paper

Yielding, shear banding and brittle failure of amorphous materials

arXiv:2103.06782 · doi:10.1103/PhysRevResearch.4.043037

Abstract

Widespread processes in nature and technology are governed by the dynamical transition whereby a material in an initially solid-like state then yields plastically. Major unresolved questions concern whether any material will yield smoothly and gradually (ductile behaviour) or fail abruptly and catastrophically (brittle behaviour); the roles of sample annealing, disorder and shear band formation in the onset of yielding and failure; and, most importantly from a practical viewpoint, whether any impending catastrophic failure can be anticipated before it happens. We address these questions by studying the yielding of slowly sheared athermal amorphous materials, within a minimal mesoscopic lattice elastoplastic model. Our contributions are fourfold. First, we elucidate whether yielding will be ductile or brittle, for any given level of sample annealing. Second, we show that yielding comprises two distinct stages: a pre-failure stage, in which small levels of strain heterogeneity slowly accumulate, followed by a catastrophic brittle failure event, in which a crack quickly propagates across the sample via a cooperating line of plastic events. Third, we provide an expression for the slowly growing level of strain heterogeneity in the pre-failure stage, expressed in terms of the macroscopic stress-strain curve and the sample size, and in excellent agreement with our simulation results. Fourth, we elucidate the basic mechanism via which a crack then nucleates and provide an approximate expression for the probability distribution of shear strains at which failure occurs, as determined by the disorder inherent in the sample, expressed in terms of a single annealing parameter, and the system size.

arXiv comment18 pages, 11 figures

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