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 within the precipitate is included using the error and rectangular functions. Due to the presence of precipitates, the critical thermal driving forces (athermal friction) remarkably differ between the direct and reverse PTs, resulting in a hysteresis behavior. For many cases, the critical thermal driving force increases like cx, x=0.5–0.6, vs. the precipitate concentration c for both the direct and reverse PTs. This is similar to c0.5 for the known effect of solute atoms on the athermal friction, which are also dilation centers, but without surface energy. Change (40% reduction) in the precipitate surface energy during PT significantly changes the PT morphology and the critical thermal driving forces. 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. In the opposite case, 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 for the direct PT while it is almost independent of it for the reverse PT. For any concentration, the VSE BCs result in higher thermal critical driving forces, but a smaller hysteresis range, and a larger transformation rate. The obtained critical microstructure and thermal driving forces are validated using the thermodynamic phase equilibrium condition for stationary interfaces. Increase in the interface width reduces the interphase friction. After neglecting misfit and transformation strain and change in surface energy, our simulations describe well the Zener pinning pressure for the grain boundary. The obtained results give an important generic understanding of athermal friction mechanism for phase interfaces for various PTs at the nanoscale.