Phase field simulations of plastic strain induced phase transformations under high pressure and large shear
Pressure and shear strain induced phase transformations (PTs) in a nanograined bicrystal at the evolving dislocations pile up have been studied utilizing a 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 the finite element method (FEM) The nucleation pressure for the high pressure phase (HPP) under hydrostatic conditions near a single dislocation was determined to be 15.9 GPa. Under shear, a dislocation 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 applied pressure, the least corresponding shear strain depends on pressure nonmonotonously. Surprisingly, the ratio of kinetic coefficients for PT and dislocations affect the stationary solution and the 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, no effect was found on the average pressure and shear stress and HPP nanostructure, despite the different number of dislocations in a pile up. The obtained results represent a nanoscale basis for understanding and description of PTs under compression and shear in a rotational diamond anvil cell and high pressure torsion.