Influence of Friction in Simple Upsetting

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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

Available online at: w ww.astm.org

Copyright © 2008 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. 1



Ring Compression Test (RCT) —For defining the friction

condition occurring in the metal forming process, it is common

practice to follow either the concept of the interface friction factor

m (m = / k ; where =interface shear strength, and k =shear yield

stress of the material) or the Coulomb’s law concept ( µ = / P ; where

µ=friction coefficient, =interface shear strength, and P =stress nor-

mal to interface) [1]. Since m is independent of normal shear stress

and friction tests are available to evaluate the m value easily duringforging operations, it is widely used to predict the forging behavior.

In order to predict the forging behavior of any material, it is nec-

essary to quantify friction factor during the forming process. There

are various laboratory friction tests to perform this activity. The

most commonly used method for evaluating frictional conditions in

cold forging is the Ring Compression Test (RCT). In this test, a thin

ring specimen is forged axially (or compressed) between two rigid

patterns (top and bottom). As a result, the ring specimen deforms

and metal flows in the radial direction such that for low friction

conditions (good lubrication) the inner diameter of the ring in-

creases like that of solid sample, while for high friction conditions

(poor lubrication) the inner diameter is found to decrease [2]. Dur-

ing compression, the percentage change in inner diameter is mea-

sured for every known reduction in sample thickness or height. Thecalibration curves are drawn between percentage height reduction

and percentage change in inner diameter [1]. Thus the curves cor-

respond to varied friction conditions and therefore can be quanti-

fied in terms of “friction factor– m or friction coefficient– µЈ [3] for

standard ring geometry. The popularly used ring geometry is

ID:OD:H=3:6:2. Since this method (RCT) of friction quantifica-

tion depends only on the physical measurement of the ring sample

and the requirement of forming loads, material properties, etc., are

avoided, it is widely accepted to measure friction during bulk form-

ing operation. Some of the factors that influence the friction factor

(or friction coefficient) in RCT are the ring geometry, barreling ef-

fect, changing friction condition, strain rate, temperature, percent-

age reduction, surface conditions, etc., [4–7] and their effects arelisted below.

1. Effect of geometry: With an increase in ring thickness, the

friction factor was found to increase for the same lubricant

and material. This effect is studied in Ref [4] that for the

same temperature 300 K , reduction percentage (app. 40

to 47 %), and material (Al-5Si forged, cast alloy and

Al-4Mg forged, cast alloy), the change in ring geometry

(thickness) from 6:3:1 to 6:3:2 (OD:ID:H), leads to an in-

crease in the m value for the 6:3:2 case.

2. Effect of barreling: Avitzur in his analyses [8] assumed that

there is no barreling (or bulging) effect during ring forging

and the calibration curves are developed based on this. But

this was disproved by Sofouglu et al. [5,6] that the bulgingeffect showed significant effect on the friction factor devel-

oped during deformation by conducting experiments on

plasticine material. This was demonstrated by monitoring

the inner diameter both at the interface and at the middle of

thickness for every percentage reduction and the friction

coefficient changes are found to be significant.

3. Effect of changing friction conditions at interface: The

RCT calibration curves were developed with the assump-

tion that the friction will remain constant along the inter-

face during forging [8]. But this is not the case as friction

conditions change along the interface. This issue of chang-

ing friction conditions has not been critically analyzed, but

the “constant friction factor assumption” can be adopted as

long as the iteration process is carried out using small stepsin height reduction and the final dimensions obtained in

one step are considered as the initial geometry for the next

step [4].

4. Effect of strain rate: The strain rate effect on the friction

coefficient is also found to be significant from RCT on

plasticine material [5,6] by considering rate dependent and

rate independent FE models.

5. Effect of temperature: The temperature effect is quite inter-

esting. Under lubricated conditions, in general, with an in-

crease in temperature, the friction factor is found to in-

crease [4]. This could be because of the change in viscosity

of the lubricant at higher temperatures. With an increase in

temperature, lubricant viscosity will decrease making it

watery and hence holding of lubricant is reduced resulting

in a higher friction coefficient (or friction factor). But

under dry lubrication, temperature effect is not significant

on friction factor [7]. It should also be noted that in Ref [4],

it is mentioned that the effect of temperature on the friction

condition is uncertain.

In RCT, the die geometry and metal flow are simple, the forging

pressure is relatively low, and the new surface generated during de-

formation is small [9,10]. Therefore, in a ring test the frictional

characteristics of the forging lubricant cannot be adequately evalu-

ated. Also, the friction factor evaluated from RCT can be used

mainly for open die forging operations, where degree of deforma-

tion is less. In order to overcome the problem involved in RCT, a

double cup extrusion test was developed [9,10].

Double Cup Extrusion (DCE) Test —The Double Cup

Extrusion (DCE) Test (Fig. 1, [11]) involves combined forward and

backward extrusion of the billet. In this test, the bottom punch is

kept stationary and the top punch is moved in the downward direc-

tion, such that it deforms the cylindrical sample as shown in Fig. 1.

As a result, both forward and backward extrusion takes place re-

sulting in an “H”-shaped deformed sample. The ratio of backward

h1 to forward h2 extrusion cup heights is controlled by the fric-

tional conditions at the container-billet interface. The calibration

curves can be obtained by plotting the height ratio with percentage

deformation [9] for varied friction conditions (or friction factors).

The tool dimensions involved in the DCE test are given in Ref [10].

FIG. 1— Double Cup Extrusion Test [11].

2 JOURNAL OF TESTING AND EVALUATION



The DCE test can be simulated using the FE code and the height

ratio h1 / h2 —percentage deformation data can be obtained for

varied friction factors m . By comparing the experimental curves

for different lubricants with that of from FE simulations for differ-

ent friction factors, the m values for lubricants can be evaluated

[10]. Also, by comparing the deformation of grids in the extruded

specimen experimentally and numerically, one can evaluate the

friction factor of the lubricant more accurately [10].

In order to find the suitability of the ring test and double cup

extrusion test, a cold forging process which involves extrusion in

the axial direction and upsetting in the radial direction was ana-

lyzed with grease lubrication whose m values were obtained both

from the ring compression test and double cup extrusion test. The

deformed patterns were compared at different stages of the process

[12]. It was concluded that the m values given by double cup tests

were more appropriate for deformation predictions in cold forging

operations. Ring compression tests are suitable for simple upsetting

operations [12]. Similar to RCT, factors influencing the friction

factor in DCE test, i.e., billet height, reduction ratio, reduction in

area on cup height can be understood from Refs [9,13].

Prediction of Hardness Distribution

Efforts have been taken to predict the hardness change by relating it

to plastic strain during forging. The earlier attempt was made by

Hartley et al. [14], where in the hardness distribution during Rim

Disk forging was predicted by knowing the stress distribution

by FE analyses and relating the stress to hardness by a known

(Hardness-) relation. But the hardness prediction is not accurate

at higher deformation levels. A better approach to predict the hard-

ness distribution was suggested by Kim et al. [15]. In their work,

the hardness-effective strain distribution during a simple upsetting

test was initially established. Hardness was obtained from experi-

ments and effective strain from FE simulations. Then the effective

strain pattern at known regions during cup extrusion was obtained by FE simulations and hardness pattern at the same regions were

established using the empirical relationship developed earlier by

upsetting tests. Their approach showed good agreement between

the experimental and predicted hardness pattern during cup extru-

sion. Also in their work, an attempt has been made to study the

effect of varied friction conditions on the hardness and effective

strain variation during simple upsetting. Petruska et al. [16] per-

formed similar work, but their aim was to compare the hardness

prediction accuracy between hardness-mean strain and hardness-

local strain relations during forward extrusion. Both of them agreed

well with each other. Recently, analytical models were developed

for Brinell hardness and Vickers hardness by Sonmez et al. [17]

such that properties obtained from simple compression tests K , ncan be directly related to hardness, so that hardness distribution can

be evaluated independent of material and deformation. These ana-

lytically predicted hardness distributions were related to effective

strain predictions from FE simulation empirically. From this, a

hardness pattern can be predicted for any cold working operation. It

is found that their predictions were accurate and the models devel-

oped were quite satisfactory.

The authors feel important that the following issues can be ad-

dressed during the prediction of the hardness pattern in any cold

forging process.

• The above presented literature relates hardness and effective

strain quantities without knowing the effect of varied friction

conditions on them during the initial upsetting process. The

basis for projecting this as an issue is because of the depen-

dency of hardness and strain evolution on the varying fric-

tion conditions (or lubricants) during upsetting and hence

supporting the necessity of understanding the effect of dif-

ferent lubricating conditions on the hardness, effective strain

distribution in a simple upsetting process.Though an attempt

has beenmade in Kim et al. [15] to address this issue to some

extent, further critical experimental analyses is necessary to

make unified conclusions.• Relating hardness and plastic strain using a simple upsetting

operation and predicting the hardness distribution in a typi-

cal forging process using this relationship is explored only

for a particular lubricating condition. This methodology is

not examined for varied friction conditions. From the pub-

lished literature, one can say that the same procedure has to

be adopted for each lubricant to predict the hardness distri-

bution, which is quite time consuming and cumbersome.

Hence, exploring and understanding the applicability of the

hardness-plastic strain relationship for varied lubricating

conditions is an important issue.

• The hardness-plastic strain relationship was developed from

a simple upsetting process involving only radial metal flow.The applicability of this relation for a cold forging process,

say cup extrusion, involving axial metal flow is the general

trend. How good the developed empirical relation is for pre-

dicting the hardness distribution in a forging process involv-

ing both radial and axial metal flow can also be addressed.

By considering the above issues as important, the present work

aims at:

1. Investigating the influence of various lubricants (or friction

conditions) on the hardness and effective strain variation

during the simple upsetting operation.

2. Inter-relating hardness and effective strain evolution in a

simple upsetting operation for different lubricants and vali-dating the applicability of this empirical relation for chang-

ing lubricating conditions.

3. Validating the applicability of the developed empirical re-

lation for predicting the hardness distribution in a cold

forging process which involves both axial and radial metal

flow (for different lubricating conditions).

Influence of Varied Friction Conditions on the

Hardness, Effective Strain Distribution During

Simple Upsetting Operation

This part of the analysis deals with the effect of friction on the

variation of hardness and effective strain in a simple upsetting pro-

cess for different lubricating conditions. Different lubricants, viz.,

castor oil m =0.33 , soap m =0.25 , grease m =0.2 , and Teflon

m =0.16 are used for performing the experiments. Here, the fric-

tion factor m values for the lubricants were obtained through ring

compression tests conducted earlier [18].

Selected Material

Commercially available pure aluminum was used as the billet ma-

terial in this study. In order to ensure identical properties all the test

specimens were annealed at 623 K for a period of one hour.

NARAYANAN ET AL. ON INFLUENCE OF FRICTION IN A COLD FORGED PRODUCT 3



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).




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).




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.




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).




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).




VHN = 29.15 + 74.5 (1)

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 ¯ .




cating conditions. Two trials were conducted for each condition.

The hardness variation was found to be within ±5 % limit in these

experiments also.

The schematic representation of tooling used for experimental

purpose is shown in Figs. 13 and 14. The tooling consists of upper

and lower dies with respective pins. These pins are fitted into the dieas shown in Fig. 14.After deformation, pins can be easily taken out

and hence the billet can be removed easily from the pin. The arrow

marks show the metal flow direction (Fig. 14). The radial metal

flow represents the “forging” operation and the downward metal

flow represents the “extrusion” operation. Hence, this particular

process combines both radial and axial metal flow as mentioned

earlier. But in FE simulations, lower and upper die pins are not pro-

vided separately and the die is considered as a single unit.

Effective Strain Evolution During Combined

Forging-Extrusion Process and Hardness Prediction

The effective strain distribution in the cold forged product was pre-

dicted at the same locations where hardness was measured earlier,

by conducting FE simulation using DEFORM ver3.0 package. The

FE simulation was conducted for 50 % deformation for four lubri-

cating conditions with varied friction factors noted earlier. The

rigid plastic, plane strain, and axisymmetric analyses were followed

for simulations. The elements selected were four-noded quadrilat-

eral in shape.The effective strain values thus obtained from FE simula-

tions of the “combined forging-extrusion process” for varied lubri-

cants at different locations were substituted in the empirical rela-

tion, VHN=29.15 + 74.5, developed from the simple upsetting

tests. The hardness (VHN) values thus obtained are equivalent to

that of from “combined forging-extrusion” experiments. The hard-

ness distribution from the empirical relation were compared with

the hardness (VHN) obtained experimentally. Thus, the hardness

distribution in a cold forged product can be predicted just by deter-

mining the effective strain distribution using FE simulations at the

design stage itself for varied lubricating conditions.

Comparison between Experimental and Predicted Hardness Values

The experimental and predicted hardness values (from empirical

Eq 1) for the combined forging-extrusion product for four different

lubricants in the radial and axial directions were compared by find-

ing the correlation coefficient r . The correlation coefficient r , is

determined using the formula,

Correlation coefficient, r = n xy − x y /ͱ r xr y

where:

r x

= n

x2 −

x

2

; r y

= n

y2 −

y

2

Here, x and y are the variables considered for comparison, and n is

the number of readings. Table 1 presents the correlation fit between

the experimental and predicted hardness. Lubricants soap, grease,

and Teflon show a better correlation fit, while hardness predictions

for castor oil show a larger discrepancy (r = 0.45 and 0.44).

The graphical comparison between the experimental and pre-

dicted hardness for four different lubricants is shown in Figs.

15–18.The graphical comparison shows a similar pattern of predic-

tion with castor oil depicting a larger discrepancy between the ex-

perimental and predicted hardness values, while other lubricants

show predictions with acceptable accuracy. Moreover, the predic-

tions are more accurate in the axial direction, rather than in the ra-

dial direction.

FIG. 13— Schematic representation of tooling for experiments (cold forging =extrusion process) (all dimensions in mm; not to scale).

FIG. 14— Schematic of assembled view of thetooling used for combined forging

extrusion experiments (symmetric with horizontal axis A-A).

TABLE 1— Correlation coefficient between the predicted and experimental

hardness values.

Correlation Coefficient r

Lubricant Radial Direction Axial Direction

Castor Oil 0.45 0.44

Soap 0.95 0.93

Grease 0.65 0.93

Teflon 0.80 0.92




In whole, the hardness predictions using the empirical equation

which is common for a four lubricants is not accurate for a lubricant

with lesser holdability, i.e, castor oil, while other lubricants (Teflon,

soap, grease) with better holdability show good prediction levels.

Hence, it can be said that the empirical relation, VHN=29.15

+ 74.5 is more suitable for lubricants (soap, grease, and Teflon) ap-

proaching sliding friction conditions as they represent the semi-

solid and solid lubricant category, wherein holdability is relatively

better than in the case of the castor oil lubricant.

Conclusions on Hardness Prediction

Hardness variation was predicted from the empirical equation and

the applicability of the equation was tested under two different con-ditions: (1) a forming process involving both radial and axial metal

flow, and (2) varied friction conditions or lubricants. The following

are the conclusions from this part of the work.

FIG. 15— Comparison of experimental hardness to predicted hardness (from Eq 1) for castor oil m=0.33 lubrication.

FIG. 16— Comparison of experimental hardness to predicted hardness (from Eq 1) for soap m=0.25 lubrication.

FIG. 17— Comparison of experimental hardness to predicted hardness (from Eq 1) for grease m=0.2 lubrication.




• The empirical relation, VHN= 29.15 + 74.5, established

during the simple upsetting operation (having only radial

metal flow) is found to be good for hardness prediction dur-

ing the combined forging-extrusion process, involving both

radial and axial metal flow. The predictions are more depen-dent on the lubricating conditions at the interface, rather than

the typical forging process used for prediction.

• The empirical relationship between hardness and effective

strain obtained from the simple upsetting operation, which is

common for all the lubricants, predicts the hardness distribu-

tion during the forging-extrusion process with moderate ac-

curacy. In general, predictions are good in the case of lubri-

cants with better holdability, viz., Teflon, soap, grease, rather

than a lubricant with lesser holdability, i.e., castor oil. This

can be related to sticking and sliding friction conditions ex-

isting at the interface.

Perspective

• The hardness and effective strain variation for four differ-

ent lubricants are related to sticking and sliding friction

conditions resulting in differential strain hardening and

differential straining during upsetting operation. Some of

the results are similar to that presented in Kim et al. [15].

A similar trend is expected in the case of other lubricants

also and, hence, one can visualize the influence of lubri-

cants on the hardness and effective strain during the up-

setting operation to be similar to that presented in this

study.

• The friction factor of lubricants used for the simulation

purpose in this work were evaluated from the ring compression test, which may not accurately represent the in-

terfacial friction conditions during closed die forging, as

is the case in the combined forging-extrusion process. It

is expected that the friction factor obtained from the

double cup extrusion test may predict the forging behav-

ior accurately.

• Even in the case of RCT, the constant friction factor ap-

proach is considered. But the interface friction changes

with deformation and, hence, evaluating the varying fric-

tion factor will improve the accuracy of predictions.

• Also, one can develop separate empirical equations for

varied lubricating conditions to improve the prediction

accuracy.

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FIG. 18— Comparison of experimental hardness to predicted hardness (from Eq 1) for Teflon m=0.16 lubrication.


http://dx.doi.org/10.1115/1.1369601

http://dx.doi.org/10.1115/1.1369601

http://dx.doi.org/10.1115/1.1369601

http://dx.doi.org/10.1016/0924-0136(92)90313-H

http://dx.doi.org/10.1016/0924-0136(92)90313-H

http://dx.doi.org/10.1016/0924-0136(92)90313-H

http://dx.doi.org/10.1016/0924-0136(92)90313-H

http://dx.doi.org/10.1016/0924-0136(92)90313-H

http://dx.doi.org/10.1115/1.1369601

http://dx.doi.org/10.1115/1.1369601



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http://dx.doi.org/10.1016/0924-0136(96)02292-3

http://dx.doi.org/10.1016/0924-0136(96)02292-3

http://dx.doi.org/10.1016/0924-0136(96)02292-3

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Documents

Influence of Friction in Simple Upsetting