Using finite element modeling to examine the flow processes in quasi-constrained high-pressure torsion

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Abstract

Finite element modeling was used to examine the flow processes in high-pressure torsion (HPT) when using quasi-constrained conditions where disks are contained within depressions on the inner surfaces of the upper and lower anvils. Separate simulations were performed using applied pressures from 0.5 to 2.0 GPa, rotations up to 1.5 turns and friction coefficients from 0 to 1.0 outside of the depressions. The simulations demonstrate the distribution of effective strain within the depressions is comparable to the prediction by ideal torsion, and the applied pressure and the friction coefficient outside the depressions play only a minor role in the distribution of effective strain. The mean stresses during processing vary linearly with the distance from the center of the disk such that there are higher compressive stresses in the disk centers and lower stresses at the edges. The torque required for rotation of the anvil is strongly dependent upon the friction coefficient between the sample and the anvil outside the depressions.

Highlights

Finite element modeling was used to examine flow in quasi-constrained HPT. ► The simulations predict the effective strains and mean stresses during processing. ► Simulations show torque required for anvil rotation depends on friction coefficient.

Introduction

The processing of metals through the application of severe plastic deformation (SPD) has become important in the production of bulk solids having grain sizes in the submicrometer and nanometer range [1]. Several different SPD techniques are available for fabricating these ultrafine-grained materials [2], [3] but it is now generally recognized that high-pressure torsion (HPT) is especially effective for producing exceptional grain refinement [4], [5], [6].

High-pressure torsion was first developed over seventy years ago [7], [8] and the basic principles of this technique are now well established [9]. The HPT sample is generally in the form of a very thin disk and it is processed in an HPT facility where it is subjected to a compressive load and concurrent torsional deformation. The compressive load produces compressive stresses that are effective in preventing cracking of the sample while the torsional straining of the thin disk produces severe plastic deformation. Although HPT is usually conducted with thin disks, there have been recent attempts to expand the principles of HPT processing to include small cylinders [10], [11], [12], rings [13], [14], [15] and U-shaped samples [16].

The facilities for processing by HPT may be conveniently divided into three distinct categories depending upon the precise configuration of the anvils [9]. These configurations are termed constrained, quasi-constrained and unconstrained where lateral flow of the material is not restricted in the unconstrained facility, it is partially restricted in the quasi-constrained facility and it is totally restricted in the constrained facility: illustrations and descriptions of these three procedures were given earlier [9]. Although several early experiments were conducted using constrained or unconstrained facilities, most of the current HPT processing is conducted under quasi-constrained conditions.

Very little information is available at present on the variations that may arise using these three different processing procedures. However, a recent report provides a comprehensive evaluation of the differences arising in the allotropic phase transformations in pure Zr when conducting HPT under constrained and unconstrained processing conditions [17].

Despite the considerable current interest in HPT processing, there are only very limited studies of the principles of material flow during the processing operation. For example, the evolution of strain is usually calculated considering the ideal torsion of a disk having the initial shape of the sample and the mean compressive stresses are then calculated by dividing the load in the anvils by the initial area of the disk. There has been some limited use of finite element modeling (FEM) to examine the flow processes in HPT [18], [19], [20] but, without exception, all of these earlier analyses have concentrated exclusively on unconstrained HPT. These studies have shown that the normal pressure varies as a function of the distance to the center of the sample [18], [19] and the distribution of strain varies through the thickness of the sample [20]. Nevertheless, these analyses are not easily applied to current HPT processing under quasi-constrained conditions.

The present research was therefore initiated because of the recognized importance of utilizing FEM to evaluate the distributions of stresses and strains for HPT processing under quasi-constrained conditions. Accordingly, this report examines the flow parameters in quasi-constrained HPT and considers the implications of these results in practical operations.

Section snippets

Experimental procedures

The finite element modeling was conducted using DEFORM-3D 10.0 software (Scientific Forming Technologies Corp., Columbus, OH) considering isothermal conditions. The material behavior was based on a flow curve presented earlier for commercial purity copper determined by monotonic torsion testing [21]. This experimental flow curve was approximated by an appropriate relationship between the effective flow stress, σ, and the effective strain, ɛ, such that the material behavior in the simulation was

The general characteristics of material flow

The simulations show the sample is deformed by the application of pressure and attains the shape of the depression. Although there is a gap between the top and bottom anvils the friction between the sample and the anvils and the depression walls in the anvils prevents the sample from flowing significantly through the gap at least in the early stage of the process. The reductions in the thickness of the disks were ∼10% after application of the compressive loads without rotation. As the torsional

General implications of the modeling for quasi-constrained conditions

The simulations in this study apply to disk-shaped samples subjected to compression pressures and concurrent torsional straining under conditions of quasi-constrained HPT processing. As reported recently [12], quasi-constrained HPT overcomes the drawbacks of sample thinning and increased torque when processing using unconstrained or fully constrained HPT. In the present simulations, as in experimental processing, one anvil remains static while the other anvil rotates at a constant rotation

Summary and conclusions

  • 1.

    Finite element modeling was used to examine quasi-constrained HPT processing with disks located within depressions on the inner anvil surfaces. Separate simulations were conducted for applied pressures from 0.5 to 2.0 GPa, friction coefficients from 0 to 1.0 outside of the depressions and torsional strains up to 1.5 turns.

  • 2.

    The simulations show the distribution of effective strain inside the quasi-constrained volume of the anvils is comparable to the prediction by ideal torsion. The applied

Acknowledgements

This work was supported in part by the Brazilian Research Council (CNPq) and in part by the National Science Foundation of the United States under Grant No. DMR-0855009.

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