Crystal plasticity and grain crushing in high-porosity rocks

Previous studies show the significance of considering microstructure of individual crystals in modeling the inelastic behavior of high-porosity rocks. Plastic deformation of high-porosity crystalline rocks, exemplified by limestone, is mainly attributed to crystal plasticity and cataclastic flow. Crystal plasticity is defined as the plastic deformation along potential slip systems within the crystal lattice. In the context of continuum mechanics this micro-mechanism is modeled by a nonlinear relationship between stresses and strains. Two types of nonlinearity characterize the inelastic behavior of the crystal grains: material nonlinearity and geometric nonlinearity. Material nonlinearity defines the changes in stiffness matrix due to plastic slip along slip systems. Geometric nonlinearity contributes to the changes in stiffness matrix due to changes in the geometry of the crystal grains. Geometric nonlinearity is modeled using theory of finite deformation, which assumes the geometry of slip systems to be a function of crystal deformation. This type of nonlinearity is very important in modeling crystal deformation mainly because of plastic spin induced by anisotropy in the crystal structure. However, considering the geometry of slip systems as a function of crystal slip makes the equations highly nonlinear. As a result, many studies either ignore geometric nonlinearity or make other assumptions to simplify the equations. Cataclastic flow, on the other hand, is characterized by pervasive grain crushing in which larger grains are converted into smaller ones. We model cataclastic flow as strong discontinuity in the grain scale via an assumed enhanced strain method formulated within the context of nonlinear finite elements. The method allows the individual finite elements, identified to be in critical condition, to break into two pieces along a plane identified by theory of bifurcation. We show that modeling cataclastic flow combined with finite deformation crystal plasticity can shed much light onto the mechanism of pore-scale deformation in high-porosity rocks.