James K. Knowles Lectures & Caltech Solid Mechanics Symposium
For solids undergoing inelastic deformation via the evolution of some defect structure, a portion of the mechanical energy expended in deforming the solid is associated with a change in the defect structure and is stored in the body, while the remainder is dissipated. Knowledge of the dissipation associated with inelastic deformation is needed for prediction of a variety of phenomena, such as the thermal softening behavior that promotes mechanical instabilities. A mesoscale framework, analogous to that for discrete dislocation plasticity, has been developed for modeling the deformation of amorphous metals deforming by the Shear Transformation (STZ) mechanism. The shear transformation zones are modeled as Eshelby inclusions and superposition is used to represent a quasi-static boundary value problem solution. In carrying out calculations using this framework, in some cases we found that the calculated dissipation rate was negative, which violates the Clausius-Duhem inequality (the second law of thermodynamics). To understand why a negative dissipation rate occurred in the numerical calculations, a general analysis of dissipation and dissipation rate in Eshelby transformations was undertaken. The analysis showed that there is a maximum value of transformation strain magnitude for an Eshelby inclusion that gives non-negative dissipation rate. The condition for non-negative dissipation rate can be expressed as the product of a configurational force, analogous to the Peach-Koehler force for dislocations and the J-integral for cracks, times the transformation strain rate. The resulting expression suggests a form of kinetic relation for Eshelby transformations that can guarantee a non-negative dissipation rate. Such a kinetic relation has been implemented in the mesoscale modeling framework for deformation of metallic glasses by the STZ mechanism. Results of such calculations will be presented.