Grain fragmentation in sheared granular flow: weakening effects, energy dissipation, and strain localization

We describe the shear flow of a disordered granular material in the presence of grain fracture using the shear-transformation-zone theory of amorphous plasticity adapted to systems with a hard-core interparticle interaction. To this end, we develop the equations of motion for this system within a statistical-thermodynamic framework analogous to that used in the analysis of molecular glasses. For hard-core systems, the amount of internal, configurational disorder is characterized by the compactivity X = ∂V / ∂S(C), where V and S(C) are, respectively, the volume and configurational entropy. Grain breakage is described by a constitutive equation for the temporal evolution of a characteristic grain size a, based on fracture mechanics. We show that grain breakage is a weakening mechanism, significantly lowering the flow stress at large strain rates, if the material is rate strengthening in character. We show in addition that if the granular material is sufficiently aged, spatial inhomogeneity in configurational disorder results in strain localization. We also show that grain splitting contributes significantly to comminution at small shear strains, while grain abrasion becomes dominant at large shear displacements.