A Thermomechanical Framework for Analysis of Microstructural Evolution: Application to Olivine Rocks at High Temperature

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.

Rates of Dynamic Recrystallization in Geologic Materials

“…In other words, DRX is fastest under high-temperature, low-stress conditions. This is a seemingly counterintuitive result (and contradicts the recent findings of Holtzman et al, 2018), since stress scales with dislocation density, which provides the driving force for DRX. We suggest, however, that under high-stress, low-temperature conditions, large densities of dislocations with limited mobility accumulate, leading to dislocation entanglement that inhibits DRX.…”

“…An extension of our analysis to nonisothermal conditions is beyond the scope of the present study. With that being said, we speculate that under conditions where microstructural evolution can keep pace with evolving temperatures, our findings (i.e., equation (19)) may still be applicable via a quasi-static approximation (similar to that employed by Holtzman et al (2018) for the application of steady state flow laws to transient creep). Nevertheless, further experiments are required to test this approximation.…”

“…As stated above, this assumption is sensible under experimental conditions where isothermal conditions are imposed, and any thermal perturbations due to shear heating are quickly dissipated. Natural shear zones, however, may experience complex thermal histories—during exhumation or subduction, for example—and are likely closer to adiabatic conditions such that shear heating may be significant (e.g., Foley, ; Holtzman et al, ). An extension of our analysis to nonisothermal conditions is beyond the scope of the present study.…”

“…Whereas the kinetics of static grain growth are reasonably well established (Covey‐Crump, ; Evans et al, ; Faul & Scott, ; Hiraga et al, ; Karato, ; Olgaard & Evans, ; Skemer & Karato, ; Tullis & Yund, ; Yoshino & Yamazaki, ) and are typically parameterized in the form of a normal grain growth law (Kingery et al, ), there are few empirical data on the rates of grain size reduction by DRX in geologic materials. Previous treatments of grain size evolution have considered the rate of DRX as a function of the dissipation of deformation work through grain boundary production (Austin & Evans, , ; Bercovici & Ricard, ; Rozel et al, ), the probability of grain nucleation based on the stored energy of a given grain (Jessell et al, ; Piazolo et al, ; Wenk et al, ), the minimization of a grain population's internal energy (Mulyukova & Bercovici, ), or gravitation toward a mechanistically‐bounded steady‐state grain size (Braun et al, ; Cross et al, ; Hall & Parmentier, ; Holtzman et al, ). However, few studies have explored the kinetics of DRX using empirical (i.e., experimental or field‐based) data.…”

Structural control and system-level behavior of the seismic cycle at the Nankai Trough

“…During periods of rapid change of stress or strain-rate, other deformation processes take place within the rock or mineral structure, leading to a short phase of hardening that transitions to the steady-state response, usually referred to as transient creep (Chopra 1997;Wu et al 2016). In contrast to steady-state, the micro-mechanics of transient creep are poorly understood and different constitutive relationships have been proposed (Sherburn et al 2011;Thieme et al 2018;Holtzman et al 2018), but plastic anisotropy within single crystals may be an important factor (Masuti et al 2019). Because of the rapid change imposed by the seismic cycle, transient creep may be operating during postseismic relaxation (Pollitz et al 2008;Freed et al 2010;Hoechner et al 2011;Tang et al 2019;Muto et al 2011).…”