Finite element analysis of high pressure torsion processing
Introduction
Recently, several methods of severe plastic deformation (SPD), i.e. large plastic straining realised at quite low temperature and high pressure, such as equal channel angular pressing (ECAP), high pressure torsion straining (HPT), etc., have been developed to process bulk nano-structured materials [1]. One of the main advantages of SPD, in comparison to other well-known methods such as rapid solidification, inert gas condensation or ball milling, is its capability to produce bulk samples and semi-products. This is very important for investigation of various properties and industrial application. Among various SPD methods, the HPT process involving large shear and compressive plastic deformation and being one of these methods is characterised by the distinctive possibility to deform material under high hydrostatic pressure of several GPa with permanent control of the degree of deformation. The HPT process has been the subject of many investigations as a new method of processing for nano-structured materials due to its ability to develop homogeneous nanostructures with high-angle grain boundaries [2]. Recent investigations have also shown that the HPT process can be successfully applied for both the consolidation of metal powders [3] and microstructural refinement [4].
Fig. 1 presents a schematic representation of the HPT process. A workpiece is held between anvils (upper ram and lower support) and strained in compression under an 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. Due to the specific geometric shape of the sample, the main volume of the material is strained under conditions of quasi-hydrostatic compression under applied pressure and the pressure of the outer layers of the sample. As a result, despite the large strain values, the deformed sample is not destroyed.
The shear strain, γ is proportional to the distance from the axis of the sample, r:where θ is the angle of torsion per unit length. (This assumption was investigated and proven experimentally by Grewe and Kappler [5].) According to Eq. (1), the torsion strain value changes linearly from zero in the centre of the sample to the maximum value at its surface. On the other hand, the results of numerous investigations has shown that after several rotations the deformation by the given mode often results in similar refinement of the microstructure in the centre of the samples also, and the processed nanostructure is usually homogeneous at the surface of the samples [1]. It should be noted that the initial thickness of the sample is reduced by approximately twice under high compression pressure for which the traditional use of the initial thickness of the sample under-rates the calculated strain values as compared to the true values [1]. As Valiev et al. [1] emphasised, it is more reasonable to consider the number of rotations and not the strain value calculated by the analytical equations in HPT. It is necessary to investigate the deformation behaviour considering not only complex boundary and loading conditions, but also non-linear material properties.
Although a lot of studies have been done on HPT, most of them are for microstructure and its characterisation [6], [7], [8], [9] or for processing [8], [10]. Because the mechanical properties of the deformed material are directly related to the amount of plastic deformation, i.e. the developed strain, the understanding of the phenomenon associated with strain development is very important in SPD processes. The knowledge of absolute values and the homogeneity of internal stress and strain distributions is very desirable in order to optimise the processes of grain size refinement and nano-structure development in the HPT process.
In this study, the results of the elasto-plastic finite element analysis of the plastic deformation behaviour of bulk nano-structured materials during the HPT processing are presented. The simulated geometry of the workpiece is compared with previous experimental data for pure copper samples processed by the HPT process.
Section snippets
Calculation
Pure Cu (99.9%) samples annealed at 600°C for 10 h having an initial disk shape with a diameter of 10 mm and a height of 0.7 mm were used as ingots for the following deformation in a special device [11]. In this device, the ingots were put between two flat heads under a highly imposed pressure of about 5 GPa. The lower head was rotated at the rate of 0.012 rad s−1. The friction forces between the heads and the ingot resulted in the shear deformation of the workpiece.
One ingot was subjected to pure
Results and discussion
Fig. 3 shows the deformed geometry of a copper sample after the HPT processes of: (a) compressed and unloaded state with 5 GPa; (b) compression (5 GPa)–die rotation (36°)–unloading; (c) compression (5 GPa)–die rotation (72°)–unloaded state. The outer part of the workpiece situated out of the die was thickened. Although the geometry of the deformed workpiece is not distinguishable in Fig. 3, it can be shown that the thickness profile of the unloaded workpiece is not the same as that of the loaded
Summary
In this study, the results of the elasto-plastic finite element analysis of pure copper during the HPT process using the von Mises model are presented. The deformation geometry of the workpiece was investigated. The thickness of the workpiece decreased with distance from the centre because of the higher compressive plastic stress in the centre compared to the outer part during the loading state and the elastic recovery during unloading. The circumferential displacement decreases with distance
Acknowledgements
This work was supported by Korea Research Foundation Grant (KRF-2000-042-E00095). The author would like to express his appreciation to Dr. I.V. Alexandrov who made valuable discussions that supported the experimental data.
References (16)
- et al.
Prog. Mater. Sci.
(2000) - et al.
Mater. Sci. Eng. A
(1993) - et al.
Mater. Sci. Eng. A
(2000) - et al.
Nanostructur. Mater.
(1999) - et al.
Metall. Mater. Trans. A
(1998) - et al.
Acta Mater.
(1997) - et al.
Phys. Stat. Sol.
(1964) - et al.
Nanostructur. Mater.
(1999)
Cited by (78)
Analytical and numerical approaches to modelling severe plastic deformation
2018, Progress in Materials ScienceCitation Excerpt :Cyclic extrusion-compression (CEC) was analysed by Rosochowski et al. [469]. High pressure torsion (HPT) of disks was considered by Kim [470], Figueiredo et al. [261,262,471,472] and Molotnikov et al. [384,473]. As new SPD technologies and the areas of their possible application keep emerging, the significance of FEM methods for quick and efficient design of processing routes and tools increases.
Modeling of kinematic hardening at large biaxial deformations in pearlitic rail steel
2018, International Journal of Solids and StructuresCitation Excerpt :While able to replicate the strains, the two latter processes are difficult to use for direct model evaluations due to the complex contact conditions. Several authors (e.g. Estrin et al., 2008; Wei et al., 2014; Larijani et al., 2015; Yoon et al., 2008; Kim, 2001; Draï and Aour, 2013) have simulated the HPT process, and Larijani et al. (2015) even simulated the extraction of specimens from the deformed disks and their uniaxial response. However, multiaxial loading of the extracted specimens is challenging, due to the limited size that can be extracted with a reasonable homogeneous deformation.
Large elastoplastic deformation of a sample under compression and torsion in a rotational diamond anvil cell under megabar pressures
2017, International Journal of PlasticityA new designed incremental high pressure torsion process for producing long nanostructured rod samples
2017, Journal of Alloys and CompoundsSimulation of high pressure torsion tests of pearlitic steel
2015, Journal of Materials Processing TechnologyCitation Excerpt :Simulation of unconstrained high pressure torsion process has been the subject of a few studies where the main focus are on the obtained inhomogeneous stress-strain field and contact conditions between the sample and the anvils. In Kim (2001) HPT of pure copper up to 72° torsion was analysed using isotropic elasto-plasticity and FEM in ABAQUS with axisymmetric elements with twist. A 3D FE model using rigid-plasticity in the code Deform was used in Yoon et al. (2008) to study the obtained inhomogeneous strain field of a nanostructured material up to two revolutions.