Abstract
Microstructural evolution governs transient creep processes in the Earth at high temperature, on time scales from seconds to millions of years. Many experimental constraints and empirical models have been developed for discrete pieces of this problem, including flow laws and kinetic models for grain growth and dislocation recovery. We incorporate these models into a thermodynamic framework to develop a constitutive model for transient creep. The framework employed here is a branch of nonlinear thermodynamics of irreversible processes called the generalized standard materials formalism developed in solid mechanics over the last 40 years but minimally applied to geophysical problems. The generalized standard materials formalism is designed to incorporate a broad range of nonlinearity and coupling in the constitutive equations. To describe dynamic recrystallization, the model is constructed such that information propagates upward in length scale: [dislocation density → subgrain size → grain size], with each property evolving more slowly than the one below. We demonstrate that (1) the grain size-stress piezometer may contain temperature dependence below a threshold in stress, (2) the microstructural evolution is strongly temperature dependent and thus dependent on thermal boundary conditions, and (3) the fraction of mechanical work done to the system that is diverted to changing the microstructure is not a constant but is at least a function of stress, temperature, dislocation density, and grain size. This kind of thermodynamically constrained analysis can be applied to torsional deformation experiments to extract further constraints on the subprocesses of microstructural evolution and transient creep.