The main objective in developing the new armoured steel plate... used steel A and steel B plates, is the manufacture... CHAPTER 1. INTRODUCTION

The main objective in developing the new armoured steel plate... used steel A and steel B plates, is the manufacture... CHAPTER 1. INTRODUCTION
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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University of Pretoria etd, Kasonde M (2006)
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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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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Chapter 2: Literature Review
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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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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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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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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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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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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(
)
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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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].
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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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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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Chapter 2: Literature Review
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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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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University of Pretoria etd, Kasonde M (2006)
Chapter 2: Literature Review
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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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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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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(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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University of Pretoria etd, Kasonde M (2006)
Chapter 2: Literature Review
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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Chapter 2: Literature Review
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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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Chapter 3. Experimental Techniques
•
•
•
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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Chapter 3. Experimental Techniques
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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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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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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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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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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