Rate dependent shear bands in a shear transformation zone model of amorphous solids

摘要

We use Shear Transformation Zone (STZ) theory to develop a deformation mapfor amorphous solids as a function of the imposed shear rate and initialmaterial preparation. The STZ formulation incorporates recent simulationresults [Haxton and Liu, PRL 99 195701 (2007)] showing that the steady stateeffective temperature is rate dependent. The resulting model predicts a widerange of deformation behavior as a function of the initial conditions,including homogeneous deformation, broad shear bands, extremely thin shearbands, and the onset of material failure. In particular, the STZ model predictshomogeneous deformation for shorter quench times and lower strain rates, andinhomogeneous deformation for longer quench times and higher strain rates. Thelocation of the transition between homogeneous and inhomogeneous flow on thedeformation map is determined in part by the steady state effectivetemperature, which is likely material dependent. This model also suggests thatmaterial failure occurs due to a runaway feedback between shear heating and thelocal disorder, and provides an explanation for the thickness of shear bandsnear the onset of material failure. We find that this model, which resolvesdynamics within a sheared material interface, predicts that the stress weakenswith strain much more rapidly than a similar model which uses a single statevariable to specify internal dynamics on the interface.