Grain-size Evolution During Deformation

The process of localization in a deforming solid made of grains is related to a dynamic feedback between the deformation itself and the rheology controlled by macroscopic variables (pressure, temperature) and by the grain size distribution. In this contribution, using simply the most fundamental thermodynamic requirements (mass and energy conservations and positivity of entropy production) we constrain the relationships between the evolution of grain size and the deformation. Our formalism couples a microscopic model for the evolution of grain size distribution under deformation to a macroscopic continuum approach for the deformation itself. The grain size growth can either be related to a continuous process where the number of grains remain constant but where mass is exchanged between them or to a discontinuous process where the number of grains changes by grain sticking or grain breaking. The kinetic rates are controlled by a balance between local and averaged free energies (that include contributions from grain surface and volume energies as well as from larger scale deformational work). This model predicts the increase in average grain size when no deformations are applied (i.e. the healing of a damaged matrix) by grain ripening and/or grain coagulation. This generalizes the Lifshitz-Slyozov theory and the Smoluchovski formalism. When deformation is applied, the discontinuous breaking mechanism provides small grains and a source of nuclei that decrease the average grain size while the continuous mass exchange between grains sharpens their size distribution. We will discuss the possible grain size distributions and modes that can be analytically predicted in simple cases and show more complex numerical simulations.