A continuum thermodynamic framework for grain boundary motion

Abstract

In this work, we seek to explain grain boundary motion as a dissipative process within a thermodynamic framework inspired by continuum models for crystal plasticity. This allows for a unified explanation of phenomena such as motion by driving force, shear coupling, mode switching, and stagnation. We begin with a discussion of the kinematic requirements for grain boundary motion and the compatibility of grain boundary shear transformations. The model is based on the principal of minimum dissipation potential, where the “dual dissipation potential” is the energy loss per unit transformed volume as a result of interface motion. Several analytical examples are shown to demonstrate that this model consistently recovers multiple types of grain boundary migration behavior, indicating that the dissipation potential is an intrinsic grain boundary property. It is also shown that the model predicts the phenomenon of mode-switching, and that a “yield surface” can be constructed to relate mechanical loading to mode selection and yield. Molecular dynamics is then used to measure dissipation potential values (in particular the “dissipation energy”) for a wide number of boundaries. Rate-independent dissipation energies are determined for a crystallographically diverse set of 112 Ni grain boundaries using atomistic simulations with two distinct types of physical driving forces: an applied stress and energy jump. Agreement of dissipation energies across driving forces provides verification for the framework. The model’s simplification of migration mechanisms provides a basis for unifying the observed varied grain boundary migration behavior subject to crystallography, driving force, and boundary conditions. Eventually, this framework can be used to develop experimentally calibrated models of grain boundary migration at the mesoscale.