Modeling and simulation of strain-induced phase transformations under compression in a diamond anvil cell

Abstract

Strain-induced phase transformations (PTs) under high-pressure differ fundamentally from the pressureinduced PTs under quasihydrostatic conditions. A model and finite-element approach to strain-induced PTs under compression and torsion of a sample in rotational diamond anvil cell are developed. The current paper is devoted to the numerical study of strain-induced PTs under compression in traditional diamond anvils while the accompanying paper [ V. I. Levitas and O. M. Zarechnyy Phys. Rev. B 82 174124 (2010)] is concerned with compression and torsion in rotational anvils. Very heterogeneous fields of stress tensor, accumulated plastic strain, and concentration of the high-pressure phase are determined for three ratios of yield strengths of low-pressure and high-pressure phases. PT kinetics depends drastically on the yield strengths ratios. For a stronger high-pressure phase, an increase in strength during PT increases pressure and promotes PT, serving as a positive mechanochemical feedback; however, maximum pressure in a sample is much larger than required for PT. For a weaker high-pressure phase, strong strain and high-pressure phase localization and irregular stress fields are obtained. Various experimentally observed effects are reproduced and interpreted. Obtained results revealed difficulties in experimental characterization of strain-induced PTs and suggested some ways to overcome them. Strain-induced phase transformations ͑PTs͒ under high-pressure differ fundamentally from the pressureinduced PTs under quasihydrostatic conditions. A model and finite-element approach to strain-induced PTs under compression and torsion of a sample in rotational diamond anvil cell are developed. The current paper is devoted to the numerical study of strain-induced PTs under compression in traditional diamond anvils while the accompanying paper ͓V. I. Levitas and O. M. Zarechnyy, Phys. Rev. B 82, 174124 ͑2010͔͒ is concerned with compression and torsion in rotational anvils. Very heterogeneous fields of stress tensor, accumulated plastic strain, and concentration of the high-pressure phase are determined for three ratios of yield strengths of low-pressure and high-pressure phases. PT kinetics depends drastically on the yield strengths ratios. For a stronger high-pressure phase, an increase in strength during PT increases pressure and promotes PT, serving as a positive mechanochemical feedback; however, maximum pressure in a sample is much larger than required for PT. For a weaker high-pressure phase, strong strain and high-pressure phase localization and irregular stress fields are obtained. Various experimentally observed effects are reproduced and interpreted. Obtained results revealed difficulties in experimental characterization of strain-induced PTs and suggested some ways to overcome them.

Coupled phase transformations and plastic flows under torsion at high pressure in rotational diamond anvil cell: Effect of contact sliding

“…This work can be considered as generalization of the previous works 13 for simulation of the processes in RDAC when contact sliding is taken into account or generalization of the previous work 15 on modeling of the processes in DAC with contact sliding and friction, for much more complex three dimensional (3D) case of compression and shear in RDAC. Combination of classical isotropic Coulomb friction model with plastic friction model is extended to consider phase concentration-dependent friction stress and to include small elastic slipping.…”

“…12,13,15,16,19 The applicability of the perfectly plastic and isotropic model with the yield strength independent of the deformation history is justified in Ref. 20 under monotonous loading for various classes of materials (metals, rocks, powders, etc.)…”

“…While first numerical results for modeling strain induced PTs in DAC 12,16,19 and in RDAC 13 have been very successful in interpreting multiple experimental phenomena, they involve a strong assumption: there is full cohesion on the contact surface between sample and diamond anvils. In this case, radial displacements at the contact surface are zero and circumferential displacements of material are equal to circumferential displacements of an anvil.…”

“…3 Since strain-induced defects produce much larger stress concentration than the pre-existing ones, external pressure can be significantly reduced. Strain-induced PTs in RDAC are described by three-scale theory (at the nano-, micro, and macroscales), 3 its further developments at the micro 10 and macroscales, 12,13 and within numerical simulations at the macroscale. 12,13 While there are some analytical and numerical solutions for interaction of PTs and plasticity at the nanoscale, 3,14 they cannot be directly utilized in the current study on PTs in RDAC, due to the size of the sample of the order of magnitude of 1 mm.…”

“…9 That is why finite-element method (FEM) simulations have been developed to study the evolution of all fields, including concentration of high pressure phases, and effects of material parameters on them, as well as to interpret experimental phenomena. 12,13,15,16 It is a nonlinear problem of coupled PTs and mechanics with large plastic deformations and displacements, which leads to nontrivial simulation challenges using FEM, including convergence.…”