A theoretical model for the evolution of microstructure in lithospheric shear zones

Rates of Dynamic Recrystallization in Geologic Materials

“…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.…”

The Generation of Plate Tectonics From Grains to Global Scales: A Brief Review

“…Similarly, grains with high dislocation density have large internal energy and thus diffuse mass into grains with lower dislocation density, resulting in DRX by grain boundary migration (e.g., Derby & Ashby, ). The energetically driven processes of grain growth and DRX can compete and interact, as both grain size and dislocation density and their effects on a grain's internal energy, evolve during deformation (Mulyukova & Bercovici, , see also Figure ); the evolution of dislocation density and internal energy have also been used to model the development of anisotropy (Kaminski & Ribe, ). While the basic (single‐ and two‐phase) grain damage theory describes the thermodynamics (i.e., energy conservation and positivity of entropy production) governing grain size evolution (Section ), its current formulation assumes that the migration and accumulation of dislocations by which DRX occurs is instantaneous; thus, the current theory does not capture the interaction of grain size evolution and dislocation dynamics.…”

“…Mulyukova and Bercovici () provide an instructive model using a simple system consisting of only two grains to illustrate the interaction between forces associated with the variations in dislocation density ω i and grain boundary curvature 2/ R i , where R i is again grain size and the subscript i =1 or 2 refers to the individual grains. The underlying physical processes, however, are general for systems with virtually infinite number of grains, as was demonstrated in Mulyukova and Bercovici (), albeit with some simplifications.…”

“…Using a simple parameterization of the combined effects of stress and grain size, and assuming for simplicity that the medium is isotropic, the rate of change of dislocation density in a deforming rock can be described as (see; Mulyukova & Bercovici, ): where C 2 is a constant with dimensions of m/s, R c defines the grain size below which the dislocation density becomes grain size sensitive (typically set to be equal to the field boundary grain size, which applies to either of the mechanisms that can suppress an increase in dislocation density described above), G is the shear modulus and b is the length of the Burgers vector (see Table ). Furthermore, a i determines dislocation density at the steady state, since when .…”

“…Moreover, the evolution of only one of the grains (in our case R 1 ) needs to be tracked, since the size of the other grain can be deduced from mass conservation. Assuming only diffusive mass exchange between the grains (i.e., no grain splitting or coalescence; see; Ricard & Bercovici, ), the evolution of R 1 is given by (see; Mulyukova & Bercovici, ): where C 0 and C 1 are constants with dimensions of m and m 7−2 p / s , respectively, V is the total volume of the two grains, and exponent p is generally set to p =2, which corresponds to normal grain growth behavior (Ricard & Bercovici, ). (Note that the factor ( V /2) was unintentionally omitted in Mulyukova & Bercovici, , equation (18).…”