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CHAPTER 4
EXPERIMENTAL STRESS ANALYSIS OF ALFA COMPOSITES
USING MACHINE VISION SYSTEM
4.1: INTRODUCTION
4.1.1: Upsetting Between Flat Platens
Stresses in most of the metal forming processes, such as cold heading, riveting
etc. are compressive in nature. Upset test at room temperature gives a representative
behavior during metal forming. Upsetting of solid cylinders is an important metal
forming process and an important stage in the forging sequence of many products.
Though extensive studies have been reported by various authors on friction studies
little attention has been given to the compression of taller cylinders, where the initial
height/diameter (H0/D0) ratio equals or exceeds unity. To be comprehensive and
practical, a model of the forging process should permit determination of not only the
platen forces and pressure distributions affecting tool life, but also the internal flow of
the forging influencing die-design and forging sequence and the properties of final
product dictating in-service performance.
A systematic detailed study of free deformation can be used to predict how
metal would flow under various working conditions and with various tool and work
piece geometries. This information can then be used to design better forgings, make
improved intermediated dies and to avoid the defects and failure of the materials
during plastic working. Some specific examples are as follows:
(a) Avoiding forging defects
(b) Avoiding failure of materials
(c) Design of forgings and intermediate stage dies
(d) Economic advantages
4.1.2: Machine Vision System and Its Advantages
Use of optical measuring technologies (Machine Vision System) in metal
forming and tooling industry has increased during recent years. The main
57
applications include digitizing of metal parts and tools, to perform forming analysis of
parts and tools and determination of material properties. Good interfaces to
conventional CAD/CAM and numerical simulation systems made such optical
measuring system a part of complex process chains. These process chains mainly
focus on optimizing the development of products and production processes,
improving the product quality using optical systems, considerably decreasing the
development time for products and production while improving the quality.
Conventional methods of analyzing the deformation behaviour during upsetting by
measuring grid distortions on tool maker’s microscope were available in literature.
Adoption of Machine vision system to analyze the flow behaviour of materials during
upsetting has been proposed in the present work. The advantage of this method is that
the experiment need not be intermittently stopped after certain deformation to
measure the strains from grid. When the experiment is stopped intermittently, elastic
deflections in specimen and tooling may be relieved causing inaccuracies in the next
step of deformation. By the use of vision system, the experiment need not be stopped
during deformation process. Offline analysis can be done latter.
One of the most common analysis and evaluation methods used for the metal
stamping process in measuring the extent of deformation is sometimes related to
forming severity, where the level of deformation is categorized as safe, marginal or
failure. In many press shops, strain measurement is used as a way to asses the
formability of a stamping. Surface strain data can be used effectively to diagnose
production problems, and identify potential failure sites. These data also are used to
verify predicted results from finite element analysis programs (FEA).
4.1.3: Friction in Metal Forming
Friction is the great importance in many metal forming operations. They affect
the material flow, deformation characteristics of the work piece, wear and fatigue
failure of the tool, and the mechanical properties of the formed parts. Furthermore,
minimizing friction is profitable since it reduces the force and energy required for a
given operation. This will lessen the stresses induced in the forming tool and prevent
direct tool to work piece contact, which contribute to longer tool life and better
quality control.
58
A number of studies have already been made in an attempt to obtain quantitative
data on friction in metal processing by using the actual metal working operation or by
using simulative laboratory tests. Use of the particular metal working process for
these investigations has the disadvantage that it is difficult to separate the force
necessary to overcome friction from the force necessary to give the required
deformation, and more difficult to control the secondary process variables.
Laboratory tests may furnish valuable measurements of frictional behavior under
controlled conditions provided that these tests are capable of simulating process
conditions such as temperature, deformation speed and deformation pressure.
4.1.4: The Ring Compression Test
The ring test technique involves a simple forging operation performed on a flat
ring-shaped specimen; the change in diameter produced by a given amount of
compression in the thickness direction is related to the interfacial friction condition.
If friction were equal to zero, the ring would deform in the same way as a solid disk,
with each element flowing radially outwards at a rate proportional to its distance from
the center. With a small but finite interfacial friction force, outward flow takes place
at a lower rate and for the same degree of compression; the outside diameter is
smaller than with zero friction. If the frictional force exceeds a critical vale, it is
energetically favorable for only part of the ring to flow outwards and for the
remainder to flow inward towards the center; thus the outside diameter after
compression is still further reduced.
Measurement of the final internal diameter of compressed rings provides a
particular sensitive means for studying interface friction since the internal diameter
increases if the friction is small and decreases if the friction is large. The ring test has
an advantage when applied to the study of friction at elevated temperatures and/or
high speeds; no direct measurement of force is required and no yield strength values
of the deforming material are needed, hence the major difficulties of evaluation of
compression tests under these conditions are eliminated. Correlation of changes in
internal diameter with numerical values of friction can be obtained either by
independent calibration or by the application of available theoretical analysis.
59
4.2: LITERATURE REVIEW
4.2.1: Friction and Ring Compression test
Friction is the resistance to motion encountered when one body slides over
another. In metal working processes it arises from sliding of the work piece against
the die [1]. In the interest of clarity, friction forces are often neglected. In many real
metal working processes friction is the predominant factor [2]. Shaw et al. [3]
discussed the significance of axisymmetric compression, and then the
mechanical/manufacturing properties of materials, to estimate forming limits up to
plastic instability and fracture. Considerable attention has been devoted to the analysis
of platen forces and pressure distributions in upsetting, particularly for thin discs [4-
8].
Of the many laboratory tests utilized for friction studies the ring test technique
originated by Kunogi [9] and further developed by Male and Cockroft [10] has the
greatest capability for quantitatively measuring friction under normal processing
conditions. Before a satisfactory mathematical solution for the compression of a ring
was available, a pioneering independent calibration was made by experimentation
[11]. Subsequent theoretical analyses [12, 13] have made possible more accurate and
less laborious calibration of the ring test by mathematical computation.
The first satisfactory analysis of the compression of a flat ring was made by
Avitzur [12] through an optimum upper bound mathematical solution and later
verified by Hawkyard and Johnson [13] using a stress analysis approach. Both
solutions are based on assumptions that (a) there is no non-uniform distortion of
cylindrical elements due to frictional constraint, i.e., no barreling; (b) the ring material
obeys Mises’ stress-strain rate laws, implying no strain hardening effect, no elastic
deformation and no volumetric change; and (c) a constant friction factor, m, for a
given die and material under constant surface and temperature conditions such that the
interfacial frictional shear stress, τi, is given by
3
0στ mi =
Where σ0 = basic yield stress of the ring material. The assumptions of
constant m and constant σ0 automatically means that τi is constant. Certain
investigations [14-16] on friction indicate that, for metal working conditions, the
assumption of a constant interfacial friction stress may be reasonably justified. When
60
strain hardening of ring material occurs (i.e., assumption (b) is violated) it is
necessary that interpretation of the ring test results with the mathematical solution
should be cautious.
The theoretical solutions of Avitzur [12] and Hawkyard and Johnson [13] both
yield the following mathematical relationships for a ring specimen under compression
(Figure 4.1), where Rn is the radius of the metal flow divide within the ring
(sometimes referred to as the neutral or “no-slip”):
1. When Rn ≤ Ri
4
2
20
1/ 24
0
4
0
1
3
2( 1) 1
+ =
− −
i
n
i
RX
RR
R RX X X
R
2
0 0
0
exp 1 − − −
i
i
R R RX m
R T R ---------------(1)
2. When Ri ≤ Rn ≤ R0
4 4
02
00 0
4
0
0 0
1 1 31
ln2
2 1 1 1 3
+ + = × + − + +
i
n
ii n
n
R R
R RR RmT RR R R
R R R
------(2)
Eq.(1) is valid when Rn lies between Ri and O and
2
0 0
4
0
0
3( / )1ln
2 1 1 1 3
≤ − + +
i
i
i
mR R R
T R RR R
-------------------------(3)
Eq.(2) is valid when Rn lies between 0
2
+ iR R and R0 and
61
2
0 0
4
0
0
3( / )1ln
2 1 1 1 3
≥ − + +
i
i
i
mR R R
T R RR R
--------------------------(4)
Figure 4.1: Compression of flat ring-shaped specimen between flat dies.
Neither the basic yield stress of the material, σ0, nor the interfacial shear
stress, τ, appear in the final equations in terms of absolute values, only as a ratio, m.
The basic assumption in the analysis is that this ratio remains constant for the material
and deformation conditions. If the analysis is carried out for a small increment of
deformation, σ0 and τ can be assumed to be approximately constant for this increment
and the solution is valid. Thus, if the shear factor m is constant for the whole
operation, it would appear justifiable to continue the mathematical analysis in a series
of small deformation increments using the final ring geometry from one increment as
the initial geometry for the subsequent increment and so on. As long as the ratio of
the interfacial shear stress, τ, and the material flow stress, σ0, remained constant it
would not be of consequence if the ring material strain hardened during deformation
provided that the increase in work hardening in any one single deformation increment
could be neglected. The progressive increase in interfacial shear stress accompanying
strain hardening would also be of no consequence provided that it could be assumed
to be constant over the entire die/ring interface during any one deformation increment.
Thus it is possible that the analysis could be justifiably applied to real materials even
though it was initially assumed that the material would behave according to the
Ring
specimen T
Rn
Ri
R0
Direction of
metal flow Upper die
Lower die
62
Mises’ stress-strain rate laws provided that the assumption of a constant interfacial
shear factor, m, is correct.
The ring compression test, developed by Male and Cockroft [10] is the most
commonly employed method for determining friction characteristics. The test
involves the compression of a hollow, thick-walled cylinder, or ring, and the
determination of the variation of the internal bore diameter with the height reduction.
The variation of the bore with height has been shown to depend on friction between
the ring and the platens, and to provide a good method for its evaluation [17]. The
test is reasonably easy to carry out at room temperature, since an interrupted
compression test (with the associated loss in accuracy because of the load reversal)
can be employed, with the bore diameter being measured at each interruption.
Calibrating curves for the ring compression test have been obtained using a
range of methods with various simplifying assumptions. Probably the most well-
known calibration curves are those determined by Hawkyard and Johnson [13]. In
their analysis of the ring, it is assumed that the material behaves with rigid perfect
plasticity and that no barreling occurs so that the deformation is completely
homogeneous, with uniform states of stress and strain. The ring compression test is
perceived by many as the standard procedure for determination of friction between the
billet and die in forging operation. In addition, it is sometimes assumed that it is a test
for which a universal calibration can be used. The friction arises due to the work piece
coming in contact with a tool or die [18, 19]. The mechanics of friction are complex.
The fundamentals of this phenomenon have been much studied [5, 14, 20-22], yet
very little that is known would facilitate formulation of exact functional relationship
between τ and the other variables. Friction can be described by a coefficient of
friction (µ), defined as:
/ / / hardnessµ = = τ = τi iF R p
Where: F = force of friction, R = normal reaction, p = interface pressure≅ σ0, and τi =
interface shear stress.
63
4.2.2: Compression Testing of Short Cylinders
The compression of a short cylinder between anvils is a much better test for
measuring the flow stress in metal working applications [23-25]. The nature of tensile
instability due to necking can be avoided and the test can be carried out to strains in
excess of 2.0 (for ductile material). Friction between the specimen and anvils play
key role. In the homogeneous upset (zero friction) test a cylinder of diameter D0 and
initial height H0 would be compressed in height to H and spread out in diameter to D
according to the law of constancy of volume.
D02
H0 = D2
H
For the selection of an upsetting process the following parameters are significant:
a) Geometry of the component
b) Strength of the component material
c) Formability characteristics of the material
d) Upset ratio
e) Accuracy
f) Surface quality, and
g) The economic considerations.
For trouble-free and economic production the work piece material must be of
uniform quality (chemical composition, mechanical properties and surface finish).
4.2.3: Engineering Stress and Engineering Strain
The engineering strain e is the ratio of the change in length to the original
length [26-28].
0
0
0 0 0
1 L
L
L LLe dL
L L L
−∆= = = ∫ -------------- (1)
The engineering stress
0
PS
A= -------------- (2)
64
4.2.4: True Stress and True Strain
The engineering stress-strain curve does not give a true indication of the
deformation characteristics of a material because it is based entirely on the original
dimensions of the specimen and these dimensions change continuously during the
test. In metal working processes the work piece undergoes appreciable change in
cross sectional area. Thus measures of stress and strain which are based on the
instantaneous dimensions are needed.
Ludwik [29-31] first proposed the definition of true strain or natural strain “ε”.
In this definition of strain the change in length is referred to the instantaneous gauge
length, rather than to the original gage length.
00
lnL
L
dL L
L Lε = =∫ -------------- (3)
0
lnL
Lε = or ln(1 )eε = + -------------- (4)
True stress is the load at any instant divided by the cross-sectional area over
which it acts. True stress will be denoted by the familiar symbolσ .
σ = 0A
p -------------- (5)
σ = 0A
P(1+e) or σ = S (1+e) -------------- (6)
where: S = engineering stress
e = engineering strain
P = applied load
A = instantaneous area
In compression equation (6) becomes
σ = 0A
P(1-e) or σ = S (1-e) -------------- (7)
65
4.2.5: Computation of Plastic Strain
Plastic strain (εp) = (Total strain) – Stress
Young's modulus
From figure 4.2 totC y mx E= − = σ − ε
( )/ tot
P
ECC m
E E
σ − ε−ε = − = = −
ε = P totE
σε = ε − --------------- (8) [27]
εp
Figure 4.2: Elastic and plastic components of total strain
4.2.6: Optical Measurements of Strains
Knowledge of material behaviour requires the measurement of mechanical
parameters. Strains are usually measured by the use of strain gauges. When the
specimen is distant, difficult to reach, in a hostile environment or does not support the
attachment of gauges, the use of measurement techniques without contact such as
optical methods, allows to determining the desired parameters. These non-contact
and non-destructive methods can represent a real advance for displacement, stress and
strain measurements. There are two types of experimental methods for strain
measurement, indirect and direct methods. Indirect techniques allow strains to be
determined by derivation of the measured displacement field. Among indirect
methods the principles of ones include digital image correlation [32], speckle
interferometry [33] or Morié techniques [34]. Direct methods give strains using an
extensometer, gauges, three element rosettes or grid [35-37]. All these tools can only
σy
εelastic
C totalε
σ
ε
y = mx + C
66
be used for strains less than 20% and also do not allow the measurement of larger
deformation. Three optical methods can be employed for large strain measurement
using a grid (lines or spots) method of mark-tracking techniques.
The optical measurement of strains on a specimen surface is generally
achieved with a grating of crossed lines obtained by engraving or die stamping from a
holographic support containing the master grating [38,39]. The mark-tracking
techniques can be implemented [40] in which four grid lines are scribed or drawn with
a fine marker pen. The specimen surface can be either transparent or opaque.
Ductility of a material is generally defined as the ability to deform plastically
without fracture. It is usually expressed as a measure of the strain at fracture in a
simple test (elongation or reduction in area being the two most commonly used). For
metal forming applications, effective ductility is not a unique property of the material;
it depends on localized conditions of stress, strain, strain rate and temperature in
combination with material characteristics such as inclusion content and grain size,
processing parameters associated with die design, work piece geometry, and
lubrication determine the local stress and strain states throughout the material. Control
of these parameters may thus be exercised to produce conditions favorable for
enhanced deformations to fracture. The compression test on cylindrical specimens has
been used by several investigators for the study of deformation behaviour under
combined stresses [41-44]. During compression of a cylinder the lateral free surface
barrels and fractures form at the barrel. The barreled surface results in the
development of a tensile stress in the circumferential direction and a decrease in the
magnitude of the axial stress below the average compressive stress in the material. In
case of severe barreling the axial stress may also become tensile. Through variations
in the cylinder height–to–diameter ratio and contact surface friction conditions, the
severity of the barrel curvature can be controlled. Thus a variety of stress and strain
states can be generated in the equatorial regions of the upset cylinders, providing a
convenient test for deformation and fracture studies.
67
4.2.7: Theoritical Background of Orthogonal Axes
The orthogonal axes of reference for the component of stress and strain
increment on the free surface of a compression specimen are as shown in figure 4.3.
It is assumed that throughout the compression test the principal axed of stress and
strain increment coincide. The reference axis, r, in a principal direction because the
shear stresses on a free surface are zero, and θ-axis is principal direction because the
flow is symmetrical about the longitudinal axis, hence the z-axis is also a principal
direction.
Figure 4.3: Showing the orthogonal axes of reference
For these conditions, the Von-Mises yiels criterion can be written in terms of
principal stresses as
σ = 23J = [2
θσ + 2
zσ - zσσ θ ] 2/1 ------------ (1)
Because the transverse stress component rσ is zero on the free surface. Here
J 2 is the second invariant of the stress deviator.
The plastic strain increment at any instant of loading is proportional to the
instantaneous stress deviator, i.e.
d ijε = ijσ ' dλ ----------------- (2)
Equator
Lo
ng
itu
din
al
ax
is
z
r θ
∆z0
∆w0
68
Where dλ is non negative constant which may vary throughout the loading history.
For rσ = 0, equation (2) yields
θ
θθ
σσσσ
εε
−
−=
z
z
zd
d
2
2 or
2
21
++
=α
ασσ θ
z
------------ (3)
Where zd
d
εε
α θ= is a parameter which can be determined by experimental
measurements of the ratio of the principal strain components in the θ and z directions
on the free surface of the specimen.
Substituting equations (3) and (1) gives the following expression for θσ and zσ .
2/12
2
21
2
211
−
++
+
++
−=α
ααα
σσ z ---------------(4)
And
++
=αα
σσ θ2
21z ----------------------(5)
By convention, compressive stresses are negative, thus the lower sign in
equation (4) is used in evaluating zσ . σ denotes the effective flow stress for an
isotropic material for the appropriate effective strain ε at the free surface.
In terms of the principal strain increments
( ) 2/122
3
2zz ddddd εεεεε θθ ++= ------------------(6)
where, the incompressibility condition 0=++ zr ddd εεε θ has been used.
The effective strain at the free surface from equation (6) is given by
ε = ∫z
dε
ε0
= 3
2 ( ) zd
z
εααε 2/1
0
21∫ ++ -----------------(7)
69
Where the integration can be performed along the strain path provided the
principal axes of the strain increment do not rotate relative to element.
The equations (4),(5) and (7), will enable us to calculate the stresses and
effective strains on the geometric centre of the bulge surface and are identical to the
equations derived by Kudo and Aoi and David et al [41,45].
Theoretically, α may take any value between -∞ and +∞ but there is no real
value of α for which θσ or zσ would increase with out bounds. In the present
experimental situation the range ofα is limited to -2 to -1/2. As α increases, the
tensile stress θσ increases but the hydrostatic stress Hσ = ( )zσσ θ + /3, becomes more
and tensile which leads to a higher probability of fracture.
70
4.3: EXPERIMENTAL DETAILS
4.3.1: Ring Compression Test
Ring compression tests were carryout to determine the friction factor ‘m’ for a
given set of flat platens and work piece while upsetting. These tests were performed
on alloy and composites in dry condition. Standard ring shaped samples were
prepared by conventional machining, turning and boring operations on a lathe
machine with the ratio of Outside Diameter (OD): Inside Diameter (ID): Height (H) =
6: 3: 2. Figure 4.4 shows the ring compression sample with OD: ID: H = 15:7.5:5 mm
(6: 3: 2). These ring samples were allowed to deform slowly up to 50% at the rate of
0.25 mm/sec by using computer controlled electrical screw driven 100 kN universal
testing machine (Model: UT 9102; Dak System Inc). The internal diameter of the ring
was measured intermittently by stopping the test up to a maximum deformation of
50% or up to fracture whichever is earlier. Figure 2.13 shows the closer view of the
ring compression experimental setup.
Figure 4.4: Ring compression specimen (OD: ID: H = 6:3:2)
71
4.3.2: EXPERIMENTAL STRAIN MEASUREMENTS
4.3.2.1: Experimental Set Up
A PC–based system consisting of a video camera (Logitech charge coupled
device) with an integrated digitizing capacity with resolution of 640x480 pixels and
256 colour full depths attached with a magnifying glass was used. The shutter speed
used was 20 pictures (full frame) per second and was sufficient enough to record the
images as the run speed of the upsetting process was a slow test performed on
computer controlled bench mark machine of 100 kN capacity. Figure 4.5
demonstrates the experimental setup.
4.3.2.2: Materials
The upsetting tests were performed on four different materials viz., AA2024
alloy , and AA2024-2% fly ash, AA2024-6% fly ash and AA2024 –10% fly ash
composites in the following conditions.
(i) Aspect ratio (H0/D0) of 1.0, and
(ii) Aspect ratio (H0/D0) of 1.5.
4.3.2.3: Compression Testing
The upset tests were performed at room temperature between two flat platens
on a computer controlled UTM of 100 kN capacity universal testing machine (Model:
UT 9102; Dak System inc). The compression dies of H11 grade are used for
compression and the sample is placed axi-symmetrically in between the dies. The
tests were conducted at a constant cross head speed for both the alloy and composites
for all the specimens. Details of the process control parameters and necessary
precautions were discussed in chapter 2. The compression tests were carried out until
either 50% reduction in height or initiation of the fracture on the specimen surface
whichever is earlier. A PC based data logging system was used to record and store
the loads and displacements continuously.
72
Figure 4.5: Experimental set up of computer controlled 100 kN compression testing
machine with on line video recording system (Model: UT 9102; Dak
System inc).
73
(a)
(b)
Figure 4.6: (a) Closer view of the experimental set up of computer controlled 100 KN
compression testing machine with on line video recording system (b)
Closer view of the Upset sample.
Top Platen
Upsetting
Specimen
Bottom Platen
Top Platen
Bottom Platen
CCD Camera
Upsetting
Specimen
74
4.3.3: PREPARATION OF SAMPLES, GRID MARKING AND
MEASUREMENTS
Several workability tests are available to study the deformation behaviour
under the combined stress and strain conditions usually found in bulk deformation
process. The deformation behaviour obtained from upsetting test to a deformation
50% is worth studying to determine the flow pattern. In most of the upset forging
processes such as in cold heading, riveting, plate bending, stud welding, the
deformations are limited to 50% in a single stroke in order to check the die filling.
The parameters that affect the die filling are friction conditions, material ductility, and
aspect ratio and strain rate. In case of cold and warm forging processes the effect of
strain rate can be discarded, within the reasonable limits of strain rate variation that is
caused in press forging operation.
Deformation behaviour for two limiting values of aspect ratio 1.5 (to avoid
buckling) and 1.0 (which is used in most of the forging applications) are chosen to
conduct the tests. The specimens were machined from 18 mm diameter gravity die
cast and homogenized fingers to a diameter of 12 mm and to lengths 12 mm and 18
mm. Grid lines were marked at the mid height of the surfaces (4 mm x 900). The
measurement and strain calculations scheme was shown in figure 4.7. Online video
images of grid were recorded during the deformation process. The tests were
continued till 50% deformation or till the appearance of an appreciable crack which
ever is earlier. The images of grids before and after deformation for Ho/Do = 1.0 were
shown in figure 4.8 (a) and (b) respectively. The distortions of grid from recorded
images were analyzed offline after the experiments at desired reductions. The camera
was calibrated for the corresponding distances of grid to yield a fixed magnification
and to take care of distortions in the images. The images were selected at deformation
steps of 5% using the software animation shop 3.0 and are transported to paint shop
pro 7.0 for further processing to get the enhanced noiseless images of high clarity
grid. Axial ( zε ) and circumferential strain ( θε ) values were calculated from these
measurements according to:
zε = ln
0h
h, and θε = ln
0w
w
75
Where: h0 and w0 are the initial height and width of an element (Figure 4.7a),
respectively, and hi and wi are the current height and width of the element respectively
(Figure 4.7b).
Figure 4.7: (a) Schematic diagram of upset tests showing grids for strain
measurements
(a) (b)
Figure 4.8: Images of grids drawn at equatorial plane for Ho/Do = 1.0 (a) before
deformation (b) after deformation
w
h0
D0
H0
D
w
h
76
4.4: RESULTS AND DISCUSSION
4.4.1: RING COMPRESSION TEST
The decrease in internal diameter of the ring compression test was plotted
against % of deformation on Male and Cockcroft calibration curves in increments of
10% deformation. The experimental values obtained for AA2024 alloy and fly ash
composites was fitted into the Male and Cockcroft calibration curves, as shown in
Figure 4.9 (a-d). These experimentally obtained curves were coinciding with the
calibration curve at the friction factor ‘m’ value of 0.36. Hence the friction factor ‘m’
for this AA 2024 alloy and the composites in dry condition was equal to 0.36. The
same set of flat platens was used for upsetting alloy and the composites under
investigation. The same surface roughness for alloy and composites samples was
maintained. Hence, the friction factor ‘m’ for alloy and the composites under
investigation was found to be 0.36. Figure 4.10 shows the photographs of ring
specimen before and after 50% deformation. The end face of a ring specimen after
deformation has a polished finish; this phenomenon evident the existence of friction
between the ring specimen and die during deformation under dry condition.
77
(a)
(b)
-60
-40
-20
0
20
40
60
80
100
0 10 20 30 40 50 60 70 80 90
% Deformation
% Decrease in Internal Diameter AA 2024 alloy
m=1
m=0.8
m=0.6
m=0.4m=0.2
m=0.12
m=0.08
m=0.04
m=0.02m=0
-60
-40
-20
0
20
40
60
80
100
0 10 20 30 40 50 60 70 80 90
% Deformation
% Decrease in Internal Diameter
AA2024 -2% Fly Ash Composite
m=1
m=0.8
m=0.6
m=0.4m=0.2
m=0.12
m=0.08
m=0.04
m=0.02m=0
78
(c)
(d)
Figure 4.9: Ring test calibration curves for AA 2024 alloy and composites showing
the changes of the minimum internal diameter as a function of the
reduction in height for dry (Unlubricated) condition. (a) AA 2024 alloy
(b) AA 2024 alloy- 2% Fly ash Composite (c) AA 2024 alloy- 6% Fly ash
Composite, and (d) AA 2024 alloy- 10% Fly ash Composite.
-60
-40
-20
0
20
40
60
80
100
0 10 20 30 40 50 60 70 80 90
% Deformation
% Decrease in Internal Diameter
AA2024- 6% Fly Ash Composite
m=1m=0.8
m=0.6
m=0.4
m=0.2
m=0.12
m=0.08
m=0.04
m=0.02m=0
-60
-40
-20
0
20
40
60
80
100
0 10 20 30 40 50 60 70 80 90
% Deformation
% Decrease in Internal Diameter
AA 2024-10% Fly Ash Composite
m=1
m=0.8
m=0.6
m=0.4
m=0.2
m=0.12
m=0.08
m=0.04
m=0.02m=0
79
(a)
(b)
Figure 4.10: Ring compression test specimen (OD: ID: H = 6:3:2) (a) Before
deformation (b) after 50% deformation in dry condition
80
4.4.2: Compressive Properties of the AA2024 alloy and Al-Fly Ash Composites
Figure 4.11 shows the hardness of the AA 2024 alloy and AA 2024 alloy fly
ash (ALFA) composites before and after 50% deformation. As the amount of fly ash
is increasing the hardness of the composite is increasing. This increase was observed
from 73 VHN for AA 2024 alloy to 130 VHN for AA 2024–10% fly ash composite.
This could be due to the presence of fly ash particulates which consists of majority of
the alumina and silica which are hard in nature.
Further, figure 4.11 also illustrates the hardness values for 50% deformed of
AA 2024 alloy and AA 2024 alloy–fly ash composites (2, 6 & 10 wt. % fly ash) under
compression loading. The increased hardness values were observed for all the tested
samples under deformed condition. This increase in hardens was higher for higher the
amount of fly ash presence in the matrix. This increase was attributing from the
presence of high hardness fly ash powder, which act as reinforcing phase, are
dispersed in AA 2024 alloy matrix and become the obstacles to the movement of
dislocation when plastic deformation occurs. From the present investigation the
increase in hardness value at before and after 50% deformation for alloy and
composites was observed as: for AA2024 alloy: 73 to 89 VHN, whereas for AA2024-
2% fly ash composite was 85 to 115 VHN, for AA2024-6% fly ash composite was118
to 132 VHN, and for AA2024-10% fly ash composite 130 to 143 VHN respectively.
Compressive properties of the synthesized Al-Fly ash (ALFA) composites
(2, 6 and 10 wt. % fly ash) can be understood by studying the load– displacement
curves. Figure 4.12 and 4.13 shows the load–displacements curves for AA2024 alloy
and fly ash composites during compression testing with aspect ratios of 1.0 and 1.5
respectively; and figures 4.14 and 4.15 shows the true stress–true strain curves of AA
2024 alloy and ALFA composites with aspect ratios of 1.0 and 1.5 respectively. The
load requirement increased with increase in displacement for both the alloy and
composites. The composites show higher loads than the unreinforced alloy; and this
increase in load is more for higher the amount of fly ash, as shown in figures 4.12 and
4.13. The same is confirmed from the true stress and true strain results, as shown in
figures 4.14 and 4.15.
81
This indicates that the fly ash addition leads to improvement in the strength of the
composites. The strength of the metal matrix composites (MMC) is expected to
increase by addition of solid ceramic particles due to the strengthening effects
occurred in particulate reinforced composites. These effects include the transfer of
stress from the matrix to the particulate, the interaction between individual
dislocations and particulates, grain size strengthening mechanism due to a reduction
in composite matrix grain size, and generation of a high dislocation density in the
matrix of the composite as a result of the difference in thermal expansion between the
metal matrix and particulates [46-48]. Further the experimental results shows that
increased in aspect ratio decreases the load required for the same amount of
deformation. For a fixed diameter, a shorter specimen will require a greater axial
force to produce the same percentage of reduction in height, because of the relatively
larger undoformed region [49].
Figure 4.11: Comparative hardness bar chart for AA 2024 alloy and AA 2024–2-10%
fly ash composites before and after 50% deformation
0
20
40
60
80
100
120
140
160
0 2 6 10
Ha
rdn
ess
(V
HN
)
Wt. % of fly ash
Before Deformation 50% Deformation
Figure 4.12: Load –
composites at the aspect ratio
Figure 4.13: Load –
composites at the aspect ratio
82
– displacement curves for AA 2024alloy and Al
composites at the aspect ratio (Ho/Do) =1.0
– displacement curves for AA 2024 alloy and Al
composites at the aspect ratio (Ho/Do) =1.5
alloy and Al-Fly ash
y and Al-Fly ash
Figure 4.14: True stress vs true plastic strain curves for AA 2024alloy and Al
composites at the aspect ratio (Ho/Do) =1.0
Figure 4.15: True stress vs true plastic strain for AA 20
composites at the aspect ratio (Ho/Do) =1.5
83
Figure 4.14: True stress vs true plastic strain curves for AA 2024alloy and Al
composites at the aspect ratio (Ho/Do) =1.0
Figure 4.15: True stress vs true plastic strain for AA 2024alloy and Al
composites at the aspect ratio (Ho/Do) =1.5
Figure 4.14: True stress vs true plastic strain curves for AA 2024alloy and Al-Fly ash
24alloy and Al-Fly ash
84
4.4.3: HOLLOMON POWER LAW PARAMETERS
True stress vs true strains were calculated from equation (7) and (8) of section
4.2.4 with the help of the Load – displacement data; which was generated during the
cold upsetting of alloy and composites. The calculated true stress vs true strains were
fit into well established Hollomon power law [50-56] given by:
σ = K ε n
Where: σ = true stress
ε = true plastic strain
K= strength coefficient, and
n = strain hardening exponent
Figures 4.14 and 4.15 shows the representative plots of σ vs ε generated
from the upsetting test data carried out at slow speed with aspect ratios (H0/D0) = 1.0
& 1.5 of the AA2024 alloy and composites respectively. This data was treated to be
material property [57] and used as input for finite element analysis discussed in
chapter 5.
Hollomon parameters ‘K’ and ‘n’ are used widely to assess behaviour in both
uniaxial tension and compression at room temperature [58-60]. These constants have
also been used to relate properties in metal forming [61-67]. The strength coefficient
(K) gives the flow stress at unit strain and it is the measure of elastic spring-back. The
strain hardening exponent ‘n’ is an important in metal forming. It signifies the strain
hardening or work hardening characteristic of a material, that is, the higher the value
of ‘n’, higher is the rate at which the material work hardens. A material with high
value of ‘n’ is preferred for process, which involves plastic deformation. The larger
the ‘n’ value, the more the material can deform before instability [68].
The strength coefficient, K found to be increasing with increasing fly ash
content, figure 4.16 (a). A rise in ‘K’ value was observed from 402 MPa for AA2024
alloy to 890 MPa for AA2024-10% fly ash composite. The obtained values were at
50% deformation by cold upsetting process.
85
Figure 4.16(b) shows the effect of fly ash particle on strain hardening
exponent ‘n’. The value of ‘n’ found to be increasing with fly ash addition. The
strength of the metal matrix composites (MMC) is expected to increase by addition of
solid ceramic particles due to the strengthening effects occurred in particulate
reinforced composites. The presence of second phase particles in the continuous metal
matrix phase resulted in localized internal stresses which modify the plastic properties
to a great extent [69, 70]. Hence, the presence of hard fly ash particles made the
composites high strength subsequently increase in strain hardening exponent ‘n’
values for larger fly ash content.
During metal forming the dislocation density increased by several orders of
magnitude. By this, zones of higher dislocation density emerge, which represent a
hindrance for moving dislocations. Therefore the dislocations can only pass by or cut
across one another at an increases stress. The inner stress also cause the dislocation
sources to be activated again only at higher stresses. The stress fields of the
dislocations, which act against the emergence and movement of further dislocations,
must be considered as the main cause of strain hardening. In polycrystalline metals,
gain boundaries and the difference in orientation of the slip planes between grains act
as additional obstacles for the dislocation movement.
If there has no thermally activated action, such as recrystallization or recovery,
during the deformation process, the exponent ‘n’ was a measure of the work
hardening observed in all metallic materials. This represents the increase of flow
stress σ with increase in natural strainε . Based on this phenomenon, the work
hardening coefficient ‘n’ was a measure of achievable maximum formability for
different materials during forming with the same external restraints. A higher work
hardening coefficient means a higher uniform elongation value, there by reducing the
tendency for local straining in the material. Although slip planes occasionally cross
grain boundaries, especially if the crystals have twin orientation or close to it as a rule
deformation stops whenever a change of orientation is present not only grain
boundaries but also sub boundaries acts as barriers for movement, and a pile-up of
dislocations with distortion of the crystal results [71-73].
Figure 4.16: (a) Variation of strength coefficient (K) wit
AA2024
addition of
86
(a)
(b)
Variation of strength coefficient (K) with addition of
AA2024 alloy; (b) Variation of strain hardening exponent (n) with
addition of fly ash to AA2024 alloy
h addition of fly ash to
Variation of strain hardening exponent (n) with
87
4.4.4: MEASUREMENT OF EXPERIMENTAL STRAIN PATH EQUATIONS
Surface strains, θε and zε were evaluated for the geometric mid-sectional grid
of the specimens (figure 4.8) and the results were plotted in figures 4.17 to 4.20, for
AA2024 alloy and AA2024-2 to 10 wt. % fly ash composites respectively.
Homogeneous deformation corresponds to ideal condition, that is, deformation
without friction or barreling with a constant slope of2
1−=
Zεεθ .
Homogeneous compression resulted in straight strain paths of slope nearly
equal to -1/2. From the figures 4.17 to 4.20, it was evident that upset tests with
friction produced curved strain paths. The tendency of this curved strain paths was
increasing with increasing frictional constraint and decreasing aspect ratio. The slope
of the experimentally determined relationship between axial strain zε and
circumferential strain θε deviated from that corresponding to homogeneous
deformation as barreling develops. The strain paths for H0/D0 = 1.0 in dry conditions
were much steeper than H0/D0 = 1.5 of same frictional condition. This was true for the
alloy and all the composites under investigation. Also it was observed that the strain
path deviations from homogeneous line was less for H0/D0 = 1.5 compared to H0/D0 =
1.0.
The line with a slope2
1−=
Zεεθ on θε vs zε plot and which intersects the
ordinates at ≅θε 0.3 is an estimate of a fracture line for upsetting test performed on
circular cylinders [74]. Though the intercept 0.3 on the ordinate may be
approximately correct for steels, but may differ for material to material. Brownrigg et
al [75] and H. A. Kuhn et al [76] reported these values of intercepts as 0.29, 0.32, and
0.18 for the 1045 steel, 1020 steel and 303 stainless steel respectively. In the present
work these intercept values were observed to be 0.30 for AA2024 alloy and all the Al-
fly ash composites.
Upset tests with friction produce curved strain paths. The deviation of slope
from that of homogeneous deformation to ratio between axial strain ( θε ) and
88
circumferential strain ( zε ) represents barreling. This deviation was less when the
specimen – die interface friction was low. From the experimental results, it was
evident that the strain paths obtained from cylindrical specimens with aspect ratios 1.0
and 1.5 deviated from the slope −0.5 (which represents the homogeneous
deformation). It was also observed that all strain paths obtained from different
specimens exhibited nonlinearity from the beginning to the end of the strain path. And
also it was shows that the slope at a point on the strain path increases as that point
moves toward the end of the strain path or the fracture point. This means that at the
fracture point, the incremental axial strain component was almost zero, while the
incremental circumferential strain component was very high. This change in the slope
of the strain path has a great effect on the stress state at the surface of the specimen.
The curve fitting technique was used (because of the scatter in the experimental data
for axial and circumferential strains) to obtain a smooth relationship between the axial
strain and circumferential strain. This relationship represents the equations of the
strain paths. Some of these equations of strain paths obtained from different
specimens were given in table 4.1. The ends of the strain paths represent the fracture
points. Joining all the fracture points on all strain paths gives the workability limit for
the materials under considered.
Table 4.1: Experimental strain path equations obtained by the best curve fit technique.
The compression tests were carried at the friction factor ‘m’= 0.36 (Dry condition).
S. No Material Aspect ratio Strain path equations
1. AA2024 alloy
H0/D0=1.0 θε =0.218 zε2 -0.5426 zε
2. H0/D0=1.5 θε =0.0938 zε2 -0.5223 zε
3. AA2024 alloy- 2%
fly ash composite
H0/D0=1.0 θε =0.2135 zε2 -0.6884 zε
4. H0/D0=1.5 θε =0.1579 zε2 -0.5558 zε
5. AA2024 alloy- 6%
fly ash composite
H0/D0=1.0 θε =0.0929 zε2 -0.9262 zε
6. H0/D0=1.5 θε =0.6439 zε2 -0.3569 zε
7. AA2024 alloy- 10%
fly ash composite
H0/D0=1.0 θε =0.2958 zε2 -0.7729 zε
8. H0/D0=1.5 θε =0.4193 zε2 -0.4283 zε
89
Figure 4.17: Circumferential strain θε as a function of axial strain zε at the equatorial
free surface for AA2024 alloy
Figure 4.18: Circumferential strain θε as a function of axial strain zε at the equatorial
free surface for AA2024–2% fly ash composite.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Axial Strain
Circumferential Strain
H/D = 1.0
H/D = 1.5
Fracture Line
Homogeneous Deformation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Axial Strain
Circumferential Strain
H/D = 1.0
H/D = 1.5
Fracture Line
Homogeneous Deformation
90
Figure 4.19: Circumferential strain θε as a function of axial strain zε at the equatorial
free surface for AA2024–6% fly ash composite.
Figure 4.20: Circumferential strain θε as a function of axial strain zε at the equatorial
free surface for AA2024–10% fly ash composite.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Axial Strain
Circumferential Strain
H/D = 1.0
H/D = 1.5
Fracture Line
Homogeneous Deformation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
Axial Strain
Circumferential Strain
H/D = 1.0
H/D = 1.5
Fracture Line
Homogeneous Deformation
91
4.4.5: DETERMINATION OF STRESS COMPONENTS
Estimation of the effective strain,ε , on the geometrical mid section of the free
surface were made from equation (7) of section 4.2.7. The effective strain obtained
by this method allowed estimates of the effective stress from the stress - strain power
law relationship discussed in section 4.2.7. The appropriate value of effective stress
was then used in equation (4) and (5) of section 4.2.7 to calculate the stresses θσ and
zσ . The hydrostatic component of the stress, Hσ =( )
++
3rz σσσ θ was then
computed. The magnitude of the free surface stress components Hzandσσσ θ , for
various test conditions like deformation in dry condition with aspect ratio (Ho/Do) of
1.0 and 1.5 were plotted against effective strains which were shown given in figure
4.21 to 4.24. The drawn figures represent the AA2024 alloy and Al-2-10% fly ash
composites respectively. As the value of rσ on free surface was assumed to be zero,
Hσ becomes ( θσ + zσ )/3.
In an idealized situation of uniaxial compression, the circumferential stress θσ ,
was zero and the axial stress zσ was equal to the yield stress, 0σ . Under this
condition the hydrostatic component of the stress, Hσ would be equal to Zσ /3 and
would always be compressive; a state of instability will never occur in homogeneous
deformation. Hence according to an instability theory of fracture ductile fracture will
never occur in homogenous deformation. On the other hand if the friction between
the specimen and platens is such that the deformation departed from the homogeneous
case and barrel was developed. The tensile circumferential surface stress component
θσ was non zero and the hydrostatic component of stress Hσ become less compressive
and in some cases tensile.
The present results referring to figures 4.21 to 4.24 of AA2024 alloy and
AA2024alloy –fly ash composites show that with the increasing effective strain the
circumferential stress component θσ increasingly becomes tensile with continued
deformation. The increase in its value was found to be more in case of specimens
deformed for lower aspect ratio compared to the higher aspect ratio conditions. On
92
the other hand the axial stresses zσ , for AA 2024 alloy as well as all the fly ash
composites increased in the very initial stages of deformation but started becoming
less compressive immediately as barreling developed. For unfractured specimens the
axial stress zσ , was always be compressive. However for the specimens where
surface fracture occurred both zσ and Hσ stress components became less and less
compressive as deformation progressed and became tensile. This gave rise to the so
called normal fracture.
Kudo and Aoi [41] and Kobayashi [43] observed both the normal and shear
type of fractures in their ductile failure studies; the shear type of fracture was
observed when the axial stress, zσ on the surface is compressive. It is possible to
speculate that when friction at the interface is so negligible that the axial stress zσ is
always compressive and the circumferential stress θσ never reaches the critical value,
shear type of fracture should occur. To verify this hypothesis Samantha [74] made his
study on an Al specimen of H0/D0 = 1.5 which was incrementally deformed without
any strain measurements. New Teflon film was used at each incremental deformation,
and the deformation was continued until shear crack appeared, after 93% reduction in
height. This result gives an indication that, if the cold heading wire does not contain
longitudinal surface defects such as seams and laps, and is well lubricated, ductile
fracture should not be a problem in a similar process such as bolt heading, plate
bending and other cold forming operations.
The hydrostatic stress involves only pure tension or compression and yield
stress is independent of it. But fracture strain is strongly influenced by hydrostatic
stress [77, 78]. Increase in friction constraint and decrease in aspect ratio caused
hydrostatic stress to be tensile and instability starts. As the hydrostatic stress becomes
more and more tensile, a state of tensile instability will occur. The transformation in
nature of the hydrostatic stress from compressive to tensile depends on the shape and
size of the specimen and the frictional constraint at the contact surface of the
specimen with the die block.
In the present work, the upsetting tests were performed in dry condition for
predicting the deformation to fracture. Due to practical difficulties in observing the
93
crack initiation the maximum deformation is limited to 50%. For AA2024 alloy and
AA2024 alloy -2% fly ash composites, no crack was observed. In case of AA2024–
6% fly ash composite, the crack was observed at 48% deformation for aspect ratio of
1.0 and no crack was observed for aspect ratio of 1.5. Referring to the result obtained
for AA2024-10% fly ash composite, the crack appearance was observed at 46% and
48% deformation for the aspect ratios of 1.0 and 1.5 respectively
From the observation of figures 4.21 to 4.24, showing hydrostatic stress as a
function of effective strain, it was concluded that for the same amount of strain the
tendency of hydrostatic stress changes from compressive to tensile under for small
aspect ratios. For AA2024 alloy, the extent of deformation from instability to fracture
was large. But in case of all the fly ash composites (AA2024 alloy - 2 to 10 wt. %),
due to presence of large portion of second phase particles, the post instability strain to
fracture was small. Similar results were found with the experimental works of
Edelson and Baldwin [79]. However this post instability strain to fracture can be
increased by changing the microstructure via proper heat treatment as it is influenced
by the grain size and inter particle distance. Such study is beyond the scope of present
work.
Figure 4.21: Effective stress
effective strain
condition with aspect
94
(a)
(b)
Effective stressσ , stress components θσ , zσ and σ
effective strain ε for AA2024 alloy; up to 50% deformed in dry
condition with aspect ratio: (a) H0/D0 = 1.0, (b) H0/D0
Hσ as a function of
alloy; up to 50% deformed in dry
0 = 1.5.
Figure 4.22: Effective stress
effective strain
deformed in dry condition with aspect ratio:
= 1.5.
95
(a)
(b)
Effective stressσ , stress components θσ , zσ and σ
effective strain ε for AA2024 alloy- 2% fly ash composite; up to 50%
deformed in dry condition with aspect ratio: (a) H0/D
H as a function of
2% fly ash composite; up to 50%
/D0 = 1.0, (b) H0/D0
Figure 4.23: Effective stress
effective strain
deformed in dry condition with aspect ratio:
1.5.
96
(a)
(b)
Effective stressσ , stress components θσ , zσ and σ
effective strain ε for AA2024 alloy-6% fly ash composite; up to 50%
deformed in dry condition with aspect ratio: (a) H0/D0
H as a function of
6% fly ash composite; up to 50%
0 = 1.0, (b) H0/D0 =
Figure 4.24: Effective stress
effective strain
deformed in dry condition with aspect ratio:
1.5.
97
(a)
(b)
Effective stressσ , stress components θσ , zσ and σ
effective strain ε for AA2024 alloy-10% fly ash composite
deformed in dry condition with aspect ratio: (a) H0/D0
H as a function of
fly ash composite; up to 50%
0 = 1.0, (b) H0/D0 =
98
4.5: CONCLUSIONS
1. The friction factor ‘m’ was found to be 0.36 for the given set of compression dies
in dry condition.
2. Irrespective of alloy composition the friction factor values were found to be same
for a given set of dies.
3. Load requirement increased with decrease in aspect ratio for given frictional
condition.
4. Strength coefficient (K) increased with increase in fly ash content for all the fly
ash composites compare to AA 2024 alloy.
5. Strain hardening exponent (n) increased with in fly ash content for all the fly ash
composites compare to AA 2024 alloy.
6. Machine vision system was successfully employed in the measurement of grid
distortion at equatorial plane for the analysis of stress components.
7. Implementation of Machine vision system reduced the extent of experimentation.
8. AA2024 alloy and AA2024 alloy–fly ash composites show that with the
increasing effective strain the circumferential stress component θσ increasingly
becomes tensile with continued deformation.
9. The increase in circumferential stress component θσ value was found to be more
in case of specimens deformed for lower aspect ratio compared to the higher
aspect ratio conditions.
10. The axial stresses zσ , for AA 2024 alloy as well as all the fly ash composites
increased in the very initial stages of deformation but started becoming less
compressive immediately as barreling developed.
11. At the beginning of deformation axial compressive stress increased in magnitude
but as the deformation progress the magnitude reduced.
12. Hydrostatic stress also reduced in magnitude as the deformation increased; in
some cases it even became tensile.
13. Increase in fly ash content and decrease in aspect ratio caused hydrostatic stress to
be tensile leading to normal type of fracture.
99
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