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Materials Science and Engineering A 489 (2008) 363–372

The role of the friction during the equal channelangular pressing of an IF-steel billet

N. Medeiros, J.F.C. Lins ∗, L.P. Moreira, J.P. Gouvea

Programa de P´ os-graduac˜ ao em Engenharia Metal´ urgica, Universidade Federal Fluminense, Avenida dos

Trabalhadores 420, Volta Redonda, RJ 27255-125, Brazil

Received 23 August 2007; received in revised form 14 December 2007; accepted 2 January 2008

Abstract

It is well known that high levels of friction induce adherence effects in materials processed by equal channel angular pressing (ECAP) promotingsome degree of heterogeneity along the deformation zone. In the present paper, the role of the friction in relation of die geometry considering

frictionless, ideal lubrication and severe friction conditions of an interstitial free (IF) steel deformed by ECAP technique using plane strain finite

element models was investigated in details. The analysis of adherence at the billet–die contact region during only one pass of deformation was

carried out in a quasi-static form at room temperature. Independent of the die channels intersection angle (90 ◦ or 120◦) analyzed an adherence

phenomenon was observed under determined friction conditions. It can be concluded that it is necessary to establish an upper limit to the friction

coefficient in order to avoid the adherence effect in two-dimensional finite element simulations.

© 2008 Elsevier B.V. All rights reserved.

Keywords: Equal channel angular pressing; Friction; Finite element method; Interstitial free steel

1. Introduction

ECAP is nowadays considered as one of the most promising

severe plastic deformation (SPD) technique that can be appro-

priated to produce ultrafine-grained materials at industrial scale

[1,2]. This technique is defined as a straightforward operation

that a well-lubricated billet is forced to pass into a die with two

channels of identical cross-sections. The microstructure of the

material is refined by the action of simple shear imposed at the

channels intersection.

It is well known that the shear stress yield and the fric-

tion conditions play an important role on mechanical properties

of the deformed material [3–5]. In this sense, the theoretical–

experimental works available in the literature [6,7] have beenreported the existence of a macroscopic relation between the

material flow and the friction during ECAP multi-pass process-

ing.

Thenumerical simulation of ECAP hasbeen extensively used

to predict the pressing loads and the effective plastic strain levels

∗ Corresponding author. Tel.: +55 24 3344 3012; fax: +55 24 3344 3029.

E-mail addresses: [email protected](N. Medeiros),

[email protected] (J.F.C. Lins).

induced in several materials during the deformation with the aidof finite element method (FEM) [8–13]. One of the first numer-

ical works that reports the sensitivity of this SPD technique in

relation of the friction conditions was done by Semiatin et al.

[14]. In this work, the authors reported that an uniform effective

plastic strain zone placed at the middle portions of the deformed

billet could be affected directly by strain homogeneity.

Theaim of the present work was to investigate the appearance

of adherence at the billet–die contact regions during the defor-

mation via ECAP of an interstitial free (IF) steel billet using a

plane strain FEM models. The models were developed assum-

ing frictionless, ideal lubrication and severe friction conditions

at the billet–die contact region considering four distinct friction

coefficient (μ) values of 0, 0.05, 0.10 and 0.20, respectively. Thesimulations were carried out using two distinct situations of the

die channels intersection angle (Φ), 90◦ and 120◦, respectively.

2. The finite element analysis

The simulation of the pressing of an IF-steel billet was done

isothermally at room temperature. The numerical simulations

were performed quasi-statically using a commercial finite ele-

ment code (ANSYS 8.1).

0921-5093/$ – see front matter © 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.msea.2008.01.011

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364 N. Medeiros et al. / Materials Science and Engineering A 489 (2008) 363–372

2.1. Modeling of the die

The outer intersection angle (Ψ ) of the die was assumed to

be zero. In addition, each modeling of the die was considered

as rigid-elastic piece which mechanical properties employed

referred to an H13 tool-steel with the Young modulus ( E ) equal

to 200 GPa and the Poisson’s ratio (ν) about 0.3. In both mod-

els, incompressible 2D finite elements were employed assuming

a plane strain condition. The die geometries used in the sim-

ulations are shown in Fig. 1, where the presence of a small

fillet radius of 1.5 mm placed at the inner channels intersection

can be noted. Also, in all the cases, the channels have square

cross-sections with 10 mm of side. The literature reports that the

introduction of a small inner fillet radius in the die geometry can

avoid theproblem of divergencein ECAP simulation [15,21,22].

Also, the value used in the present work to the inner filler radius

maintains the character of deformation by simple shear asso-

ciated to the ECAP technique, once the limits suggested by

Rosochowski and Olejnik [23] are taking into account.

2.2. Modeling of the billet

The billet geometry adopted in each model was a two-

dimensional (50 mm×9.8 mm) one with a unitary thickness

since a plane-strain condition was assumed. The IF-steel was

considered as an isotropic elastic–plastic material which the

elastic properties employed were E =195GPa and ν = 0.29;

whereas, the plasticity is defined by the von Mises or J2 asso-

ciated flow rule. In relation of the hardening behavior, the

experimental uniaxial stress–strain data was adjusted by means

of the Swift model [16], providing the plastic parameters pre-

sented as follows [17]:

σ eq = 544.96(0.004852+ εeq)0.235 (1)

where σ eq is the von Mises stress obtained from the effective

plastic strain εeq.

In relation of the billet mesh, it was described by the same

type of finite elements employed in the die modeling. For the

billet geometry model, 4590 2D plane strain elements were

introduced.

2.3. Loadings and billet–die contact

A displacement boundary condition was imposed to the topline of the billet. In order to assure the quadratic convergence of

the Newton–Raphson method used in the code, the compressive

displacements imposed on the billet top region in the vertical

direction were fixed in increments of 0.10 mm up to a total

displacement of 45 mm.

Fig. 1. Schematic diagrams of the two-dimensional ECAP die FEM modeling showing: (a) intersection angle equal to 90◦; (b) intersection angle equal to 120◦; (c)

contact region for Φ equal to 90◦; (d) contact region for Φ equal to 120◦.



N. Medeiros et al. / Materials Science a nd Engineering A 489 (2008) 363– 372 365

Concerning the friction in the billet–die interface, the friction

coefficient (μ) values of 0, 0.05, 0.1 and 0.2 were attributed for

the models. To represent the friction behavior as a consequence

of the shear stress and the contact pressure, the generalized

Coulomb’s lawwas used. It is well known that this law statespro-

portionality between shear yield stress and the contact pressure

due to the presence of the friction. Specifically in the ANSYS

code, this relation is verified by means of von Mises yield crite-

rion corrected to the simple shear condition and is given by

τ MAX = μσ Y√

3(2)

where τ MAX and σ Y are the yield stresses in pure shear and

uniaxial tension, respectively. Also, μ denotes the static friction

coefficient. Thus, to stress values lesser than τ MAX, sliding of

the workpiece is observed andto higher or equal values of τ MAX,

one should observe an adherence condition like a weld.

A flexible contact between workpieceand tool was employed.

The contact regions assumed in the present work are represented

in Fig. 1 by the lines placed at the billet–die interfaces. The con-tact status was updated after each load step to avoid inaccurate

results. In addition, the contact algorithm was described by the

augmented Lagrangian method employed that permits a small

amount of slip under sticking friction conditions. This method

enables the material flow toward to the second channel.

2.4. Friction and effective plastic strain curves

TheCoulomb’s friction curves were obtained by means of the

mapping of the contact pressure and shear stresses in function

of the billet displacement and the friction conditions. The map-

ping was done in the most external nodes at the two billet sides.

Fig. 2a shows the left side of the billet that comprehends both

left-hand height and bottom and, the respective right side that

was composed by the right-hand height. Fig. 2b shows the nodes

configuration used to evaluate the appearance of adherence dur-

ing the deformation process. In the billet left and right sides

were mapped the displacements corresponding to the loading

direction (negative y-axis). The nodal displacements along the

Fig. 2. (a) Schematic drawing of the billet sides used in the determination of

the Coulomb friction curves. (b) Nodes used in the mapping of displacement,

contact pressure and friction stress along the simulation time.

Fig. 3. Effective plastic strain path used in the nodal mapping corresponding to

the deformed geometry for: (a) die channels intersected at 90◦; (b) die channels

intersected at 120◦.

billet bottom side in the direction of the second channel (positive

x -axis) were also evaluated.

The effective plastic strain curves were obtained by a map-

ping of the nodal values in function of the friction conditions.

Nevertheless, the procedure adopted consisted in the choice

of the strain paths that was defined by two nodes placed

in the middle-portion of the billet, in the vertical and hori-

zontal directions. As well known, the middle-portion of the

deformed billet contains the uniform deformation zone that

exhibits the improved mechanical properties. Thus, regarding

the final deformed geometry of the billet, the effective plastic

strain curves were carried out along the respective deformation

zones from the beginning until the end, in intervals about 25%

(Fig. 3).

3. Results and discussion

3.1. Shear resistance as function of the μ-value

Fig.4 presents the numerical predictions for the friction stress

and the contact pressure as a function of the μ-value obtained

for Φ= 90◦ from the most external nodes located at the billet left

and right sides. An inversion of the friction stresses sign, which

canbe attributed to thepassage of the billet towards to the secondchannel and associated to the simple shear, was observed. The

friction stress and the subsequent contact pressure increase with

the friction coefficient. In particular, when μ is equal to 0.20,

an adherence or sticking friction condition at the billet left side

for displacements higher than 10 mm was detected. In this case,

the friction conditions were sufficiently huge to permit that the

material achieved its shear yield stress about 90 MPa (see the

left-side of Fig. 4c). In addition, the plots corresponding to left

side (Uy) showed dispersed results for 1 mm of displacement.

This behavior can be associated to abrupt increasing in both

contact pressure and friction stress. For die geometries in which

the channels are intersected at 90◦, the billet initially under-




Fig. 4. Friction stressand diecontact pressure obtained forΦ= 90◦ from thenodal values located at theleft andbillet right sides referent to:(a) μ= 0.05; (b)μ= 0.10;

(c) μ= 0.20.

goes a uniaxial compression before its plastic yielding causedby simple shear. Thus, the initial dispersion of the results for

1 mm is linked to the die response due to the billet compression

that is increased for high μ-values. Also, specifically in the left

side plot of Fig. 4b, dispersions can be verified in some results

obtained for 30, 40, and 45 mm of displacement. The deviations

are related to bending of billet layers during the passage forward

to thesecond channel. In theright-side plots of Fig.4, the appear-

ance of intermediary values can be related to unloading regions

placed along the billet surface after crossing the deformation

zone.

The adherence phenomenon can be evidenced when the

billet–diecontact regions are analyzed separately. In this context,

Fig. 5 shows the evolution of displacements, contact pressureand friction stress of the nodes located at the billet bottom, left

and right sides previously defined in Fig. 2b. In these cases, the

most severe condition for friction and die configuration were

employed, i.e., the parameters μ and Φ were assumed as 0.20

and 90◦, respectively. In Fig. 5a, along billet left side, one can

observe the presence of compressive displacements that falls

continuously from the top node 1347 to 1345 located at the bot-

tom side. In addition, the nodes 1491, 1451, and 1413 showed a

behavior that suggests a stabilization tendency in their displace-

ments with time. It is clear that the motion of the bottom node

(1345) was practically zero. This behavior can be explained by

the abrupt increasing in the contact pressure from the bottom to




Fig. 5. Nodal results for displacement, contact pressure and friction stress, and die contact pressure with time obtained for Φ= 90◦ and μ= 0.20: (a) billet left side;

(b) billet right side; (c) billet bottom side.

top parts of the billet after starting the pressing process due to

highμ-value adopted. Following thenode 1347, onecan observe

that the pressure contact increases from zero to about 1.1 GPa

when the time increases from 0 to 50. Also, at this interval, the

regions with high contact pressure exhibited a most intense char-

acter of adherence, i.e., thenodes 1347, 1491, and1451 remained

completely adhered while the nodes 1413 and 1345 does not pre-

sented a relevant dependence with the sticking friction condition.

After this interval and until the end of the simulation (time equal

to 450), the nodes showed evidences of a decrease in the contact

pressure accompanied by an elevation of the friction stress. Thiseffect is related to the augmented Lagrangian contact algorithm.

Thefriction stress peaks displayed after time of 300 by the nodes

1347 and 1491 can be correlated with billet bending during its

passage through the inferior channels intersection.

The billet right side behavior during the simulation was

marked by a positive contribution to the material plastic yielding

toward thesecond channel. It canbe appreciated in Fig.5b, when

one observes an expressive increase of the nodal displacements

from the top (node 1348) to the bottom (node 1346) during the

simulation without tendency of stabilization previously men-

tioned. In relation to the frictional behavior, one can note that

the material crossing along the channels intersection is char-

acterized by peaks of contact pressure and an increase in the

friction stress followed by an unloading step. In addition, the

work-hardening of the material is responsible by the elevation

in the contact pressure from the bottom to the top regions of the

workpiece, i.e., from the node 1346 to the 1348. In summary,

the right side of the billet can deform under simple shear con-

ditions displaying peaks of contact pressure for the nodes 1565,

1603, 1643 and 1348. These peaks is related with the material

shear yield stress when the billet crosses the deformation zone

located at the channels intersection undergoing friction stress

levels close to 90 MPa.Along the billet bottom side the nodal displacements were

considerably small in comparison with the values corresponding

to the left andright sides.It was probably a directconsequenceof

the severe friction conditionadopted. Besides, the initial bending

of theworkpiece causedan intense adherencein thenodesclosed

to the billet left side (see nodes 1345 and 1355) with elevated

friction stress levels. From the node 1362 to 1346, the positive

character associated to the right side contributed to the decrease

in the contact pressure and friction stress after time equal

to 50.

The friction behavior during the passage of the billet into the

die with 120◦ of channels intersection angle was analogue to the




most severe tool configuration (Φ= 90◦). Therefore, the nodal

behaviors with the time are not presented in this work. However,

a smooth channels intersection was responsible by the fall of

the shear stress intensity at the billet–die contact interface to the

most severe friction condition and after 10 mm of displacement,

asshown in Fig.6. This condition strongly suggests that theplas-

tic strain imposed in the material during the deformation was

inferior in comparison of the severe die configuration (Φ= 90◦)

simulated. In this context, is reasonable to deform the IF-steel at

Φ = 90◦ accompanied for values of the friction coefficient down

to 0.20 in order to avoidthe appearance of adherence. In addition,

the die geometry with Φ=120◦ promoted a less severe deforma-

tion of the billet and, therefore, the dispersion of the results was

less intense. However, in the beginning of the pressing the billet

bottompart is supportedby a small regionof thedie, as presented

in Fig. 1d. Consequently, an increase of contact pressure during

the uniaxial compression of the billet can be observed for 1 mm

of displacement (Fig. 6). Lastly, the unloading zones associated

to thedouble bending of thebillet canbe used to explain thegrad-

ual decrease in the contact pressure observed in the right plots of Fig. 6.

The literature reports several alloys deformed by ECAP via

finite element method simulation [5,10–12,24,25] using dies

with channels intersected at 90◦ and severe friction conditions to

improve the final mechanical properties. These results indicated

that under these conditions high levels of plastic strain per pass

could be achieved with appreciable homogeneity. Nevertheless,

the adherence effects were not taken into account in all of the

works.

3.2. Dependence of the pressing force with the friction

conditions

Fig. 7 compares the nodal reaction forces determined forΦ= 90◦ and 120◦ as a function of the μ-value and the billet dis-

placement. As expected, the increase in the friction coefficient

requires highpressing pressures and this factwasearlier reported

by Dumoulin et al. [5] and, recently reinforced by Son et al. [18].

Also, one can observe an increasing of the reaction forces up to

about 7.5 and 5 mm for the both intersecting angles evaluated

followed by a decreasing up to about 10 mm. This effect corre-

sponds to the channels width and is due to the first bending of

the billet edge. For Φ= 90◦, as presented in Fig. 7a, a common

initial behavior was observed for all the extrusion forces with

a peak due to the inwards rounded shape of the billet followed

by an immediate unloading probably caused by the inversion

of the shear stresses sign. A progressive and approximately lin-ear increase of the nodal extrusion force was also noted when

μ = 0.05 close to 15 until near 44 mm of displacement, whereas

a drop for μ-values of 0.10 and 0.20 can be observed due to the

adherence of the billet right side at the secondchannel.However,

the force evolution displayed for Φ=120◦ shows a reloading up

to 15 mm due to the second bending needed to complete the

rotation of the billet (Fig. 7b).

Fig. 6. Friction stress and die contact pressure obtained for Φ=120◦ from the nodal values located at the left and billet right sides with: (a) μ= 0.05; (b) μ= 0.10.




Fig. 7. Results of the pressing forces in function of the friction conditions for: (a) die channels intersected at 90 ◦; (b) die channels intersected at 120◦.

3.3. Distribution of the effective stresses and strains on the

billet

Fig. 8 shows the iso-contour plots of the effective von Misesplastic strains and stresses determined for Φ= 90◦ and 120◦,

regarding μ= 0.20. At 90◦ intersection angle, one should firstly

observe that either the bottom or the top of the billet present the

smallest effective strains since these regions do not pass through

the 45◦ shear zone between the channels. It is important to note

that this extremely high value of the effective plastic strain is

close to 2.4 (Fig. 8a). This value is due to Ψ being equal to zero

and this condition leads to the mesh folding. Finally, the uniform

regions of the effective plastic strains are originated by the stress

flow lines (Fig. 8b) normal to the direction of the displacement

applications, as previously reported by Kim et al. [8] and also

by each Coulomb’s curve presented in Fig. 4c.

At 120◦, as depicted in Fig. 8c, the aspects observed can be

explained analogously to 90◦, e.g., the initial and final portionsof the billet display the smallest plastic deformation since they

do not cross the deformation zone placed at the intersection of

the channels. The presence of the flow lines (Fig. 8d) normal

to the direction of the displacement applications, as reported

earlier by Kim et al. [8], can explain the plastic strain uniform

zone. However, when one compares the effective plastic strains

obtained by means of the models, it is possible to verify that

these values decrease as function of increasing the Φ angle. In

this point, the importance of the Coulomb’s curves became clear

since the fall of the friction stresses mentioned previously and

Fig. 8. (a) Distribution of effective plastic strains to die channels intersected at 90◦. (b) Distribution of correspondent von Mises stresses to die channels intersected

at 90◦. (c) Distribution of effective plastic strains to die channels intersected at 120◦. (d) Distribution of correspondent von Mises stresses to die channels intersected

at 120◦. In all the simulations, the friction condition adopted was equal to 0.20.




caused by the increasing of the Φ can be responsible by the

decrease of the effective plastic strains.

3.4. Mapping of the nodal effective plastic strains along the

uniform strain zone

Fig. 9 presents the nodal effective plastic strains obtained

along the uniform deformation zone in the vertical and horizon-

tal directions from the die channels intersected at 90◦ and 120◦

with distinct friction conditions. It can be observed for the die

configuration at 90◦ that forμ-values of 0.05 and 0.10, the effec-

tive plastic strains are independent of the friction conditions in

both directions considering the maximum value equal to 1.15

in the half of the deformation zone. The relative invariance of

the effective plastic strains with the friction conditions associ-

ated to the dependence with the die geometric parameters agrees

completely with the upper bound-based analytical solutions to

the ECAP pressure calculations proposed recently by Eivani and

Taheri [19]. In this work, the authors reported that the expres-

sions obtained by the effective plastic strains determinations are

functions that depend exclusively of the die geometry adopted.

In Fig. 9a, it is worth to mention the presence of homogeneous

deformation zone in the horizontal direction. It is clear that the

beginning and the end of the zone also showed small values due

to influence of the billet boards and to the portions of 25, 50

and 75%. We have noted that the zone displays homogeneity in

the distribution of the strains, as also reported recently by Yoon

et al. [20]. On the other hand, in the vertical direction, only the

beginning of the strain zone presented small values due to the

fact of the influence of minor board effects.

For μ equal to 0.10, a reasonable heterogeneity in terms of

the strains distribution is a direct consequence of the perturba-

Fig. 9. Curves of nodal effective plastic strains along the uniform plastic zone considering die channels intersected at 90◦ under friction condition equal to: (a) 0.05;

(b) 0.10; (c) 0.20.




Fig. 10. Curves of nodal effective plastic strains along the uniform plastic zone considering die channels intersected at 120◦ under friction condition equal to: (a)

0.05; (b) 0.10.

tions induced on the billet surface. It is associated to the contact

interface, as previously presented in Fig. 4b. For this reason,

in the horizontal direction the maximum value of the effective

plastic strains were observed at the end of the uniform zone.

In the vertical one, the small effect of the billet boards exhib-

ited a tendency analogue that mentioned to the ideal lubrication

(μ= 0.05).

In the most severe friction condition, i.e., for μ equal to

0.20, the oscillations along the horizontal direction (see Fig. 9c)

were intensifiedby the appearance of sticking friction conditions

when the material moves in the direction of the second channel.

On the other hand, some regions displayed a huge homogeneity

along the vertical direction, e.g., the portions from 25 to 75%

of deformation zone. At the beginning (0%) and end (100%) of

the billet is possible to observe a proximity effect with the con-

tact surfaces revealing some degree of heterogeneity of plasticstrains.

The die channels intersected at 120◦ also showed the influ-

ence of the geometric parameters on the effective plastic strains

once the maximum values were about 0.7 (see Fig. 10). These

results are in agreement with the results reported earlier by

Eivani and Taheri [19]. In the case of ideal lubrication and

μ about 0.10, the absence of adherence induced a significant

homogeneity of strains due to the inexistence of perturbations

along the deformation zone, mainly in the horizontal direc-

tion where these effects were most evident. However, when

μ is equal to 0.20 the oscillatory effects along the horizon-

tal direction also promoted a large heterogeneity of strains

along the deformation zone. On the other hand, the vertical

direction exhibited the homogeneity of strains, analogously to

Φ= 90◦

.

4. Conclusions

The quasi-static two-dimension FEM simulations of an IF-

steel deformed by means of the ECAP technique after a single

pass at room temperature make possible some conclusive obser-

vations, as follows:

• The Coulomb’s curves were determined to the die channels

intersected at 90◦ and 120◦ for nodal points placed in the right

andleft billetsidesas function of thefriction conditions. It was

possible to observe a critical adherence condition for Φ= 90◦

and 120◦, when the μ-value was equal to 0.20. This conditionpromotes an increase in the pressing force to press the billet

towards to the second channel.

• The nodal displacements, contact pressure and friction stress

levels confirmed the sticking friction conditions when μ

assumes a value of 0.20. This phenomenon was independent

of the Φ-value adopted.

• The effective plastic strain distributions along the billet mid-

dle portions induced an extended deformation uniform zone.

This effect wasnot only a consequence of the von Mises stress

flow lines normal to the load application direction but also due

to combined effects of contact pressure and the friction stress

at the billet–die contact region.




• The mapping of the effective plastic strain distributions along

the uniform deformation zone was a very useful tool to

observe the relative independence of the maximum strain

values with the friction when moderate conditions were con-

sidered. These results displayed a good agreement with the

literature to both cases of the die geometry investigated. Nev-

ertheless, for the most severe friction condition adopted in the

present work, the presence of oscillations on the strain zones

distributed along the billet horizontal direction can be asso-

ciated to the appearance of adherence at the workpiece–tool

contact interfaces.

• Finally, considering the Coulomb’s curves and the mapping

of the effective plastic strains distributions along the uniform

deformation zone was possible to conclude that thebest condi-

tion to deform bulk materials via ECAP is when one employs

a die with channels intersected at 90◦ associated to a μ-value

equal or less than 0.10.

Acknowledgement

The authors would like to thank to CAPES for the financial

support. J.F.C. Lins and L.P. Moreira thank to CNPq (Grant No.

400609/2004-5).

References

[1] R.Z. Valiev, T.G. Langdon, Prog. Mater. Sci. 51 (2006) 881–981.

[2] V.M. Segal, Mater. Sci. Eng. A 386 (2004) 269–276.

[3] T.G. Langdon, Mater. Sci. Eng. A 462 (2007) 3–11.

[4] J.R. Bowen, A. Gholinia, S.M. Roberts, P.B. Prangnell, Mater. Sci. Eng. A

287 (2000) 87–99.

[5] S. Dumoulin, H.J. Roven, J.C. Werenskiold, H.S. Valberg, Mater. Sci. Eng.

A 410/411 (2005) 248–251.



[8] H.S. Kim, M.H. Seo, S.I. Hong, Mater. Sci. Eng. A 291 (2000) 86–90.

[9] H.S. Kim, Mater. Sci. Eng. A 315 (2001) 122–128.[10] H.S. Kim, Mater. Sci. Eng. A 328 (2002) 317–323.

[11] S.J. Oh, S.B. Kang, Mater. Sci. Eng. A 343 (2003) 107–115.

[12] A.V. Nagasekhar, Y. Tick-Hon, Comput. Mater. Sci. 30 (2004) 489–495.

[13] W.J. Zhao, H. Ding, Y.P. Ren, J. Wang, J.T. Wang, Mater. Sci. Eng. A

410/411 (2005) 348–352.

[14] S.L. Semiatin, D.P. Delo, E.B. Shell, Acta Mater. 48 (2000) 1841–1851.

[15] C.J.L. Perez, Scripta Mater. 50 (2004) 387–393.

[16] H.W. Swift, J. Mech. Phys. Solids 1 (1952) 1–18.

[17] L.P. Moreira, E.C. Romao, G. Ferron, L.C.A. Vieira, A.P. Sampaio, AIP

Conf. Proc. 778 (2205) 667–672.

[18] I.H.Son, Y.G.Jin, Y.T. Im,S.H. Chon, J.K.Park, Mater.Sci. Eng.A 445/446

(2007) 676–685.

[19] A.R. Eivani, A.K. Taheri, J. Mater. Proc. Technol. 182 (2007) 555–563.

[20] S.C. Yoon, P. Quang, S.I. Hong, H.S. Kim,J. Mater. Proc. Technol. 187/188

(2007) 46–50.[21] S. Li, M.A.M. Bourke, I.J. Beyerlein, D.J. Alexander, B. Clausen, Mater.

Sci. Eng. A 382 (2004) 217–236.

[22] F. Yang, A. Saran, K. Okazaki, J. Mater. Proc. Technol. 166 (2005) 71–78.

[23] A. Rosochowski, L. Olejnik, J. Mater. Proc. Technol. 125/126 (2002)

309–316.

[24] R.K. Oruganti, P.R. Subramanian, J.S. Marte, M.F. Gigliotti, S.

Amancherla, Mater. Sci. Eng. A 406 (2005) 102–109.

[25] T. Suo, Y. Li, Y. Guo, Y. Liu, Mater. Sci. Eng. A 432 (2006) 269–274.

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