A simple model for material's strengthening under high pressure torsion

Highlights

• Solved confined high pressure torsion process' governing equations

• Enabled estimation of friction induced deformation by the process

• Estimated friction's contribution into the total consumed power

• Verified the solution using experimental case studies

Abstract

Constrained high pressure torsion (CHTP) is a promising route to fabricate ultra-fine structured bulk and powder materials. It was recently proposed as a mechanical test for large strains. Only a few models are available on “friction induced deformation” during CHTP. A number of closed form models were derived in this work to estimate a sticking friction condition during CHPT. The models also correlate CHPT's torque-twist-pressure response and its constitutive parameters. To verify the accuracy of the derivations, the response for Armco iron samples were estimated under three different pressures of 1.9, 3.8 and 7.5 GP and compared with experimental data. Contribution of frictional power dissipated at the specimen's circumferential surface was evaluated and compared with the total deformation power.

Introduction

Severe plastic deformation (SPD) refers to the processing of metals under a combination of extensive hydrostatic pressure and large strains [1]. This produces ultra-fine grained material with a very high dislocation density and modifies properties of the original material. Several new SPD techniques have been developed recently including accumulative roll bonding (ARB) [2], equal channel angular extrusion (ECAE) [3], high pressure torsion (HPT) [4], twist extrusion [5] and axisymmetric forward spiral extrusion [6].

Un-constrained and (semi)constrained modes of high pressure torsion, (semi)CHPT, are widely used by several researchers. A CHPT, allows establishing an effective back-pressure, reduces bulging effect and decreases surface defect. The constrained mode, in its ideal sense, is not practical due to the brittle nature of the punches and the manufacturing errors. A semi-constrained version of HPT has been commonly employed in the existing literature to minimize the implementation problems. Analytically, the constrained mode is reasonably close to the semi-constraint mode. Both semi-constrained and constrained modes are considered in this article. CHPT has been viewed [7] as the realisation of an ideal torsion test in which the fracture of the sample is being postponed indefinitely due to the presence of high hydrostatic pressure. Such a process permits a defined continuous variation of strain and is applicable to relatively brittle materials. Compared to many other SPD processes, CHPT can develop a higher hydrostatic pressure in its sample allowing a more efficient grain refinement even in high strength materials.

CHPT was recently utilized for physical simulation of contact problems [8], [9]. Conventional simulation of the problems is typically expensive, in many cases impractical and therefore should be simulated physically (e.g. rolling contact fatigue [10], [11], [12]). A real contact problem usually closely relates to “friction induced non-linear deformation”. Thus conventional simulators (such as tensile or torsion tests) cannot adequately represent the problem. Advantages of using CHPT as a physical simulator include development of a friction induced deformation mechanism in the test sample in a “zero shape change” and non-linear fashion. CHPT was also proposed recently as a mechanical test [13] to identify stress strain curves of material under very large strains. Both of these new applications are interesting paradigm shifts but they have to develop well analytically before they can be seriously used at the experimental stage.

A key challenge to utilize CHPT as a mechanical test or a physical simulator is to reduce the uncertainties surrounding slippage between the sample and its upper/lower anvils. Very little is known about the boundary conditions in the CHPT including the distribution of loads, velocity fields and possible local slippage at the tool-sample interface. Slippage during CHPT was studied by [14]. In-process observations of the test sample are extremely difficult due to the transient nature of the conditions and inaccessibility of the sample during the process. For a better understanding of the slippage, the boundary conditions could be indirectly monitored by studying the measured overall torque-twist-pressure response. Embossing CHPT's die-sample interface, as suggested by Yogo et al. [13], suppresses sliding between the specimen and the upper\lower die. However the significantly modified geometry requires a proper (complex) post processing of the test measurements. In an ideal CHPT, the main deformation mechanism is pure shear under a high hydrostatic pressure while the modified interface produces a multi-axial and complex deformation route. Given the small size of the sample (~ 1 mm in thickness), the embossing and material flash-out through the die-sample gaps are significant and result in multi-axial deformation. Use of FEM to describe the complex deformation (Yogo et al. [13]) is questionable. A mechanical test (CHPT in this case) is to identify material's constitutive behaviour but the constitutive description is a pre-requisite for a sound and reliable FE analysis. The numerical simulations of the test also require critical assumptions on boundary conditions and constitutive parameters of the test material as priori known information. Experimental observations [15] and numerical studies [16] showed that the plastic deformation is highly heterogeneous along the thickness direction due to the die geometry and high friction, as well as along the radial direction due to the characteristics of torsion. They showed that plastic deformation increased from the centre to the edge in the middle zone in the thickness direction of the disk processed by the CHPT. Also, they found that the deformation vanished in the “dead metal zone” due to the vertical wall constraint under high pressure. More realistic boundary conditions could be defined based on experimental observations. Due to such doubts, typically CHPT's induced strain is simply reported in terms of the numbers of revolutions.

There are several advantages in developing a closed form relationship between the torque-twist-pressure and the flow parameters of CHPT under sticking friction condition. The relationship is useful to quickly design the test, to predict its requirements and to optimize the die geometry. This analytical tool allows a better understanding of microstructure evolution during CHPT processing. To optimize the final properties, through microstructure control, detailed understanding of grain refinement mechanisms is essential. This involves proper simulation of driving forces for grain refinement using crystal plasticity models (e.g. [17], [18]) at a sub grain scale. To calibrate such models by inverse method (e.g. [19]), the sample's load-displacement response can be used. The closed form solution is also useful as a guide to constitutive specification, driving forces for dislocation velocity, nucleation rates and the boundary conditions needed for a crystal plasticity formulation.

This work aims to estimate the minimum pressure to initiate a sticking friction between a CHTP's anvil and its sample. It also estimates a “threshold torque” required to start the friction induced plastic deformation. A bi-linear kinematically admissible velocity field is employed to estimate effective strain rate and strain in the sample and to derive an upper bound solution of the problem. This correlates the torque twist response during CHPT to its constitutive and test parameters. Finally to assess the accuracy of the derivations, a comparison is made between the predicted torque-twist-pressure response and the experimental measurements for three cases of Armco iron samples deformed under pressures of 1.9, 3.8 and 7.5 GPa, respectively.