Abstract
By analyzing the problem of high pressure torsion (HPT) in the rigid plastic formulation, we show that the power hardening law of plastically deformed materials leads to self-similarity of HPT, admitting a simple mathematical description of the process. The analysis shows that the main parameters of HPT are proportional to βq, with β being the angle of the anvil rotation. The meaning of the parameter q is: q = 0 for velocity and strain rate, q = 1 for shear strain and von Mises strain, q = n for stress, pressure and torque (n is the exponent of a power hardening law). We conclude that if the hardening law is a power law in a rotation interval β, self-similar regimes can emerge in HPT if the friction with the lateral wall of the die is not too high. In these intervals a simple mathematical description can be applied based on self-similarity. Outside these ranges, the plasticity problem still has to be solved for each value of β. The results obtained have important practical implications for the proper design and analysis of HPT experiments.
Highlights
High pressure torsion (HPT) is a severe plastic deformation process, which is widely used for producing nanocrystalline metals and alloys [1,2,3]
In subsection 2 of the section “Model” it has been shown that if the hardening law of the material has a power-law form, the HPT process must evolve in a self-similar fashion, and its parameters must have a power dependence on the torsion angle of the anvil
We have shown in subsection 2 of the section “Model” that the uniform simple shear state along the height of the specimen is a solution of the HPT problem in the case of ideally plastic material when there is no friction on the cylindrical surface of the anvil
Summary
High pressure torsion (HPT) is a severe plastic deformation process, which is widely used for producing nanocrystalline metals and alloys [1,2,3]. The generally accepted theory of HPT is based on the assumptions of uniformity of simple shear deformation along the height of the specimen and that there is no slippage between the sample and the anvils. This theory gives a simple expression for the shear strain (1). In [4,5] a problem of coupled phase transformations and plastic flows under torsion at high pressure in a rotational diamond anvil cell was investigated. It has been shown that the assumption of no slippage between the sample and the anvils is too simple in some cases, and leads to significant errors in the description of phase transformations. The same result was obtained experimentally in [7]
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