ecap friction
TRANSCRIPT
7/29/2019 Ecap Friction
http://slidepdf.com/reader/full/ecap-friction 1/10
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
7/29/2019 Ecap Friction
http://slidepdf.com/reader/full/ecap-friction 2/10
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◦.
7/29/2019 Ecap Friction
http://slidepdf.com/reader/full/ecap-friction 3/10
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-
7/29/2019 Ecap Friction
http://slidepdf.com/reader/full/ecap-friction 4/10
366 N. Medeiros et al. / Materials Science and Engineering A 489 (2008) 363–372
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
7/29/2019 Ecap Friction
http://slidepdf.com/reader/full/ecap-friction 5/10
N. Medeiros et al. / Materials Science a nd Engineering A 489 (2008) 363– 372 367
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
7/29/2019 Ecap Friction
http://slidepdf.com/reader/full/ecap-friction 6/10
368 N. Medeiros et al. / Materials Science and Engineering A 489 (2008) 363–372
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.
7/29/2019 Ecap Friction
http://slidepdf.com/reader/full/ecap-friction 7/10
N. Medeiros et al. / Materials Science a nd Engineering A 489 (2008) 363– 372 369
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.
7/29/2019 Ecap Friction
http://slidepdf.com/reader/full/ecap-friction 8/10
370 N. Medeiros et al. / Materials Science and Engineering A 489 (2008) 363–372
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.
7/29/2019 Ecap Friction
http://slidepdf.com/reader/full/ecap-friction 9/10
N. Medeiros et al. / Materials Science a nd Engineering A 489 (2008) 363– 372 371
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.
7/29/2019 Ecap Friction
http://slidepdf.com/reader/full/ecap-friction 10/10
372 N. Medeiros et al. / Materials Science and Engineering A 489 (2008) 363–372
• 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.
[6] V.M. Segal, Mater. Sci. Eng. A 271 (1999) 322–333.
[7] V.M. Segal, Mater. Sci. Eng. A 345 (2003) 36–46.
[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.