Finite element analysis of plastic deformation behavior during high pressure torsion processing
Introduction
Recently, several methods of severe plastic deformation were developed to process bulk nanostructured materials with a grain size from 20 to 200 nm depending on a number of factors (Valiev et al., 2000, Jing et al., 2007, Atienza et al., 2007). The high pressure torsion (HPT) process has been subject of many investigations as a new method of processing bulk nanostructured materials. By this method, nanostructures can be formed both by the consolidation of nanopowders (Valiev et al., 1993) and the refinement of the coarse-grained microstructures (Alexandrov et al., 1998). The presence of high angle grain boundaries (Valiev et al., 1997) and high intrinsic stresses are the main features of the obtained nanostructured materials (Valiev et al., 2000).
Fig. 1 shows a schematic representation of the HPT process. A workpiece is held between anvils (upper ram and lower support) and strained in compression under the applied pressure of several GPa. After pressing and holding the workpiece using the upper holder, the lower holder rotates and surface friction forces between the workpiece and the rotating lower die deform the workpiece by shear force.
Because the mechanical properties of the deformed material are directly related to the amount of plastic deformation, i.e. the developed strain, understanding the phenomenon associated with the strain development is very important in severe plastic deformation processes. The knowledge of absolute values and the homogeneity of internal stress and strain distributions is still very desirable in order to optimize the processes of grain size refinement and nanostructure development in the HPT process. For systematic analysis of deformation behavior of materials, numerical approach is useful (Kong et al., 2007a, Kong et al., 2007b).
In this study, the results of the finite element analysis of the plastic deformation behavior of bulk materials during the HPT processing are presented. Simulation for strain distribution is attempted for a sample with the thickness that is larger than the thickness of a general disk-shaped sample by a factor of about 10.
Section snippets
Dislocation cell evolution constitutive model
A main deformation mechanism in polycrystalline metallic materials at room temperature is motion of dislocations and its interaction with grain boundaries (Han, 2007). The workpiece material used in the calculations was the annealed copper, for which the flow curve was calculated up to large strains using the dislocation cell evolution model, a kind of phenomenological approach (Slycken et al., 2007).
Here, we briefly review the 3D version of the constitutive model (Tóth et al., 2002) used in
Results and discussion
Fig. 4 shows the deformed geometry of a copper sample after the HPT processes of (a) compressed state, (b) compressed and one turn rotated and (c) compressed and two turns rotated states. After simple compression, the center regions are less deformed and the corner regions are highly deformed reaching ɛmax = 1.4, as conventional upsetting cases. After applying torsion of one turn shown in Fig. 3(b), strain is high on the punch contacting areas. It should be noted that this axially non-uniform
Conclusions
In this study, the results of the finite element analysis of pure copper during the HPT process using the dislocation cell evolution constitutive model were presented. The deformation geometry of the workpiece was investigated. Equivalent strain distribution was investigated. Torque history was investigated. This axially non-uniform deformation is more remarkable than the radially non-uniform deformation.
Acknowledgement
This work was supported by the Korea Science and Engineering Foundation Grant (F01-2006-000-10051-0) – JSPS international collaboration program.
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