A comparative study of severe plastic deformation techniques by finite element analysis.
Comaneci, Radu
1. INTRODUCTION
Severe Plastic Deformation methods were developed as a new way of
manufacturing UFG materials. Among various SPD methods, ECAP and MF
processes are specially designed to obtain UFG structures in bulk
materials (Valiev et al., 2006).
ECAP process involves the extruding of the workpiece through a die
consisting of two channel intersecting at a specify angle [phi] (see
Fig.1). Because of identical cross section of the two channels, one can
re-insert the billet into the entry die channel and impose more severe
plastic strain.
[FIGURE 1 OMITTED]
In the vertical channel, the billet moves as a rigid body while all
deformation is localized in the small area around the channel's
meeting line (the bisect plane). The metal is subjected to a simple
shear strain which produces the refinement of the structure. The billet
removal involves a new development of ECAP procedure. The theoretical
effective strain s according to the die geometry (Fig.1) for each pass
is given in Eq. (1):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
MF process involves multiple forging by changing the axis of the applied strain between passes (see Fig.2) by billet rotation along the
axis.
The geometry of specimen and the die channel are in principal
designed in that way, that the material flows only in direction of the
channel at applied compressive load--thus the width of channel and
sample have to be equivalent, Figure 2. Additionally the geometry of the
specimen remains about equal before and after a processing step if
initial height of the specimen and length of channel are identical.
Thus, it is possible to subject the same specimen several times to the
MF process by rotating the material by 90[degrees] around the transverse
direction and/or normal direction of the channel.
[FIGURE 2 OMITTED]
The theoretical effective strain s of the workpiece in each pass,
obtained by compression in the die channel is given by Eq. (2):
[epsilon] = [2/[square root of 3]ln (H/W) (2)
In both procedures, the samples cross section are not changed
during the processing which allows to induce large plastic strain into
material until the accumulated deformation reaches a desired level.
Comparison of different SPD techniques was very rarely reported
previously and only in terms of achieved properties (Cherukuri et al.,
2005) or microstructure changes (Cabibbo et al., 2007). The aim of this
paper is the comparison of two processes in terms of load and strain
distribution by FEA.
2. FINITE ELEMENT ANALYSIS
Annealed Al99,7% specimen with dimensions of 10mmx10mmx60mm was
used. Simulations were based of the constitutive curves and material
constants from DEFORM 3D material library. The deformations were
conducted at RT. The friction factor between the inner surfaces of the
die channels and the specimen was assumed to be 0.12. This value was
experimentally established. All simulations were carried out at a
constant speed of 8.75mm/s, for a 50mm stroke of punch. The isothermal conditions can be fulfilled at that low pressing speed. The workpiece
was dicretized in 8000 tetrahedral elements. The tolerance, positioning
of both workpiece and top/bottom die, convergence criteria, re-meshing
conditions, and boundary conditions must be specified before the
execution of the simulation process. In order to estimate strain
distribution, a few tracking points ([P.sub.1], [P.sub.2] ...) are
defined in longitudinal section of the workpiece.
3. RESULTS AND DISCUSSION
A simulated load-displacement curve for Al99.7 in the mentioned
conditions shows that the load level increases dramatically during the
last stage of the full-filling of the die channel for MF process. (see
Fig.3). That is typically for the die work process. The load level for
ECAP process is instead about five times lower.
[FIGURE 3 OMITTED]
Note that theoretical effective strain for a pass and for the
sample with dimensions of 10x10x60mm, has the value of 2.06, according
to Eq. (2), in frictionless conditions. The strain becomes maximum
(2.30) at the contact region of material with the punch ([P.sub.2]) and
it is minimum (1.03) at the contact with bottom die (P8). In the steady
state, the strain is in the range of 0.73 ... 1.42. That is explained
taking into account the friction: because of this, the strain for all
tracking points (except [P.sub.2]) is smaller than the theoretical
value. As we see, dead zone formation ([P.sub.2], P5, P8 region) is the
major factor for non-uniform strain distribution in MF of strain
hardening material. Lack of free flow of the sample causes strain
heterogeneity.
[FIGURE 4 OMITTED]
Between the inevitable non-uniformly deformed head and tail region,
Fig.5 shows clearly a steady-state region in ECAP, where the strain is
uniform along the axis. Within this steady-state region, however,
deformation inhomogeneity still exists along the transverse direction
(e.g. bottom to top along the width) to a degree that varies with
material and *P (Li et al., 2004). In ECAP, the channel angle plays a
very important role in distribution of strain and material flow.
Generally, larger channel angle leads to lesser average strain but
better homogeneity (Nagasekhar et al., 2007).
[FIGURE 5 OMITTED]
4. CONCLUSIONS
According to FEA results, there are important differences between
ECAP and MF processes in terms of estimated load and strain
distribution. In both cases, as we expect, the mean strains are under
theoretical values because of strain hardening, friction conditions and
gap formation. The estimated strains are in good agreement with real
experiments.
The ECAP process has the advantage of smaller forces and more
homogenous strain reached in an earlier steady state of plastic
deformation.
For the same imposed strain it is preferably to perform ECAP
process with extrapasses than MF process even if the last one is more
effectively in strain terms.
5. REFERENCES
Cabibbo, M.; El-Mehtedi, M.; Scalabroni, C.; Balloni, L. and
Evangelista, E. (2007). A comparative study of microstructural
refinement by torsion-compression and equal channel angular pressing,
Metallurgia Italiana, Vol 99, Issue 7-8, 2007, pp. 9-14
Cherukuri, B.; Nedkova, T.S. and Srinivasan, R. (2005). A
comparison of the properties of SPD-processed AA-6061 by equal channel
angular pressing, multi-axial compressions/forgings and accumulative roll bonding, Materials Science and Engineering A, 410-111, 2005, pp.
394-397
Li, S.; Bourke, M.A.M.; Beyerlein, I.J.; Alexander, D.J. and
Clausen, B. (2004). Finite element analysis of the plastic deformation
zone and working load in equal channel angular extrusion, Materials
Science and Engineering A, 382, 2004, pp. 217-236
Nagasekhar, A.V.; Tick-Hon, Y. and Seow, H.P. (2007). Deformation
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extrusion/pressing, Journal of Materials Processing Technology 192-193,
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Valiev, R.Z.; Estrin, Y.; Horita, Z.; Langdon, T.G.; Zehetbauer,
M.J. and Zhu, Y.T. (2006). Producing Bulk Ultrafine-Grained Materials by
Severe Plastic Deformation, JOM, Vol. 58 (4), 2006, pp. 33-39