Phase field simulations of plastic strain-induced phase transformations under high pressure and large shear

Abstract

Pressure and shear strain-induced phase transformations (PTs) in a nanograined bicrystal at the evolving dislocations pile-up have been studied utilizing phase field approach (PFA).The complete system of PFA equations for coupled martensitic PT, dislocation evolution, and mechanics at large strains is presented and solved using finite element method (FEM). The nucleation pressure for high pressure phase (HPP) under hydrostatic condition near single dislocation was determined to be 15.9 GPa. Under shear, a dislocations pile-up that appears in the left grain creates strong stress concentration near its tip and significantly increases the local thermodynamic driving force for PT, which causes nucleation of HPP even at zero pressure. At pressures of 1.59 and 5 GPa and shear, a major part of a grain transforms to HPP.When dislocations are considered in the transforming grain as well, they relax stresses and lead to a slightly smaller stationary HPP region than without dislocations. However, they strongly suppress nucleation of HPP and require larger shear. Unexpectedly, the stationary HPP morphology is governed by the simplest thermodynamic equilibrium conditions, which do not contain contributions from plasticity and surface energy. These equilibrium conditions are fulfilled either for the majority of points of phase interfaces or (approximately) in terms of stresses averaged over the HPP region or for the entire grain, despite the strong heterogeneity of stress fields. The major part of the driving force for PT in the stationary state is due to deviatoric stresses rather than pressure. While the least number of dislocations in a pile-up to nucleate HPP linearly decreases with increasing the applied pressure, the least corresponding shear strain depends on pressure nonmonotonously. Surprisingly, the ratio of kinetic coefficients for PT and dislocations affect stationary solution and nanostructure. Consequently, there are multiple stationary solutions under the same applied load and PT and deformation processes are path dependent. With an increase in the size of the sample by a factor of two, 2 no effect was found on the average pressure and shear stress and HPP nanostructure, despite the different number of dislocations in a pile-up. Obtained results represent a nanoscale basis for understanding and description of PTs under compression and shear in rotational diamond anvil cell and high pressure torsion.

Shear driven formation of nano-diamonds at sub-gigapascals and 300 K

“…The external pressure can be even smaller than the equilibirum pressure. Such a mechanism has been confirmed more quantitatively utilizing an analytical model of nucleation at the dislocation pile up in [11,12] and phase field simulations of strain-induced transformations in a bi-crystal in [13,14]. The G to D transition occurs without barrier as shear increases but nuclei cannot grow significantly because the stresses decrease with distance away from the defect tip.…”

Review on Recent Advancements in Severe Plastic Deformation of Oxides by High‐Pressure Torsion (HPT)

“…It was suggested that the large fraction of these lattice defects and their interactions (especially interaction between the dislocations and grain boundaries) lead to enhanced localized pressure which finally results in the formation of high‐pressure phases under lower pressures . Recent theoretical studies by phase field approach and finite elements method confirmed that a dislocation pile‐up under shearing creates strong stress concentration and significantly increases the local thermodynamic driving force for pressure‐induced phase transformation at significantly low pressures . It should be noted that the reduction of pressure by shearing was also reported in some other phase transformations such as α ‐ ω transition in Zr and hexagonal‐wurtzite transition in BN …”

High-Pressure Phase Transformations under Severe Plastic Deformation by Torsion in Rotational Anvils

“…The developed PFA was implemented in a finite element method (FEM) code COMSOL and was utilized for the first study of nucleation and growth of the HPP under normal stress and shear strain ( Fig. 3) 31,39,41,42) in a bicrystal. The obtained results prove that the superimposed plastic shear can reduce PT pressure by a factor of 10 and more.…”