steel Q
Steel R
Steel S
Plate
Firing distance
thickness
(Meter)
4.7
4.9
5.1
5.2
30
30
30
30
Firing
angle
(°)
0
0
0
0
Projectile
Velocity
(m/s)
Ballistic
performance
580
933
928
931
955
952
Passed well
Passed well
Passed well
Passed well
Passed well
615
947
943
937
948
938
Passed well
Passed well
Passed well
Passed well
Passed well
610
947
939
946
935
947
Passed well
Passed well
Passed well
Passed well
Passed well
578
942
940
947
942
952
Hardness
(VHN)
941
Passed well
Passed well
Passed well
Passed well
Passed well
Failed
Clean Penetration
Failed
Clean Penetration
Failed
Clean Penetration
Failed
Clean Penetration
Failed
Clean Penetration
Failed
Clean Penetration
939
941
951
951
961
Passed well
Passed well
Passed well
Passed well
Passed well
938
947
947
948
952
952
Passed well
Passed well
Passed well
Passed well
Passed well
Passed well
944
945
Steel T
5.4
30
0
610
945
945
935
Steel U
Steel V
4.9
5.1
30
30
0
0
578
595
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Chapter 5: Improvement in the Ballistic Performance
Table 5.2 Continued
Steel W
4.8
30
0
(a) Image of the front face of steel Q plate
565
942
935
941
941
931
Passed well
Passed well
Passed well
Passed well
Passed well
(b) Image of the rear face of steel Q plate
Figure 5.1: Photographs of the impact regions of the 4.9 mm steel Q plate that passed the ballistic testing
It is concluded from Table (5.2) that only steel T, containing the lowest volume fraction of
retained austenite of about 0.6% did not pass the ballistic test.
5.3 The Ballistic Parameters
Visual observation of the areas affected by the ballistic impact revealed three concentric
domains around the incidence point of the fired round in the armour plate. These three domains
may also be observed around the penetration hole in plate T that failed the test. The size of
these domains indicates the resistance to localised yielding of the armour plate. The existence
of these three domains in the perforated plate of steel T that failed the ballistic test, may be
explained by the relatively high velocity of the “slower” plastic wave that follows the precursor
“faster” elastic wave compared to the longitudinal movement of the fired round through the
thickness of the plate.
The inner domain, zone 1, that may be seen from the rear face in Figure 5.1(b), is penetrated
more into the plate and had almost the same diameter in all eight plates, irrespective of whether
the plate passed or failed the test. The thickness of the plates and the volume fraction of
retained austenite in these steels seemed to have very little effect on the diameter of this inner
zone 1. The diameter of the intermediate domain, zone 2, on the other hand differed while the
diameter of the outer domain, zone 3, differed significantly.
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The zones 2 and 3 are distinguishable on the front face as shown in Figure 5.1(a). The
diameters of these three circular domains within the ballistic impact-affected areas are given in
Table (5.3) for these eight steels.
Table (5.3): Diameters of the three concentric zones within the ballistic impact affected areas
of the armour plates tested
Steel P
Steel Q
Steel R
Steel S
Steel T
Steel U
Steel V
Steel W
Thickness Volume fraction
Ballistic
Diameter zone 1 Diameter zone 2 Diameter zone 3 parameter
of the plate
of retained
[mm]
austenite [%]
[mm]
[mm]
[mm]
BP
4.7
6
13
26
54
0.0546
4.9
4
12
24
46
0.0298
5.1
2
13
28
48
0.0061
5.2
3
12
27
44
0.0165
5.4
0.6
7
8
24
0.0027
5.1
2
13
28
40
0.0061
5.1
5.3
13
26
50
0.0323
4.8
6
12
30
56
0.0494
The differences between these diameters as well as their variations are shown by plotting their
values versus a ballistic parameter, defined as follows:
BP =
RA (% )
EXP(δ )
(5.1)
where RA is the volume fraction of retained austenite and δ is the thickness of the steel plate in
millimeters. The choice of this expression for the BP parameter is based, firstly on the
proportional lowering of the ratio of YS/UTS by the retained austenite and secondly, on the
increase of the effective penetrating weight when the thickness of the plate increases because
of the direct transmission of the linear momentum to the cylinder of material ahead of the fired
round within the plate. Figure 5.2 is a graphic presentation of the diameters of the three zones
as functions of the ballistic parameter BP.
More ballistic testing is necessary before determining an accurate mathematical description of
the diameters of the three zones in terms of the ballistic parameter BP. Nevertheless, the
general shape of the curves in Figure 5.2 may suggest that within the range of the experimental
parameters used, including the impact velocity, the firing angle, the volume fraction of the
retained austenite and the thickness for the martensitic steel armour plates, the optimum
ballistic performance is realised for values of the ballistic parameter BP between 0.0180 and
0.060.
The ballistic performance may decrease again at higher values of the parameter, whose limit is
yet to be determined experimentally, because of a too high volume fraction of retained
austenite or because of a too low thickness of the steel plate. The minimum hardness and the
minimum thickness requirement of the armour steels should then be determined and the
feasible region for the ballistic application redefined.
The ballistic parameter BP of the steels P through to W calculated as defined by Equation (5.1)
are shown in Table (5.3). Plotting the measured diameters of the three concentric zones 1, 2
and 3 also shown in Table (5.3), produces the following Figure 5.2.
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60
Diameter [mm]
50
40
zone 1
30
zone 2
Zone 3
20
10
0
0
0.01
0.02
0.03
0.04
0.05
0.06
Ballistic Parameter bp
Figure 5.2: Variation of the diameters of the concentric zones 1, 2 and 3 within the ballistic impact affected
domains as functions of the BP parameter.
The material in zone 1 is heated up to high temperatures during the impact as suggested by the
scanning electron microscopy of the surface of the armour plates that are covered by the
molten lead from the fired rounds. The temperature and pressure within these zones was high
enough to cause welding of the copper and the lead from the fired round to the steel plates. The
effect of the temperature rise on the microstructure within these zones was examined through
thin foil electron microscopy after the ballistic testing by cutting specific localised 3 mm discs
from these zones with a spark erosion wire cutting machine.
Cu
Zone1
steel
5.3(a)
5.3(b)
5.3(c)
Formatted
Figure 5.3: Secondary electron scanning electron microscopy of zone 1’s front face of steel plate R covered with
molten lead form the fired round ( Figures 5.3 (a) and 5.3( b), label mark: 500μm). A polished cross section of
zone 1 showing the copper from the fired round welded to the plates (figure 5.3(c)).
Figure 5.3(a) also illustrates the wavelike separation of the material within zone 1 by being
dragged into the plate thickness. This illustrates the known theory, which predicts that at high
strain rates and high temperatures the solid steel behaves like a dynamic liquid. Scanning
electron microscopy of the cross-section of some impact regions revealed the presence of a tridimensional crack, the so-called Hopkinson sphere [5], formed where the compressive elastic
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wave was reflected from the outer edges of the plate. This composed an additional interference
wave together with the slow compressive plastic wave, which produced a tensile stress higher
than the true fracture stress of the armour steel. Closer observation of the crack demonstrates
that the crack was composed of micro-cracks propagating along the grain boundaries outwards
from the impact sphere. Figure 5.4 shows a typical cross section cut from one of the plates after
ballistic testing.
Figure 5.4: Cross section throughout the affected impact region showing the copper from the round attached on to
the front face of a 4.8 mm steel W plate. The bending of the plate in the affected impact region is also observable.
Figure 5.5 shows the tri–dimensional crack and the dynamic micro-cracks along the grain
boundaries within the cross-section of the impact region. The surfaces in Figures 5.5(a) and
5.5(b) were not etched whereas the one in Figure 5.5(c) was etched.
crack
5.5(a)
Micro-cracks
5.5(b)
5.5(c)
Figure 5.5: Backscatter scanning electron microscopy of the Hopkinson sphere and the micro-cracks formed
dynamically within the tensile region
The micro-cracks along the grain boundaries demonstrate the significance of the grain
boundary properties on its ballistic performance of an armour steel. Clean grain boundaries
without segregated particles or precipitates will have a higher cohesion strength and, therefore,
a better resistance against the pull-out of grains due to the high tensile stress that occurs near to
the spherical crack. The micro-crack substructures were encountered within the cross sections
of steel R that passed the ballistic test and also in the plate of steel T that failed the ballistic
test. These two steels were similar in their lower volume fraction of retained austenite. This
observation may confirm that the retained austenite also arrests the propagation of the microcracks initiated in the region where high tensile stress waves are formed during the ballistic
impact. The literature reports levels of tensile stress as high as 28 GPa [16, 17, 18] that may
develop in the steel armour plate during the ballistic impact before fracture.
The untempered armour steels U and V also complied with the requirement of the
specifications for ballistic performance but they also had macro-cracks and some parts were
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actually broken-off from the plate. The broken sections were about fifteen centimetres from the
centre of the impact region as shown in Figure 5.6.
Figure 5.6: Untempered armour plate of steel U fractured by impact loading during ballistic testing showing the
fracture some centimetres away from the impact points.
This observation agrees with the theory of an additional shock wave interference at a certain
distance from the impact point, formed between a precursor “faster” compressive elastic wave
reflected as a tensile wave by the edges of the plate and a following “slower” compressive
plastic wave. The distance at which interference between the two waves will take place and
reach such an amplitude that the true fracture strength of the material at high strain rate is
exceeded, depends on the mass and velocity of the fired round as well as the mass, Young’s
modulus and the density of the plate.
The relation between stress wave propagation and fracture has been studied for more than a
hundred years. B Hopkinson [quoted in 5], in his published paper on “ The Effects of
Momentary Stresses in Metals” where he repeated his father’s work, provided an explanation
of the rather puzzling phenomenon of spalling or scabbing. It is characteristic of the impact of
high-speed projectiles or the detonation of explosive charges in contact with brittle targets. In
this phenomenon, which takes place when an impact occurs on one side of a brittle plate, most
of the fractures are observed not near the point of impact, but at the opposite free surface of the
plate away from the impact region. J. Hopkinson [quoted in 5] in his paper on “ On the Rupture
of Iron Wire by blow” had showed that the following surprising results occurred:
ƒ
ƒ
“The effects of two blows, which will break the wire, were not equal when the
momentum or the energies were equal, but when the velocity of the mass at
impact reached a certain critical value”;
In his experimental conditions the wire did not break near to the point at which
the impact took place but fractured further away.
In this Section the explanation that J. Hopkinson gave in the case of the drop weight impact
test, was adapted to the case of a ballistic impact on a steel plate as follows:
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1. The tensile stress σ 0 associated with a particle velocity V0 is ρV0c0 , where ρ is the
density of the wire. c0 is the velocity of extension waves in the wire;
2. c0 = (E ρ )
12
where E is Young’s modulus;
3. The maximum particle velocity V0 is equal to the velocity of the fired round and plate
system immediately after impact;
12
4. Then, if the impact is inelastic, V0 = [2 ghM (M + m )] , where M is the mass of the
fired round and m is the mass of the plate;
5. The falling height h is converted in to the round’s velocity V as follows: h ≈ V 2 2 g .
[
]
6. Then V0 = V 2 M (M + m )
1 2
;
7. The tensile stress associated with the velocity V0 is σ 0 = ρc0V [M (M + m )] ;
8. The peak stress in the pulse is dependent on V , M and m . The tensile stress after
superposition between the reflected pulse and the incident one is
12
2σ 0 = 2 ρc0V [M (M + m )] ;
12
9. If the tensile strength of the plate is σ, the condition for fracture near the clamping
support of the plate is σ = 2σ 0
VF =
σ
2 ρc 0 [M (M + m )]
12
(5.2)
where V f is the minimum velocity of the round at which fracture will occur. The
condition for fracture to occur near the top of the plate is σ = σ 0 or:
VF =
σ
ρc 0 [M (M + m )]1 2
(5.3)
Taylor [5] has pointed out that the situation is in fact much more complicated than J.
Hopkinson had realized, since the pulse produced by the impact has an infinitely long “tail”.
The model considered by Taylor can be adapted to the case of ballistic impact as follows:
1. The equation of motion of the fired round and the plate after impact is
M dV dt = Aσ = AρVc0 , where A is the cross sectional area of the plate and V is the
velocity of plate and round at time t. The solution of this equation is:
V = V0 exp[− ρAc0t / M ]
(5.4)
where V0 is the combined velocity at time t=0;
2. Thus, the stress at the clamp holding the plate is given
by σ = ρc0V = ρc0V0 exp(− ρAc0t M ) and a sharp-fronted pulse with an exponential
decay travels through the plate;
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3. The stress at a distance x from the clamp is given by:
σ ( x, t ) = ρc0V0 exp[ρA M (x − c0t )]
(5.5)
4. Equation (5.5) can also be written as:
σ ( x, t ) = ρc0V0 exp[β (x − c0t )]
(5.5(a))
5. These conditions apply for times up to t = L c0 , where L is the distance between the
impact point and the point where the wave front reaches the clamping support and the
pulse is reflected. Since the plate support is fixed the reflected pulse is one of tension
and in the time region L c0 < t < 2 L c0 for 0 < x < (2 L − c0t ) , one has only the tail of
the incident pulse, i.e. σ ( x, t ) = ρc0V0 exp[β (x − c0t )] ;
6. For x > (2 L − c0t ) , one has the superposition of the reflected tensile pulse and the tail of
the incident pulse, i.e.:
σ = ρc0V0 {exp β [(2 L − x ) − c0t ] + exp β (x − c0t )} .
(5.6)
7. Now, the reflected pulse will once again be reflected at the plate support but since the
mass is finite, this reflection will result in a change in the velocity of the plate and the
round’s mass M and after this reflection, there will be three superimposed waves in the
plate;
8. The process will continue and can result in stresses greater than the stress of
2 ρV0c0 postulated by J. Hopkinson. The degree to which this value is exceeded
depends on a nondimensional parameter α , which is the ratio M (LρA) , i.e. the ratio
of the mass of the fired round to the mass of the plate. Taylor has shown that this
maximum stress is given approximately by the expression:
σ = ρc0V0 ⎡1 + α
⎢⎣
−1
2
⎤
⎥⎦
(5.7)
Thus Taylor predicts σ = 4.2 ρc0V0 rather than σ = 2 ρc0V0 as postulated by J. Hopkinson and
this occurs later than at the third reflection at the plate support. Hammond and Proud [16]
recently reported stress values as high as 28 GPa, or a multiplying factor of 12 instead of 4.2 as
in the above relation of the maximum tensile stress being reached during a ballistic impact in a
12 mm thick steel plate. The common idea in all of these estimates is that the steel can resist
higher tensile stresses dynamically than statically, a conclusion that is supported by the usual
strain rate dependence of the flow stress of most metals.
It is possible to design an armoured structure in such a manner that the transmissibility between
the plates and the structure-support is higher to allow a controlled fraction of the incident
energy to flow into the structure, thereby reducing the amount of energy reflected into the
plate. But this solution should be carefully examined in order not to destroy the integrity of the
support-structure and its reliability. Another solution may be the lengthening of the
transmissibility path such that the elastic as well as the plastic waves are attenuated in such a
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way that their interference does not induce stresses higher than the true fracture stress of the
armour steel during ballistic impact.
The stress distribution within the plate as a function of the time and the distance from the platesupport is presented in Figure 5.7. For this calculation the average mass of the plates is
estimated at 4.5kg, the density of the steel is 7800kg/m3, the mass of the round is 3.5g and the
striking velocity is 940m/s. The results of the calculation are presented in Table (5.4).
Table (5.4): Predicted theoretical characteristics of the plate – round system during the ballistic impact, using the
model proposed by Taylor [5].
Velocity of the
pressure wave
front c0 [m/s]
Velocity of the
system plate-round
V0 [m/s]
5063
27.1
Characteristics
Predicted yield
strength σ 0 [MPa]
Spalling strength
S0 [MPa]
Dynamic
tensile strength
σ max [GPa]
1071
1070
38
This model predicts the uniaxial tensile strength to be at about 1071 MPa and the true fracture
stress due to dynamic impact loading, at about 38 GPa for these armour steels. The difference
between the measured maximum stress reported by Hammond and Proud [16] and others [17,
18] with the predicted value of 38 GPa, may be explained by the neglect of the influence of any
existing defects present in the material in the theoretical model. Any such defects will reduce
the effective dynamic fracture strength of the steel armour plates according to the well-known
principles of elastic fracture mechanics. The analysis of Equation (5.6) shows that the stress
distribution throughout the plate is strongly dependent on the time of stress wave travel. The
stress distribution in the region between one and two hundred centimetres wave path length
from the centre of impact is shown in Figure 5.7. The model predicts a tensile stress of between
11.7 GPa and 13.2 GPa in that region in which the fracture lines are located. This means that
the fracture occurs between the fourth and the fifth reflections of the tensile wave from the
edges of the plate.
0.014
0.0138
11707.9627
11707.9627
11707.9627
0.0136
0.0134 12010.7635
12010.7635
12010.7635
Time[s]
0.0132
12313.5643
12313.5643
12313.5643
12616.365
12616.365
12616.365
12919.1658
12919.1658
12919.1658
0.013
0.0128
0.0126
0.0124
13221.9665
0.0122
0.012
0.1
0.11
0.12
0.13
13221.9665
13221.9665
0.14 0.15 0.16
Distance [m]
0.17
0.18
0.19
0.2
Figure 5.7: Predicted tensile stress distribution within the plates tested in this study due to the ballistic impact, as
a function of the time and wave path length measured from the impact point and considering reflection at the top
end on Figure 5.6.
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5.3. The fracture mechanism due to the high strain rate during ballistic testing of plates
of steels P through to W
The shear lips of the fractured surfaces of the untempered steels U and V plates were analysed
by secondary electron scanning to identify the mechanism of the crack initiation and its
propagation. Two directions of propagation of the cracks were observed throughout the
fractured sections. The first three–dimensional crack propagated in a cylindrical surface whose
generator lies parallel to the surface of the plate. The second crack propagated in a direction
transverse to the surface of the plate and this crack determined the fractured surface. Figure 5.8
shows these three-dimensional cracks near the edges of the untempered steel U plates.
Edge of the plate
Cylindrical crack parallel
to the surface of the plate
Fractured surface
Figure 5.8: Secondary electron scanning microscopy of the shear lips of the fractured surface near the edge of the
untempered plate of steel U. Label mark 170μm.
The scanning electron microscopy also revealed shear bands that cross the fractured surfaces of
the untempered plates. These bands suggest that the ballistic impact induces cyclic loading in
the plates due to the multiple reflections of the tensile stress wave from the edges of the plates.
The shapes of the shear bands indicate that the fracture further away from the impact region,
initiates near the edge of the plate and propagates cyclically throughout the thickness resulting
in complete fracture. Such shear bands are shown in Figure 5.9. The initiation of these cracks
near the edge of the plate verifies the earlier proposal of a reflection of the compressive wave
as a high stress tensile wave from the edges as proposed by Taylor. The cracks were probably
initiated just after the first or the second reflection of the tensile wave from the edge because of
the poor mechanical behaviour of the untempered martensite under tensile stress in these
plates.
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Figure 5.9: Secondary electron scanning microscopy showing the shear bands in the fractured surface of the
untempered steel U plate at 12cm far from the impact point. Label mark 500μm.
The shear bands have two different appearances depending on the distance from the initiation
point. Near the edge of the plate the shear lips of the broken plate are smooth with very fine
dimples as shown in Figure 5.10(a), while a brittle inter-granular fracture of Figure 5.10(b),
with blocks of grains being pulled out was observed at about one millimetre depth into the
plate, as shown in Figure 5.10(c).
(a)
(b)
(c)
Figure 5.10: Secondary electron scanning microscopy of the shear lips showing two different modes of fracture in
the same fractured surface (a) smooth shear lips with fine dimples observed near the edges of the fractured
surface. (b) and (c) brittle fracture away from the edges where unstable propagation of the crack took place. Label
mark 2.8μm.
From Figures 5.10(b) and (c) it appears that the grain boundaries may be a low resistance path
for the propagation of the tensile stress wave caused by the ballistic impact through the entire
thickness of the armour plate.
The ballistic impact excites the natural vibration modes of the plates. The first natural
frequency of the armour plate should then be kept higher than the highest excitation frequency
of the firing rifle to avoid any synchronisation that will lead to a catastrophic spalling of the
plates. The mass, stiffness, damping factors and shape are the main parameters that determine
the natural resonant frequencies of the plates. The mass and the length of the plate can easily
be controlled and reduced through design so that the first natural frequency is high. The
reduction of the mass is possible by manufacturing thinner and smaller plates, as was the entire
aim of this study.
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The stiffness and the damping factors of the plate depend on the microstructure that is inherited
from the chemical composition and the heat treatment applied to the armour plate.
Considering that the microstructure is optimised for the ballistic performance, only the mass
and the shape of the plates may practically be changed to take into account the effect of the
excitation frequency of the firing rifle.
5.4. Morphology of the martensite and microstructures of the steels P through to W that
were tested ballistically
The microstructures of the above mentioned armour steels were analysed before and after the
ballistic test to identify any differences between them for the purpose of finding a direct
relationship between the microstructure and its ballistic performance. The effect of the strength
of the armour plate on the perforation of the plates using different projectile nose shapes has
been investigated recently by Dey and Borvik [15]. They found that when a blunt projectile
hits the target, the material in front of the projectile accelerates, while the rest of the target is
relatively stationary. Hence, the deformation localises in narrow shear bands under adiabatic
conditions where the shear strain, shear strain rate and temperature may locally be very high.
According to their study [15], these shear bands may either consist of only deformed material
or transformed material depending on the temperature that was reached in this localised area.
Mescheryakov and Divakov [17] have concluded from their investigation into the shockinduced structural transitions and dynamic strength of solids, following from the analysis of
peculiarities of high-velocity penetration and also from the analysis of experimental data, that
the strength-component of the resistance of solids to penetration (as a complementary factor to
the inertial forces) is determined by the resistance to plastic deformation. This means that if the
character of the plastic deformation changes, for example, because of a change in the structural
mechanism of deformation, the strength-component of the resistance to penetration changes as
well. Recent studies based on the measurement of the mechanical properties of armour steels,
confirm the need for the understanding of the ballistic performance of these armour plates
based on their microstructural behaviour. Hammond and Proud [16], in their work on the
pressure-induced ( α − ε ) phase transformation in low-alloy steels, where they have measured
and compared the ballistic performance of lower and upper bainite respectively in terms of the
Hugoniot Elastic Limits and spalling strength of these two phases, have concluded:
“ In order to understand why the materials behaved as they did and possibly to predict material
properties in the future, it is important to investigate the microstructural response to the
different impact conditions. This could take the form of microscopy, X-ray diffraction and
hardness testing. Such research may help to establish why the phase transition was not
observed in upper bainite and why the Hugoniot Elastic Limits of the two materials are so
different”.
They have found the HELs to be 3.5 ± 0.5 GPa and 2 ± 0.5 GPa for the lower and higher bainite
respectively. The lower-bainite was found to have a phase transition at 13 ± 0.5 GPa.
The eight plates from Table (5.3) were sectioned after the ballistic tests for different analyses
and micro-hardness measurements. X-ray diffraction analysis was done in the cross section of
the impact-affected zones ( Figure 5.4) to determine the volume fraction of the retained
austenite after the ballistic impact.
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Table (5.5): Volume fraction of the austenite in the impact-affected regions before and after
ballistic testing
Volume fraction
of retained
Volume fraction of austenite after
Thickness of retained austenite ballistic testing
the plate [mm] before testing [%]
[%]
Steel P
Steel Q
Steel R
Steel S
Steel T
4.7
4.9
5.1
5.2
5.4
6
4
2
3
0.6
<0.5
<0.5
<0.5
<0.5
<0.5
Steel U
Steel V
Steel W
5.1
5.1
4.8
2
5.3
6
<0.5
<0.5
<0.5
The volume fraction of the retained austenite in the impact-affected regions are systematically
lower after the ballistic testing than before, indicating a transformation process.
The Vickers micro-hardness profiles of the same cross-sections of steels P, Q R, T and W were
compared to appreciate the significance of the work hardening of the armour steel plate in
resisting ballistic perforation. The plates of the steels P, Q, R, T and W were selected on the
basis of their initial volume fraction of retained austenite, their plate thickness and the ballistic
behaviour. The comparison was then possible firstly, between the armour plates that all had
passed the ballistic test and secondly, between those that passed the tests and the plate of steel
T that had failed the test. Three lines of measurement were drawn on each cross section of the
impact-affected zones. The first line was drawn at one mm depth from the incidence surface
and the second one at 2.5 mm and the third one at 4.5 mm depth. The Vickers micro-hardness
was measured along each line with the reference zero point for the measurement along a line
intersecting the line and the incidence direction of the fired round which is also the longitudinal
axis of the deformed volume, shown by the arrow in the figure below.
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Figure 5.11: Illustration of the principle for the drawing of the iso-depth lines along which the micro-hardness
was measured and the positions from where 3mm discs were cut for thin foil TEM. The arrow shows the
incidence direction of the fired round.
The measured Vickers micro-hardnesses are given in Table 5.6:
Table (5.6): Vickers micro-hardness throughout the cross section of the deformed zones after the ballistic testing
Vickers micro-hardness
Depth from the impacted surface
Distance from the incidence direction of the fired round[mm]
Steel P (4.7mm)
1
2
3
5
7.5
10
12.5
15
17.5
20
25
1 mm
639
648
671
671
680
622
622
639
622
622
606
2.5 mm
594
626
666
652
685
639
626
639
620
606
594
4.5 mm
710
710
746
705
639
644
644
644
626
622
598
Steel Q (4.9mm)
1
2
3
5
7.5
10
12.5
15
17.5
20
25
1 mm
551
564
568
575
575
579
537
537
537
537
537
2.5 mm
564
550
564
598
554
543
537
537
530
530
530
4.5 mm
602
602
602
602
602
561
564
537
530
530
530
Steel R (5.1mm)
1
2
3
5
7.5
10
12.5
15
17.5
20
25
1 mm
496
575
583
590
583
579
571
598
588
583
598
2.5 mm
626
652
661
631
648
639
598
594
618
598
598
4.5 mm
661
635
635
690
652
639
639
610
602
586
598
Steel W (4.8mm))
1
2
3
5
7.5
10
12.5
15
17.5
20
25
30
1 mm
657
666
671
666
657
671
661
666
639
644
614
622
2.5 mm
661
622
648
657
666
648
648
648
648
639
639
626
4.5 mm
661
685
675
675
675
635
630
631
606
614
614
614
Steel T (5.4mm)
5
7.5
10
12.5
15
17.5
20
25
1 mm
614
505
481
446
427
422
422
422
2.5 mm
602
564
523
523
517
517
515
511
4.5 mm
511
514
499
505
508
505
508
508
The hardness measurements start at approximately 6 millimetres from the axis of the
perforation hole for the plate of the steel T that failed the test. These hardnesses are compared
in Figure 5.12.
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Micro Vickers hardness number
800
750
700
1 mm
2.5 mm
4.5 mm
650
600
550
500
0
5
10
15
20
25
30
Distance from the centre of the impact region
[mm]
Figure 5.12(a): Vickers micro-hardness profiles throughout the cross section of the deformed zone of the plate of
steel P
Micro Vickers hardness number
620
610
600
590
580
1 mm
2.5 mm
4.5 mm
570
560
550
540
530
520
0
10
20
30
Distance from the centre of the impact [mm]
Figure 5.12(b): Vickers micro-hardness profiles throughout the cross section of the deformed zone of the plate of
steel Q
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Micro Vickers hardness number
800
750
700
650
1 mm
600
2.5 mm
550
4.5 mm
500
450
400
0
5
10
15
20
25
30
Distance from the centre of impact [mm]
Figure 5.12(c): Vickers micro-hardness profiles throughout the cross section of the deformed zone of the plate of
steel R
Micro Vickers hardness number
700
680
660
640
620
1 mm
600
2.5 mm
580
4.5 mm
560
540
520
500
0
5
10
15
20
25
30
35
Distance from the centre of the impact region
[ mm]
Figure 5.12 (d): Vickers micro-hardness profiles throughout the cross section of the deformed zone of the plate of
steel W
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650
600
550
1 mm
2.5 mm
4.5 mm
500
450
400
0
10
20
30
Distance from the centre of the impact region
[mm]
Figure 5.12(e): Vickers micro-hardness profiles throughout the cross section of the deformed zone of the plate of
steel T that had failed the test
The following observations can be made:
(i) For the plates that withstood the fired round, the hardnesses near the incidence direction,
i.e. in zone 1, are higher for the iso-depth lines situated at 4.5 mm from the incidence
surface than for the iso-depth lines situated at 1 and 2.5 mm . For the latter two iso-depth
lines the hardness curves have a maximum at about 10 mm from the incidence direction of
the fired round while the hardnesses within zone 1 are lower. The Vickers micro-hardness
on the iso-depth-lines at 4.5 mm increased by about 100 units for the steels P, Q and W that
had a higher volume fraction of retained austenite before the ballistic testing than steel R
with only 2% retained austenite and whose hardness increased only by about 50 units.
(ii) The plate of steel R with 2% retained austenite, showed a decrease in hardness along
the 1 mm iso-depth line compared to the hardness at 25 mm further away from the impact
incidence direction. This is opposite to the tendency in the plates of steels P, Q and W with
higher volume fractions of retained austenite.
(iii) The plate of steel T that had failed the test had a higher hardness around the perforation
hole for the iso-depth lines at 1 and 2.5 mm and a lower hardness for the iso-depth line at
4.5 mm. This is again opposite to the observation in the non-perforated plates of steels P,
Q, R and W. Moreover steel T had softened during the ballistic impact.
Thin foils cut by spark erosion from the same zones were analysed in transmission electron
microscopy to examine the differences between these steels and the variation in their
hardnesses in the cross section of the same steel.
Three areas were selected on each cross section for the cutting of the thin foils, i.e. the centre
of the impacted region (center in Figure 5.11), the circumference of the deformed zone
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(exterior in Figure 5.11) and the non-deformed area. The bright field and dark field images of
these areas are compared below:
T
RA
RA
RA
(a)
T
(b)
Figure 5.13: Dark field transmission electron microscopy showing the twinned martensite with retained austenite
in steel P before the ballistic test.
Two types of shape of the retained austenite were observed in the dark field image in Figure
5.13(b), i.e. a nodular type and an interplate film type along the plate interfaces.
The microstructure of steel Q was close to that of steel P, consisting of twinned martensite with
retained austenite along the plate interfaces.
(a)
(b)
Figure 5.14: Transmission electron microscopy of steel Q, (a) dark field image and (b) corresponding bright field
image of the twinned martensite.
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The thin foil images of transmission electron microscopy from the centre of the impact and
from the circumference of the deformed region are compared below. At the centre of the
impact “new” martensite was formed. Fine carbides were precipitated within the martensite
matrix and no twins were observable.
(a)
(b)
(c)
(d)
Figure 5.15: Transmission electron microscopy of the centre of impact of steel Q; (a) and (c) bright field images,
(b) and (e) respective corresponding dark field images showing no twins and neither retained austenite after
ballistic test. Label mark 200 nm.
The absence of twinned martensite in the “new martensite” could arise from incomplete
solution of carbide, diluting the austenite and raising the Ms temperature.
Because reaustenitisation occurs transiently in the impact zone the properties of austenite will
be important in energy absorption and ballistic resistance. The kinetics of reaustenitisation will
also be composition dependent.
(a)
(b)
Figure 5.16: (a) and (b) Thin foil dark field images of the circumference of the deformed region showing twinned
martensite with dislocation pile-ups at twin interfaces in steel Q. Label mark 200 nm.
At 25mm away from the incidence direction the morphology was a twinned martensite with a
large number of dislocations piled up at the twin interfaces. It appears that the twin interfaces
are acting as dislocation barriers. This area has a higher Vickers micro-hardness than the centre
of the impact area and also higher than the plate before the ballistic test.
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The plate of steel R containing 2% retained austenite consisted of twinned martensite as well.
At 2% the retained austenite is not easily observable in the dark field thin foil transmission
electron microscopy images.
(a)
(b)
Figure 5.17: (a) Thin foil dark field image and (b) corresponding bright field image of steel R before the ballistic
test.
The bright field and dark field images of the centre of the impact area revealed untwinned
martensite and the massive formation of fine carbides within the martensite plates and on the
plate inter-faces despite its 1.03%Si content which should delay such a transformation.
(a)
(b)
Figure 5.18: Thin foil transmission electron microscopy; (a) dark field and (b) the corresponding bright field
image showing the disappearance of the twins and the formation of large aggregates of fine carbides throughout
the martensite matrix at the centre of the ballistic impact area on the plate of steel R. Label mark 200 nm.
This formation of carbides may explain the decrease in the micro-hardness observed upon
ballistic impact along the iso-depth line at one mm in Figure 5.12(c).
The plate of steel W contains 6% volume fraction of retained austenite and the nodules of
retained austenite are located on the plate interfaces.
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Figure 5.19: Dark field image thin foil transmission electron microscopy of steel W (0.98wt% Si) before the
ballistic test. Label mark 200 nm.
Fine carbide particles have precipitated throughout the martensite plates upon tempering at
250°C for 15 minutes before the ballistic test.
Figure 5.20: Thin foil TEM bright field image showing the precipitation of fine carbides in the matrix before the
ballistic test of steel W tempered at 250°C for 15 minutes. Label mark 200 nm.
The plate of steel T (the failed one) had the lowest volume fraction of retained austenite of
about 0.6%, which is almost equal to the absolute error of detection by the X-ray diffraction
equipment used. However, the thin foil transmission electron microscopy revealed elongated
films of retained austenite along the lath interfaces. The measured martensite start temperature
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of steel T was 184°C, which is comparable to those of the other seven steels successfully tested
in this second series of ballistic testing. Nevertheless, it is still the highest Ms temperature in
this series of steels. The morphology of the martensite before the ballistic testing was coarse
laths with coarse cementite.
The cementite may have formed due to auto-tempering during the quenching and then
coarsened upon tempering at 180°C. The low Silicon content of 0.4%Si was apparently not
enough in this case to delay the formation of coarser cementite. The carbide particles around
the perforation hole have coarsened further upon ballistic impact.
(a)
(b)
(c)
(d)
Figure 5.21: Thin foil transmission electron microscopy of steel T; (a) and (b) dark field and corresponding bright
field images before the ballistic test and (c) bright field image and (d) corresponding dark field image after the
ballistic test, showing the coarsened carbide particles and the films of retained austenite. Label mark 500 nm.
5.5. General observation
The microstructure of the armour steel has a definite effect on its ballistic performance for
plates with a thickness smaller than 6 mm and it is clear that there is a direct relationship
between the microstructure and the ballistic performance of martensitic steel armour plates.
The ballistic parameter BP, which takes into account the thickness of the plate and the volume
fraction of retained austenite contained in the martensitic steel, may be used for predicting the
ballistic performance and the following conclusions can be made at this stage.
(i) High ballistic performance may be achieved by combining twinned martensite with retained
austenite in the same microstructure;
(ii) Coarse carbide particles are detrimental to the ballistic performance of the armour steels;
(iii) Stress-induced transformations occur inside the shock-affected region upon ballistic
impact; and
(iv) The microstructure at the centre of the impact region does not contain any of the initial
twins after impact.
The de-twinning process may be explained as follows: Part of the kinetic energy of the fired
round is transformed into heat by entropy trapping, which raises the temperature high enough
for the twinned martensite to recrystallise and re-austenitise. The new austenite is then
quenched by the surrounding material and transforms into new untwinned martensite. This
means that there is no memory effect present between the initial state with twinned martensite
and the final state without twins. This transformation extends to a large volume around the
impact region depending on the amount of retained austenite present in the plate. The kinetic
energy of the fired round is then used to:
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Chapter 5: Improvement in the Ballistic Performance
-
heat up the surrounding material and induce the phase transformations; and
mechanically deform the affected region.
The third part of the energy is transferred to the plate’s support structure.
The phase changes during the ballistic impact should be considered in predicting the ballistic
performance of a martensitic steel, as the fraction of the kinetic energy consumed by the phase
transformation may be very important by resulting in a reduction of the effective energy
available for the perforation stage.
The susceptibility of the retained austenite to stress-induced transformation appears to depend
on its shape and location within the martensite. The nodular austenite, found when the volume
fraction is higher than 2%, gave a stronger TRIP effect than the inter-lath films. This may be
due to differences in the mechanical stability upon high strain rate impact of the two types of
retained austenite.
Thin foil TEM of the experimental armour steels considered in this study revealed a change of
the morphology of the retained austenite from film to nodular when its volume fraction
increases. The ballistic performance of the experimental martensitic armour steels also
increased as the volume fraction of retained austenite increased in the range from 1% to 6%
although an upper limit has not been found within this range.
At too high volume fraction of retained austenite, adverse effects may occur following an
excessive softening of the armour plates and the resistance to ballistic perforation. Further
studies are needed on a possible upper limit of retained austenite content and to find an
explanation on the mechanism by which retained austenite is transformed under impact, or
whether a stress-induced or a strain-induced transformation occurs. Furthermore, investigations
as to the location, the shape of the retained austenite and their mechanical and thermal
susceptibilities will be useful in predicting and simulating the ballistic performance of
martensitic armour steels containing some volume fraction of retained austenite.
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Chapter 6: Characterisation of the martensitic transformation in armour steels
CHAPTER 6. CHARACTERISATION OF THE MARTENSITIC
TRANSFORMATION IN ARMOUR STEELS
6.1. Background
6.1.1 Theories of the martensitic transformation
A number of crystallographic and thermodynamic theories of the martensite transformation
and the subsequent modifications to these theories have been briefly presented in Chapter 2.
The Phenomenological crystallographic Theories of the Martensitic Transformations (PTMT)
are concerned with the relationships that exist between the Bain strain, the invariant shape
strain, the rotation and shear processes that comprise the so-called inhomogeneous or
complementary strain. The original phenomenological approaches of Wechsler, Lieberman
and Read (WLR) [102] and Bowles and Mackenzie (BM) [103] are equivalent. The first
theory of WLR derived the shape strain as the result of the rotation R, the Bain distortion B
and an inhomogeneous shear. The second theory of BM derived the total strain S which
describes the homogeneous lattice strain occurring over a range of a few unit cells as the
result of the shape strain and a complementary shear. Bowles and Mackenzie proposed that
the complementary shear strain was part of a twinning shear in the martensite. This
hypothesis implies that oppositely directed complementary shears could possibly produce
twin orientations within a martensite plate, and it is well known that the plates produced in
many martensitic transformations are twinned on a very fine scale. The Bowles and
Mackenzie model predicts the crystallographic features such as the habit plane, the strain and
the orientation relationships between the parent austenite and the product martensite.
The Phenomenological crystallographic Theories of the Martensitic Transformations have
been successfully applied to many alloy systems, but as shown by Christian [45], in steels it
can only be applied mainly to {2 5 9} and {3 10 15} -type martensite plates; {2 2 5}
martensite plates and lath martensites have been proven difficult to fit to the theory. The
concept of the displacement vector of the lattice deformation was then advanced by Gu et al
[71]. They considered two ways to reduce the strain energy, i.e. the self-accommodation
between different martensitic variants and plastic accommodation between the parent phase
and martensite to explain the formation of {5 7 5} martensite. Kelly [59] recently
demonstrated that, when applied in a rigorous fashion, the Infinitesimal Deformation (ID)
approach is exactly equivalent to the Phenomenological crystallographic Theory of the
Martensitic Transformation (PTMT). The PTMT assumes the invariability of the habit plane.
On the other side many researchers such as Christian [45], Kennon and Dunne [46], Tadaki
and Shimizu [48], and Dunne and Kennon [49] have demonstrated that the flexibility of the
habit plane is rather a characteristic of the martensite transformation than an exception.
In this study the PTMT model proposed by Bowles and Mackenzie was used for predicting
the theoretical features of the martensite and their possible relation with the ballistic
performance of the armour steels. The atom force microscopy is then used to find
correspondences between the surface relief accompanying the martensitic transformation and
the prediction by the Bowles and Mackenzie model of the PTMT. It can be accepted that an
internally twinned martensite is mathematically equivalent to one that is internally slipped.
That is, algebraically a predeformed austenite followed by the Bain deformation is equivalent
to a martensite formed by the Bain mechanism followed by an inhomogeneous shear. When
the martensite is not internally twinned, e.g. as in lath martensite, a single correspondence
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Chapter 6: Characterisation of the martensitic transformation in armour steels
relation and Bain deformation applies to an entire lath. In general, the reasons for a particular
operative substructure (inhomogeneous shear) in a given material are rather obscure[69].
Zhang et al [98] have reported the results of many investigations made on the morphology
transition from lenticular to butterfly to lath martensites. Variables reported to influence the
martensite morphology include: transformation temperature, quench rate above Ms, chemical
composition, dispersion of particles, thermodynamic driving force, austenite defect structure
and stacking fault energy and the martensite and austenite strength. Davies and Magee [99]
supposed that the morphology differences result from the different habit planes. The lattice
invariant shear for the various martensite habit planes are as follows [99]:
{2
{2
{1
5 9} - twinning in ferrite
2 5} - slip in austenite and twinning in ferrite
1 1} - slip in ferrite and austenite
These different habit planes usually correspond to lenticular, butterfly and lath martensites.
6.1.2. Tetragonality of martensite
The tetragonality of martensite in steels containing Carbon and Nitrogen is consistent with the
correspondence implied by the Bain strain. Whereas in cubic ferrite the octahedral interstitial
sites are occupied at random, in tetragonal martensite there must be a preferred occupancy of
sites with only those octahedral sites along the martensite c-axes being filled, so producing
the observed tetragonality. It was noticed in Chapter 2 that a significant redistribution of
Carbon atoms and a disappearance of the tetragonality of a 5.1at.%C martensitic steel
occurred at room temperature during aging times of less than 50 hours [66]. Carbon atoms
segregated to lattice imperfections and also transferred from a/b-type octahedral interstices to
c-type interstices, thereby decreasing the c m parameter of the tetragonal martensite at room
temperature.
Lyssak et al [67] have found that the tetragonality of the martensite in Manganese steels is
abnormally small. Moreover, they have observed that there are several alloy systems in which
the tetragonality of martensite containing Carbon, does not obey the well-known
experimental equation:
c a = 1 + 0.046 p
where p is the mass percentage of Carbon in the steel. Kajiwara and Kikuchi [68] made a very
extensive and systematic study of the martensite tetragonality in Fe-Ni-C alloys and found
that the tetragonality is quite dependent on the mode of the lattice invariant deformation in the
martensite.
Uehara et al. [69] have investigated the tetragonality of martensite in high Carbon- Iron alloys
containing some Aluminium. From their study it appears that the tetragonality is enhanced by
Aluminium and Nickel additions that prevent Carbon atoms from moving out of octahedral
sites to tetrahedral sites during quenching (auto-tempering).
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Chapter 6: Characterisation of the martensitic transformation in armour steels
6.1.3. Techniques used in characterising the martensitic transformation
The features of the martensitic transformation may be determined by combining the
determination of the phases present in the microstructure and their lattice parameters by the
X-ray diffraction method, with the analysis of the morphologies, the spatial distribution and
shapes of the phases determined by Transmission Electron Microscopy. Recently the
introduction of Atomic Force Microscopy has brought in new possibilities of investigating the
characteristics of the martensitic transformation by analysing the surface relief accompanying
the transformation on a nanometric scale.
6.2. Characterisation methodology
(i)
(ii)
(iii)
(iv)
The inputs in the Bowles and Mackenzie model used in this study for the
characterisation of the martensite are the lattice parameters of the martensite and
of the retained austenite measured by X-ray diffraction at room temperature.
Complementary details on the martensite formation were determined by analysing
the surface relief by Atomic Force Microscopy on a nanometric scale;
Scanning Electron Microscopy was used for analysis on a micrometric scale as
complementary to the observation from the Atomic Force Microscopy; and
Transmission Electron Microscopy was used to determine the morphologies and
the location of the phases that are present in the armour steels.
6.3. Characteristics of the martensite formation in the armour steels
6.3.1. Crystallographic characteristics
The volume fraction of the retained austenite and the lattice parameters of both the austenite
and the martensite were determined by X-ray diffraction of the specimens austenitised at
900°C and quenched into water at room temperature. The martensite start temperatures were
determined by dilatometric analysis. The crystallographic characteristics of the martensite
formation were then calculated using the Bowles and Mackenzie model.
It was found from the XRD measurements of the lattice parameters that the martensite in
these armour steels, is cubic with am approximately equal to cm or, alternatively, it is
possible that the tetragonality was so small that it could not be detected. Samples were double
checked on two different XRD machines and were also stored at sub-zero temperatures
between the quenching step and the XRD analysis to prevent significant Carbon movement.
No tetragonality could be found. The measured lattice parameters and the calculated
characteristics of the martensitic transformation in the nineteen armour steels are presented in
Table (6.1).
The calculated magnitude of the complementary shear strain varies between 0.24 and 0.30 for
these steels. The calculated misorientation from the Kurdjumov-Sachs orientation relationship
is less than 1.2°. Nishiyama [36] estimated the limit of application of the calculated
Kurdjumov-Sachs orientation relationship using the Bowles and Mackenzie model, to those
cases where the calculated misorientation angle between the directions [− 1 0 1]γ in the
austenite and [− 1 − 1 1]m in the martensite are smaller than 4°. According to this prediction
the K-S orientation relationship may be applied to the martensite formation in these armour
steels. Figure 6.1 illustrates the effect of the martensite start temperature on the scattering
from the Kurdjumov-Sachs orientation relationship, on the complementary shear and on the
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Chapter 6: Characterisation of the martensitic transformation in armour steels
magnitude of the displacement vector. It appears from this figure that the Kurdjumov-Sachs
orientation relationship may be present in twinned as well as in lath martensitic armour steels.
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Chapter 6: Characterisation of the martensitic transformation in armour steels
Table (6.1). Lattice parameters and features of ferrous martensite in armour steels.
Inputs
Name of
the
armour
steel
E
Ms
temperatu
re [°C]
196
F
am [nm]
Invariant line
normal
n
0.36448
0.2867291
255
0.36559
0.2863991
G
271
0.3683
0.2865805
H
210
0.36556
0.2862345
I
309
0.368300
0.286643
J
306
0.36652
0.2866597
K
318
0.36469
0.2864401
L
259
0.36475
0.286822
N
241
0.36468
0.2863646
O
218
0.36569
0.2863932
P
115
0.35837
0.285753
Q
178
0.35781
0.285086
R
170
0.36521
0.285806
0.4876
0.7243
0.4876
0.4769
0.7384
0.4769
0.4593
0.7604
0.4593
0.4756
0.7400
0.4756
0.4598
0.7597
0.4598
0.4727
0.7438
0.4727
0.4835
0.7296
0.4835
0.4865
0.7257
0.4865
0.4829
0.7304
0.4829
0.4761
0.7394
0.4761
0.5211
0.6759
0.5211
0.5193
0.6788
0.5193
0.4742
0.7418
0.4742
aγ
[nm]
Complementary rotation
Q
[1.0000
0 0.9876
0 0.1073
[1.0000
0 0.9869
0 0.1098
[1.0000
0 0.9858
0 0.1138
[1.0000
0 0.9868
0 0.1101
[1.0000
0 0.9859
0 0.1137
[1.0000
0 0.9866
0 0.1108
[1.0000
0 0.9873
0 0.1082
[1.0000
0 0.9875
0 0.1075
[1.0000
0 0.9873
0 0.1084
[1.0000
0 0.9868
0 0.1100
[1.0000
0 0.9904
0 0.0990
[1.0000
0 0.9902
0 0.0995
[1.0000
0 0.9867
0 0.1104
0
0
-0.1073
0.9876]
0
0
-0.1098
0.9869]
0
0
-0.1138
0.9858]
0
0
-0.1101
0.9868]
0
0
-0.1137
0.9859]
0
0
-0.1108
0.9866]
0
0
-0.1082
0.9873]
0
0
-0.1075
0.9875]
0
0
-0.1084
0.9873]
0
0
-0.1100
0.9868]
0
0
-0.0990
0.9904]
0
0
-0.0995
0.9902]
0
0
-0.1104
0.9867]
Total shape strain for the
invariant line
S
[1.0807
0.0512
-0.1173
[1.0751
0.0496
-0.1109
[1.0663
0.0468
-0.1009
[1.0744
0.0494
-0.1101
[1.0666
0.0469
-0.1012
[1.0729
0.0489
-0.1084
[1.0786
0.0506
-0.1148
[1.0802
0.0510
-0.1166
[1.0783
0.0505
-0.1145
[1.0747
0.0495
-0.1104
[1.1002
0.0551
-0.1392
[1.0991
0.0549
-0.1379
[1.0737
0.0492
-0.1093
-0.0267
1.1188
-0.1191
-0.0266
1.1164
-0.1194
-0.0268
1.1122
-0.1189
-0.0266
1.1161
-0.1194
-0.0268
1.1123
-0.1190
-0.0266
1.1154
-0.1194
-0.0266
1.1179
-0.1193
-0.0267
1.1186
-0.1191
-0.0266
1.1178
-0.1193
-0.0266
1.1162
-0.1194
-0.0293
1.1256
-0.1146
-0.0290
1.1252
-0.1150
-0.0266
1.1158
-0.1194
0.0973
0.0650
0.7667]
0.0941
0.0659
0.7629]
0.0889
0.0671
0.7570]
0.0937
0.0660
0.7624]
0.0891
0.0671
0.7572]
0.0929
0.0662
0.7614]
0.0961
0.0654
0.7652]
0.0970
0.0651
0.7663]
0.0959
0.0654
0.7650]
0.0939
0.0660
0.7626]
0.1077
0.0618
0.7796]
0.1071
0.0620
0.7788]
0.0933
0.0661
0.7620]
Invariant
plane
normal
p1
0.1984
0.6680
0.7172
0.1904
0.6511
0.7347
0.1780
0.6244
0.7605
0.1895
0.6491
0.7367
0.1784
0.6253
0.7597
0.1874
0.6446
0.7412
0.1954
0.6616
0.7240
0.1976
0.6663
0.7190
0.1949
0.6606
0.7250
0.1899
0.6499
0.7359
0.2267
0.7252
0.6502
0.2249
0.7218
0.6546
0.1885
0.6470
0.7388
Magnitude
of the
complement
ary shearm2
0.28
Shear
angle
[°]
Deviation
from K-S
[°]
8.19
0.94
0.29
8.38
1.06
0.30
8.68
1.27
0.29
8.40
1.08
0.30
8.67
1.26
0.29
8.45
1.11
0.29
8.26
0.98
0.28
8.21
0.95
0.29
8.27
0.99
0.29
8.39
1.07
0.26
7.54
0.57
0.26
7.58
0.59
0.29
8.43
1.09
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Chapter 6: Characterisation of the martensitic transformation in armour steels
S
182
0.35792
0.285704
T
184
0.36559
0.286066
U
170
0.36486
0.286106
V
145
0.3578
0.2853
W
130
0.35819
0.285883
0.5238
0.6718
0.5238
0.4739
0.7422
0.4739
0.4794
0.7351
0.4794
0.5212
0.6759
0.5212
0.5235
0.6723
0.5235
[1.0000
0
0
0 0.9906 -0.0984
0 0.0984 0.9906]
[1.0000
0 0.9867
0 0.1105
[1.0000
0 0.9871
0 0.1092
[1.0000
0 0.9904
0 0.0990
[1.0000
0 0.9906
0 0.0984
0
0
-0.1105
0.9867]
0
0
-0.1092
0.9871]
0
0
-0.0990
0.9904]
0
0
-0.0984
0.9906]
[1.1019
0.0554
-0.1410
[1.0735
0.0491
-0.1091
-0.0297
1.1261
-0.1139
-0.0266
1.1157
-0.1194
0.1085
0.0616
0.7807]
0.0932
0.0661
0.7619]
0.2292
0.7301
0.6438
0.1882
0.6465
0.7394
0.26
7.49
0.55
0.29
8.4361
1.10
[1.0764
0.0500
-0.1123
[1.1002
0.0551
-0.1392
[1.1017
0.0553
-0.1408
-0.0266
1.1170
-0.1194
-0.0293
1.1256
-0.1146
-0.0297
1.1260
-0.1140
0.0948
0.0657
0.7638]
0.1077
0.0618
0.7796]
0.1084
0.0616
0.7805]
0.1923
0.6550
0.7308
0.2267
0.7252
0.6501
0.2289
0.7295
0.6446
0.29
8.34
1.03
0.26
7.54
0.57
0.26
7.50
0.55
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Chapter 6: Characterisation of the martensitic transformation in armour steels
The higher martensite start temperatures led to larger angles between the directions
[− 1 0 1]γ and [− 1 − 1 1]m . For values of this angle larger than 4°, an intermediate
orientation relationship between that of Kurdjumov-Sachs and Nishiyama-Wasserman may be
found [36].
1.4
1.2
1
scattering from K-S OR in
degrees
Complementary shear
strain
Magnitude of the
displacement vector in nm
0.8
0.6
0.4
0.2
0
100
150
200
250
300
350
Ms temperature [degree Celsius]
Figure 6.1: Dependence of the martensite formation characteristics on the measured martensite start temperature
calculated by the Bowles and Mackenzie model.
The general trends of these characteristics present a plateau for the martensite start
temperature within the range 200°C to 250°C. The values of these three characteristics are
larger when the martensite start temperatures are higher than 250°C. The plateaux of
intermediate constant values of the scattering from the Kurdjumov-Sachs orientation
relationship, of the complementary shear strain and of the magnitude of the displacement
vector may be explained by the equal probability of formation of the martensite by a slip or
by a twinning mechanism in armour steels of which the martensite start temperatures range
from 200°C to 250°C, contrary to the other two plateaux where one of the two mechanisms
predominate at the expense of the other. The data collected by Morozov and co-workers [21]
and presented in Table (2.5), show that many researchers have calculated the various
parameters using different thermodynamic models and have predicted a change in the
martensite formation mechanism at Ms temperatures between 232°C and 284°C for different
Fe-C alloys. The plateaux of the crystallographic characteristics using the Bowles and
Mackenzie model as presented in Figure 6.1, are in good agreement with these
thermodynamic predictions. The variation in the morphology of the martensite in three
armour steels is illustrated in Figure 6.2 for samples of steels H, G and I of which the
martensite start temperatures were respectively 210°C, 271°C and 309°C, and that were
austenitised at 900°C for 20 minutes in an argon atmosphere and then water-quenched to
room temperature. The samples were then polished mechanically and etched for 7 seconds
with a 2% Nital solution. In steel G whose martensite start temperature was 210°C, the
martensitic structure consisted largely of plates coexisting with large laths.
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Chapter 6: Characterisation of the martensitic transformation in armour steels
The lath substructure became slimmer as the martensite start temperature became higher as
illustrated in Figures 6.2 (a), (c) and (e) respectively for the three steels.
(a)
(b)
Figure 6.2 (a) and (b): Backscatter scanning electron microscopy of steel G (MS = 210°C).
(a) x2000 and (b) x5000
(c)
(d)
Figure 6.2 (c) and (d): Backscatter scanning electron microscopy of steel G (MS = 271°C).
(c) x2000 and (d) x5000
(e)
(f)
Figure 6.2 (e) and (f): Backscatter scanning electron microscopy of steel I (MS = 309°C).
(e) x2000 and (f) x5000
The same observation was made by scanning electron microscopy of the samples when still
unetched. Samples with thicknesses ranging from 1 to 2 mm were cut from the plates of steels
E through to I, mechanically polished using a 1 micron diamond paste and cleaned 30
seconds in an ultrasonic cell containing pure ethanol.
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Chapter 6: Characterisation of the martensitic transformation in armour steels
These samples were then austenitised at 900°C for 10 minutes in a high vacuum atmosphere
in the THETA Dilatometer and quenched to room temperature in a Helium-gas flow. The
backscatter scanning electron microscopy micrographs of these samples are shown in Figure
6.3. The free-surface features of the martensite are coarser in steel E (shown in Figure 6.3(a))
which has the lowest martensite start temperature of 196°C and is finer in steel I (shown in
Figure 6.3(e)) whose martensite start temperature is the highest at 309°C. The steels H, F and
G whose martensite start temperatures were respectively 210°C, 255°C and 271°C, had
intermediate sized free-surface martensite features as shown in Figures 6.3(b), 6.3(c) and
6.3(d) respectively. The small packets formed in steels whose martensite start temperatures
are higher than 250°C, present less resistance against the combination of dynamic loading and
localised high temperatures produced in zone 1 during ballistic impact.
It was noted in Chapter 4, that the free-surface martensite was not fully constrained during its
formation as is the case inside the bulk of the steel, hence the differences in martensite plate
widths between Figures 6.2 and Figure 6.3.
Figure 6.3(a): Backscatter scanning electron micrographs of steel E with Ms=196°C, finely polished before
austenitising at 900°C for 10 minutes in high vacuum and quenched in a helium-gas flow. The sample was not
polished or etched after quenching.
(b)
(c)
Figure 6.3: (b) Backscatter scanning electron micrographs of steel H with Ms=210°C and (c) steel F with
Ms=255°C, both finely polished before austenitising at 900°C for 10 minutes in high vacuum and quenched in a
Helium-gas flow. The samples were not polished or etched after quenching.
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Chapter 6: Characterisation of the martensitic transformation in armour steels
(d)
(e)
Figure 6.3: (d): Backscatter scanning electron micrographs of steel G with Ms=271°C and (e) steel I with
Ms=309°C, both finely polished before austenitising at 900°C for 10 in high vacuum and quenched in a Heliumgas flow. The sample was not polished or etched after quenching.
6.3.2. Quantitative analysis of the surface relief by means of Atom Force Microscopy
6.3.2.1: Plate martensite in steel E
Atomic Force Microscopy of steels E through to I was presented in Figure 4.4.36 of Chapter
4. The qualitative comparison of the surface relief apparently reveals different mechanisms of
martensite formation in these steels. In Chapter 4, a qualitative classification of the surface
relief of these armour steels was done according to their martensite start temperatures.
It was observed that in steel E which had a low martensite start temperature with Ms=196°C,
internally twinned martensite formed by a shear mechanism accompanied by sub-twins. Two
groups of twins were present and formed in two different directions A and B as shown in
Figure 6.4. The twinning ratios of these two groups as well as their frequency were analysed
using the Discrete Fourier Transform calculated by the Fast Fourier Transform algorithm of
their spatial distributions and are compared in this paragraph.
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Chapter 6: Characterisation of the martensitic transformation in armour steels
Twins
B
A
Figure 6.4: Atomic Force Microscopy of steel E with Ms=196°C, showing the twins (100 to 200 nm wide) and
other finer parallel lines (sub-twins) approximately transverse to the twins (and approximately parallel to the
habit plane)
Normal lines were considered relative to each direction A or B. The corresponding surface
relief profiles along the two directions A and B with the corresponding Fast Fourier
Transforms are illustrated in Figure 6.5 for the direction A and in Figure 6.6 for the direction
B.
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Chapter 6: Characterisation of the martensitic transformation in armour steels
Steel E ( line 1)
20
TB_1
15
TA_1
TB_2
[nm]
TA_2
10
5
0
50
100
150
200
250
[nm]
Fast Fourier Transform
300
350
400
Magnitude[nm2 ]
300
200
100
0
0
0.02
0.04
0.06
0.08
0.1
[1/nm]
0.12
0.14
0.16
0.18
0.2
Figure 6.5(a): Surface relief profile of steel E along line 1 in the direction A and the corresponding Fast Fourier
Transform
Steel E (line 9)
20
[nm]
15
10
5
0
50
100
150
200
250
[nm]
Fast Fourier Transform
300
350
400
400
[nm2]
300
200
100
0
0
0.02
0.04
0.06
0.08
0.1
[1/nm]
0.12
0.14
0.16
0.18
0.2
Figure 6.5(b): Surface relief profile of steel E along line 9 in the direction A and the corresponding Fast Fourier
Transform.
The measured widths of the twins and the twinning ratios are presented in Table (6.2) and
Appendix A6.2 where (dx) is the horizontal distance between a minimum and the following
maximum or vice versa and (dy) is the height difference between the two points.
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Chapter 6: Characterisation of the martensitic transformation in armour steels
Table (6.2): Measured geometric characteristics of the twins along lines parallel to the direction A in steel E.
line 1
TA_1
TB_2
TA_2
TB_3
TA_3
dx [nm]
35.71
79.61
33.48
24.55
95.98
Height [nm]
9.05
-6.44
8.03
-8.75
7.35
Relief angle [Degrees]
14.23
-4.62
13.50
-4.84
13.55
Width [nm]
36.84
79.87
34.43
55.84
26.42
Slope [nm/deg]
Twinning ratio
TB/(TB+TA)
2.58
-17.25
2.54
-11.6
1.94
0.69
0.68
Line 9
TA_1
TB_1
TA_2
TB_2
TA_3
TB_3
dx [nm]
35.67
79.70
26.56
92.61
31.12
55.41
Height [nm]
9.17
-6.50
6.64
-9.06
7.37
-5.60
Relief angle [Degrees]
14.43
-4.66
14.04
-5.59
13.34
-5.78
Width [nm]
36.84
79.97
27.38
93.05
31.98
55.69
Slope [nm/deg]
Twinning ratio
TB/(TB+TA)
2.55
-17.12
2.00
-16.63
2.39
-9.63
The twinning ratio
0.74
0.74
0.63
TB _ i
normal to the direction A in steel E spread from 0.6 to 0.81.
TB _ i + TA _ i
Twins TB _ i are regular shapes whose relief angle is about 5.2±0.6°. Twins TA _ i are rather
regular shapes whose relief angle is about 13.5±2.0°.
The frequency spectrum contains a narrow bandwidth peak at about 0.008 nm −1 . This
indicates that the plates are not exactly the same width but are rather continuously distributed
around the mean width value which equalled 125 nm .
The surface relief profile along the direction B is illustrated in Figure 6.6.
The geometric measurement along the lines in the direction B are shown in Table 6.3. The
TB _ i
along the normal to the direction B in steel E was spread within
twinning ratio
TB _ i + TA _ i
the range 0.55±0.03.
The surface relief was again N-shaped with twins TB _ i whose relief angle was about
5.0±1.0° and twins TA _ i whose relief angle was about 6.0±2.0°.
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[nm]
Chapter 6: Characterisation of the martensitic transformation in armour steels
80
70
60
50
40
30
20
10
0
0
100
200
300
400
500
600
700
[nm]
Figure 6.6(a): Typical surface relief profile along the direction B
Figure 6.6(b): Typical surface relief profile of the sub-twins along the direction B
The total width of the sub-twin pairs normal to the direction B ranges from 10 to 20 nm
which are smaller than 125 nm measured normal to the direction A.
Table (6.3): Measured geometric characteristics of the twins along lines in the direction B in steel E.
TA_1
TB_2
TA_2
TB_3
TA_3
TB_4
TA_4
dx [nm]
42.03
48.32
33.62
31.52
27.32
52.53
37.82
height [nm]
3.29
-4.98
3.56
-2.73
1.13
6.59
-3.91
Relief angle [Degrees]
4.477
-5.89
6.05
-4.96
2.37
7.153
-5.91
Width [nm]
42.15
48.58
33.81
31.64
27.34
52.95
38.03
Slope [nm/deg]
9.414
-8.24
5.58
-6.37
11.49
7.40
Twinning ratio TB/(TB+TA)
0.58
0.53
-6.43
0.58
The twinning ratio is also smaller normal to the direction B than normal to the direction A.
Lin Xiaoping and co-workers [47, 96] have determined the crystallographic characteristics of
the {2 2 5}γ and of the {2 5 9}γ martensite in a Fe-23%Ni-0.55%C and a Fe-8%Cr1%C alloy respectively using Atomic Force Microscopy.
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Chapter 6: Characterisation of the martensitic transformation in armour steels
They have observed that the relief angles of the {2 5 9}γ and the {2 2 5}γ martensite
range respectively from 4 to 5.8° and from 1 to 9°. The relief angles measured for steel E
which ranged from 4 to 6°, was in good agreement with those measured by Lin Xiaoping and
co-workers for the {2 2 5}γ martensite. However the widths of the plates measured for
steel E ranging from 90 to 125 nm , were at least two times smaller than those measured by
Lin Xiaoping and co-workers [95]. It seems from this comparison that the relief angle of the
{2 2 5}γ martensite may be less sensitive to the chemical composition than the width of the
plates.
The austenitisation temperature seems to have an effect on the widths of the plates but not on
the relief angles. Indeed, the data from Table 1 of the work done by Lin Xiaoping and coworkers [95] shows that the heights and the widths of the plates increase when the
austenitisation temperature increases from 1173K to 1473K.
A number of areas of the steel E consist of zigzag-shaped, while the rest consisted of twin
martensite. The adjacent plates of zigzag-shaped martensite share the same conjugate habit
plane. According to the Nishiyama-Wasserman-I (NW-I) and Nishiyama-Wasserman-II
(NW-II) orientation relationships, the adjacent plates that share the same conjugate habit
plane may grow in two symmetrical directions, so a tent-shaped surface relief is formed by
their mutually back-to-back accommodation growth [93].
0
1
2
μm
3
4
5
6
7
0
1
2
3
4
5
6
7
μm
Figure 6.7: Zigzag-shaped martensite appears to have been formed in some parts of steel E
6.3.2.2: Lath martensite in the steel I
The martensite start temperature of steel I is 309°C. Figure 4.4.35(e) of Chapter 4 showed the
thin foil TEM bright field image of this steel. Lath morphology of the martensite in this steel
was found after austenitisation at 900°C for 20 minutes and water quenching. Figure 6.8
illustrates the surface relief accompanying the martensite formation in this steel. Contrary to
steel E’s surface relief, is that of steel I irregular and N-shaped, which is not in agreement
with the prediction of the invariant plane strain [95, 96].
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Chapter 6: Characterisation of the martensitic transformation in armour steels
Figure 6.8 (a): Surface relief accompanying the formation of slipped martensite in steel I showing the irregular
N-shape.
Figure 6.8 (b): Surface relief accompanying the formation of slipped martensite in steel I (Ms =309°C) showing
the irregular N-shape.
A typical surface relief profile accompanying the formation of the martensite in steel I is
illustrated in Figure 6.9. Relief deterioration is possible in the case of this relatively high Ms
temperature through thermal smoothing and oxidation.
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Chapter 6: Characterisation of the martensitic transformation in armour steels
Figure 6.9: Typical surface relief profile after martensite formation in steel I and the corresponding
geometric characteristics. The number in the first column indicates the segment number, i.e. 1 correspond to
segment 1-2, 2 corresponds to segment 2 –3.
The laths are larger than 1.1 μm. This is about 2 times the width of the martensite plates
formed in steel E. The size of the laths or of the plates may have an effect on the effective
“grain size” in resisting fracture or perforation due to ballistic impact.
The transition of the martensite morphology in the armour steels as determined by Atomic
Force Microscopy was illustrated in Figure 4.4.36 of Chapter 4. AFM images reveal three
different morphologies of the martensite formed in these armour steels depending on the
specific martensite start temperatures. Based on the work of Davies and Magee [99], the
AFM results presented in Figure 4.4.36 and the crystallographic parameters using the Bowles
and Mackenzie model as presented in Table (6.1) and Figure 6.1, the lattice invariant shear
for the various martensite habit planes for the armour steels E through to I would be as
follows:
Table (6.4): Habit planes of the armour steels E through to I as defined using the AFM results, the work of
Davies and Magee and the crystallographic parameters from the BM model
Illustrated in
Habit plane
Steel E
Steel H
Steel F
Steel G
MS
[°C]
196
210
255
271
Figure 4.25(a)
Figures 4.25(b); 6.2(a)
Figure 4.25(c)
Figures 4.25(d); 6.2(c)
{2 2 5}- twinning in ferrite
Steel I
309
Figures 4.25(e); 6.2(e)
{2 2 5}and {5 7 5} slip in
austenite and twinning in
ferrite
{5 7 5} or{1 1 1}- slip in
austenite and ferrite
Invariant lattice shear
angle [°]
8.19
8.40
8.38
8.48
Total strain
8.47
0.30
0.28
0.29
0.29
0.30
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Chapter 6: Characterisation of the martensitic transformation in armour steels
6.4. Orientation relationship between martensite and retained austenite
The orientation relationship between martensite and retained austenite in the armour steels W
(Ms =130°C), U (Ms =170°C), and H (Ms =210°C), were determined by the electron
diffraction technique. It is concluded in Figure 6.10 that, in the Steel W, the orientation
between the martensite and the retained austenite obeys the Nishiyama-Wasserman
orientation relationship with:
(1
0 0 )α // (1 1 0 )γ
0 1 1 α // 1 1 1 γ
Figure 6.10(a): TEM thin foil bright field of the steel W (Ms = 130°C). Label mark: 500 nm
Figure 6.10(b)
Figure 6.10c
Figure 6.10(b): Selected Area Diffraction Pattern from Figure 6.10(a). Figure 6.10(c): Corresponding indexing
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Chapter 6: Characterisation of the martensitic transformation in armour steels
The dark field images corresponding to the spots
0 1 1 bcc and 2 2 0 fcc are
shown in Figure 6.10(d) and 6.10(e ) respectively.
Figure 6.10(d)
Figure 6.10(e)
Figure 6.10(d): TEM thin foil dark field image corresponding to the spot
0 1 1 bcc showing the
martensitic matrix. Figure 6.10(e): TEM thin foil dark image corresponding to the spot
2 2 0 fcc
showing nodular retained austenite. Label mark: 500 nm
The same orientation relationship was observed in the Steel U, with Ms = 170°C. The typical
TEM thin foil bright image of this steel is shown in Figure 6.11(a).
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Chapter 6: Characterisation of the martensitic transformation in armour steels
Figure 6.11(a): TEM selected area bright field of the steel U. Label mark: 500 nm
The Selected Area Diffraction Pattern and the indexing map of this steel are presented in
Figure 6.11(b) and 6.11(c).
Figure 6.11(b)
Figure 6.11(c)
Figure 6.11(b): Typical SADP of the Steel V, Ms = 145°C. Figure 6.11(c): corresponding indexing map.
It is concluded from this mapping that the Nishiyama-Wasserman orientation between the
parent austenite and the martensite is obeyed in this steel.
(1
0 0 )α // (1 1 0 )γ
0 1 1 α // 1 1 1 γ
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Chapter 6: Characterisation of the martensitic transformation in armour steels
The spacing of the planes that produced the extra spots A, B and C are close to
the lattice parameters of cementite, however the corresponding angles differ by
about 2°. They may be formed by the reflexions from a structure that is very
close to the orthorhombic cementite, possibly an iron carbide formed by
autotempering during the quenching.
Figure 6.11(d)
Figure 6.11(e)
Figure 6.11 (d) and (e): TEM dark field images corresponding to the spots
martensitic matrix and
0 1 1 bcc showing the
2 2 0 fcc revealing the retained austenite along the martensite twinned plates.
Label mark: 500 nm
Formatted
b
In steel H, Ms = 210°C, the SADP presents the orientation relationship
(1
0 0)α // (1 1 2 )γ
0 1 1 α // 1 1 1 γ
which deviates from the Nishiyama-Wasserman by 7°.
In this steel also the spacing of the planes that produced the extra spots A,B,C,D and E are
close to those of cementite and suggest the possibility of autotempering and the formation of
fine carbide particles of a carbide such as Fe2.4C or ε-carbide.
Figure 6.12(a) presents a typical TEM thin foil bright field image of the steel H. The SADP
corresponding to the region near the boundary indicated with an arrow, is shown in Figure
6.12(b) and the indexing map in Figure 6.12(c).
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Chapter 6: Characterisation of the martensitic transformation in armour steels
Figure 6.12(a): TEM selected area bright field of the steel H (Ms = 210°C)
Figure 6.12(b)
Figure 6.12(c)
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Chapter 6: Characterisation of the martensitic transformation in armour steels
The dark field images corresponding to the spots 0 2 0 α and 3 1 1 γ are presented in
Figure 6.12(d) and Figure 6.12(e).
Figure 6.12(d)
Figure 6.12(d): Dark field image from the spot 0
Figure 6.12(e)
2 0 α showing the martensite. Figure 6.12(e) from the
spot 3 1 1 γ showing the retained austenite
The N-W orientation relationship seems to prevail in these martensitic armour steels where
the Ms temperature is lower than 200°C. The orientation relationship deviates from the N-W
when the Ms temperature is higher. Spots suggesting autotempering appear in steels with Ms
temperatures higher than 170°C.
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Chapter 7: Requirements For Advanced Performance Armour Steels
CHAPTER 7. REQUIREMENTS FOR ADVANCED PERFORMANCE ARMOUR
STEELS
7.1 Introduction
The optimisation of the microstructures and mechanical properties of the armour plates in a
quenched and tempered condition has been undertaken with the intention of improving the
ballistic performance of the steels A, B, C and D currently produced and used for military,
civil and security purposes. Standardised ballistic testing of plates of new armour steels
with 6 mm thickness assessed the improved resistance against ballistic impact. The
reliability of the 6 mm armour plates was assessed by the ability of thinner plates ranging
from 4.7 to 5 mm to withstand the direct impact of 5.58 mm rounds fired by a R4 rifle at
zero degree obliquity from a distance of 30m at muzzle velocities ranging between 930 and
1050 m/s, as specified currently for civil and military applications with armour plates
thicker than 8.5 mm. Since armour plates with thickness of 8.5 to 20 mm are currently
being used to obtain the same ballistic performance, this makes the new alloys a significant
improvement in weight reduction. It represents a reduction in weight of the plate used in
manufacturing light vehicles for security and combat purposes from 66.3 kg/m2 to less than
35.1 kg/m2, a possible reduction of almost 50% in weight of the protected areas in these
vehicles. This will reduce fuel consumption and increase the maximum speed attainable in
these vehicles and will also open new global markets for the local steel industry. Thirteen
advanced performance armour plate steels have been tested successfully in the conditions
mentioned above. Through thin foil transmission electron microscopy, scanning electron
microscopy and X-ray diffraction techniques from carefully sectioned samples at and near
the impact areas after ballistic testing, it was confirmed that the success of these new alloys
lies in their ability to undergo Transformation Induced Plasticity or “TRIP” of retained
austenite upon impact together with a transition from twinned plates to slipped lath
martensite that consume a significant part of the kinetic energy of the fired rounds.
Three groups of armour steels were identified by considering together the martensite start
temperature, the volume fraction of retained austenite and the morphology of the
martensite.
7.2.
Group 1: consists of armour steels containing 1 to 6% volume fraction of retained
austenite. Steels of this group have a higher ability to withstand rounds from R4
rifles fired from a distance of less than or equal to 30 metres from the plate. The
martensite start temperatures of these steels range from 130 to 210°C. The
morphology of the martensite formed in this temperature range is twinned plates
containing nodules of retained austenite in the plate interfaces and on grain
boundaries. Thin foil Transmission Electron Microscopy of the regions of the 4.5 to
5.0 mm thick plates of Group 1 deformed upon multiple ballistic impacts reveals the
combination of two operating mechanisms in resisting ballistic perforation. The
kinetic energy of the fired rounds is absorbed in the impacted regions in two ways:
ƒ
ƒ
The transformation of the retained austenite to martensite by the well known
TRransformation-Induced Plasticity or TRIP effect; and
through reaustenitisation subsequent to the heating up of the plate martensite
by entropy trapping inside the so called “adiabatic region” at the centre of
the impacted zone and the formation of new slipped martensite upon being
cooled down by the surrounding material. It needs to be recognized,
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Chapter 7: Requirements For Advanced Performance Armour Steels
however, that the reaustenitised material probably has a higher Ms
temperature than originally as little carbide dissolution may take place under
the dynamic conditions of shock wave propagation
7.3. Group 2: comprises armour steels whose martensite start temperatures are between
210 and 280°C. This Group 2 armour steels has a combination of high strength, high
Charpy-V impact energy at -40°C and a high hardness. The yield strengths of the steels in
this group are higher than 1500 MPa, the ultimate tensile strength higher than 2000 MPa,
the elongations on 50 mm gauge length are higher than 7% at room temperature, the
Charpy-V impact energies of sub-sized specimens is above 13 Joules at -40°C and the
hardness values are higher than 570 BHN.
The combination of high mechanical properties has inspired the design of armour steels in
the past. The current martensitic armour steels such as steels A, B, C and D belong to
Group 2. The minimum thickness of the plates of these armour steels required to withstand
the R4 rifles fired in the same conditions than above, is 8.5 mm. The volume fraction of
retained austenite in these plates is less than 1% and the martensite formation is generally
accompanied by slip of dislocations. Some regions of the martensite contain twins on a
background of laths. The coexistence of the laths and the twinned regions within the
martensite was clearly observed in the three-dimensional surface relief AFM images and
was also observed by thin foil transmission electron microscopy. The retained austenite in
these steels is present as thin films along the lath interfaces and does not appear to undergo
any TRIP. It remains untransformed upon ballistic impact, contrary to the nodular austenite
located on plate interfaces and grain boundaries of the Group 1 armour steels.
7.4 Group 3: comprises armour steels whose martensite start temperatures are higher than
280°C. They contain less than 1% retained austenite and have the highest Charpy-V impact
energy at -40°C and % elongation at room temperature. Their yield and ultimate tensile
strength are intermediate between those of Group 1, the lowest, and those of Group 2, the
highest. Armour steels of Group 3 are very sensitive to auto-tempering upon quenching.
7.5. General requirements of high performance armour steels
The location and the morphology of the retained austenite in all of these steels seem to be a
function of the martensite start temperature. The TRansformation Induced Plasticity effect
appears to be more effective when the martensite is formed at lower temperatures rather
than at higher temperatures. Furthermore, nodular retained austenite seems to transform
more readily by the strain-induced mechanism. Further investigation is needed for a better
understanding of the conditions that determine the location and the morphology of the
retained austenite in these martensitic armour steels.
The mechanical properties and ballistic performance of martensitic armour steels are
strongly dependent on the chemical composition and the heat treatment cycle. The tensile
properties are difficult to measure in untempered conditions for the armour steels of Groups
1 and 2 because of their brittle behaviour. On the other hand the martensitic armour steels
of Group 3 are ductile from auto-tempering during quenching and their tensile properties
are measurable in the as-quenched condition. The steels of Group 3 also have a high
Charpy-V impact energy of sub-sized specimens in the untempered condition. The tensile
properties as well as their impact energy at -40°C of all of these armour steels are improved
by tempering between 200°C and 250°C for times less than 1 hour. Tempering above
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Chapter 7: Requirements For Advanced Performance Armour Steels
300°C for the same time leads to a reduced tensile strength due to the precipitation of
coarse cementite particles in the martensitic matrix.
Thin foil transmission electron microscopy of the tempered steels confirmed the wellknown effect of Silicon in retarding the decomposition of the supersaturated martensite and
the formation of cementite. Martensitic armour steels containing 0.8 to 1.2%Si may resist
over-tempering at 300 to 350°C without forming coarse cementite that is detrimental to the
mechanical properties as well as to the resistance against ballistic perforation. Thin
carbides start precipitating along the twinned plate interfaces upon tempering of these
armour steels, which is in agreement with the results published by Kelly [100], who has
confirmed that the cementite thus formed obeys the Bagaryaski orientation relationship
with the ferrite.
7.6. Design philosophy of high performance armour steels
From the comparison between mechanical properties and ballistic performance of the 13
steels tested in the conditions described in Chapters 4 and 5, it appears that the highest
ballistic performance is reached by heat treatment conditions that are contrary to those
required for the combination of the highest mechanical properties for a given chemical
composition of the steel. This observation is in agreement with the published results on the
ballistic performance of armour steels in general and, thereby, constitutes the basis for the
development of advanced performance armour steels. This observation is, therefore, in
contradiction to the current design philosophy for armour steels used hitherto. Neither the
high tensile properties nor the high Brinell hardness number of the steel are ideal criteria
within themselves in predicting the ballistic performance of armour plates or the dynamic
resistance of structures to impact loading [6,7, 12, 13, 14, 15, 16, 17, 18]. Instead, the ratio
of the yield strength to the ultimate tensile strength of the material and the volume fraction
of retained austenite contained in the martensite are an improved indication of the steel’s
ability to resist localised yielding that favours ballistic perforation. The steels whose
YS/UTS ratio is lower than 0.6 and contain 1% to 7% of retained austenite in twinned
martensite, appear to present a low tendency to localised yielding upon high velocity
impact loading.
This behaviour may be quantified through a function that includes the diameters of the
impact affected zones around the incidence point after ballistic testing. However, it is
difficult to establish a direct relationship between mechanical properties and ballistic
performance of armour steels. The differences between mechanical properties and ballistic
performance for a given armour steel and the reason why an armour steel plate performs
ballistically better than another, should rather be explained in terms of their microstructures
as well as their response to high velocity dynamic loading. Indeed, published data have
reported measured dynamic tensile stresses in steel plates subjected to ballistic impacts of
as high as 28 GPa [16,17,18]. The dynamic measurable maximum stress is, therefore, 12
times higher than the ultimate tensile strength of current high strength steels. This fact
renders the current criteria that are largely based on the absolute values of the yield or the
ultimate tensile strength in predicting the ballistic performances of armour steels,
inappropriate.
In this study the resistance to localised yielding by the ballistic impact has been quantified
by the diameters of three concentric zones formed around the incidence point. It appears
that the diameter of the inner zone 1 is almost equal for all the steels and is slightly larger
than the fired round’s diameter. On the other hand the diameters of the outer zone 3 are
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Chapter 7: Requirements For Advanced Performance Armour Steels
larger for those steels whose volume fraction of retained austenite is higher and their yield
strength to ultimate strength ratios are lower. The relationship between the volume fraction
of retained austenite in the martensitic steel, the diameter of the outer zone 3 and the
thickness of the plate may then be used in defining a criterion for its ballistic performance.
The yield strength to ultimate tensile strength ratio (YS/UTS), which also appears to be a
function of the volume fraction of retained austenite in the martensitic steel through the
TRIP effect, may be introduced as a dependent variable in this relationship. The uncertainty
in predicting the ballistic performance of the steels considered in this study using the
Ballistic Performance Index (BPI) proposed by Srivathsa and Ramakrishnan [6,7] may be
explained by the lack of a relationship between the independent variable, i.e. the volume
fractions of the phases present in the microstructure and the dependent variable, expressed
as the yield strength to ultimate tensile strength ratio. The Ballistic Parameter BP has,
therefore, been defined in Chapter 5 to account for the effect of the volume fraction of
retained austenite and the thickness of the steel plates on the diameters of the outer zone 3
of the ballistic impact-affected regions, which indicate the resistance to localised yielding
due to impact loading upon high velocity ballistic impact. It has been observed in this study
that the combination of a high austenitisation temperature ranging between 870 and 950°C
together with a low tempering temperature ranging between 170 and 200°C, is favourable
for a low YS/UTS ratio and this provides a high resistance to localised yielding of the
plates in thicknesses smaller than 5 mm. When the Silicon content of the armour steel is
high the plates may be tempered at 350°C and still have a high ballistic performance.
Contrary to this design philosophy, a low austenitisation temperature of 800 to 850°C and a
high tempering temperature of 250 to 300°C, generally improve all the tensile properties
and the sub-zero impact energy but reduce the steel’s resistance to ballistic perforation.
7.7 Localised microstructural features of impact loading
Shock induced transformations and transitions occur respectively inside zones 1 and 3 of
the impact affected regions. Quasi-adiabatic conditions prevailing inside zone 1 are
favourable for the conversion of kinetic energy into heat. The localised temperatures in
those zones are high enough to induce melting and welding of the fired round’s material
onto the steel plates, dynamic reaustenitisation of the twinned plate martensite and
subsequent formation of slipped lath martensite together with auto-tempering. The new lath
martensite forms from austenite with likely a higher Ms than originally as it is unlikely that
carbides will fully dissolve during the brief and dynamic temperature rise. The Vickers
micro-hardness profiles across the sections of the impacted regions show global hardening
of these regions but with relative softening of zone 1 compared to zones 2 and 3. Inside
zone 3 many dislocations are produced. Thin foil transmission electron microscopy of zone
3 shows dislocation pile-ups at twinned plate interfaces, demonstrating the high resistance
of the twin interface to shear by slip of dislocations. New martensite is formed by a straininduced mechanism of the retained austenite, i.e. the TRIP effect. No retained austenite was
detected by X-ray diffraction of the impact-affected regions after ballistic testing. Rather,
thin foil transmission electron microscopy of the same regions revealed new untwinned
martensite that was formed by transformation of nodular retained austenite located in plate
interfaces.
Scanning electron microscopy of the three-dimensional cracks revealed the character of
dynamic cracking with microscopic cracks propagating along the grain boundaries. This
observation may be a consequence of the high resistance provided by the twinned plate
interfaces against the movement of dislocations throughout the martensite crystals and
throughout the grains. Former parent austenite grain boundaries are then less resistant for
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Chapter 7: Requirements For Advanced Performance Armour Steels
the propagation of microcracks induced by the transmission of that part of the kinetic
energy of the fired round that is converted into potential energy of the compressive and
tensile stress waves crossing the plates. From the simulation using an adaptation of the
stress distribution model in space and time upon impact loading proposed by Hopkinson
and modified by Taylor [5] and taking into account the likely true fracture stress as
reported in the literature, the fracture of the untempered plates is predicted to occur 11 to
20 cm away from the incidence point for an incidence velocity of the fired rounds between
930 and 950 m/s. Tensile stresses near to 12 GPa may be developed within the armour plate
after three or four reflections of the tensile stress wave from the edges of the plates, which
were 30 cm long and 20 cm wide. The profiles of the shear bands across the fractured
sections of the untempered plates suggested a vibratory dynamic response of the plates to
the ballistic impact loadings that excited some natural frequencies within the plates
according to their harmonics. The sizing of the plates to be used should then consider a
lowest natural frequency of the plate structure larger than the highest firing frequency of
the R4 to avoid synchronisation. Smaller and thinner plates may be the remedy for
mechanical resonant failures.
7.8 Martensite characterisation in these advanced performance armour steels
The martensite was characterised using the lattice parameters of the martensite and of the
retained austenite as measured by X-ray diffraction, as inputs in predicting the
crystallographic features by the Bowles and Mackenzie model of the Phenomenological
crystallographic Theory of the Martensitic Transformation. This was found to be in good
agreement with the predictions of the existence of three plateaux distinguishing the
martensite formed by an internal twinning mechanism, {2 2 5}γ butterfly martensite
formed by a slip mechanism in the austenite and {1 1 1}γ lath martensite formed by a
slip mechanism in both the austenite and the ferrite. The three formation mechanisms of the
martensite were observed by qualitative AFM analysis of the surface relief accompanying
the martensite formation.
•
Surface relief of armour steels in Group 2 whose martensite start temperatures
ranged from 210 to 280°C, were irregular N-shaped which revealed no character of
the IPS. The three-dimensional AFM images and the thin foil TEM of these steels
showed the coexistence of twinned plates and dislocated lath martensite.
Thermodynamic data reported by Morozov et al [21] suggest that this transition in
morphology is likely to occur between 232 and 284°C for Fe-C-X systems.
•
The surface relief accompanying the formation of martensite at temperature above
300°C in Group 3, indicated high plastic strain accommodation. However, relief
deterioration is also possible in the case of this relatively high Ms temperature
through thermal smoothing and oxidation.
•
The Bowles and Mackenzie model of the PTMT predicts a crystallographic
orientation between the martensite and the austenite close to the Kurdjumov-Sachs
orientation relationship in the armour steels of Group 1.
For the other two groups the PTMT predicts a larger deviation from the Kurdjumov-Sachs
orientation relationship, suggesting the existence of an influence from the relative
crystallographic orientation between the martensite and austenite crystals within the plates
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Chapter 7: Requirements For Advanced Performance Armour Steels
or laths on the ability that grain boundaries have in resisting spallation and crack
propagation by dynamic loading. Indeed, backscattered scanning electron microscopy in
Figures 6.2 and 6.3 show big differences between the plates and laths formed within the
grains that may have some influence on the microscopic geometric configuration of the
grain boundaries. It is well known from the theory of formation and growth of martensite
that the growth of plates and laths is arrested at parent austenite grain boundaries. The
microscopic configuration of the grain boundaries will then be the result or consequence of
the formation history of the martensite inside the grains.
An effective control of the state of the grain boundaries and of the subsequent ballistic
performance or of the mechanical properties, depending on the application, may then be
achieved by controlling what is happening inside the grains through appropriate design of
the chemical composition of the armour steel and by applying the relevant heat treatment.
7.9. Proposed revised specification for advanced performance armour steels
The specifications for the advanced performance plate armour steels may be revised as
follows:
•
The optimum chemical composition should range between:
Element
Range in
weight
percentage
%C
0.38 0.43
%Mn
0.4 2.0
%Si
0.4 1.2
%Mo
0.4 0.6
%Cr
0.4 1.5
%Ni
1.0 4.5
%Cu
<0.2
%P
<0.005
%S
<0.005
•
The martensite start temperature of the steel should be lower than 210°C;
•
The volume fraction of retained austenite in plate martensite should be higher than
1%;
•
The heat treatment should consist of austenitisation at temperatures between 850
and 950°C for less than 1 hour, followed by water quenching to room temperature;
•
Tempering should be undertaken at temperatures ranging from 150 to 180°C for 20
to 60 minutes when the Silicon content is lower than 0.6%. The tempering
temperature may be raised to 300°C when the Silicon content is higher than 1%;
•
The design methodology should be based on the YS/UTS ratio which should
preferably be below 0.6 as well as on a value of the Ballistic Parameter of 0.018 to
0.060 to predict the ballistic performance;
•
Small size and thin armour plates should be preferred to reduce the risk of
mechanical resonance of the armour plate with the firing frequency;
•
Manganese sulphide and coarse carbides are detrimental to ballistic performance as
well as to mechanical properties of the tempered plates; and
•
Under these conditions armour steels with a Brinell hardness of 475 BHN and a
Charpy impact energy at -40°C as low as 10 Joules, are acceptable.
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Chapter 7: Requirements For Advanced Performance Armour Steels
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Chapter 8: Conclusion
CHAPTER 8: CONCLUSION
From this experimental and theoretical study, it is concluded that:
ƒ There is a constitutional/morphological dependence of the ballistic
performance of martensitic armour steels;
ƒ A high hardness or strength are not accurate indicators for good ballistic
performance;
ƒ The lack of correlation between high strength and high ballistic performance
may be explained in terms of the effect of retained austenite on the YS/UTS,
which determines the resistance to localised yielding;
ƒ The Ballistic Parameter BP which takes into account the volume fraction of
retained austenite RA and the thickness of the armour plate, gives a better
prediction of the ballistic performance;
ƒ The combination of twinned martensite and nodular retained austenite
appears to be favourable to a good ballistic impact resistance;
ƒ Reaustenitisation of the twinned plate martensite in the centre of the impact
region absorbs a significant part of the kinetic energy of the fired round;
ƒ Twinned plate interfaces act as barriers for dislocation movement upon
ballistic impact. This produces a high hardness in zone 3 of the ballistic
affected region;
ƒ Lath martensite with films of RA have poor ballistic resistance;
ƒ Coarse carbides and needlelike manganese sulphide are also detrimental;
ƒ The impact loading induces transient vibration within the steel plates. The
mechanical design of the structure should optimise their size to avoid
resonance with the frequency of the firing rifle.
Further work
It was observed in this study that the nodular retained austenite in plate interfaces or on
grain boundaries is more susceptible to strain induced transformation than RA with a film
morphology in lath interfaces. The stabilisation of the austenite upon quenching of the
armour steels and the reason why the retained austenite is nodular or film shaped were not
analysed in this study. Further investigation on the conditions of formation, the location
and the morphology of the retained austenite in the martensitic steel armour plates will be
necessary for further improvement of the ballistic performance and reduction of the plate
thickness by exploiting the TRIP effect in these steels.
Analyse the following:
Effect of increased Mo, C and Si
Effect of Cobalt
Ballistic limit in terms of %RA and thickness of the plates
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References
REFERENCES
1. ISCOR, Technical notes, 2003
2. SP WOLSKY and AW CZANDERNA, Methods and Phenomena 5, Ballistic Materials
and Penetration Mechanics, Elsevier Scientific Publishing Company, 1982
3. von F. Wever, W. Peter; Atlas zur Warmebehandlung der Stahle. Hrsg. Vom MaxPlanck-Institut fur Eisenforschung in Zusammenarbeit mit dem Werkstoffausschuss
des Vereins Deutscher Eisenhuttenleute; Dusseldorf 1954-1958.
4. Isao Kozasu. Metallurgical Framework of Direct-Quenching of steel; The Minerals,
Metals & Materials Society; 1997
5. Jonas A ZUKAS, T NICHOLAS, Halloock F SWIFT, Longin B GRESZCZUK, Donald
R CRRAN, Impact Dynamics, John Wiley and Sons editors,1982
6.
B. Srivathsa and N Ramakrishnan, Ballistic performance maps for thick metallic
armour, International Journal of Impact Engineering, Volume 24, Issue 2, 2000.
7. B. Srivathsa and N Ramakrishnan, A ballistic performance index for thick metallic
armour, Computer Simulation Modelling in Engineering, 3(1998), pp. 33-40
8. N Ramakrishnan, Ballistic test procedures for armour materials, Technical Report
DMRL, Hyderabad, India, 1986
9. Young-Wong Lee and Tomasz Wierbicki,Fracture prediction of thin plates under
localized impulsive loadind. Part II: discing and petalling, International Journal of
Impact Engineering, Volume 31, Issue 10, 2005 pp. 1277-1308
10. AG Atkins and YW Mai, Crack and craze nucleation In: elastic and
Ellis Horwood, Chichester (1985), p. 369-431.
plastic fracture,
11. AK Takuda, K. Mori, N Takakura and K Yamaguchi, Finite element analysis of limit
strains in biaxial stretching of sheet metals allowing for ductile fracture, Int J Mech
Sci 42 (2000), pp. 785-798
12. T Borvik, M Langseth, OS Hopperstad and KA Malo, Ballistic penetration of steel
plates, International Journal of Impact Engineering 22,(1999), pp. 855-886.
13. T Borvik, OS Hopperstad,T Berstad and M Langseth, A computational model of
viscoplasticicty and ductile damage for impact and penetration, Eur J Mech A/Solids
20(2001), pp 685-712
14. T Borvik, OS Hopperstad,T Berstad and M Langseth, On the influence of stress
triaxiality and strain rate on the behaviour of a structural steel. Part II. Numerical
study, Eur J Mech A/Solids 22(2003), pp. 15-32
202
University of Pretoria etd, Kasonde M (2006)
References
15. S Dey, T Borvik, OS Hopperstad, JR Leinum and M Langseth, The effect of target
strength on the perforation of steel plates using three different projectile nose shapes,
Engineering Fracture Mechanics, Volume 70, Issue 18, December 2003, pp. 25432558
16. B.I. Hammond and W.G. Proud, Does the pressure-induced alpha-epsilon transition
occur for all low-alloy steels, The Royal Society, 2004
17. Yu I Mescheryakov, A K Divakov and N I Zhigacheva, Shock induced structural
transitions and dynamic strength of solids, International Journal of Solids and
Structures, Volume 41, Issue 9-10, May 2004
18. Z Rosenberg and E Dekel, On the role of material properties in the terminal ballistic of
long rods, RAFAEL, Ballistic Center, Haifa, Israel, 2004
19. Fisher JC, Trans. AIME, 1949, 185, 688
20. T.Y. Hsu (Xu Zuyao), J. Mater. Sci. 20, 23 (1985)
21. Yiwen Mou and H.I. Aaronson, The carbon-carbon interaction energy in alpha Fe-C
alloys, Acta Metallurgica, Volume 37 No. 3 pp. 737-765, 1989
22. G J. Shiflet, J.R. Bradley and H.I. Aaronson, Metall. Trans. 9A, 999, 1978
23. C. Zener, Trans. Am. Inst. Min. Engrs 203, 619(1955)
24. J Wang, PJ van der WOLK, S van der ZWAAG, Metals Trans JIM: 41 (2000) p. 761
25. Pickering FB, Physical Metallurgy and the Design of Steels, London, Applied Science
Publication, 1978
26. M. Tanino, C. . Liu, A. Tsuchiya, and T. Matsuo; Effect of C, N, Mn and Mo on the
Ms and Md temperatures in High Purity Fe – 18% Cr – 10% Ni stainless steels; The
Minerals, Metals and Materials Society, 1977
27. P Payson and C.H. Savage, Trans. ASM33 (1944), pp. 261-281
28. R.A. Grange and H.M. Stewart, Trans. AIME 167 (1945) pp. 467-494
29. KW Andrews, JISI 203 (1965), pp. 721-727
30. T Sourmail and C. Garcia-Mateo, Critical assessment of models for predicting the MS
temperature of steels, Computational Materials Science, Volume 34, Issue 4,
December 2005
31. Hayzelden et al, The martensite transformation in Fe-Ni-C alloys, Acta Metallurgica,
Vol. 34, No 2, pp. 233-242, 1986
32. Ueda M, Yasuda H Y, Umakoshi Y, Controlling factor for the nucleation of martensite
at grain boundary in Fe-Ni bicrystals, Acta Materialia 51 (2003) 1007-1017
203
University of Pretoria etd, Kasonde M (2006)
References
33. Eshelby J, Proc R Soc 1957; A241:376
34. Christian J., Acta Metallurgica 1958; 6:377
35. Borgenstam A and Hillert M, Driving Force for fcc → bcc martensite in Fe-X alloys,
Acta Metallurgica, Volume 45, No 5, PP. 2079-2091, 1997.
36. Nishiyama Z, Martensitic Transformation, Materials Science and Technology,
Academic Press, New York, 1978
37. Johnsson, CH, Arch Eisen., 1937, 11, 241
38. Zener C, Trans. AIME, 1949, 1167, 550
39. Kaufman L. and Hillert M., in Martensite – A Tribute to Morris Cohen, ed. Oslon and
WS OWEN. ASM International, Materials Park, Ohio, 1992
40. Koistinen DP, Marburger RE, Acta Metallurgica 1959; 7; 59
41. Magee CL. The nucleation of martensite. Phase transformations. Metals Park, OH:
American Society of Metals; 1970. p. 115
42. Fisher JC, Hollomon JH, Turnbull D, AIME Trans 1949; 185,:69
43. SMC van Bohemen, J Sietsma, MJM Hermans, IM Richardson, Kinetics of the
martensitic transformation in low-alloy steel studied by means of acoustic emission,
Acta Materialia 51 (2003) 4183-4196
44. Christian, J.W. Martensite, A tribute to Morris Cohen, (G.B Olsen and W.S. Owen.
Eds.), ASM International, 1992, p103.
45. Christian, J.W. Theory of Transformations in Metals and Alloys, Pergamon, Oxford,
1965, p.869
46. Kennon, N.F. and Dunne P. Druce. Acta Met., 1982, 30, p.429
47. Xiaoping Lin, Y. Zhang, N. Gu and Z Meng, Crystallographic analysis of {225}
martensite in Fe-Cr-C alloy, Hebei University of Technology, Tiajin, China, 2003
48. Tadaki and Shimizu. Scripta Met., 1971, 9, p.771
49. Dunne P. Druce and N.F.Kennon, Materials Science Forum Vols. 189-190(1995) pp.
273-278
50. Morito, H. Tanaka, R. Konishi, T. Furuhara and T. Maki , The morphology and
crystallography of lath martensite in Fe-C alloys, Acta Materialia 51 (2003) 19781999.
204
University of Pretoria etd, Kasonde M (2006)
References
51. George Krauss, Martensite in steel: strength and structure, Materials science and
Engineering A 273 – 275 (1999) 40-57
52. J.M. Marder, A.R. Marder, Trans. ASM 62 (1969) 1
53. T. Maki, K. Tsuzaki, I. Tamura, Trans. Iron Steel Inst. Jpn. 20 (1986) 207
54. P.M. Kelly, A. Jostsons, R.G. Blake, Acta Metall. Mater. 38 (1990) 1075
55. Dongyu Liu, Bingzhe Bai, Hongsheng Fang, Wenzheng Zhang, Jailing Gu, Kaidi
Chang, Effect of tempering temperature and carbide free bainite on the mechanical
characteristics of a high strength low alloy steel, Materials Science and Engineering
A, Volume 371, Issues 1-2, 25 April 2004, p. 40-44
56. T. Inoue, S. Matsuda, Y. Okamura, K. Aoki, Trans Jpn Inst. Metals 11 (1970) 36.
57. S. Matsuda, T. Inoue, H. Mimura, Y. Okamura, Trans. Iron Steel Inst. Jpn. 12 (1972)
325
58. G.B. Olson, in: G. Krauss, Deformation, Processing and Structure, ASM, Materials
Park, OH, 1984, p. 391
59. Patrick M. Kelly, Martensite Crystallography – the Apparent controversy between the
Infinitesimal Deformation Approach and the Phenomenological Theory of
Martensitic Transformations; Metallurgical and Materials Transactions A; Volume
34A; September 2003 – 1783
60. R.H. Aborn, Trans. ASM 48 (1950) 51
61. C.S. Roberts, Trans. TMS-AIME 197 (1953) 203
62. L. Chang, S.J. Barnard, G.D.W. Smith, in: G. Krauss, P.E. Repas.
Fundamentals of
aging and Tempering in Bainitic and Martensitic Steel Products, ISS-AIME,
Warrendale, PA, 1992, p. 19
63. G. Krauss and A. R. Marder, Met. Trans., 2, 2243-2257 (1971)
64. J. McMahon and G. Thomas, in Proc. Third Int. Conf. on Strength of Metals and
Alloys, The University of Cambridge (UK), 1973, PP. 180-184
65. Daozhi Liu and Druce Dunne.
Interfacial Structure of Twinned Martensite in Shape-Memory Alloys
Materials Science Forum Vols. 394-395 (2002) pp. 201-204
2002 Trans Tech Publications, Switzerland
66. Liu Cheng, N.M. van der Pers, A BöTTGER, Th. H. de Keijser and E.J. Mittemeijer,
Lattice Changes of Iron-carbon martensite on aging at Room-Temperature, Delft
University of Technology, The Netherlands, 1990
67. L.I. Lyssak and O Andrushchik, Fiz. Metal. Metalloved, 28(1969), 348
205
University of Pretoria etd, Kasonde M (2006)
References
68. S. Kajiwara and T. Kikuchi, Acta Metall. Mater. 39(1991) 1123
69. S Uehara, S Kajiwara, and T Kikuchi, Origin of abnormally large tetragonality of
Martensite in High Carbon Iron alloys containing Aluminium, Materials
Transactions, JIM, Volume 33, No 3, (1992), pp. 220 to 228.
70. M. Bowles and C. M. Wayman, Bain Strain, Lattice Correspondences, and Rotations
Related to Martensitic Transformations, Metallurgical Transactions, Volume 3, May
1972
71. N. Gu, X. Song, J. Zhang, F. Yin and R. Wang, Effects of Self-Accommodation and
Plastic Accommodation in Martensitic Transformations and morphology of
Martensites, Metallurgical and Materials Transactions A, volume 26A, August 1995.
72. STEEL. A Handbook for Materials Research and Engineering. Volume 1:
Fundamentals, Verein Deutscher Eisenhuttenleute, Dusseldorf 1992
73. Waldo Sumpf, Lecture notes on Phase transformations in Metals and their Alloys,
2003, University of Pretoria
74. S.D. Antolovich, R.O. Ritchie, W.W. Gerberich, MECHANICAL Properties and
Phase Transformations in Engineering Materials, Committees of the Metallurgical
Society, TMS Annual Meeting in New Orleans, Louisiana,, 1986
Article: W.M. Garrison, Jr.; The micromechanisms of Ductile Fracture and the
Design of Ultra High Strength Steels
75. Badeshia HKDH. Bainite in steels. London: The Institute of Materials, 2001
76. R.E. Schramm and R.P. Reed, Stacking fault energies of Austenitic Stainless Steels;
Metall. Trans. A, 6A(1975), 1345-1351
77. Bhadeshia HKDH. Carbon content of retained austenite in quenched steels. Metal
Science 1983; 17 (March): 151-2
78. Woie-Shyan Lee and Tzay-Tian Su, Mechanical properties and microstructural features
of AISI 4340 high-strength alloy steel under quenched and tempered conditions,
Journal of Materials Processing Technology, Volume 87, Issues 1-3, 15 March 1999,
Pages 198-206.
79. P.K. Ray, R.I. Ganguly and A.K. Panda, OPTIMIZATION of Mechanical Properties of
an HSLA-100 Steel through control of Heat Treatment variables; Materials Science and
Engineering A, Volume 346, Issues 1-2, 15 April 2003, Pages 122-131
80. J. Speer, DK Matlock, BC De Cooman, JG Schorth, Carbon partitioning into austenite
after martensite transformation, Acta Materialia 51 (2003) 2611-2622
81. Hillert M, Purdy GR. On the misuse of the term bainite. Scripta Materialia 2000; 43(9);
831-3
206
University of Pretoria etd, Kasonde M (2006)
References
82. Kozasu, I., T. Shimizu, K. Tsukada: Trans. Iron Steel Institut Japan 12(1972) S. 305/13
83. Magonon, O.L.; Metallurg. Trans. 7A (1976) S. 1389/400
84. Edwards, R.H., N.F. Kennon: Metallurg. Trans. 9A(1978) S. 1801/09
85.
Pietikainen, Considerations about tempered martensite embitterment, Materials
Science and Engineering A, 1999, pages 466-470
86. A. Nakashima and J.F. Libsch, Trans. ASM 53 (1961), p. 753]
87. F. Zia-Ebrahimi and G. Krauss. Acta metal. 32 (1984), p. 1767
88. Bimal K. Jha and Nirmalendu S. Mishra, Materials science and
(1999 42-55)
engineering A 263
89. R.C. Thomson and M.K. Miller ,Carbide precipitation in martensite during early stages
of tempering Cr- and Mo-containing low alloy steels, Acta materialia, Vol 46, pp.
2203-2213, 1998,
90. A.J. McEvily, R.C. Ku, T.L. Johnston, Trans. TMS-AIME 236 (1966) 108
91. R.H. Richman, Trans. TMS-AIME 227 (1963) 159
92. G. Krauss, ISIJ International 35 (1995) 349
93. Gu Baozhu, J.M.B. Losz, G. Krauss, Proceedings ICOMAT, The Japan Institute of
Metals, 1986, p. 367
94. Enders A. Robinson, Least squares regression analysis in terms of
Goose Pond Press, Texas, 1981
Linear algebra,
95. J Speer, D.K. Matlock, B.C. De Cooman, J.G. Schroth; Carbon partitioning into
austenite after martensite transformation. Acta Materialia 51 (2003) 2611-2622.
96. Lin Xiaoping, Gu Nanju, Zhang Yong, Meng Zhaowei and Ma Xiaoli, AFM
quantitative analysis and determination of shear angle of {2 5 9} f martensite surface
relief, Progress in Natural Science, March 2002.
97. Yu D.G. et al, Bainite transformation theory, Shangai Jiaotong University Press, 1998
98. Zhang X.M., Gauthier E. and Simon A., Martensite morphology and habit plane
transitions during tensile tests for Fe-Ni-C alloys, Acta Metallurgica, Volume 37, N0. 2,
1989.
99. Davies R.G. and Magee C.L., Metallurgical Transactions, 2. 1939 (1971)
100. Kelly PM, Acta Metallurgica; 1965; 13; 635
207
University of Pretoria etd, Kasonde M (2006)
References
101. Waldo Stumpf, Lecture notes on Mechanical Metallurgy, 2003, University of Pretoria
102. M.S. Wechsler , D.S. Lieberman and T.A. Read, Trans AIME 197, 1503 (1953)
103. J.S. Bowles and J.K. Mackenzie, Acta Metall. 2, 129, 224 (1954)
208
University of Pretoria etd, Kasonde M (2006)
APPENDIX 2
A2: Fitting parameters and equations of the mechanical property surfaces
A2.1:Steel F
Table A2.1(a): The fitting parameters for the YS/UTS ratio of steel F, in Equation (4.3)
Fitting parameters in
Equation (4.3)
Normalised
austenitisation
Austenitisation temperature
temperature
T
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
0.0365
0.0298
0.0134
0.0148
b
c
0.0495 0.5224
0.0477 0.5094
0.0522 0.496
0.0501 0.4786
Correlation
coefficient
0.992
0.979
0.975
0.982
Table A2.1(b) The fitting parameters for the YS/UTS ratio of steel F, in Equation (4.4)
a
b
c
Correlation
Fitting parameters in (4.4)
coefficients
A
B
C
D
0.0155 0.0046 -0.0263 0.0211
1
-0.0073 -0.0002 0.0076
0.05
1
-0.002 -0.0025 -0.0199 0.503
1
Table A2.1(c): Fitting parameters for the ultimate tensile strength of steel F in Equation (4.3)
Fitting parameters in Equation
(4.3)
Normalised
Austenitisation austenitisation
temperature temperature
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
117.6
202.71
122.3
13.969
Correlation
coefficients
b
c
d
-390.52 33.642 2163.8
0.97
-452.26 -230.58 2348.8
0.939
-316.52 -316.87 2365.8
0.996
-195.43 -74.625 2029
0.978
Table A2.1(d): Fitting parameters for the tensile strength of steel F in Equation (4.4)
a
b
c
d
Fitting
parameters
in
Correlation
Equation (4.4)
coefficients
A B
C
D
0 -108.81 -58.695 174.6
0.95
0 102.84 108.15 -395.82
0.94
0 284.89 -61.664 -305.38
0.99
0 -293.51 -58.11 2389.9
0.98
209
University of Pretoria etd, Kasonde M (2006)
Table A2.1(e): Fitting parameters for the Charpy impact energy of steel F in Equation (4.3)
Fitting parameters in
Equation (4.3)
Normalised
austenitisation
Austenitisation temperature
temperature
T
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
-1.6946
-0.2232
0.3044
0.3809
b
2.3901
1.2026
0.3166
0.5326
c
5.3945
2.9669
2.3285
1.4276
Correlation
coefficients
d
10.33
0.995
6.2403
0.9946
8.6423
0.97
7.5503
0.906
Table A2.1(f): Fitting parameters for the Charpy impact energy of steel F in Equation (4.4)
a
b
c
d
Fitting parameters in Equation
Correlation
(4.4)
coefficients
A
B
C
D
0.2771 -0.7846 0.7606 0.1278
1
0.4503 0.7895 -1.379 0.6719
1
-1.1541 0.8588 -0.8294 2.5523
1
-5.617 1.68682 4.2271 7.2539
A2. Eq1. Equations for the mechanical properties of steel F
(
)
(
)
YS
3
2
3
2
= 0.0155Tan + 0.0046Tan − 0.0263Tan + 0.0211 × Ttn + − 0.0073Tan − 0.0002Tan + 0.0076Tan + 0.05 ×
UTS
3
2
Ttn + − 0.002Tan − 0.0025Tan − 0.0199Tan + 0.503
(
)
(A2.Eq1(a))
(
)
(
+ (− 293.51T
)
UTS = − 108.81Tan − 58.695Tan + 174.6Tan × Ttn + 102.84Tan + 108.15Tan − 395.82 × Ttn
(
2
3
)
+ 284.86Tan − 61.664Tan − 305.38 × Ttn
2
2
2
an
− 58.11Tan + 2389.9
)
2
(A2. Eq1(b))
(
) (
)
(
+ 2.5523)×T + (− 5.617T
)
CIE − 400 C = 0.2771Tan − 0.7846Tan + 0.7606Tan + 0.1278 ×Ttn + 0.4503Tan + 0.7895Tan −1.379Tan + 0.6419
(
3
2
×Ttn + −1.1541Tan + 0.8588Tan − 0.8294Tan
3
2
3
tn
an
3
3
2
)
+1.68682Tan + 4.2271Tan + 7.2539
2
(A2.Eq1©)
210
University of Pretoria etd, Kasonde M (2006)
A2.2: Steel G
Table A2.2(a): The fitting parameters for the yield to tensile strength ratio of steel G in Equation
(4.3)
Fitting parameters in
Equation (4.3)
Normalised
Austenitisation austenitisation
temperature temperature
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
0.0287
0.0273
0.0271
0.0069
b
0.0442
0.0621
0.0592
0.0739
Correlation
coefficients
c
0.6758
0.99
0.6844
0.81
0.5196
0.9881
0.5166
0.9249
Table A2.2(b): Fitting parameters for the objective function for Steel G
Fitting parameters in Equation
Correlation
(4.4)
coefficients
A
B
C
D
1
a -0.0119 -0.0106 0.001 0.0284
1
b 0.0216 -0.0018 -0.0067 0.0609
1
c 0.1885 -0.0065 -0.2681 0.6027
Table A2.2(c): Fitting parameters for the tensile strength of steel G in Equation (4.3)
Normalised
austenitisation
Austenitisation temperature
temperature
T
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
Fitting parameters in (4.3)
a
265.22
122.37
38.471
123.55
b
-670.08
-308.53
-166.74
-289.29
c
-92.36
-261.59
-245.45
-282.04
Correlation
coefficients
d
2177.8
0.963
2110.8
0.962
2090
0.965
2036.6
0.986
Table A2.2(d): Fitting parameters for the tensile strength of steel G in Equation (4.4)
a
b
c
d
Fitting parameters in Equation
Correlation
(4.4)
coefficients
A
B
C
D
0
128.21 -76.336 66.175
0.98
0
-272.31 192.62 -207.38
0.999
-133.93 74.61 39.091 -261.81
1
-44.325 7.65 -26.275 2099.6
1
211
University of Pretoria etd, Kasonde M (2006)
Table A2.2(e): Fitting parameters for the Charpy impact energy of the sub-sized specimens of
steel G
Fitting parameters in Equation
(4.3)
Normalised
Austenitisation austenitisation
temperature temperature
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
1.4866
0.1438
0.7649
-0.275
b
-4.2306
-2.0506
-2.7295
-1.0173
c
2.6199
3.9178
3.1999
3.5676
Correlation
coefficients
d
18.178
0.9968
15.008
0.995
16.611
0.986
14.176
0.993
Table A2.2(f): Fitting parameters for the Charpy impact energy of steel G in Equation (4.4)
a
b
c
d
Fitting parameters in Equation
Correlation
(4.4)
coefficients
A
B
C
D
-2.039 0.1704 1.1582 0.4354
1
2.95531 -0.2631 -1.3465 -2.3608
1
1.7445 -0.5232 -1.2707 3.617
1
-4.9562 0.4134 2.9552 15.764
1
A2. Eq2. Equations for the mechanical properties of steel G
(
YS
)
(
)
= − 0.0119Tan − 0.0106Tan + 0.001Tan + 0.0284 × Ttn + 0.0216Tan − 0.018Tan − 0.0067Tan + 0.0609 ×
UTS
3
2
Ttn + 0.1885Tan − 0.0065Tan − 0.2681Tan + 0.6027
3
2
(
2
3
2
)
(A2.Eq2(a))
(
)
(
− 261.81) × T + (− 44.325T
)
UTS = 128.21Tan − 76.336Tan + 66.175 × Ttn + − 272.31Tan + 192.62Tan − 207.38 × Ttn
(
2
+ − 133.93Tan + 74.61Tan + 39.091Tan
3
2
3
2
tn
3
an
2
+ 7.65Tan − 26.275Tan + 2099.6
2
)
(A2.Eq2(b))
(
) (
)
(
)
CIE − 400 C = − 2.039Tan + 0.1704Tan +1.1582Tan + 0.4354 × Ttn + 2.955Tan − 0.2631Tan −1.3465Tan − 2.3608
(
3
2
)
(
3
3
2
)
× Ttn + 1.7445Tan − 0.5232Tan −1.2707Tan + 3.617 ×Ttn + − 4.9562Tan + 0.4134Tan + 2.9552Tan +15.764
2
3
2
3
2
(A2.Eq2©)
212
University of Pretoria etd, Kasonde M (2006)
A2.3: Steel H
Table A2.3(a): The fitting parameters in Equation (4.3) for the YS/UTS ratio of steel H
Fitting parameters in
Equation (4.3)
Normalised
Austenitisation austenitisation
temperature temperature
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
0.0224
0.0193
0.0137
0.0129
b
0.0545
0.058
0.0378
0.0273
Correlation
coefficients
c
0.4888
0.92
0.4754
0.95
0.4662
0.99
0.4444
0.9833
Table A2.3(b): The fitting parameters in Equation (4.4) for the YS/UTS ratio of steel H
Fitting parameters in Equation
Correlation
(4.4)
coefficients
A
B
C
D
0
0.0013 -0.0051 0.0164
a
b 0.0188 -0.0079 -0.0324 0.0488
0
-0.0047 -0.0214 0.4713
c
0.96
1
0.99
Table A2.3(c): The fitting parameters for the ultimate tensile strength of steel H in Equation (4.3)
Fitting parameters in Equation (4.3)
Normalised
Austenitisation austenitisation
temperature
temperature
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
231.81
230.63
262.13
166.59
b
-791.9
-704.14
-668.63
-563.7
c
489.98
388.36
100.07
286.23
d
1932.8
1864.1
2151.2
1839.1
Correlation
coefficients
0.994
0.996
0.992
0.996
Table A2.3(d): The fitting parameters for the ultimate tensile strength of steel H in Equation (4.4)
a
b
c
d
Fitting parameters in Equation
Correlation
(4.4)
coefficients
A
B
C
D
-89.842 -53.078 57.232 252.28
1
68.439 9.6581 45.661 -687.46
1
371.88 161.88 -473.75 226.23
1
-537.19 -136.91 490.34 2022.9
1
213
University of Pretoria etd, Kasonde M (2006)
Table A2.3(e): The fitting parameters of the Charpy impact energy for steel H in Equation (4.3)
Fitting parameters in (4.3)
Normalised
Austenitisation austentisation
temperature temperature
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
b
1.9032 -7.6936
2.2313 -5.9804
3.3711 -9.3431
0.597 -4.4147
c
2.2175
-0.9373
-0.2485
1.8897
d
19.296
15.176
18.372
13.246
Correlation
coefficients
0.988
0.972
0.9657
0.926
Table A2.3(f): The surface fitting parameters of the Charpy impact energy for steel H in Equation
(4.4)
a
b
c
d
Fitting parameters in Equation
Correlation
(4.4)
coefficients
A
B
C
D
-2.6581 -1.745 2.005 2.9951
1
7.5189 1.8086 -5.8795 -7.8627
1
-1.3467 2.9773 1.1828 -0.9237
1
-8.7964 -0.5659 5.7714 16.837
1
A2. Eq3. Equations for the mechanical properties of steel H
(
)
)
(
)
YS
2
2
3
2
= 0.0013Tan − 0.0051Tan + 0.0164 × Ttn + 0.0188Tan − 0.0079Tan − 0.0324Tan + 0.0488 ×
UTS
2
Ttn + − 0.0047Tan − 0.0214Tan + 0.4713
(
(
)
(
)
− 687.46)
(A2.Eq3(a))
× Tan + 371.88Tan + 161.88Tan − 473.75Tan + 226.23 × Ttn + − 537.19Tan −136.91Tan + 490.34Tan + 2022.9
2
(
3
2
)
(
3
2
UTS = − 89.842Tan − 53.078Tan + 570232Tan + 252.28 × Ttn + 68.439Tan + 9.658Tan + 45.661Tan
3
2
3
3
2
(A2.Eq3(b))
(
) (
)
(
)
CIE − 400 C = − 2.6581Tan −1.745Tan + 2.005Tan + 2.9951×Ttn + 7.5189Tan +1.8086Tan − 5.8795Tan − 7.8627
(
3
2
)
3
(
3
2
)
×Tan + −1.3467Tan + 2.9773Tan +1.1828Tan − 0.9237 ×Ttn + − 8.7964Tan − 0.5659Tan + 5.7714Tan +16.837
2
3
2
3
2
(A2.Eq3©)
214
University of Pretoria etd, Kasonde M (2006)
A2.4: Steel I
Table A2.4(a): The fitting parameters for the yield strength to ultimate tensile strength ratio of
steel I in Equation (4.3)
Fitting parameters in
Equation (4.3)
Normalised
Austenitisation austenitisation
temperature temperature
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
0.0018
0.005
0.0117
0.0147
b
0.069
0.1014
0.0737
0.063
Correlation
coefficients
c
0.7226
0.96
0.702
0.96
0.5473
0.9577
0.5193
0.98
Table A2.4(b): The fitting parameters for the yield strength to ultimate tensile strength ratio of
steel I in Equation (4.4)
Fitting parameters in Equation
Correlation
4.4
coefficients
A
B
C
D
1
a -0.004 -0.0001 0.0105 0.0084
1
b 0.0434 -0.0242 -0.0464 0.0902
1
c 0.1467 -0.0042 -0.2484 0.6251
Table A2.4(c): The surface fitting parameters for the tensile strength of steel I in Equation (4.3)
Fitting parameters in Equation
(4.3)
Normalised
Austenitisation austenitisation
temperature temperature
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
89.705
60.44
62.015
64.553
b
-159.9
-135.38
-127.64
-226.13
c
-370.57
-284.47
-284.9
-110.66
Correlation
d
coefficients
1982.3
0.992
1869
0.971
1859
0.99
1725.3
0.993
Table A2.4(d): The fitting parameters for the tensile strength of steel I in Equation (4.4)
a
b
c
d
Fitting parameters in Equation
Correlation
4.4
coefficients
A
B
C
D
-16.806 17.889 4.2298 59.24
1
-50.316 -69.193 17.201 -123.82
1
146.92 49.579 -16.97 -290.19
1
-127.69 -11.475 -0.8125 1865.3
1
215
University of Pretoria etd, Kasonde M (2006)
Table A2.4(e): Fitting parameters for the Charpy impact energy of steel I in Equation (4.3)
Fitting parameters in
Equation (4.3)
Normalised
Austenitisation austenitisation
temperature temperature
-1
800°C
-0.33333
850°C
0.333333
900°C
1
950°C
a
0.3737
0.5935
0.5948
0.5647
b
-1.0494
-1.1198
-1.1983
-0.9749
c
0.8835
0.519
0.7491
0.9475
d
18.097
18.97
19.246
19.273
Correlation
coefficients
0.87
0.95
0.92
0.95
Table A2.4(f): Fitting parameters for the Charpy impact energy of steel I in Equation (4.4)
a
b
c
d
Fitting parameters in Equation
Correlation
4.4
coefficients
A
B
C
D
0.1052 -0.1406 -0.0097 0.6098
1
0.1744 0.1653 -0.1371 -1.1774
1
-0.3523 0.3166 0.3843 0.5989
1
0.1958 -0.4759 0.3923 19.161
1
A2. Eq4. Equations for the mechanical properties of steel I
(
)
(
)
YS
3
2
2
3
2
= − 0.004Tan − 0.0001Tan + 0.0105Tan + 0.0084 ×Ttn + 0.0434Tan − 0.0242Tan − 0.0464Tan + 0.0902
UTS
3
2
×Ttn + 0.1467Tan − 0.0042Tan − 0.2484Tan + 0.6251
(
)
(A2.Eq4(a))
(
+ (14.92T
)
(
UTS = − 16.806Tan + 17.889Tan + 4.2298Tan + 59.24 × Ttn + − 50.316Tan − 69.193Tan + 17.201Tan − 123.82
× Ttn
2
3
3
an
2
)
3
(
3
2
)
)
+ 49.579Tan − 16.97Tan − 290.19 × Ttn + − 127.69Tan − 11.475Tan − 0.8125Tan + 1865.3
2
3
2
(A2.Eq4(b))
(
) (
)
(
)
CIE − 400 C = 0.1052Tan − 0.1406Tan − 0.0097Tan + 0.6098 ×Ttn + 0.1744Tan + 0.1653Tan − 0.1371Tan −1.1774
(
3
2
)
3
(
3
2
)
×Ttn + − 0.3523Tan + 0.3166Tan + 0.3843Tan + 0.5989 ×Ttn + 0.1958Tan − 0.4759Tan + 0.3923Tan +19.161
2
3
2
3
2
(A2.Eq4©)
216
University of Pretoria etd, Kasonde M (2006)
APPENDIX A6.2:
Geometric characteristics of the steel E measured by means of Atomic Force Microscopy
Line 4
dx
39.1997
79.168 33.8193 11.5293
dy
9.259
-7.058
8.343 -0.06741
Inclination(Degrees) 13.29647 -5.09716 13.86483 -0.33517
Width
40.27835
79.482 34.83318 11.5295
Slope (nm/deg)
3.029251 -15.5934 2.512342 -34.3994
TB/(TB+TA)
0.69
Line 5
dx
32.98 80.6177 40.3089
dy
9.4593
-6.142
9.3723
Inclination(Degrees) 16.01203 -4.35897 13.09602
Width
34.30975 80.85133 41.38414
Slope(nm/deg)
2.142748 -18.5483 3.160055
TB/(TB+TA)
0.66
109.1442 29.2076 58.4152
-10.5198
7.2356 -5.4776
-5.50821 13.92083 -5.35968
109.65 30.09049 58.67146
-19.9067 2.161545 -10.9468
0.78
115.4299
-10.5284
-5.21419
115.9091
-22.2295
29.3155
5.9052
11.39481
29.90435
2.624384
102.6044
-9.158
-5.10303
103.0123
-20.1865
0.79
Line 6
dx
29.6402 67.3642 15.2692 26.0475
126.6447 27.8439 142.8121
dy
6.6714 -4.1958 0.019344
8.0066
-8.614
6.9449 -13.2485
Inclination(Degrees) 12.69115 -3.56589 0.072623 17.09529
-3.89307 14.01221 -5.30278
Width
30.38172 67.49474 15.26921 27.25028
126.9373 28.69694 143.4253
Slope(nm/deg)
2.39393 -18.9279 210.2539 1.594023
-32.606 2.047995 -27.0472
TB/(TB+TA)
0.61
0.74
Line 7
dx
36.6428 75.1648 33.8241
dy
7.9903 -4.7493
7.9828
Inclination(Degrees) 12.30755 -3.61727 13.28607
Width
37.50386 75.31469 34.75334
Slope(nm/deg)
3.047224 -20.8209 2.615772
TB/(TB+TA)
0.68
Line 8
dx
32.071
69.153 13.0288
dy
9.8142 -7.1363 0.48034
Inclination(Degrees) 17.02352 -5.89482 2.11247
Width
33.53905 69.52024 13.03765
Slope(nm/deg)
1.97016 -11.7935 6.171757
TB/(TB+TA)
0.60
124.9614
-8.4291
-3.86092
125.2454
-32.4393
27.2472
6.9117
14.24101
28.11017
1.973889
147.5109
-13.1597
-5.10054
148.0967
-29.0355
0.81
34.0754 116.2573
32.071
9.4498 -11.4269
7.3269
15.50764 -5.6164 12.87539
35.36144 116.8175 32.8973
2.28026 -20.7993 2.555052
0.77
217
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