A continuum theory of grain size evolution and damage
Authors: Ricard Y. , Bercovici D. 
Published: January 2009

Lithospheric shear localization, as occurs in the formation of tectonic plate boundaries, is often associated with diminished grain size (e.g., mylonites). Grain size reduction is typically attributed to dynamic recrystallization; however, theoretical models of shear localization arising from this hypothesis are problematic because (1) they require the simultaneous action of two creep mechanisms (diffusion and dislocation creep) that occur in different deformation regimes (i.e., in grain size stress space) and (2) the grain growth (“healing”) laws employed by these models are derived from normal grain growth or coarsening theory, which are valid in the absence of deformation, although the shear localization setting itself requires deformation. Here we present a new first principles grained‐continuum theory, which accounts for both coarsening and damage‐induced grain size reduction in a monomineralic assemblage undergoing irrecoverable deformation. Damage per se is the generic process for generation of microcracks, defects, dislocations (including recrystallization), subgrains, nuclei, and cataclastic breakdown of grains. The theory contains coupled macroscopic continuum mechanical and grain‐scale statistical components. The continuum level of the theory considers standard mass, momentum, and energy conservation, as well as entropy production, on a statistically averaged grained continuum. The grain‐scale element of the theory describes both the evolution of the grain size distribution and mechanisms for both continuous grain growth and discontinuous grain fracture and coalescence. The continuous and discontinuous processes of grain size variation are prescribed by nonequilibrium thermodynamics (in particular, the treatment of entropy production provides the phenomenological laws for grain growth and reduction); grain size evolution thus incorporates the free energy differences between grains, including both grain boundary surface energy (which controls coarsening) and the contribution of deformational work to these free energies (which controls damage). In the absence of deformation, only two mechanisms that increase the average grain size are allowed by the second law of thermodynamics. One mechanism, involving continuous diffusive mass transport from small to large grains, captures the essential components of normal grain growth theories of Lifshitz‐Slyosov and Hillert. The second mechanism involves the aggregation of grains and is described using a Smoluchovski formalism. With the inclusion of deformational work and damage, the theory predicts two mechanisms for which the thermodynamic requirement of entropy positivity always forces large grains to shrink and small ones to grow. The first such damage‐driven mechanism involving continuous mass transfer from large to small grains tends to homogenize the distribution of grain size toward its initial mean grain size. The second damage mechanism favors the creation of small grains by discontinuous division of larger grains and reduces the mean grain size with time. When considered separately, most of these mechanisms allow for self‐similar grain size distributions whose scales (i.e., statistical moments such as the mean, variance, and skewness) can all be described by a single grain scale, such as the mean or maximum. However, the combination of mechanisms, e.g., one that captures the competition between continuous coarsening and mean grain size reduction by breakage, does not generally permit a self‐similar solution for the grain size distribution, which contradicts the classic assumption that grain growth laws allowing for both coarsening and recrystallization can be treated with a single grain scale such as the mean size.