Implications of Viscosity and Strain-Gradient Effects for the Kinetics of Propagating Phase Boundaries in Solids

Abstract

This paper is concerned with the propagation of phase boundaries in elastic bars. It is known that the Riemann problem for an elastic bar capable of undergoing isothermal phase transitions need not have a unique solution, even in the presence of the requirement that the entropy of any particle cannot decrease upon crossing a phase boundary. For a special class of elastic materials, the authors have shown elsewhere that if all phase boundaries move subsonically with respect to both phases, this lack of uniqueness can be resolved by imposing a nucleation criterion and a kinetic relation for the relevant phase transition. Others have singled out acceptable solutions on the basis of a theory that adds effects due to viscosity and second strain gradient to the elastic part of the stress. It is shown that, for phase boundaries that propagate subsonically, this approach is equivalent to the imposition of a particular kinetic relation at the interface between the phases.