Finite element analysis of high pressure torsion processing

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Abstract

Bulk nano-structured materials processed by methods of severe plastic deformation (SPD) have attracted the growing interest of researchers in materials science. The high pressure torsion straining (HPT) process, which involves large shear and compressive plastic deformation, has been the subject of intensive study in recent years due to its capability of producing fully dense samples having an ultrafine grain size. Because the evolution of the microstructures and mechanical properties of plastically deformed materials are directly related to the amount of plastic deformation, the understanding of the phenomenon associated with the strain development is very important. In this process, knowledge of the internal stress and strain distribution is fundamental to the determination of the optimum process conditions for a given material, such as the number of rotations, the rotational speed and the temperature. In this study, the commercial elasto-plastic finite element method (ABAQUS) is applied to obtain a better understanding of the plastic deformation behaviour of the workpiece during the torsion straining process. The simulated geometry (thickness distribution) of the workpiece is compared with previous experiment data obtained using copper specimens with different number of rotations. The thickness of the workpiece decreased with distance from the centre because of the higher compressive plastic stress state in the centre region compared to the outer part during the loading stage and the elastic recovery during unloading.

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:γ=θrwhere 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.

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