Hierarchical Nonequilibrium Thermodynamics of Thermally Activated Dislocation Plasticity of Metals and Alloys

The Gibbs equilibrium thermodynamic framework has demonstrated high utility in computational thermodynamics for prediction of stable phases and a wide range of properties of metals and alloys. Hillert nonequilibrium thermodynamics is a generalization of the Gibbs framework suitable for nonequilibrium evolution processes, including nucleation and migration of defects (Liu, 2024a,b). Based on a sequence of local equilibrium states that reflect the heterogeneity of material structure, including defect distribution, Hillert nonequilibrium thermodynamics considers the increment of both thermal and configurational entropy changes associated with irreversible processes along a nonequilibrium trajectory. In the context of thermally activated dislocation plasticity (McDowell, 2024a,b,c), the present paper considers the Hillert generalization of Gibbs equilibrium thermodynamics in terms of internal state variable theories based on evolving constrained local equilibrium states of subsystems such as grains and phases that comprise the overall system or ensemble. We discuss the enumeration of configurations of defects to construct configurational entropy, distinguish between driving forces and probabilities of pending reactions based on local constrained equilibrium states and the entropy change due to nonequilibrium state transitions, and provide insights into both the second law of thermodynamics and the heuristic principle of maximal internal entropy production. Finally, we discuss the use of this framework as a strategy to inform reduced order internal state variable models for crystal plasticity relations of hierarchically structured alloys.