Criticality in sheared, disordered solids. I. Rate effects in stress and diffusion

Rate effects in sheared disordered solids are studied using molecular dynamics simulations of binary Lennard-Jones glasses in two and three dimensions. In the quasistatic (QS) regime, systems exhibit critical behavior: the magnitudes of avalanches are power-law distributed with a maximum cutoff that diverges with increasing system size L. With increasing rate, systems move away from the critical yielding point and the average flow stress rises as a power of the strain rate with exponent 1/β, the Herschel-Bulkley exponent. Finite-size scaling collapses of the stress are used to measure β as well as the exponent ν which characterizes the divergence of the correlation length. The stress and kinetic energy per particle experience fluctuations with strain that scale as L-d/2. As the largest avalanche in a system scales as Lα, this implies α