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7/28/2019 Influence of Friction in Simple Upsetting
R. Ganesh Narayanan,1 M. Gopal,2 and A. Rajadurai3
Influence of Friction in Simple Upsetting
and Prediction of Hardness Distribution in a ColdForged Product
ABSTRACT: Predicting inhomogeneous deformation in any forging process will definitely be helpful in deciding the tool, billet material, lubri-
cation, annealing sequences, and number of stages to make products. In this work, the influence of varied friction conditions on the hardness and effective strain variation during simple upsettingis studied.Also,hardnessvariation in a typical cold forging process is predicted by relating hardnessand effective strain evolution in a simple upsetting operation empirically. Four different lubricants, viz., castor oil ( m=0.33), soap (m=0.25), grease(m=0.2), teflon (m=0.16), are considered for experimentation. The friction factors of these lubricants were obtained from a Ring Compression Test(RCT) and are used in FE simulations of upsetting and forging operations. It is found from the analyses that: (1) Teflon shows relatively less variation
in hardness and effective strain depicting homogeneous upsetting operation, whereas other lubricants show a larger variation in hardness and effec-tive strain in radial and axial directions; (2)hardnessis observed to vary linearly with effective strain; (3) the empirical relationship between hardnessand effective strain obtained from a simple upsetting operation, which is common for all the lubricants, predicts the hardness distribution during theforging-extrusion process with moderate accuracy. This depends on the interface friction conditions, i.e., solid and semi-solid lubricants with better holdability like Teflon and soap show good correlation between experimental and predicted hardness values than liquid lubricant, i.e., castor oil.
KEYWORDS: forging, forming, hardness, lubricant
Introduction
Need for Hardness Prediction
Metal forming operations involve a complex interaction of the
metal and the dies and equipment used to deform it. The physical
phenomena describing a forming operation are difficult to expresswith quantitative relationships. The metal flow in any metal form-
ing operation is influenced by the process variables, viz., billet ma-
terial, tooling, conditions at tool/material interface, deformation
zone, equipment, used, and number of stages to make the product.
In producing discrete parts, several forming operations are required
to transform the initial “simple” geometry into a “complex” geom-
etry without causing material failure or undesirable material prop-
erties. Inhomogeneous deformation can occur in such forging op-
erations, and leads to failure or reduced fatigue life of the product
in service. A prior knowledge about the deformation characteristics
in a particular forging process is necessary in deciding the appro-
priate lubricants, tool/die design, load, forming and annealing se-
quences. Also, this assists in producing either a homogeneousstructure or a prescribed distribution of properties (like hardness,
strain, etc.) during the course of deformation. Most of the forged
parts are produced in multi-stages that in each stage the product
undergoes severe plastic deformation and hence strength/hardness
increases because of strain hardening. Sometimes the forged mate-
rial becomes so hard that one needs to anneal it before subsequent
forging operations to avoid early failure. It is cumbersome and time
consuming to measure the properties distribution at every stage to
assess the deformation characteristics of the component. Conse-
quently, the most significant objective of any method of analysis
could be to predict the forging behavior at the design stage itself
and assist the forming engineer in designing the forming and pre-forming sequences. For a given operation, such design essentially
consists of relating the undeformed part properties with that of the
deformed one, either by analytical, numerical predictions or
through empirical relations.
Hardness is the direct measure of resistance given by the mate-
rial to plastic deformation and hence is a better candidate to mea-
sure the deformation behavior of any cold forged product. If it is
possible to predict the hardness distribution at the design stage it-
self, without performing experiments or with minimum experi-
ments, one can monitor and control the cold forging process in the
design stage itself. Moreover, the heterogeneity involved in any
forging operation is influenced by the frictional conditions at the
material-die interface. Therefore it is conceivable to say that hard-
ness distribution during the forging operation will also be affected
by the interface friction conditions. So, predicting the hardness dis-
tribution at the design stage itself, for varied friction conditions,
will be of great concern and an interesting point to be explored.
Brief Description of Friction Tests for Cold Forging
This section briefly describes two friction tests, Ring Compression
Test (RCT) and Double Cup Extrusion (DCE) test, generally used
to evaluate the interface friction condition during forging opera-
tion. Also the literature status on predicting the hardness distribu-
tion during any cold forging operation is presented.
Manuscript received September 20, 2007; accepted for publication March 10,
2008; published online May 2008.1Department of Mechanical Engineering, Indian Institute of Technology,–
Guwahati, Guwahati 781 039, India, e-mail: [email protected] of General Engineering, DMI College of Engineering, Palanchur,
Nazrethpet (P.O.), Chennai 602 103, India.3Department of Production Engineering, Madras Institute of Technology,
Chrompet, Anna University, Chennai 600 044, India.
Journal of Testing and Evaluation, Vol. 36, No. 4Paper ID JTE101443
Annealing was conducted after the test specimens were machined.
In order to ensure uniform hardness distribution before deforma-
tion, hardness was measured at three different points in the axial
and radial directions.Average hardness of 60 VHN was found in all
the test specimens with a variation of ±2 VHN. Cylindrical speci-
mens with the dimension of 20 mm diameter and 30 mm height
were prepared for conducting simple upsetting tests.
Flow Curve of the Testing Material
In order to perform the FE simulations, the material properties of
the billet (strength coefficient, K, and strain hardening coefficient,
n) and stress-strain values should be given as input. Basically, it is
assumed here that the metal flow in a cold forging operation follows
the constitutive equation, = K T n where =true stress (MPa), T
=true strain, K = strength coefficient (MPa), n =strain hardening
exponent.
In order to establish this constitutive equation, a true stress-true
strain graph was drawn by conducting compression tests on pure
aluminum billet of size 20 mm diameter and 30 mm height. Load
and height deformation values were obtained from a 30-ton hydrau-lic press. By using volume constancy during plastic deformation,
true stress and true strain values were calculated. A graph was
drawn between true stress and true strain in log-log plot. The slope
of the line gives the n value and the stress at T =1.0 gives the K
value. Teflon was used as the lubricant for compression testing
which in general gives homogeneous deformation with a lesser
bulging effect. The bulging effect is neglected for simplicity.
Finally, the constitutive equation was found to be
= 180T 0.13
This constitutive equation was used as the input for the FE simula-tions.
Simple Upsetting Test
Commercially available pure aluminum billet (annealed) of size
20 mm diameter and 30 mm height was compressed for different
lubricating conditions in a 30-ton hydraulic press. The four lubri-
cants selected for the upsetting process are castor oil, grease, Te-
flon, and soap. The crosshead speed was maintained at 0.1 mm/s.
Upsetting was conducted for 50 % height reduction of the initial
billet. After 50 % height reduction, upset specimens were sectioned
axially into two halves and the flat surface was polished. Hardness
values were measured along the axial and radial directions.
Hardness Test
The distribution of hardness in the cold upset specimen was mea-
sured using the Vickers Hardness Tester, which employs a diamond
pyramid indenter. Hardness values were measured on the deformed
sample at a regular interval of 1.2 mm along the radial direction
and 1.3 mm along the axial direction from the geometrical center
of the upset specimen. Also, hardness was measured on the top cir-
cular face at a regular interval of 1.2 mm from the surface center of
the upset specimen. A load of 5 kg for a duration of 10 seconds was
used for hardness testing. A schematic representation of the loca-
tions of hardness measurement after the simple upsetting operation
is shown in Fig. 2. Hardness measurements were performed on both
sides of the horizontal and vertical axis. The same experimental
procedure was followed for all the lubricating conditions men-
tioned earlier. Two sets of experiments were conducted for each
condition and the average hardness was considered for analyses.
The variation of hardness was found to be within ±5 VHN with
repetitions in all the lubricants.
Effective Strain Evolution During Simple Upsetting Operation
The simple upsetting operation was simulated using a commercial
finite element code, DEFORM ver3.0 and the effective strain was
predicted. The FE simulations were conducted for 50 % height re-
duction for four different lubricants with corresponding friction
factor m values.
The given specimen was discretized into 600 number of ele-
ments, which were four-noded quadrilateral in shape. Axisymmet-
ric, plane strain, rigid plastic analyses was performed using simu-
lations. After 50 % height reduction, once the simulation was
completed, the effective strains were obtained at the same locations
where the hardness (VHN) values were previously obtained
through experiments. The same FE simulation procedure was fol-lowed for all four lubricating conditions.
Effective Strain
During forging of complex parts, the stress and strain at each point
during deformation is of a complex nature, unlike in uniaxial ten-
sile testing. The total strain at any point of the deforming sample
involves an elastic and plastic part, i.e.,
ij = ij e + ij p
Since the elastic strains are very small, when compared to that of
large plastic strains during forging, the total strain can be approxi-
FIG. 2— Schematic representation of location of hardness measurement on an upset sample; axially sectioned sample; surface hardness was measured at the surfacecenter line of the sample ( =location of hardness measurement; not to scale).
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mated to plastic strains only and hence, ij Ϸij p .The 3-D nature of plastic strain during forging can be repre-
sented by a single quantity “Effective strain=” which is a func-
tion of plastic strains in normal and shear directions. The effective
strain can be obtained by equating the plastic work done in 1-D to
the plastic work done in the general state, i.e.,
d = 1d 1 + 2d 2 + 3d 3
So, the plastic strain increment can be written as, d = 1 / 1d 1
+2d 2 +3d 3 .
Now, by following von Mises plasticity theory, and normality
condition, one can find the strain increments, viz., d 1, d 2, d 3.
From this, the plastic strain increment can be obtained as, d
= 2 / 3 d 12 + d 22 + d 32 1/2.Representing in general coordinate system,
d = 2/3 d 112 + d 22
2 + d 332 + 2d 12
2 + 2d 132 + 2d 23
2 1/2
Finally in terms of total plastic strains,
Effective strain, = 2 / 3 112 +22
2 +332 + 212
2 + 2132 + 223
2 1/2
Results of Upsetting Experiments
The variation of hardness and effective strain in the radial and axial
directions with respect to the distance from the geometrical center
to the periphery of the billet for different lubricants were analyzed
and the results are given below.
Variation of Hardness and Effective Strain in Radial
Direction
The variation of hardness with distance from the center to the pe-
riphery for different lubricants in the radial direction is shown in
Fig. 3. It is evident from the figure that Teflon m =0.16 shows a
relatively smaller change in hardness throughout the radial dis-
tance. The hardness varies within a span of 114 VHN at the center
to 103.75 VHN at the end. The smaller variation in hardness is
mainly because of the good lubricating ability of Teflon, resulting
in the homogeneous deformation. This is reflected in the friction
factor value m =0.16 obtained from RCT for Teflon as it is the
lowest of all the lubricants. In general, the lesser friction factor
value reflects the sliding friction condition existing at the interface
and hence homogeneous deformation (i.e., lesser bulging) is ex-
pected. This could have possibly resulted in uniform strain harden-
ing throughout the radial distance, leading to even distribution of
hardness.
Other lubricants, viz., grease, castor oil, and soap show nonuni-
form deformation and a large decrease in hardness is seen from the
center of the billet to its periphery (Fig. 3). (Local hardness in-
crease in a few cases is neglected.) For example, soap lubricant
showed comparatively more variation from 115 VHN at the center
to 92.5 VHN at the end. This is due to the bulging or barreling of
the billet during compression. During bulging, metal near the pe-
riphery of the billet (bulge surface) can be seen as the “easy de-formed region” and material near to the geometric center (or verti-
cal axis) can be seen as the “difficult deformed region,” at a
particular deformation height. It is expected that the “easy de-
formed region” strain harden less, when compared to the “difficult
deformed region,” as metal flows outward without any restriction.
In other words, the strain hardening ability should decrease from
the billet geometric center to its periphery. As a result, the decreas-
ing trend in hardness is seen from the center to the bulge surface (or
periphery) (Fig. 3). In the case of Teflon, the bulging or barreling
effect is comparatively less. The schematic of “easy and difficult
deformed regions” are shown in Fig. 4, where in the maximum de-
formed grids near the periphery are “easy deformed grids” and
minimum deformed grids near the geometric center are “difficultdeformed grids.”
It is found from the Fig. 5 that: (1) the effective strain decreases
from the center towards the periphery of the upset billet; and (2)
with increase in m values, the effective strain variation is more from
the center to periphery. First, the decrease in effective strain is simi-
lar to the hardness distribution along the radial direction. Secondly,
with an increase in m value, the resistance to metal flow at the in-
terface increases, as it approaches the sticking friction condition
m =1.0 . But the metal flows easily along the horizontal axis (A-B
in Fig. 4) of the sample. So, the higher the m value, the more will be
the bulging effect and hence more variation in effective strain from
the vertical axis (or geometric center) to the periphery of the upset
billet is expected, i.e., from A to B in Fig. 4 (for the same deforma-
FIG. 3— Variation of hardness from the geometrical center to the surface in the radial direction (inset shows the hardness measurement locations schematically).
NARAYANAN ET AL. ON INFLUENCE OF FRICTION IN A COLD FORGED PRODUCT 5
7/28/2019 Influence of Friction in Simple Upsetting
tion height). This variation is depicted in Fig. 5. The effect of the m
value on the bulging of the upset sample is schematically presented
in Fig. 6(a). With an increase in the m value, the ratio of diameter of
bulge
D B
to diameter of initial billet
Do
, say D B
/ Do
, will in-
crease, either linearly or nonlinearly, as shown in Fig. 6(b). This
leads to more effective strain variation from the geometric center to
the periphery of the upset sample, with an increase in the m value.
This behavior of effective strain concurs with the analyses by Kim
et al. [15], where in the m =0 case shows nil variation in effective
strain, with the m =1 case showing maximum effective strain varia-
tion from center to periphery.
Variation of Hardness and Effective Strain in Axial Direction
Figure 7 shows the variation of hardness with the distance from the
center to the surface of the upset billet for four different lubricants
in the axial direction. It is observed from the figure that Teflon
shows almost uniform hardness distribution from the geometric
center to the surface, except the initial local increase.This is similar
to the case in the radial direction presented earlier. While grease,
castor oil and soap show a relatively larger variation in hardness
(i.e.,) there exists a significant decrease in hardness from the geo-
metric center to the billet surface. This is due to the differential
straining of the billet near to the surface (or interface) and in the
center. Since movement of metal near to the interface is restricted
(because of nonholdability of lubricant and sticking friction condi-
FIG. 4— Schematic representation of “easy and difficult deformed regions” inupset sample (not to scale).
FIG. 5— Variation of effective strain from the geometrical center to the periphery in the radial direction (inset shows the effective strain measurement locations schematically).
FIG. 6— Schematic representation of influence of the m value on the bulging of the upset sample (not to scale); (a) Influence of m on the bulging of the upset sample,
(b) Effect of m on the D B / Do ratio.
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tion), deformation is less in that region, whereas metal deforms
easily without any restriction away from the interface. As a result,
the material hardening is severe near to the horizontal axis (or geo-
metric center), rather than at the interface. Hence, when hardness ismeasured in the axial direction from the geometric center to the
surface, it is likely to decrease as shown in Fig. 7.
One can imagine this similar to the deformed grids presented in
Fig. 4. The schematic of the deformed grid pattern for this case is
shown in Fig. 8, wherein the elements near to the geometric center
(or horizontal axis) deform more when compared to that of near the
interface. As a result, the hardness decreases from the center to the
interface (or billet surface). One should observe similar hardness
variation behavior, even if the hardness locations are other than the
vertical center axis. For example, if the hardness values are mea-
sured along the line AA as shown in Fig. 8(b), a similar decrease in
hardness is expected from the horizontal axis to the interface. The
hardness variation in the axial direction correlates with what is ob-served in Ref [15], wherein hardness decreases from the center to
the interface.
Figure 9 shows the variation of effective strain with respect to
distance from the center to the periphery of the billet in the axial
direction. It is understood from the figure that the effective strain
decreases from the center to the periphery of the upset specimen. It
also demonstrates that higher friction factor lubricant, i.e., castor
oil, m =0.33, generates higher effective strain at the center and
lower effective strain at the interface i.e., the range of effective
strain variation in the axial direction increases with increase in fric-
tion factor value. Teflon with m =0.16 shows lesser variation in ef-
fective strain (Fig. 9). One can visualize this as a result of inhomo-
geneous deformation (i.e., more bulging) occurring due to thehigher friction condition existing at the interface when castor oil is
used as the lubricant, whereas this is minimal in the case of Teflon.
Moreover, since castor oil is a liquid lubricant, its holdability dur-
ing the forging operation is of greater concern, which may not be an
issue in the case of Teflon.
Variation of Hardness and Effective Strain on the
Flat Surface (or Interface)
The variation of hardness (VHN) and effective strain from the cen-
ter to the periphery on the flat surface of the billet is presented in
Figs. 10 and 11, respectively. Teflon and other lubricants as wellshow more or less constant variation in hardness and effective
strain throughout the surface, except at the end. An important ob-
servation is that with increase in the m value, the effective strain
variation on the surface is decreasing. For example, in Fig. 11, cas-
tor oil with a higher m value m =0.33 shows lesser effective strain
throughout the surface, in comparison to that of Teflon with a lower
m value m =0.16 . This typical behavior can be related to the hold-
ability of the lubricant and, in turn, existence of sticking or sliding
friction conditions at the interface.
FIG. 7— Variation of hardness from geometrical center to the surface in the axial direction (inset shows the hardness measurement locations schematically).
FIG. 8— Schematic representation of initial billet and deformed grids during upsetting; Initial undeformed billet with grid pattern, (b) Deformed grids in one-quarter
of the upset sample (not to scale).
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For a lubricant with lesser holdability at the interface, say in cas-
tor oil m =0.33 , since the surface exhibits more resistance for ex-
pansion (or deformation), it undergoes lesser straining, leading to
minimum effective strain throughout the surface. Whereas Teflon m =0.16 exhibits better holdability because of the interface ex-
pands (or deforms easily) more, and hence more straining is expe-
rienced, resulting in higher effective strain throughout the surface.
Since hardness and effective strain are measured at the surface,
they remain constant, unlike in the billet inner region presented in
earlier sections. In the inner region of the upset billet, material de-
forms severely and hence undergoes (a) differential straining—
resulting in an increase and decrease of effective strain, and (b) dif-
ferential strain hardening—resulting in an increase and decrease of
hardness, which is not the case in the surface (or interface).
To summarize, the effect of varied friction conditions (or lubri-
cants) on the hardness and effective strain variation during the
simple upsetting operation is unified, i.e., decrease in hardness and effective strain is observed in the radial and axial directions. The
decrease in hardness and effective strain can be related to “differ-
ential strain hardening” and “differential straining,” respectively,
between the billet center region and periphery. This differential
hardening and straining is because of the holdability of the lubri-
cant and, in turn, the prevalence of sticking and sliding friction con-
ditions existing at the interface, i.e., whether bulging is minimum
or maximum. It is observed that the case with lesser holdability,
i.e., castor oil with m =0.33, depicted maximum variation of hard-
ness and effective strain, while Teflon with better holdability m=0.16 showed more or less uniform variation. Other lubricants,
viz., grease and soap follow a similar trend accordingly. Some of
the results are similar to that presented in Ref [15]. A constant
variation in hardness and effective strain is seen on the billet
surface.
Interrelating Hardness and Effective Strain
Figure 12 shows the scatter diagram of hardness (VHN) to effective
strain . All the experimental hardness (VHN) values were plot-
ted with the effective strain values from FE simulations for var-
ied lubricants. The scatter diagram indicates a linear variation be-tween the effective strain and hardness (VHN). Therefore, a
straight line fit was developed for hardness (VHN) as a function of
effective strain by the least square curve fitting method. The
empirical relationship established between hardness (VHN) and ef-
fective strain is,
FIG. 9— Variation of effective strain from geometrical center to the surface in axial direction (inset shows the schematic of effective strain measurement locations).
FIG. 10— Variation of surface hardness (VHN) from the center of the circular face to the outer surface (inset shows the hardness measurement locations
schematically).
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This empirical relation is common for all four lubricants, viz., Te-
flon, grease, soap, and castor oil, considered for experimentation.
This relationship is valid within the band of hardness values
±10 % within the line contour.The strain values on or near to the
fit line VHN=29.15 +74.5 will yield accurate hardness values.
A more accurate relationship can be obtained with more experi-
mental trials.
Conclusions on Upsetting Test
The influence of different lubricants on the variation of hardness
and effective strain during the simple upsetting operation is stud-
ied. An empirical relation has been established between the hard-
ness and effective strain during the simple upsetting operation. Fol-
lowing are the conclusions made from this part of the investigation.
• Teflon shows more or less uniform hardness distribution in
the axial and radial directions indicating homogeneous de-
formation. Other lubricants show a large decrease in hard-
ness.
• Effective strain decreases from the center towards the periph-
ery of the specimen for all the lubricants in the radial and
axial directions, with Teflon showing minimum variation in
effective strain. In the axial direction, high friction factor
lubricant—castor oil, m = 0.33, generates higher effective
strain at the center and lower effective strain at the periphery,
showing a larger variation is effective strain. This typical be-
havior is due to the “differential straining” of material near to
the billet geometric center and at the interface.
• All the lubricants show constant variation is hardness and
strain when measured on the surface (or upper interface).
• Hardness varies in linear proportion with effective strain for
all the friction conditions (or lubricants) and this follows an
empirical relation, VHN=29.15
¯ +74.5.
Prediction of Hardness Distribution in a Cold
Forged Part and Validating the Empirical
Relationship
The next part of the study deals with the prediction of hardness
distribution in a cold forging process, which involves both radial
and axial flow of metal. The equation interrelating hardness and
effective strain was developed from simple upsetting tests, which
involves radial metal flow only. In order to predict the hardness dis-
tribution and to validate the developed equation, a forging process
that involves both axial and radial flow of metal, combined forging-extrusion process was selected. By considering the empirical rela-
tion (Eq 1), by evaluating the effective strain at different locations,
the designer can predict the hardness of the forged part at the design
stage itself.
Experimentation and Hardness Measurement
Commercially available pure aluminum billet (annealed) of size
24 mm diameter and 42 mm height was selected as the specimen
for validating the equation and for predicting the hardness distribu-
tion. After 50 % deformation, the hardness values were obtained
using the Vickers hardness testing machine at regular intervals of
1.2 mm along the radial and axial direction for four different lubri-
FIG. 11— Variation of surface effective strain from the center of the circular face to the outer surface (inset shows the effective strain measurement locations schematically).
FIG. 12— Variation of hardness (VHN) with effective strain ¯ .
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