Evaluation of friction condition in cold forging by using T-shape compression test

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Journal of Materials Processing Technology 209 (2009) 5720–5729

Contents lists available at ScienceDirect

Journal of Materials Processing Technology

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valuation of friction condition in cold forging by using T-shapeompression test

. Zhanga,∗, E. Feldera, S. Bruschib

CEMEF, UMR CNRS/Mines ParisTech 7635, B.P. 207, F 06904 Sophia Antipolis Cedex, FranceDIMS, University of Trento, Via Mesiano 77, 38050, Trento, Italy

r t i c l e i n f o

rticle history:eceived 22 May 2008eceived in revised form 25 May 2009ccepted 2 June 2009

eywords:riction test

a b s t r a c t

Friction plays an important role in metal forming, and numerical simulation of forging processes requiresprecise informations about the material properties and the value of the friction factor m or coefficient �.This paper describes the T-shape compression, a new friction testing method by combined compressionand extrusion of a cylinder between a flat punch and a V-grooved die. It can realize actual cold forgingcondition and allows measuring the friction on the cylindrical surface of the billet during forging process.The results of experiments and simulations show that the stroke–load curve and the height of the extruded

umerical simulationold forgingow carbon steel

part are both sensitive to friction. In order to obtain the highest sensitivity to friction, a FE parametricstudy of this test has been performed: it indicates that small corner radius and V-groove angle in thedie should be chosen. Two commercial FE codes, FORGE 3D and ABAQUS, were used and provided verysimilar results for a given friction condition. Low carbon steel drawn bar with phosphate and soap coatingwas chosen as specimens. Friction tests with three different lubrication conditions (solid coating, oil andoil + solid coating) were carried out, and then friction factor m and friction coefficient � were determined

. Introduction

Cold forging processes, such as extrusion, upsetting, heading andrawing, have been widely used to realize the net-shape manufac-ure in the automotive and transportation industry, since the 1950s.n cold forging of steel, the interface pressure between die andorkpiece may reach values up to 2500 MPa, the surface expansion

atio (surface area expansion/initial surface area) of the workpieceo 3000% and the local temperature of interface to 200 ◦C (Bay,994). Friction condition has a large effect on cold forging pro-esses, because it not only influences the forming force but alsoetermines the quality of workpiece and tool life. A lubricant that isble to withstand arduous interfacial conditions is essential in coldorging. The most common lubricants are solid coatings, but oilsnd mixed lubricants are sometimes used. The most widely usedubricant for cold forging steel consists of a solid coating of zinc

∗ Corresponding author at: Research Institute of Tool&Die Technology and Metalorming, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi10049, PR China. Tel.: +86 29 82668607x607.

E-mail address: henryzhang@mail.xjtu.edu.cn (Q. Zhang).

multi-stage processes, such as drawing or extrusion, the phosphateand soap coating on the workpiece surface may be worn away, sooften oil is used in forging steel billets coated with phosphate andsoap layer, resulting in a mixed lubricant.

To reduce cost and time of manufacture, FE simulation is almostuniversally used for process planning and prediction of flow defectsin forged parts. However, the mechanism of friction, particularly inthe effect of a lubricant is not clearly understood and so the choiceof a friction model for FE simulation is often a matter of guessworkbased on experience. A wrong choice can lead to poor predictionsof forming loads and metal flow. To obtain relevant friction charac-terization, several experimental methods for determining frictioncoefficient � or factor m during cold forging have been presented.Prominent among them are ring compression, forward extrusion,double cup extrusion, upsetting-sliding and spike tests, as shownin Fig. 1. In order to reflect the actual cold forging process, a suitablefriction test should involve high surface pressure, extensive metalflow, large new surface generation (Altan et al., 2004). In addition,Wagener and Wolf (1994) and Zhang et al. (2008a,b) proposed thatto obtain a representative value of friction factor m or friction coef-ficient � for a given real forging operation, the contact condition

Q. Zhang et al. / Journal of Materials Processing Technology 209 (2009) 5720–5729 5721

tests f

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eelftZtstNfiotp

wBdppc

Fig. 1. Friction

Many studies have shown that the ring compression test is aimple way to determine the shear friction factor m, or the frictionoefficient �, since it was developed by Male and Cockcroft (1964).n the ring compression test, a flat ring specimen is compressed andhe change in internal diameter of the ring indicates the frictionevel, as shown in Fig. 1(a). However, this test induces a very simpleeformation path and relative small new surface expansion ratio,hich nearly equals to 20% (the standard ring-test proportions; out-

ide diameter:inside diameter:height = 6:3:2 and half compressionf the initial ring height).

As a real industry operation, forward extrusion can be used tovaluate friction in cold forging, because the friction force gen-rated along the surface of container decreases with the billetength, after the die region has been filled with the metal. Thenriction factor m, or friction coefficient �, can be determined fromhe slope of decreasing stroke–load curve of extrusion. However,hang et al. (2008a,b) found that contact conditions in the con-ainer and die, such as material, roughness, normal pressure andurface expansion ratio are different and it can induce different fric-ion phenomena. According to the work of Gouveia et al. (1999) andoorani-Azad et al. (2005), the load curve found from simulation of

orward extrusion, in which the same friction condition is appliedn the die and container, does not fit well with the experimentalne. Therefore, two friction conditions, die/workpiece and con-ainer/workpiece, should be considered in the forward extrusionrocess (see Fig. 1(b)).

Double cup (combined forward and backward cup) extrusion,as initially explored by Geiger (1976) and then developed by

or cold forging.

ity with respect to the upper punch, container friction force caninduce preferential metal flow into the upper cup, compared tothe lower one. Therefore, the ratio of top cup height to bottomcup height (H1/H2), depends on the friction along the container.Cup height ratio will increase with large friction along the con-tainer/specimen interface. The minimum cup height ratio is equalto one, if no friction force is generated along the container innersurface. However, Schrader et al. (2007) found that the maximumcontact pressure between specimen and container is rather small(for example <700 MPa for low carbon steel). In addition, Arentoft etal. (1996) found strain hardening rate of material has a large influ-ence on cup height ratio and the evaluation of friction coefficient.

The upsetting-sliding test, proposed by Lazzarotto et al. (1997,1998), is similar to the scratch test. The test includes three maincomponents: indenter, die and specimen. The indenter plays therole of a drawing or extrusion die, whose surface roughness shouldbe the same as that of the tool to be used in the cold forging pro-cess. The specimen with lubricant layer is fixed in the die (seeFig. 1(d)). Before the test, the position of indenter is adjusted to givethe required penetration depth between the extremity of indenterand surface of specimen. Then the indenter moves along the spec-imen with a constant speed and deforms its surface. The normaland tangential forces are measured to evaluate the friction condi-tion between indenter and specimen. The advantage of this test isthat some process conditions, such as sliding speed and temper-ature, can be readily adjusted. However, this method is not like areal forging process as only a local region of the specimen deformssignificantly and the surface expansion ratio is small.

Spike forging is an axisymmetrical forging process combin-ing extrusion and upsetting. It can be used to determine friction,because the load and spike height increases with friction. The spiketest requires a bottom die with a sharp-corned tapered orifice ofcircular cross-section and a flat-top die. A circular billet squeezed

5722 Q. Zhang et al. / Journal of Materials Processing Technology 209 (2009) 5720–5729

bfetpmasb(w

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Fig. 2. The principle

etween the dies flows both sideways and into the orifice. Higherriction restricts sideways flow and therefore a longer spike isxtruded (see Fig. 1(e)). In this test, like in ring compression test,he ends of the cylindrical specimen are in contact with the die andunch directly. However, contact condition on cylindrical surfaceay be different with the ones on end surfaces. For example, in

lmost all multi-stage cold forging operations, the billet is directlyheared from a drawn coated wire, so unlike cylindrical surface ofillet, end surfaces are not coated with the lubricant layer. Petty1994) proposed that spike test and ring compression test, usuallyere used for estimating friction in hot metal forging.

In this paper, we study the T-shape compression, a new methodo determine friction in cold forging, by numerical simulation andxperiments. The paper is divided as following:

The principle of this test is presented.It is demonstrated by finite element codes that the friction influ-ences the forming load and the formed part shape.The geometry of the tools is optimized by FE simulation in orderto maximize the sensibility of the test to friction.The results of two FE codes, Forge 2005® and ABAQUS®, are com-pared in order to validate the numerical study.T-shape compression tests with three different lubrication condi-tions, solid lubricant (phosphate + soap), oil and mixed condition,have been carried out on low carbon steel sample. This validatesthe numerical study and provides the friction factor m and coef-ficient � of these various lubrication conditions.

. The principle of T-shape compression

T-shape compression includes three parts: punch, cylindricalpecimen and die with a V-groove, as shown in Fig. 2. The sectionalhape of a formed part is ‘T-shaped’, hence the test is named T-shapeompression.

In this test, the specimen is first located in the groove as shownn Fig. 2(a). During deformation by the top punch, some metal isxtruded into the groove and some is upset and moves sidewaysetween the flat surfaces (see Fig. 2(b)). The friction force, gener-ted along the wall of groove, restricts metal flow into it, so the

shape compression.

ity of the lubricant. For solid lubrication condition, the cylindricalsurface of the specimen was coated with zinc phosphate and soaplayer, contact with die and punch directly. For the oil lubricationcondition test, the V-groove is filled with the lubricant, so the billetsurface is easily lubricated during the test.

For this new friction test, some potential advantages are evident:

• The forming load and shape of formed specimen are sensitive tothe friction condition.

• Only cylindrical surface of billet is in contact with punch and die.• Oil lubricant can easily be applied in the test by filling in the die

groove.• Severe deformations, including both extrusion and compression,

are involved in this test. Surface expansion ratio of specimen mayreach to 50%. The maximum contact pressure can attain 4 timesthe initial flow stress of the material.

• Specimens with different diameters can be tested by using thesame die. In addition, the cost and time of die manufacture aresmaller than the ones of other friction tests, such as forwardextrusion and double cup extrusion.

3. FE model

The commercial implicit FE software FORGE 2005® 3D was usedto simulate this forming process for test design and evaluation offriction. It has automatic remeshing capabilities, which is importantin the simulation of metal forming operations with large mate-rial deformations and displacements. Because the operation hastwo planes of symmetry, only one quarter of specimen was mod-elled by 5875 four node tetrahedron elements and an elastic–plasticmaterial model was assigned to specimen.

The material of specimens was AISI 1010. It was providedby industrial manufacturer as cold drawn cylindrical bar. Thestrain/stress relationship of AISI 1010 steel was obtained by uniaxialcompression test (see Fig. 3). In the large strain region of this mate-rial (ε > 0.64), the flow stress is assumed constant. In order to verifythis assumption, tension tests were performed on this material. Itsreduction in area at the rupture surface is high and corresponds toa strain of about 1.4; the related microhardness is near the micro-

Fig. 3. The strain/stress curve of AISI 1010 by uniaxial compression test.

Fig. 6. Load curves with different friction factors.

Fig. 4. The sectional shape of die.

0 mm. The height and the diameter of the samples were equal tomm.

In order to compare calculated results from different FE codes,ne forming simulation using ABAQUS/Explicit was performed, inhich the 8700 C3D8R element was used to model one quarter of

he specimen, and the die and punch were modelled as rigid ele-ent R3D4. In addition, Arbitrary Lagrangian Eulerian (ALE) adap-

ive meshing was used to control mesh distortion (ABAQUS, 2003).There are two friction laws, Coulomb and shear, which are

pplied widely to calculate the tangential stress between speci-

ses a friction coefficient � to quantify the interface friction, and isxpressed as follows:

= �p (1)

Fig. 5. Specimen defor

Fig. 7. Effects of friction factor on height of extruded part with different loads.

where � is the friction stress and p is the normal pressure. This lawis valid for forming process with either low contact pressure or lowfriction stress. The Coulomb expression does not limit the shearstress. Because the friction stress cannot exceed the shear strengthof the material, the shear friction law (constant friction or Trescalaw) was developed as

� = m√3

�̄ (2)

where m is the friction factor and �̄ is the flow stress of the deform-ing material.

mation process.

ad curve and its sensitivity (V-groove angle ˇ = 20◦).

Fig. 8. Effects of corner radius on the slope of lo

In this paper, these two friction laws were used in order to obtainhe friction coefficient � and factor m related to three differentubrication conditions in T-shape compression experiments. How-ver, in the parametric study of T-shape compression test, only thehear friction law was used.

. Effect of friction condition on load and formed parthape

Specimen deformation is shown in Fig. 5. The whole deformationf specimen in T-shape compression includes two stages.

In the first stage, the metal is pushed into the die groove and nolateral expansion appears between the punch and flat-top surfaceof die, due to small contact area between specimen and punch.Also it can be observed that the load changes almost linearly withpunch stroke when the ratio of punch stroke to billet diameterincreases from 0.15 to 0.43 (see Fig. 6).In the second stage, the contact region of specimen/punchbecomes larger, then the compression of metal occurs betweenthe flat surfaces of the tools, so load will increase shapely.

When the punch stroke is equal to 0.65 times the specimen ini-

Load curves with different friction factors are shown in Fig. 6.esults illustrate that the load increases with friction factor and

Fig. 10. Effects of V-groove angle on the slope of load c

Fig. 9. Effect of corner radius on the height of extrusion part (V-groove angle ˇ = 20◦).

the sensitivity of load to friction factor becomes larger at a higherpunch stroke. This is because contact area and contact pressurebetween specimen and die become large with the punch moving

urve and its sensitivity (corner radius R = 1 mm).

teftthf

chosen for this test. Because die cavity becomes smaller when cor-ner radius reduces, the more metal is filled into the groove. Thusthe height of extruded part and the friction force generated alongthe wall of V-groove become less.

Table 1Lubrication conditions.

ig. 11. Effect of V-groove angle on the height of extruded part (corner radius= 1 mm).

nown only with some error, and also friction factor, evaluated at aiven stroke, only can present the friction condition at this moment.herefore, according to these considerations, we choose the slopef load curve as a reference for determining friction in this work.

The height of extruded part H is measured from the flat-top ofhe die to the middle point of the extruded head. Fig. 7 shows theffect of friction factor on the height of the extruded part, for dif-erent loads which corresponds to various punch strokes. It is seenhat the extruded height increases with decrease in the friction fac-or. For instance, when the load is 55 kN, the ratio of extruded parteight to billet diameter reduces from 0.59 to 0.52 with increasing

riction factor m from 0 to 0.2.

. An FE parametric study of T-shape compression test

To be useful, a friction test must be sensitive to friction factorn practical range of values. Therefore, to maximize the sensitivityf the T-shape compression test, the influence of two geometricalarameters, such as corner radius and V-groove angle, was investi-ated.

In order to estimate the sensitivity of friction on the load, theoad curve slope sensitivity �k is defined as

k = km − km=0

km=0(3)

here km is the slope of load curve with friction factor m and km = 0s the slope of load curve without friction. In this parametric study,

Fig. 12. Equivalent strain distribution on the middle section of speci

Fig. 13. Load curves simulated by FORGE 3D and ABAQUS/Explicit (die: R = 1 mm,ˇ = 20◦; � = 0.05; punch stroke = 4.6 mm).

the depth of the groove was constant as 10 mm (see Fig. 4). Thediameter and length of specimen were both 7 mm.

5.1. Effects of corner radius R

Fig. 8 shows the effects of the groove corner radius on the slopeof load curve and its sensitivity. Three different corner radii R (seeFig. 4), of 1 mm, 2 mm and 3 mm were considered. The results showthat when a small corner radius is chosen, the slope of load curvedecreases, but it becomes more sensitive to friction factor. Mean-while, the height of extruded part increases with decrease in thecorner radius, as shown in Fig. 9. So small corner radius should be

Lubrication condition Lubricant

Solid lubrication condition Phosphate/soap layerOil lubrication condition Sinol draw 891 (viscosity � = 0.23 Pa s, at 25◦C)Mixed lubrication condition Phosphate/soap layer + sinol draw 891

men (die: R = 1 mm, ˇ = 20◦; � = 0.05; punch stroke = 4.6 mm).

Fig. 14. Experimental die and formed specimens.

.2. Effects of V-groove angle ˇ

In order to investigate the effect of V-groove angle ˇ in die, threeifferent angles were selected as 15◦, 30◦ and 90◦. Fig. 10 shows thathen the die angle becomes large, the slope of load curve increases,hile its sensitivity to friction decreases. Fig. 11 shows the effect of-groove angle on the height of extruded part with different fric-

Fig. 16. Effects of friction factor and friction coefficient on slop

Fig. 17. Friction factor and coefficient evaluated by slope of

Fig. 15. Load curves under different lubrication conditions.

tion factors. It can be seen that the height of extruded part andits sensitivity to friction decrease when the V-groove angle in thedie increases. Especially, when the V-groove angle is as large as90◦, the height of extruded part cannot be used to verify the fric-tion condition due to its low sensitivity to friction. This is because

e of load curve (0.2 ≤ punch stroke/billet diameter ≤ 0.4).

load curve (0.2 ≤ punch stroke/billet diameter ≤ 0.4).

Q. Zhang et al. / Journal of Materials Processi

tests. They were machined directly from drawn bar, which had

ig. 18. Friction factor calibration curves with experimental height of extruded part.

. Simulation results by different FE codes

An FE model with friction coefficient � = 0.05 was used in theORGE 3D and ABAQUS codes. Fig. 12 shows the equivalent strain

Fig. 19. Comparison between the experi

ng Technology 209 (2009) 5720–5729 5727

distribution on the middle section of specimen at a 4.6 mm punchstroke. Results calculated from these two codes are very similar,in which the strain of the specimen near to the die corner is thehighest, and the strain in the compression region is larger than thatin the extrusion region. After loading, the quality of the specimenmesh in FORGE 3D is better than the one in ABAQUS, because ofthe remeshing capability of FORGE 3D. From Fig. 13, it also can beobserved that the load curves calculated by the two codes are quitesimilar, therefore, the same friction values will result regardless ofwhich of the two codes is used, if the same material properties andfriction model are chosen.

7. Experimental procedure and evaluation of frictionconditions

7.1. Experimental procedure

AISI 1010 low carbon steel specimens 6.85 mm diameter and7 mm long, were used for performing the T-shape compression

a phosphate and soap coating on the cylindrical surface, appliedduring the previous drawing operation. The machined flat surfaceswere not coated. That is the main reason why only the cylindricalsurface was allowed to be in contact with die and punch in this test.

mental and simulated load curves.

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728 Q. Zhang et al. / Journal of Materials Pr

The three lubrication conditions in tests are shown in Table 1. Inrder to evaluate the effect of the lubricant oil without the phos-hate/stearate coating, the coating was electrochemically removedrom the pretreated metal. The tool material was cemented tung-ten carbide, chosen for its high strength and hardness, which wasnserted in a steel shrink ring. The sectional shape of the exper-mental die is shown in Fig. 4. The loading speed of testing was.1 mm/s and the maximum stroke was 4.5 mm. Experimental diend formed specimens are shown in Fig. 14.

.2. Evaluation of friction conditions

Fig. 15 shows the load curves obtained using the three differ-nt lubrication conditions. It can be seen that the forming loadrom mixed lubrication is a little lower than that from solid lubri-ation. The load using oil is the largest one because the lubricants squeezed out of the contact zone by the specimen/tool pres-ure, so metal-to-metal contact occurs, which induces the largeriction. On the contrary, with solid lubrication, the phosphatend soap coating can suffer large normal pressure. Hence a solidayer remains between tool and specimen, which can promote aow friction force during forming. For the mixed lubrication con-ition, the die is in contact with the phosphate and soap coatinghen the oil film is pushed out of the contact zone. Therefore, the

oad curves from mixed and solid lubrication condition are simi-ar.

Shear and Coulomb friction law were used in the numerical sim-lations of these tests in order to determine the friction factor m andoefficient � for the three different lubricant conditions, by com-aring the simulated and experimental results. Fig. 16 shows theffects of friction factor m and friction coefficient � on the slope ofhe load curve k. It can be seen that the friction factor m and coeffi-ient � have linear relationship with load curve slope k, which cane fitted with following equations:

k = 5.7 + 6.8mk = 5.8 + 15.2�

(0.2 ≤ punch stroke/billet diameter ≤ 0.4) (4)

t can be seen that the friction factor m is near 2.3 times the frictionoefficient � for the same slope of load curve. Therefore, the frictionoefficient can be easily obtained, if the friction factor has beenvaluated.

Slopes of experimental load curves with punch stroke/billetiameter from 0.2 to 0.4 were calculated. Then, the friction factornd coefficient were determined by comparison with the simu-ation results (see Fig. 16). Fig. 17 shows the friction factor andoefficient for the three lubrication conditions, evaluated by slopef load curve, and coefficient � is about half factor m.

When the punch stroke was near to 4.5 mm, the deformed spec-men was removed from the die. Then, the height of extruded partas measured from the middle surface of cut specimen. The heightf extruded part versus the forming load and friction factor arelotted in Fig. 18. According to these experimental data, the aver-ge friction factors for oil, solid and mixed lubricant are near to.22, 0.12 and 0.09, respectively. They are in close agreement withhose determined by the slope of load curves in the first stage ofxperiments.

In order to verify the values of the friction factor m andoefficient � determined by the slope of load curves and theeight of extruded part, the experimental and simulated load

ng Technology 209 (2009) 5720–5729

8. Conclusions

A T-shape compression test has been developed as a new simplefriction testing method for cold forging. Based on the numericaland experimental results obtained, the following conclusions canbe drawn:

1. T-shape compression test is suitable to evaluate the friction con-dition because the slope of load curve and the shape of formedspecimen are both sensitive to friction for certain die geometry.Meanwhile, this test induces a complex deformation path, largecontact pressure and rather large surface expansion.

2. In this test, the sensitivity of load curve slope to friction conditiondecreases with increase in the corner radius and V-groove anglein the die.

3. Simulated results provided by Forge 3D and ABAQUS agree well,so the friction factor or coefficient, evaluated by two different FEcodes, is the same.

4. The solid lubricant produces lower friction than oil lubricant,because the oil can be easily squeezed away from the high-pressure contact zone. The lubrication performances of solidlubricant and mixed lubricant are similar. The experimental val-ues of the slope of the load curve and the height of the formedspecimen shape were compared to the results of the numeri-cal simulations. So the friction factors m for mixed, solid and oillubricant conditions are about, 0.09, 0.12 and 0.23. In addition,the friction coefficients � for these three conditions are 0.04, 0.05and 0.11, respectively.

Acknowledgements

The authors would like to thank the VIF (Virtual IntelligentForging-CA) project for financing the research on measurement offriction condition in forging. And also to thank Mr. G. Fiorucci andMr. B. Triger, CEMEF, for kind help in experiment and measurementof formed specimens. In addition, we want to thank Dr. P. Montmi-tonnet, CEMEF, for his interest in this work and helpful discussions,advices and suggestions.

References

ABAQUS, 2003. User’s Manual for Version 6.4. Karlson & Sorensen Inc., Hibbitt.Altan, T., Ngaile, G., Shen, G.S., 2004. Cold and Hot Forging: Fundamentals and Appli-

cations. ASM International Press, pp. 67–86.Arentoft, M., Vigsø, C., Lindegren, M., Bay, N., 1996. A study of the double cup extru-

sion process as a friction test. In: Proceedings of the Advanced Technology ofPlasticity, vol. I, 5th ICTP, pp. 243–250.

Bay, N., 1994. The state of the art in cold forging lubrication. J. Mater. Process. Technol.46, 19–40.

Buschhausen, A., Lee, J.Y., Weinmann, K., Altan, T., 1992. Evaluation of lubricationand friction in cold forging using a double backward extrusion process. J. Mater.Process. Technol. 33, 95–108.

Dubois, A., Lazzarotto, L., Dubar, L., Oudin, J., 2002. A multi-step lubricant valu-ation strategy for wire drawing–extrusion–cold heading sequence. Wear 249,951–961.

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Gouveia, B.P.P.A., Rodrigues, J.M.C., Bay, N., Martins, P.A.F., 1999. Finite-element mod-elling of cold forward extrusion. J. Mater. Process. Technol. 94, 85–93.

Lazzarotto, L., Dubar, L., Dubois, A., Ravassard, P., Oudin, J., 1997. Identification ofCoulomb’s coefficient of friction in real contact conditions applied to a wiredrawing process. Wear 211, 54–63.

Lazzarotto, L., Dubois, A., Dubar, L., Verleene, A., Oudin, J., 1998. Testing of a zinc phos-phate stearate coating according to true conditions of contact in wire drawing.Surf. Eng. 14, 335–338.

Male, A.T., Cockcroft, M.G., 1964. A method for the determination of the coefficientof friction of metals under conditions of bulk plastic deformation. J. Inst. Metals93, 38–45.

Noorani-Azad, M., Bakhshi-Jooybari, M., Hosseinipour, S.J., Gorji, A., 2005. Experi-mental and numerical study of optimal die profile in cold forward rod extrusionof aluminum. J. Mater. Process. Technol. 164–165, 1572–1577.

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chrader, T., Shirgaokar, M., Altan, T., 2007. A critical evaluation of the double cupextrusion test for selection of cold forging lubricants. J. Mater. Process. Technol.189, 36–44.

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Zhang, Q., Felder, E., Arentof, M., Dubar, L., Borsetto, F., Bruschi, S., 2008b. On theresults of friction benchmark in cold conditions. In: Proceedings of the 12thInternational Conference, Metal Forming 2008, September 21–24, Kraków, Pol-ska.

Evaluation of friction condition in cold forging by using T-shape compression test

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