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JMEPEG (2013) 22:3222–3227
DOI: 10.1007/s11665-013-0632-x
Finite Element Analysis of Deformation Homogeneity
During Continuous and Batch Type Equal Channel
Angular Pressing
Jaimyun Jung, Seung Chae Yoon, Hyun-Joon Jun, and Hyoung Seop Kim
(Submitted March 3, 2013; in revised form May 17, 2013; published online June 29, 2013)
Equal channel angular pressing (ECAP) is the most promising and interesting process for refining the grain
size to an ultrafine grain or nanosize by imposing severe plastic deformation into the workpiece and
repeating the process while maintaining the original cross-section of the workpiece. In this paper, we
simulated the batch type ECAP and the continuous type equal channel multi-angular pressing (ECMAP),
which can impose large deformation by repeating the shear deformation, using the finite element method
and investigated the similarity and difference of the two processes. In particular, modified die design of the
continuous type ECMAP was proposed for strain uniformity.
Keywords
batch type and continuous type pressing, die optimization, equal channel angular pressing, equal channel
multi-angular pressing, finite element method, strain
uniformity
1. Introduction
Equal channel angular pressing (ECAP) is a process that
enhances physical properties of a material by applying severe
plastic deformation (SPD), and is a widely used technique for
processing bulk ultrafine grained (UFG) or nanostructured
metallic materials (Ref 1-4). Unlike powder metallurgical
technique for producing bulk materials, ECAP is capable of not
only preventing emergence of pores, secondary phases, or any
unwanted contamination to the materialÕs integrity, but also of
emanating variety of novel and interesting material properties
by controlling the materialÕs plastic deformation without
changing its original cross-section (Ref 5-7). In general, the
ECAP technique is an intermittent process that progresses using
various routes with repetitive and rotational workpiece motions:
route A represents purely repetitive processing without any
workpiece rotation, route B represents a process with 90°
rotation, and route C represents a process with 180° rotation of
the workpiece (Ref 1, 2).
Jaimyun Jung, Department of Materials Science and Engineering,
Pohang University of Science and Technology (POSTECH), Pohang
790-784, Korea; Seung Chae Yoon, Research & Development Team,
Hyundai HYSCO, Chungnam 343-831, Korea; Hyun-Joon Jun, Power
Reactor Fuel Development, Korea Atomic Energy Research Institute,
Daejeon, Korea; and Hyoung Seop Kim, Department of Materials
Science and Engineering, Pohang University of Science and Technology
(POSTECH), Pohang 790-784, Korea; and Center for Advanced
Aerospace Materials, Pohang University of Science and Technology
(POSTECH), Pohang 790-784, Korea. Contact e-mail: hskim@
postech.ac.kr.
3222—Volume 22(11) November 2013
The actual ECAP that is often used is a modified version to
fit industrial appliances, and an active field of research has been
dedicated in designing ECAP channel and die to optimize the
process. In fact, adding various channels to maximize effective
strains imposed by the process has been an ongoing research,
and equal channel multi-angular pressing (ECMAP) (Ref 8) or
parallel-ECAP (Ref 9) represents the very core of the research.
It is considered that ECMAP is apt in enhancing materialsÕ
physical properties because ECMAP, even in a single process,
provides more effective strain than the conventional batch type
ECAP processes offer.
In reducing the grain size of a workpiece material, ECAP
demands repetitive processing in which the development of the
material deformation takes on a new aspect, especially in the case
of deformation uniformity. Also, for effectively controlling the
strain that develops in each channel of ECAP, KimÕs proposals on
deformation behavior of materials through the ECMAP processes of routes A and C (Ref 8) and the consecutive ECAP
process (Ref 10) have been considered, and the finite element
method (FEM) analysis for such processes was introduced. The
physical properties of the processed materials strongly depend
on processing routes and conditions, which is why a precise
analysis of processing routes and conditions should be precedent. Notably, processing conditions regarding the materialÕs
strain uniformity are essential (Ref 11-13). That is, the route A of
batch type ECAP processes is not the same as the route A of
continuous ECMAP process in terms of strain uniformity, and
thus a modified design of ECMAP becomes necessary.
Therefore, in this paper we will investigate the deformation
homogeneity and behavior of materials through FEM analysis
with modified design for route A of ECAP applied to the
continuous ECMAP process.
2. FEM Analysis
Figure 1(a) represents the original ECAP process with width
of W and height of 6W. Figure 1(b) represents the formerly
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500
Stress, MPa
400
10W
300
200
100
6W
0
W
0
1
2
3
4
5
6
Strain
Fig. 2 Stress-strain curve used in the FEM simulation
W
(a)
W
(b)
Fig. 1 Finite element mesh system for (a) batch type ECAP and
(b) continuous ECMAP
suggested design of route A for continuous ECMAP with width
of W, height of 10W, and distance between each channel of W
(Ref 8). Here, W is 10 mm. The die consists of 90° channel
angle and 0° corner angle so that the ECAP and ECMAP
processes can offer greatest degree of deformation. The friction
coefficient is designated as 0.1 the common value for cold
metal forming. The mesh number of ECAP is assigned to be
3000, while that of continuous ECMAP is 5000. Plane strain
condition is assumed with isothermal strain rate of 1 mm/s. The
specimen used for the calculations is pure Cu with stress-strain
data extracted from the dislocation cell evolution model (see
Fig. 2) because data measured from tensile tests is not capable
of providing large strain data that is necessary for SPD process
simulations (Ref 14). The analysis software used for the
simulations is commercial FEM package DEFORM-2D
(Scientific Forming Technologies Corporation, USA).
3. Results and Discussion
3.1 The Deformation Behavior of Materials Processed Under
Original Continuous ECMAP
The original U-type continuous ECMAP process was
designed to exhibit twice the performance compared to the
repetitive ECAP processing through route A in a single
procedure (Ref 8). To observe the deformation homogeneity,
the ECAP processes with single and repeated procedures were
executed. Figure 3 shows the effective strain distributions of
processed specimens after ECAP process through route A:
Fig. 3(a) represents the effective strain distribution of the single
pass, while Fig. 3(b) represents the strain distribution of the pass
2 sample without any rotation. Figure 3(a) reveals an overall
well-matched result compared to the original work (Ref 13): the
arrow A indicates the folding defect (Ref 11). Figure 3(b)
represents the repeated procedure through route A, and shows an
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overall increase in effective strain compared to single procedure
and a diminished corner gap (Ref 13). Less sheared zone (LSZ)
becomes evident near the bottom of the specimen where a lower
strain distribution is observed. More so, in the case of repeated
procedure through route A, from the arrow, one can observe the
preliminary folding defect has retreated back with the emergence
of a new folding defect where arrow B points to. The general
shear deformation behavior seems to be an elongation along the
extruding direction (Ref 15-17).
Figure 4 shows the effective strain from top to bottom in a
steady state region in ECAP where the single procedure curve
coincides with the general results (Ref 18), but not in the case
of repeated procedure. The specimen processed through the
repeated procedure through route A has a significantly less
deformed region at the bottom. In fact, while the difference in
effective strains of top and bottom in single procedure case is
only 0.76, the case of repeated procedure renders a significant
difference 1.403, indicating an increase in effective strain
deviation in repeated procedure through route A. Based on this
information, Fig. 5 shows the average effective strain and
standard deviation: the lower the standard deviation, the more
the homogeneity of deformation (Ref 11). The single procedure
case holds to a 0.884 average effective strain with standard
deviation of 0.352, while the repeated procedure case estimates
to a 1.8 average effective strain with standard deviation of
0.586, which is 0.23 higher than the value from the single
procedure. It is considered that the repetitive processing
without any rotation forms corner gaps due to accumulation
of LSZ, which leads to limited strain near the bottom (Ref 13).
Figure 6 displays each stage of the continuous ECMAP
process that is designed to exhibit twice the performance
compared to the repetitive ECAP process through route A in a
single pass. Stage (A) is the initial stage, (B) is the stage after
first deforming zone, (C) is the stage through the second
deforming zone and a moment before the specimen exits, (D) is
right after the specimenÕs head exits the second deforming zone,
and (E) is the final stage. Like each stage, stage (B) is very
similar to the single procedure ECAP with a corner gap. At
stage (C), when the specimen head is just about to pass through
the second deforming zone, the material in the first deforming
zone experiences a back stress developed in the second
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Fig. 3
Deformed geometry and effective strain distribution for the batch type multi-pass ECAP
Route A 2 Passes
Initial 1 Pass
2.5
Effective strain
Effective strain
2.5
2.0
1.5
1.0
*SD: Standard Deviation
*AES: Average Effective Strain
SD:0.586
2.0
AES:1.8
1.5
SD:0.352
1.0
AES:0.884
0.5
0.5
1 Pass
0
2
4
6
8
Distance, mm
Fig. 4
2 Passes
10
Fig. 5 Average effective strain and standard deviation values after
1 pass and 2 passes of ECAP route A
Path plot of effective strain along the thickness direction
deforming zone to the direction of the arrow (Ref 12). Due to
the back stress, the corner gap shrinks. At stage (D) most of the
corner gap in the first deforming zone vanishes, but another
corner gap arises from the second deforming zone. However,
the corner gap in the second deforming zone is smaller than the
first corner gap at stage (B) due to low strain hardening of the
already deformed material. At the final stage (E), the specimenÕs bottom edge features a very different behavior in regions
F and G, both of which have an approximate length of 3.5W
(Ref 12, 13). The corner gap developed at first and second
deforming zones accumulates LSZ near the bottom of the
specimen, leading to a low effective strain at the bottom of the
specimen in region (F). The bottom of the specimen in region
(G), on the other hand, contains high effective strain due to the
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back stress that filled up the corner gap at the first deforming
zone.
Figure 7 shows path plots of the effective strain from
bottom to top in regions (F) and (G). The figure indicates no
significant discrepancy in effective strain distribution at the
upper region, but it did present a conflicting deformation
behavior between regions (F) and (G) 0-3 mm near the bottom
of the specimen. The effective strain value at the bottom region
of region (F) is approximately 1.03, while in region (G) the
effective strain is approximately 4.23. This disparity seems to
be originated from the back stress that filled up the corner gap
at the first deforming zone (Ref 12, 13).
Hence, the continuous ECMAP process that was designed as
an improvement to the ECAP process is, within the region from
the specimenÕs tip to 4W, similar to the repeated procedure of
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Fig. 6
Deformed geometry and effective strain distribution for the continuous type ECMAP
4.5
G part steady state
F part steady state
4.0
Effective strain
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0
2
4
6
8
10
Distance, mm
Fig. 7 Path plot of effective strain along the thickness directions in
regions F and G
ECAP through route A, but the development of effective strain
is dissimilar beyond 4W.
3.2 Deformation Behavior of Materials Processed Under
Modified Continuous ECMAP
For continuous ECMAP to accurately represent two pass
route A ECAP in terms of overall deformation homogeneity
and deformation behavior, a design that has an out corner angle
of 20°, illustrated in Fig. 8, was considered after trying various
angles for the optimum combination of deformation homogeneity and pressing load. The stages (A)-(E), like the ones
previously mentioned, are specified. One can notice from stages
(C) and (D) that by setting an out round corner, despite the back
stress derived from the second deforming zone, the localized
deformation at bottom region of the specimen can be manipulated. Figure 9 compares the effective strain distribution of the
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original ECMAP process to the modified ECMAP process.
From this figure one can detect a distinct difference in strain
distribution from the specimenÕs tip to 4W under. Figure 10
plots the effective strain from bottom to top region of the
specimen based on the information from Fig. 9. According to
Fig. 10, the bottom region of the specimen processed through
the modified ECMAP has an effective strain of 1.26, a
significantly lower value than the 4.23 of the specimen
processed through the original ECMAP. Average effective
strain and standard deviation were employed to examine the
homogeneity (Fig. 11), and the results indicate lower average
effective strain and standard deviation for the case of modified
ECMAP. Moreover, while the maximum difference in standard
deviation of effective strain from the original ECMAP was
1.67, the modified ECMAP was 1.396, establishing the
importance of the corner angle of the first channel in terms of
deformation homogeneity. Hence, it seems reasonable to state
that design that incorporates corner angles at every channel
except the last should be considered in order to achieve
deformation homogeneity.
Figure 12 shows the comparison of load histories for ECAP,
original ECMAP, and modified ECMAP. The load change for
ECAP process can be divided into three stages. First stage is the
increase in load due to the initial deformation of the specimen.
The second stage is when the specimen tip exits the initial
channel, causing a decrease in load. Lastly, the third stage is
when the specimen deformation reaches a steady state condition (Ref 19). The specimen processed through the repeated
procedure of ECAP through route A experiences a longer
second stage compared to the one processed through the single
procedure of ECAP because the former one consists of folding
defect (Ref 11, 19). Also, the load histories of the original
ECMAP and the modified ECMAP seem similar, but the latter
one shows a smaller load because the folding defect was
avoided due to the corner angle. Nevertheless, the overall load
of modified ECMAP is still large because of the back stress
caused by the multi-angular channel.
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Fig. 8
Deformed geometry with effective strain distribution under the modified ECMAP die
4.5
Modified-ECMAP
ECMAP
4.0
Effective strain
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0
2
4
6
8
10
Distance, mm
Fig. 10 Path plot of effective strain along the thickness directions
in regions indicated in Fig. 9
3.5
Fig. 9 Effective strain distribution (a) in the original die and (b) in
the modified ECMAP die
3.0
SD:0.835
3226—Volume 22(11) November 2013
Effective strain
4. Conclusions
This research discussed about the effective design and the
deformation homogeneity of the continuous ECAP process,
which has been a heated research topic for processing bulk
materials for ultrafine grains. Previously proposed design of the
continuous ECMAP process that was designed to maximize the
efficiency of the original batch type ECAP failed to maintain
deformation homogeneity due to the back stress of multi-angle
channels. To resolve the matter, this research has proposed a
modified design of ECMAP that contains an out corner angle of
20°. The results presenting decreased average effective strain
and standard deviation suggest that the proposed design is in
*SD: Standard Deviation
*AES: Average Effective Strain
2.5
2.0
SD:0.698
AES:1.98
AES:1.8
1.5
1.0
0.5
ECMAP
ECMAP-Modified
Fig. 11 Average effective strain and standard deviation values after
original ECMAP and modified ECMAP
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Fig. 12 Comparison of load histories for batch type ECAP, ECMAP of original die, and ECMAP of the modified die
fact successful in controlling the degree of back stress, and thus
the conservation of deformation homogeneity.
Acknowledgments
This study was supported by a grant from the Fundamental
R&D Program for Core Technology of Materials (10037206)
funded by the Ministry of Knowledge Economy, Korea.
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