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

摘要

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, we have shown elsewhere that, if all phase boundaries more subsonically with respect to both phases, we have shown elsewhere that, if all phase boundaries more subsonically with respect to both phases, this lack of uniqueness can be resolved by imposing a nucleation criterion and a kinetic relation relation for the relevant phase transition. Here we investigate an alternative approach that singles 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. We show that, for phase boundaries that propagate subsonically, this approach is equivalent the imposition of a particular relation at the interface between the phases.