Control of nonlinear bulk deformation and large shear strain on first-order phase transformation kinetics

Abstract

Phase transformations play a key role for many coupled natural processes and they are important for many industrial applications. However, the kinetics of phase transformations taking place in coupled chemo-mechanical systems undergoing large mechanical deformations still need to be better quantified. Here, we study phase transformation kinetics for two phases having each two chemical components. We couple a Cahn-Hilliard type model with a mechanical model for compressible viscous flow. The bulk compressibility is a nonlinear function of the pressure and the shear viscosity is a nonlinear function of the concentration. The mechanical coupling is done by considering a pressure-dependent mechanical mixing term in the equation for the Gibbs energy. We derive a dimensionless system of equations which we solve numerically with a pseudo-transient method using conservative finite differences for discretisation. We perform 1D and 2D numerical simulations and consider far-field simple shear and pure shear. For a chemo-mechanically coupled system, we show that the velocity of the phase boundary is a linear function of the degree of metastability and, hence, confirm the hypothesis of “normal growth”. A stronger mechanical coupling and a larger volumetric effect of the chemical reaction cause slower phase boundary velocities. The 2D results show a significant impact of the mechanical coupling and the far-field deformation on the orientation and kinetics of the phase transformations. Under far-field simple shear and pure shear, the phase transformations generate string-like patterns. The orientation of these patterns is controlled by the applied far-field deformation and orientations differ by 45 degrees between simple shear and pure shear.