Athermal resistance to phase interface motion due to precipitates: A phase field study

Abstract

Athermal resistance to the motion of a phase interface due to a precipitate is investigated. The coupled phase field and elasticity equations are solved for the phase transformation (PT). The volumetric misfit strain due to the precipitate is included using the error and rectangular functions. Due to the presence of precipitates, the critical thermal driving forces remarkably differ between the direct and reverse PTs, resulting in a hysteresis behavior. For the precipitate radius small compared to the interface width, the misfit strain does not practically show any effect on the critical thermal driving force. Also, the critical thermal driving force value nonlinearly increases vs. the precipitate concentration for both the direct and reverse PTs. Change in the precipitate surface energy significantly changes the PT morphology and the critical thermal driving forces. The critical thermal driving force shows dependence on the misfit strain for large precipitate sizes compared to the interface width. For both the constant surface energy (CSE) and variable surface energy (VSE) boundary conditions (BCs) at the precipitate surface, the critical thermal driving force linearly increases vs. the misfit strain coefficient for the direct PT while it is almost independent of it for the reverse PT. For larger precipitates, the critical thermal driving force nonlinearly increases vs. the precipitate concentration for the direct PT. For the reverse PT, its value for the CSE BCs linearly increases vs. the precipitate concentration while it is independent of the precipitate concentration for the VSE BCs. Also, for any concentration, the VSE BCs result in higher thermal critical driving forces, a smaller hysteresis range, and a larger transformation rate. The critical microstructure and thermal driving forces are validated using the thermodynamic phase equilibrium condition for stationary interfaces.