Scripta Materialia 49 (2003) 185–190
www.actamat-journals.com
Effect of deformation histories on texture
evolution during equal- and dissimilar-channel
angular pressing
Jin-Yoo Suh
a
a,*
, Jun-Hyun Han
a,b
, Kyu-Hwan Oh b, Jae-Chul Lee
a
Division of Materials Science and Engineering, Korea Institute of Science and Technology (KIST), P.O. Box 131,
Cheongryang, Seoul 130-136, South Korea
b
School of Materials Science and Engineering, Seoul National University, San 56-1, Shinlim-dong, Kwanak-gu,
Seoul 151-744, South Korea
Received 14 January 2003; received in revised form 24 March 2003; accepted 8 April 2003
Abstract
Finite element analyses and full constraint Taylor analyses based on the rate sensitivity model were performed to
analyze deformation history and corresponding texture evolution during equal- and dissimilar-channel angular
pressing, respectively.
Ó 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.
Keywords: Equal-channel angular pressing (ECAP); Texture; Finite element analysis; Texture simulation
1. Introduction
It is known that the formability of the metallic
sheets with a fcc structure can be greatly improved
by the presence of the h1 1 1i//ND textures. This is
because the h1 1 1i//ND textures exhibit the highest
plastic strain ratio while the planar anisotropy of
these textures is the lowest [1]. In general, the
h1 1 1i//ND textures can be generated by applying
shear deformation. Therefore, equal-channel angular pressing (ECAP), which has been known to
*
Corresponding author. Tel.: +82-29586805; fax: +8229585449.
E-mail address: [email protected] (J.-Y. Suh).
introduce the simple shear deformation into the
workpiece [2,3], can be used as a technique for
generating the h1 1 1i//ND textures in fcc metals. In
spite of its potential for enhancing formability of
various metals with the fcc structure, the ECAP
process introduced in the earlier studies is unable
to handle a long and thin strip, limiting wider
applications of this technique for producing metallic sheets with high formability.
To apply the deformation characteristics revealed by ECAP for the sheet-forming process,
Lee et al. [4], referring to earlier work of Segal et al.
[5], introduced a continuous confined strip shearing (C2S2) process, which can impart the shear
deformation to a long and thin metallic sheets
without significant changes in their cross sectional
area. This newly developed technique was termed
1359-6462/03/$ - see front matter Ó 2003 Acta Materialia Inc. Published by Elsevier Science Ltd. All rights reserved.
doi:10.1016/S1359-6462(03)00208-2
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J.-Y. Suh et al. / Scripta Materialia 49 (2003) 185–190
dissimilar-channel angular pressing (DCAP) 1 to
distinguish this technique with the conventional
ECAP.
The deformation behavior of ECAP including
DCAP has long been thought to be simple shear.
In recent years, however, a couple of studies have
shown that the deformation behavior due to
ECAP is not the ideal simple shear deformation.
Seok et al. [6], based on the finite element analyses,
demonstrated that the deformation behavior resulted by ECAP is characterized by the complex
mode of deformation consisting of shear, tension,
and compression components. Gholinia et al. [7],
based on the experimental results obtained from
ECAP of an Al billet and the corresponding texture analysis, observed the formation of
{0 0 1}h1 1 0i rotated cube and the {1 1 2}h1 1 0i
component, which have been rotated by 15–20°
with respect to the transverse direction (TD). If the
deformation imparted to the workpiece due to
ECAP is the ideal simple shear deformation as
reported in the earlier studies [2,4], these rotations
in the textures would not have taken place.
Therefore, they claimed that the rotations have
occurred as a result of the additional plane-strain
compression during ECAP. Such a fact indirectly
indicates that the deformation characteristic due
to ECAP may not be the ideal simple shear deformation.
Likewise ECAP, the deformation history resulted by DCAP and its influence on the texture
evolution is of special interest, since controlling
textures is one of the major issues in various sheet-
1
The DCAP die considered in this study consisted of two
channels, whose thickness are dissimilar to each other, such that
the thickness of the outlet channel is slightly larger than that of
the inlet channel, as shown in Fig. 1 [4]. The oblique angle (U),
which is the intersecting angle of the inlet and the outlet
channel, is fixed to 120°. The workpiece, a 1.55 mm thick strip,
is fed into the rolls, where it is reduced to a 1.45 mm thick strip
upon escaping the roll nip, and continues to proceed toward the
outlet channel along the gap between the upper die and the
feeding roll. Upon exiting the shear plane, which is defined as
the plane connecting the outer and the inner corner of the die,
the strip is subjected to a certain amount of shear deformation
corresponding to the oblique angle of the die. Once the strip
passes through the shear plane and exits through the outlet
channel, it retains its initial thickness, i.e., 1.55 mm.
forming processes. The objective of this work is to
study and compare the effect of the deformation
histories on the texture evolution during ECAP
and DCAP predicted using the finite element analyses and the full constraint Taylor analyses
based on the rate sensitivity model.
2. Procedures for calculating the deformation
history and the texture evolution
Deformation behaviors of the workpieces during ECAP and DCAP were simulated using the
commercial finite element analysis software
ABAQUS. The die angles considered in this study
were 90° and 120° for ECAP and DCAP, respectively, because they are the typical die angles
adopted for the processes. A two-dimensional
problem was considered, since the processes,
DCAP in particular, satisfies the plane-strain
condition. General conditions used for simulating
DCAP were identical to those used in the earlier
studies [6,9] to calculate the deformation process
during ECAP except for the difference in the inlet
and the outlet thickness of the DCAP channel. The
material considered for the elasto-plastic analyses
was regarded as a perfectly plastic one with the
von Mises yield strength of 100 MPa. The die was
assumed to be rigid and frictionless. As already
reported by the authors [8], the calculated results
were accurate enough to represent the experimental results.
The full constraint Taylor analyses based on the
rate sensitivity model [10] were carried out to investigate the detailed texture evolution sequence
during ECAP and DCAP. The strain rate sensitivity of 0.05 was adopted since it is typical for
aluminum at room temperature [11]. The shear
strains imparted to the specimens were assumed to
be 2 [12] and 1 [8] for ECAP and DCAP, respectively. Other details, such as equations, solving
procedures, etc., can be found elsewhere [10,11].
To take the actual deformation history into account for predicting the texture evolution, the deformation gradient matrices [13] corresponding to
every finite element steps were extracted from the
ABAQUS results. The texture evolution sequence
corresponding to this actual deformation history
J.-Y. Suh et al. / Scripta Materialia 49 (2003) 185–190
was analyzed according to the full constraint
Taylor analysis based on the rate sensitivity model.
This result was then compared with that analyzed
based on the ideal simple shear deformation,
which, previously, has been considered to be true.
To trace how the individual grains are rotating
under the actual deformation and the ideal simple
shear deformation, 400 crystallographic orientations representing random distribution were generated before the analyses. To be consistent with
rolling, the long axis of the strip along the direction of DCAP is referred as RD and the TD parallel to the surface of strip is defined as TD.
187
Fig. 2. Finite element calculations of DCAP showing how the
shape of the tracer element is evolving with respect to different
locations.
3. Results and discussion
3.1. Deformation history of ECAP and DCAP
To investigate how the workpiece undergoes
deformation during forming, one tracer element
was selected from the middle of the specimen
thickness as shown in Figs. 1 and 2. The coordinates were given to the four nodal points of the
selected element before the calculation and traced
during the whole deformation process. Deformation period valid for the analyses was extracted
from the whole deformation history acquired from
the calculations; the deformation history was
considered to start when the element, initially located at point A, reached at point B in Fig. 2 and
to complete at point C. Fig. 3(a) and (b) are a
series of deformation patterns of the square tracer
In
Guide roll
Thin strip
Upper die
o
φ =
120oo
100
=100
ω
Feeding
Feedingroll
roll
Out
(b)
Lower die
1.45 mm
y
1.55 mm
z
Feeding
Feedingroll
roll
Die
x
1.55 mm
(a)
Fig. 1. (a) A schematic of the C2S2 process based on DCAP and
(b) the detail configuration of the channels.
Fig. 3. Superimposed grids elucidating how the deformation
takes place during (a) ECAP (U ¼ 90°) and (b) DCAP
(U ¼ 120°) analyzed by the finite element method.
element, showing how the shape of the element is
evolving with time steps during ECAP and DCAP,
respectively. The step numbers denoted in Fig. 3(a)
and (b) indicate the finite element analysis steps.
It is clear from Fig. 3 that the extent of the effective strain imparted to the workpiece is significantly larger in ECAP (e 1:15) [12] than DCAP
(e 0:58) [8]. As in Fig. 3(a), general deformation
feature exhibited by ECAP is characterized by a
considerable amount of tension and compression
in addition to shear strains. In this specific case, as
illustrated in Fig. 3(a), the deformation due to
ECAP starts from step 4; the element starts to
experience compression along the ECAP direction
so that the height of the grid becomes elongated
along the thickness direction. Beyond step 14,
changes in the deformation mode have occurred
such that tension along the ECAP direction takes
place, resulting in the recovery of the grid height to
the original value. During the whole deformation
process, i.e., from step 4 to step 19, considerable
amount of the shear deformation takes place in a
continuous manner.
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J.-Y. Suh et al. / Scripta Materialia 49 (2003) 185–190
On the other hand, as compared to the deformation behavior characterized by ECAP, the deformation due to DCAP appeared to deviate
slightly from the ideal simple shear deformation as
seen in Fig. 3(b). This is believed to be due to the
two factors. One is the difference in the die angles
employed in the processes, which, in turn, resulted
in different strains. The other is considered to
originate from the different thickness between the
inlet and the outlet channel. It is noted that the
final height of the deformation grid is higher than
the initial one. This is simply because the outlet
thickness of the channel is thicker than the initial
one.
The deformation behaviors, as visualized in Fig.
3, can be used as the input data for predicting the
texture development. Therefore, it is necessary to
quantify these deformation patterns so that they
can be used as the input data for the full constraint
Taylor analyses. For this purpose, four different
deformation gradient components [13], i.e., Fxx , Fyy ,
Fxy , and Fyx where the subscript ÔijÕ denotes the
direction component as defined in Figs. 1 and 3,
were adopted. The variations in the deformation
gradient components as a function of the calculation steps (or time) are shown in Fig. 4. The step
numbers denoted in the graphs are the same as
those denoted in Fig. 3(a) and (b).
The physical meaning of the each deformation
gradient component can be explained in terms of
elongation and rotation of fibers [13] consisting the
initial square grid. Changes in the value of Fxx ,
averaged x-direction (i.e., ECAP direction as denoted in Fig. 3) component of elongation of fibers
initially directed to the x-direction, reflect the
0.5
The predictions of the texture development were
made based on (i) the ideal simple shear deformation and (ii) the actual deformation histories
characterized by ECAP and DCAP. Since the
texture development is largely dependent on the
deformation history, the results associated with
two different deformation routes, i.e., the ideal
simple shear and the actual deformation, were
compared and analyzed.
Fig. 5(a) and (b) are the h1 1 1i pole figures
predicted by assuming that the workpiece experiences the ideal simple shear deformation during
ECAP and DCAP, respectively, showing how the
textures were developed after deformation. As can
be seen in Fig. 5, two pole figures are almost
identical except for the fact that distributions of
poles are slightly broader in DCAP. Considering
that the only difference in the input data used for
the simulations is the magnitude of the simple
shear strain (c ¼ 2 for ECAP vs. c ¼ 1 for DCAP),
the difference in the shear strains considered in this
2.0
Fxy
(a)
Fyy
1.5
1.0
3.2. Texture evolution
13 14
9
1 34
17
5
Fyx
18 19
Fxx
0.0
Time
Deformation Gradient
Deformation Gradient
2.0
compression and tension of grid along the x-direction during the deformation process, while
changes in Fxy reflects averaged degree of rotation
of the fibers initially directed to the y-direction. It
is noted from Fig. 4(a) that the values of Fxy vary
from negative to positive values since the fibers
directed to the y-direction rotate counterclockwise
until step 9 as shown in Fig. 3(a). The higher
values of deformation gradient components in
ECAP than those of DCAP indicate the difference
in the extent of strains imparted to the workpieces.
(b)
Fyy
1.5
1.0
0.5
1
3
5
14
9
17
11
Fxy
Fxx
Fyx
0.0
Time
Fig. 4. Variations in the deformation gradient components during (a) ECAP (U ¼ 90°) and (b) DCAP (U ¼ 120°) analyzed by the finite
element method.
J.-Y. Suh et al. / Scripta Materialia 49 (2003) 185–190
TD
(b)
(a)
TD
RD
RD
Fig. 5. The h1 1 1i pole figures of the deformation texture after
(a) ECAP (U ¼ 90°) and (b) DCAP (U ¼ 120°) analyzed based
on the simple shear assumption.
study does not make any notable difference in the
texture evolution.
As already discussed in Section 3.1, the actual
deformation behaviors resulting from ECAP and
DCAP are characterized by the complex mode of
deformation consisting of shear, tension, and
compression components rather than the ideal
simple shear deformation. Therefore, it is believed
to be more realistic to simulate the texture evolution as a result of ECAP and DCAP by taking the
actual deformation history into account. Fig. 6(a)
and (b) are the h1 1 1i pole figures calculated based
on the actual deformation histories, showing that
how the textures were developed after ECAP and
DCAP, respectively. In the case of ECAP, as can
be seen from Figs. 5(a) and 6(a), significant differences were noted from the h1 1 1i pole figures
calculated based on the simple shear deformation
and the actual deformation; when the actual deformation history was considered for calculating
the texture evolution during ECAP, poles were
observed to distribute more discretely with a ro-
(a)
TD
(b)
RD
189
tation by 15–20° with respect to the TD. These
final textures shown in Fig. 6(a) agreed well with
the experimental and analytical results obtained by
Gholinia et al. [7].
On the other hand, unlike the results obtained
from ECAP, the h1 1 1i pole figures calculated
based on the actual deformation history caused
by DCAP were observed to be almost identical to
those calculated based on the simple shear deformation as can be seen from Figs. 4(b) and
5(b). To verify the calculated results, the commercially pure Al strip prepared by warm rolling
at 250 °C was processed through the DCAP die
with U ¼ 120°. The specimens before and after
DCAP were then thinned to half in a NaOH
solution to evaluate textures by X-ray diffractometry. The textures of the samples were determined by measuring pole figures by means of an
automated X-ray goniometer of the X-ray diffractometer with Cu-Ka radiation. Fig. 7(a) and
(b) are the h1 1 1i pole figures obtained from the
specimens before and after DCAP, showing that
the positions of the major textures are almost
identical to those predicted based on the simple
shear deformation (Fig. 5(b)) and the actual deformation history (Fig. 6(b)).
Considering the results obtained so far, it can be
inferred that, in ECAP, the texture prediction
based on actual deformation history is considered
to be appropriate, while the texture prediction
based on the simple shear deformation is erroneous. On the other hand, however, the textures
predicted based on the simple shear deformation
was almost identical to those predicted based on
the actual deformation history. Although further
studies are needed to understand texture evolution
TD
RD
Fig. 6. The h1 1 1i pole figures of the deformation texture after
(a) ECAP (U ¼ 90°) and (b) DCAP (U ¼ 120°) analyzed based
on the actual deformation history acquired from the finite element calculations.
Fig. 7. The {1 1 1} pole figures obtained from the warm rolled
specimen (a) before and (b) after DCAP.
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J.-Y. Suh et al. / Scripta Materialia 49 (2003) 185–190
mechanisms due to ECAP and DCAP in greater
detail, the results obtained from the simulations
were considered to represent the actual texture
development to some extent.
deformation are significantly different with
those calculated based on the actual deformation history and, therefore, cannot be used for
predicting the texture development.
4. Conclusion
References
According to the analyses of the deformation
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a result of ECAP and DCAP, the following conclusions were drawn;
1. ECAP (U ¼ 90°) introduces the complex mode
of deformation consisting of tension, compression, as well as shear. Such a deformation pattern characterized by ECAP is considered to be
far from the ideal simple shear deformation.
On the other hand, DCAP (U ¼ 120°) produces the shear deformation, which is slightly
deviated from the ideal simple shear deformation.
2. In the case of DACP, the texture evolution sequences calculated based on the simple shear
deformation are almost identical to those calculated based on the actual deformation history.
However, in ECAP, the texture evolution sequences calculated based on the simple shear
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