COMPRESSION TEST OF ALUMINIUM AT HIGH TEMPERATURE

COMPRESSION TEST OF ALUMINIUM AT HIGH TEMPERATURE
COMPRESSION TEST OF ALUMINIUM AT HIGH TEMPERATURE
A THESIS SUBMITTED IN PARTIAL FULFILMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
Bachelor of Technology
In
Mechanical Engineering
By
TAPAN KUMAR HALDIGUNDI
108ME030
Under the Guidance of
Prof. S.K.SAHOO
Department of Mechanical Engineering
National Institute of Technology
Rourkela
2012
1
National Institute of Technology
Rourkela
CERTIFICATE
This is to certify that thesis entitled, “COMPRESSION TEST OF ALUMINIUM AT HIGH
TEMPERATURE” submitted by Mr. TAPAN KUMAR HALDIGUNDI in partial fulfillment of
the requirements for the award of Bachelor of Technology Degree in Mechanical Engineering at
National Institute of Technology, Rourkela is an authentic work carried out by him under my
supervision and guidance.
To the best of my knowledge, the matter included in this thesis has not been submitted to any
other university/ institute for award of any Degree or Diploma.
Date: 10th may, 2012
Prof. S.K.SAHOO
Dept. of Mechanical Engineering
National Institute of Technology
Rourkela-769008
2
ACKNOWLEDGEMENT
I express my deep sense of gratitude and indebtedness to my project guide Prof S.K.Sahoo,
Department of Mechanical Engineering, NIT Rourkela for introducing the present topic and for
his excellent guidance, consistent encouragement and constant supervision throughout the course
of this work.
I would like to give special thanks to Mr. L.N. Patra, PhD Scholar,Department of
Mechanical Engineering, who gave his valuable time and support for this project work.
I also express my sincere gratitude to Mr. Susant Sahu and Mr. B.R. Maharana, PG
Scholars in Mechanical Engineering, for providing their valuable time and guidance, which
made it possible to complete the work contended in this thesis.
I am grateful to Prof. K.P.Maity, Head of the Department of Mechanical
Engineering for providing me the necessary facilities in the department.
Last but not the least, I express my hearty gratitude to the omnipotent and my
parents for their blessings and support without which this work could have never been
accomplished.
Date: 10th may, 2012
TAPAN KUMAR HALDIGUNDI
108ME030
Dept. of Mechanical Engg.
3
ABSTRACT
Compression test of aluminum alloy at high temperature were experimentally
carried out on universal testing machine at specified temperatures ranging from
35oC (room temperature) to 225oC and under a constant strain rate of 0.001/s using
powdered graphite mixed with machine oil as lubricant throughout the tests. True
Stress and strain values were calculated using the engineering equation, which
were used to plot the true stress-strain curve for different temperatures, which
indicates the mechanical properties of the metal for industrial applications. A
common characteristic equation considering true stress, true strain and temperature
has been found out using regression analysis .Generalized characteristic equations
for each temperature have also been developed by regression analysis, which
indicates that the strain hardening exponent first increases, then decreases with
increasing temperature, while strength coefficient decreases with increase in
temperature.
Keywords—Compression, High Temperature, True Stress, True Strain, Regression
Analysis
4
CONTENT
Abstract................................................................................................................. 4
Chapter 1
1. Introduction ................................................................................................................... 6
1.1 compression test......................................................... ....................................................7
1.2 Standard for compression............................................................................................... 8
1.3 Effect of different parameters on compression ............................................................ 10
1.3.1 Effects of Temperature ............................................................................................. 10
1.3.2 Effects of Rate of Deformation ....................................... ..........................................10
1.4 Material used .................................................................................................................11
Chapter 2
2. Literature Reviews..........................................................................................................14
Chapter 3
3. Experimental Details ......................................................................................................17
3.1 Experimental Setup ........................................................................................................17
3.1.1 INSTRON SATEC KN 600 Specifications ............................... ................................17
3.1.2 Furnace........................................................................................................................ 19
3.1.3 Hydraulic Power Supply ....................................................................................... ......21
3.2 Graphite as lubricant.............................................................................................. .........21
3.3 specimen preparation........................................................................................................22
3.4 Description.......................................................................................................................23
Chapter 4
4. Result and Discussions ....................................................................................................24
4.1 Flow Curve ..................................................................................................................... 24
4.2 Non-linear least square Regression analysis....................................................................30
4.3 Behaviour of flow curve at different temperatures......................................................... 37
Chapter 5
5. Conclusions ...................................................................................................................... 39
References ............................................................................................................................ 41
5
Chapter 1
Introduction
6
1. INTRODUCTION
1.1 Compression Test
The use of any material or alloy in a specific fabrication operation is subjected to various
parameters related to them. Thorough assessment of these parameters and the corresponding
behavior of the materials and resulting properties for the operating conditions need to be
analysed properly. Various thermo-mechanical treatments are to be conducted before these alloys
undergo different industrial applications. Compression Tests are of extremely high commercial
importance, because it helps determining different material properties pertaining to hot as well as
cold metal forging employed in a number of metal forming applications. It becomes important to
determine suitable load to carry out the operations. Load depends on the flow stress of materials,
friction at the tool-workpiece interface and the geometry of the die. Therefore, prediction of hot
deformation behavior correlating process variable such as strain, strain rate and temperature to
the flow stress of the deforming materials is necessary.
Flow behavior of different alloys at various temperatures can be
determined by establishing a relationship among flow stress, strain, strain rate and temperature.
So compression tests need to be conducted for a wide variety of strain rates and temperatures.
The experimental stress strain data can then be employed to relate true stress, true strain,strain
rate & temperature. This relation can then be crosschecked with other experimental data
generated.
When a simple compressive load is applied on a
particular specimen, the following types of deformation may take place: elastic or plastic
compression as in the case of ductile materials, crushing and fracture in brittle materials, or a
sudden bending deformation called buckling in long, slender bars, or a combination of these.
Ductile materials, such as aluminium lack compressive strength. So lateral expansion and thus an
increasing cross-sectional area along with axial shortening takes place. The specimen won‟t
break, rather excessive deformation occurs instead of loss of strength demonstrating failure
characteristics. This behaviour is demonstrated in the figure below.
7
fig 1.1 (flow stress-strain curve for compression test)
1.2 Standard for Compression
In order that test results may be compared easily, the dimensions of test specimens and the
methods of applying loads are standardized. One of the major standards organizations is the
American society for Testing and Materials (ASTM), a national technical society that publishes
specifications and standards for materials and testing. Other standardizing organizations are the
American Standards Association (ASA) and Bureau of Indian Standard. For compression testing
of aluminium cylinders and foils, ASTM-E9 standard is adopted.
8
1.3 Effect of Different Parameters on Compression
1.3.1 Effects of Temperature
Increasing temperature generally has the following effects on stress strain curves:
a. It raises ductility and toughness, and
b. It lowers the yield stress and modulus of elasticity
Temperature also affects the strain hardening exponent of most metals.
1.3.2 Effect of strain rate
The rate at which strain is applied to a specimen can have an important influence on the
flow stress. Strain rate is defined as :
strain rate =
It is conventionally expressed in units of sec-1 i.e. per second. Generally, increasing strain rate
increases flow stress. Moreover, the strain rate dependence of strength increases with increasing
temperature. The true strain rate is given by
=
=
=
(1)
Where v is the crosshead velocity
h is the final height of specimen
ho is the initial height of specimen
The above equation indicates that for a constant crosshead speed the true strain rate will increase
as the specimen length decreases. So in order to make true strain rate constant, crosshead
velocity should be decrease with decrease in specimen height.
9
1.4 MATERIAL USED -Aluminium (or aluminum)
It is a silvery white and ductile member belonging to the boron group of chemical elements.
Its symbol is Al and its atomic number is 13. It is insoluble in water under normal circumstances.
Aluminium is highly reactive chemically to occur in nature as a free metal. Instead, it is found
combined in more than 270 different minerals. The primary source of aluminium is bauxite ore.
Aluminum alloys are alloys in which aluminum (Al) is the predominant metal.
Commercial purity of aluminum is 99.5 to 99.79%, but pure aluminum is too soft to be of
structural value. The primary reason for alloying aluminum is to increase strength without
significantly increasing weight. Other reasons are to improve machinability, weldability, surface
appearance and corrosion resistance. The typical alloying elements are copper, magnesium,
manganese, silicon, and zinc.
 Properties of Al
Aluminium is unique and unbeatable combination of properties making its use versatile.It is
highly usable and attractive construction material.
Weight: Al is the light material compare to other material like steel. Its Density is 2.700 kg/m3
Strength: Aluminium is strong with the tensile strength 70 to 700 MPa .its strength depends on
the alloying materials and manufacture process.
Elasticity: The Young‟s modulus of Al is one-third of steel (E = 70,000 MPa).
Formability: Aluminium has the good formability characteristic ,that may be used to the form in
extrusion. Aluminium may also be cast, drawn and milled.
Machinability: Aluminium is very simple to machine. Ordinary machining equipments may be
used such as saws and drills. Al is also suitable for forming (both hot and cold process) .
Joining: Aluminium may be joined applying all the normal methods available as the welding,
soldering, Adhesive bonding and riveting.
Corrosion resistance: A thin layer of oxide is formed when Al is in contact with air, which
provides good protection against the corrosion in the corrosive environment . Its layer may also
be given further strength by surface treatment such the powder coating.
Conductivity: Its thermal and electrical conductivities are good compared with copper.
Furthermore Al conductor is only half the weight of an equivalent Cu conductor.
10
Linear expansion: Aluminium has relatively higher coefficient of linear expansion compared to
other metals. This shall take into account the design stage of the compensate for difference in the
expansion.
Non toxic: Aluminium is not poisonous; therefore it is highly suitable for the preparing and
storage of the meal
Reflectivity: Aluminium is the best reflector of the light and heat. Its reflectivity is very high.
 Applications:
Aluminum alloy has wide range of application. Followings are some of them.
I. In aircraft and other aerospace structures
II. for boat and shipbuilding, and other marine and salt-water sensitive shore
III. for cycling frames and components
IV. for automotive body panels
V. As a packaging materials.
VI. In making household components etc.
11
applications
CHAPTER 2
LITERATURE SURVEY
12
2 Literature Survey
Because of widespread use of aluminium in electrical conductors, radiator fin material,
air conditioning units, optical and light reflectors and foil and packaging materials, the high
temperature behavior of aluminium is essential to know. So to know about it various literatures
have been reviewed. Out of them some important literatures are discussed here:
Jin Nengping. et.al. [1], showed that, the peak stress level of 7150 aluminum alloy
decreases with increasing deformation temperature and decreasing strain rate. The deformed
structures exhibit elongated grains with serrations developed in the grain boundaries Dynamic
recovery and recrystalization are the main reasons for the flow softening at low Z value. Zhang
Hui et.al. [2], found out that, the true stress strain curves of Al-Mg-Si-Cu aluminum alloy exhibit
a peak stress at a small strain, after which flow stress decrease monotonically until high strain.
The substructure in the deformed specimens consists of very small amount and fine precipitates
with equaxied polygonized subgrains in the elongated grains and developed serrations in the
grain boundaries. Xiu-yu WEI. et.al. [3], concluded that, the flow stress of 2197 Al-Li alloy
decreases with the increase of deformation temperature and increases with the increase of strain
rate. The peak flow stress during high temperature deformation can be represented by Z
parameter in a hyperbolic sine function.
Aluko O. et.al. [4], found out that the compression curves of aluminum alloy
obtained using the barrel correction factor method and the Bridgman re-machining technique (no
barreling allowed during the test) are found to have close values, even at higher temperatures.
The true-stress versus true-strain curves and the barrel sizes obtained follow empirical power
laws, even at higher test temperatures. Chen. Z.Y. et.al. [5], has taken Hill‟s general method to
calculate the flow stress of a cylindrical specimen of AA6063 aluminum alloy under uniaxial
simple compression and also to consider the friction effect at the die-specimen interface. Both
the results of FEM analysis and compression test were combined to evaluate the friction
coefficient.
Ramanathan. S. et.al [6], found out the optimum working regions and flow instable
regions of 2124 Al alloy manufactured by powder metallurgy method, by using processing maps.
They also found the power dissipation efficiency and instability parameters of the material.
13
Narayanasamy and Pandey studied the effect of barreling in aluminium solid
cylinders during cold upsetting which most significantly pertains to the work to be done in this
particular experimentation [7]. M. Oktay ALNIAK and Fevzi BED_IR et.al [8] have studied the
Changes of Grain Sizes and Flow Stresses of AA2014 and AA6063 Aluminum Alloys at High
Temperatures in Various Strain Rates.
Matruprasad Rout et.al[9] studied the flow stress and barreling behavior of
aluminum alloy solid cylinder during upset forging at elevated temperature and found that flow
stress, strain hardening exponent n and strength coefficient A all decreases with the increase in
temperature and the radius value increases with the increase in test temperature and decreases
with the increases in amount of strain.
Vaibhav Dash et. Al[10] has performed the bulging test of Aluminium billets (of
hexagonal cross-section) under constant conditions of friction at room temperature and has
found that with an increase in the percentage of height reduced the compressive load required
shows an increasing trend with a rapid increase toward the end of compression and the bulging
and barreling diameter of the specimen does not only depend on the height of the deformed
specimen but also on the percentage reduction.
14
Chapter 3
Experimental Details
15
3. Experimental Details
3.1 Experimental Setup
The experiments were carried out in the universal testing machining of INSTRON SATEC 600
KN. 600 KN Models of INSTRON are ideal for high capacity tension, compression, flex and
shear testing. These models feature an ultra large, single test space and so users can easily and
safely load and unload specimens. This design offers the ultimate versatility by accommodating a
large variety of specimen sizes, grips, fixtures and extensometers. Models include: 300KN, and
600KN, 1200KN, 1500KN, 2000KN and 3500KN.
3.1.1 INSTRON SATEC KN 600 Specifications
Followings are the specifications of the machine
Table 3. 1 Specifications of INSTRON SATEC 600 KN
maker
type
software
Max. Loading capacity
Max. Vertical test opening
Horizontal test opening
Actuator stroke
Max testing speed at full load
Stiffness deflection
Load accuracy
Strain accuracy
Position accuracy
Instron,UK
hydraulic
Bluehill EM Console
600 KN
1625 mm
711 mm
508 mm
200 mm/min
<1.0 mm
±0.5% of reading down to 1/500 of
Load cell capacity
±0.5 of reading down to 1/50 of
Full range to ASTM E83 class B-1,B-2
0r ISO9513 class 0.05 extensometer
±0.5% or 0.13 mm
16
Figure 3.1 INSTRON static
Fig 3.2 Figure 3. 3 Experimental set up for high temperature compression test
17
3.1.2 Furnace
It is an induction furnace having refractory ceramic fibre. These three zone resistance wire
wound furnaces are of split construction to facilitate fast and easy loading of a pre-assembled
specimen train. The case is constructed from stainless steel with aluminum and hardened
insulation board end plates. The optional front cut-out allows the use of side-entry hightemperature extensometer. Adjustable stainless steel latches keep the furnace halves locked
together during use, but are then easily opened once testing is complete. The furnace is available
with optional heavy duty brackets or mountings, which attach to a wide range of testing systems.
The resistance wire is wound on to recrystallized alumina tube in three independent zones to
form the furnace element. This three-zone format allows the user to tailor the furnace
temperature gradient, creating a uniform central zone. High-performance ceramic fiber insulation
is used to reduce heat losses and provide fast heating rates.
Model and Style
SF- 16, 2230
Heat Zone Length
280 mm
No. of Zones
3
Element Resistance per Zone
17.6 Ohms
Furnace Length
330 mm
Furnace Outside Dia.
255 mm
Internal Bore Dia.
75 mm
Weight
21 Kg. (approx.)
Operating Temperature
1200°C
No. of Thermocouples
3
Thermocouples Type
K
Voltage
115 Vac.
Watt
2250 W, 750 W/ Zone
Phase
Single
Ampere
21 A, 6.52A/ Zone
Hertz
60 Hz/ 50 Hz
Temperature Controller
Type Eurotherm 2416
No. of Controller
3
18
Fig 3.3 furnace
Fig 3.4 temperature controller
19
3.1.3 Hydraulic Power Supply
Table 3. 3 Hydraulic Power Supply
Model
V22a
Height
1030 mm
Required Floor Space
(1220×935) mm
Weight
522 Kg. (approx.)
Required Flow at Maximum Testing Speed
12.37 Lpm
Ideal Pressure
28 bar
System Relief Pressure
179 bar
Motor Power
5 hp
3.2 Graphite as a lubricant:
Graphite is one of the allotropes of carbon. It is structurally composed of planes of polycyclic
carbon atoms that are hexagonal in orientation. The distance of carbon atoms between planes is
longer and therefore the bonding is weaker. Graphite is best suited for lubrication in a regular
atmosphere. In an oxidative atmosphere graphite is effective at high temperatures up to 450ºC
continuously and can withstand much higher temperature peaks. Graphite is characterized by two
main groups, natural and synthetic. Graphite as a lubricant is used as dry powder or mixed with
water or oil. When mixed with water, it is called 'aqua-dag' and when mixed with oil, it is called
'oil dag'. Graphite powder and machine oil in a proper ratio were mixed properly to form the
lubricant for the test.
Graphite lubrication is used so that the specimen doesn‟t get forged to the anvil and
ram at high temperature.
20
3.3 Specimen Preparation
Fig 3.5 specimen
Compression Test to be conducted requires the testing of nine specimens prepared from the raw
aluminium rod.
Specimen Specifications:
L/Deff
1.5 for to assure a geometrical dimensional factor and homogeneous deformation
L = Length of the Specimen
Deff = Effective Diameter of the Cross Section of the Specimen
Hence if Deff =10 mm, L should be approximately 15 mm
In the current experiment, L has been taken as 18 mm
Specimens of the required dimensions (figure 3.5) were cut from the aluminum alloy bar using
hacksaw and filing operation was carried out to make the two ends parallel.
21
3.4 Description
After applying graphite lubricant coating on both the sides of the specimens, they are placed in
between the top and bottom platen of the setup such that the axis of the cylindrical specimen is
concentric with the axis of the ram. Furnace is now closed and the specimen is heated up to the
desired temperature. Specimens are held on the testing temperature for 2-3 min after achieving
the desired temperature to get well-proportioned and homogenous microstructure. Then
hydraulic load is applied on the test specimen. The test is carried out at constant temperature. For
each test temperature, one specimen was taken and deformed to different strain levels. The loads
used during each deformation were recorded automatically by the BLUEHILL software
incorporated with the UTM machine. Compressive test was carried out by giving a deformation
of 10 mm, at a uniform strain rate of 0.001s-1 and at nine different temperatures of 35°C, 50°C,
75°C, 1000C, 125°C, 1500C, 175°C, 2000C and 2250C. At the end of each experiment time
taken(sec), compressive extension(mm), compressive load(N), compressive stress(Pa),
compressive strain(%), true stress(Pa) and true strain(%) were recorded automatically in the
database of the computer, which was further used by the software to generate True stress vs.
True strain graph .
22
Chapter 4
Results and Discussions
23
4 Result and Discussion
4.1 Flow curve (true stress vs. true strain)
Actually the metal continues to strain harden all the way, so that the stress required to
produce further deformation should also increase. If the true stress based on the actual crosssectional area of the specimen is used, it is found that stress-strain curve increases continuously
until plastic deformation occurs. If the strain measurement is also based on instantaneous
measurement, the curve is called true stress-strain curve. It is also known as flow curve, since
It represents the basic plastics flow characteristics of the material. Many attempts have been
made to fit mathematical equations to this curve. The most common is a power expression of the
form
n
.......................................(1)
Where , = true stress, A is strength coefficient,
n is the strain hardening exponent
Fig 4.1 deformed specimens
24
BLUEHILL software incorporated with the UTM machine automatically generates the flow
curve for each specimen instantaneously after the experiment using the true stress and true strain
data saved in computer‟s database. It uses the engineering equation to generate the flow curves.
 FOR TEMPERATURE -35oC
Fig 4.2 flow curve of specimen-1
 FOR TEMPERATURE -50oC
Fig 4.3 flow curve of specimen-2
25
 FOR TEMPERATURE -75oC
Specimen-3
Fig 4.4 flow curve of specimen-3
 FOR TEMPERATURE -100oC
Specimen-4
Fig 4.5 flow curve of specimen-4
26
 FOR TEMPERATURE -125oC
Specimen-5
Fig 4.6 flow curve of specimen-5
 FOR TEMPERATURE -150oC
Specimen-6
Fig 4.7 flow curve of specimen-6
27
 FOR TEMPERATURE -175oC
Specimen-7
Fig 4.8 flow curve of specimen-7
 FOR TEMPERATURE -200oC
Specimen-8
Fig 4.9 flow curve of specimen-8
28
 FOR TEMPERATURE -225oC
Specimen-9
Fig 4.10 flow curve of specimen-9
Overall flow curve or True stress-strain curve for different Temperatures
Fig 4.11 flow curve for different temperatures in kelvin
The figure shows the flow curve of the material at different temperatures. Data taken in regular
interval during the experiment by the BLUEHILL software were taken to plot the flow curve. It
was clear from the graph that the flow stress decreases with the increase in temperature, as the
material get soften with the increase in temperature or flow-ability of the material increases.
29
4.2 Non linear least square regression analysis
Regression analysis is a technique used for modeling and analyzing variables, which establish
mathematical relationship between a dependent variable and one or more independent variables.
It demonstrates how the value of the dependent variable changes when any one of the
independent variables is varied, while the other independent variables are held fixed. A large no
of techniques have been developed for carrying out regression analysis. Out of all those, linear
regression and least squares regression are more commonly used. Least squares problems fall
into two categories: linear least squares and non-linear least squares, depending on the nature of
variation of the dependent variable with the independent variables. The main difference between
these two is linear least square has a closed-form solution where as the nonlinear has no closedform solution and is usually solved by iterative refinement; at each iteration the system is
approximated by a linear one.
The purpose of using Regression Analysis here is to establish a mathematical
relationship between true stress and true strain, which will define the flow stress behaviour of the
material. Many attempts have been made to fit mathematical equations to this curve. The most
common is a power expression of the form
n
.........................................(1)
Taking natural logarithm on both the sides of eqn-1, we get
=>ln( ) = lnA + n×ln( ) ................................(2)
eqn-2 represents the equation of a straight line (Y = C+ mX),which can be solved by linear
regression analysis in order to find values of strength coefficient A and strain hardening
exponent „n‟ at different temperatures.
The following relationships have been determined by linear regression analysis with the
help of MINITAB software.
30
o
 Temperature-35 C: (specimen-1)
ln( ) = 18.6 + 0.0620 ln(
 Temperature-50oC: (specimen-2):
ln( ) = 18.6 + 0.0884 ln( )
31
 Temperature-75oC: (specimen-3) :
ln( ) = 18.6 + 0.144 ln( )
o
 Temperature-100 C: (specimen-4)
ln( ) = 18.3 + 0.124 ln( )
32
 Temperature-125oC: (specimen-5)
ln( ) = 18.6 + 0.0926 ln( )
o
 Temperature-150 C: (specimen-6)
ln( ) = 18.6 + 0.0796 ln( )
33
o
 Temperature-175 C: (specimen-7)
ln( ) = 17.6 + 0.295 ln( )
 Temperature-200oC: (specimen-8)
ln( ) = 17.8 + 0.227 ln( )
34
o
 Temperature-225 C: (specimen-9)
ln( ) = 18.2 + 0.179 ln( )
From above nine number of equations, we can easily find the strength coefficient A simply by
taking exp{ln(A)}.The strength coefficients A and strain hardening coefficients „n‟ for different
temperatures have been tabulated below:-
A
119640264
119640264
119640264
88631688
119640264
119640264
44013194
53757836
80197267
n
0.062
0.0884
0.144
0.124
0.9626
0.0796
0.295
0.227
0.179
Table 4.1
35
T(K)
308
323
348
373
398
423
448
473
498
Fig 4.21 n vs.T (kelvin)
Fig 4.22 A vs. T(kelvin)
36
4.3 Behaviour of flow curve at different temperatures:
Our objective is to establish a single mathematical relationship among true stress, true strain and
temperature, which will show the flow stress behaviour of the material at different temperature
ranges.
Fig 4.23 ( flow curve at different temperatures in Kelvin)
We are looking to obtain a relation that will precisely describe the characteristics of flow curves
in the above figure at corresponding temperatures,which will have following form:n
k
.........................................(3)
Taking natural logarithm on both the sides of eqn-1, we get
=>ln( ) = lnA + n×ln( ) + k×ln(T)...........................(4)
37
Again using linear regression analysis using MINITAB, we obtain following equation:
ln(Stress) = 19.9 + 0.186 ln(Strain) - 0.281 ln(Temperature)
…………….Eqn-3
Residual Plots for Stress
Normal Probability Plot of the Residuals
Residuals Versus the Fitted Values
99
0.2
90
0.1
Residual
Percent
99.9
50
10
0.1
-0.50
-0.25
0.00
Residual
0.25
0.50
18.4
Histogram of the Residuals
18.6
18.8
Fitted Value
19.0
Residuals Versus the Order of the Data
24
0.2
18
Residual
Frequency
-0.1
-0.2
1
12
6
0
0.0
0.1
0.0
-0.1
-0.2
-0.2
-0.1
0.0
Residual
0.1
0.2
1 10
20
Fig 4.24 regression analysis
38
30 40 50 60 70 80
90 100 110 120 130
Observation Order
Chapter 5
Conclusions
39
5. Conclusions
Following conclusions were made from the above work:
(1)True stress or flow stress increases with increasing true strain.
(2) True stress decreases with increasing temperature.
(3) Strain hardening exponent n found increasing and then decreasing with increase
in temperature and strength coefficient A decreases with the increase in
temperature.
(4) The true stress, true strain and temperature can be correlated by the following
empirical formula
Where
= true stress
=true strain
T=temperature in Kelvin
40
6. Reference
[1] Jin Nengping. et. al Hot deformation behavior of 7150 aluminum alloy during compression at
elevated temperature, Journal of Materials characterization 60 (2009)530-536.
[2] Zhang Hui et.al, Hot deformation behavior of the new Al-Mg-Si-Cu aluminum alloy during
compression at elevated temperatures, Journal of Materials characterization58 (2007) 168-173.
[3] Xiu-yu WEI. et.al, Flow stress of 2197 Al-Li alloy during hot compression deformation,
Transaction of non ferrous metals society of China 17 (2007) s280-s284.
[4] Aluko. O. et.al, Warm Compression Tests of Aluminum Alloy, Journal of Materials
Engineering and Performance 7 (1998) 474-478.
[5] Chen. Z.Y. et.al. Deformation Behavior of Aa6063 Aluminium Alloy After Removing
Friction Effect under Hot Working Conditions, Acta Metall. Sin. (Engl. Lett.) Vol.21 No.6
(2008) 451-458.
[6] Ramanathan. S. et.al. Hot Deformation Behavior of 2124 Al Alloy, Journal of Material
Science Technology, Vol.22 No.5, (2006) 611-615.
[7]. Narayanasamy R, Pandey KS (1997) Phenomenon of barreling in Al solid cylinders
during cold upset-forging. J Mater Proc Tech 70: 17–27
[8] ]. M. Oktay ALNIAK and Fevzi BED_IR et.al. The Changes of Grain Sizes and Flow
Stresses of AA2014 and AA6063 Aluminum Alloys at High Temperatures in Various Strain
Rates. Turkish J. Eng. Env. Sci.27 (2003) , 59 { 64.
[9]Matruprasad Rout et.al. The flow stress and barreling behavior of aluminum alloy solid
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