Nanoscale mechanisms for high-pressure mechanochemistry: a phase field study

Abstract

Coupled evolution of a high-pressure phase (HPP) and dislocations, including dislocation pileups and dislocations generated due to phase transformation (PT), under compression and shear of a nanograined bicrystal, is considered as a model for high-pressure mechanochemistry. Recently developed phase field approach for the interaction between PTs and dislocations at large strains and a finite element analysis are utilized. Periodic boundary conditions for displacements are applied to the lateral surfaces. It is confirmed that the shear-induced dislocation pileups may reduce the PT pressure by an order of magnitude in comparison with hydrostatic loading, and even below phase equilibrium pressure, as it was observed in some experiments. In contrast to the formulation with boundary conditions for lateral stresses, which do not exhibit the sample size effect, periodic boundary conditions lead to some suppression of PT with decreased grain and sample sizes. The local transformation work-based phase equilibrium condition is met for most of the points of the stationary phase interfaces. The interface configurations also correspond in the most cases to the constant pressure contour but with different values for different loadings. Rarely, the same is true for the constant shear stress contours. Similar phase equilibrium conditions are satisfied for the transformation work expressed in terms of stresses averaged over the transformed grain and HPP. These conditions can be used to scale up results of the nanoscale studies to the coarse-grained microscale theory. During unloading, the PT, dislocations, and plastic shear are fully reversible. Even if one pins all the dislocations before unloading starts, still the entire HPP returns back. Thus, problem with modeling metastability of the HPPs still remains open. Obtained results are applicable for interpretation of experiments on high-pressure torsion with diamond or ceramic anvils, friction, surface processing, and probably on ball milling.