Analysis of shear banding in metallic glasses under bending

An analytical model is proposed for studying the formation of shear bands in metallic glasses over a wide range of size scales when subjected to plane strain bending. The model is based on elasto-plastic beam bending and the evolution of shear offset in shear bands. The spacing of shear bands is assumed to be governed by a scaling law depending on a non-dimensional material parameter which is determined from experiments. The macroscopic inelastic deformation due to bending is thought to be accommodated by slip along shear bands. The model is based on comparison of the energy dissipated along shear bands with the macroscopic dissipation obtained from the elasto-plastic theory of beam bending. The model is able to capture the following experimentally-observed scaling laws: (i) for a given thickness, the shear band spacing varies linearly with curvature; (ii) for a given curvature, the shear band offset varies as the square of the thickness; (iii) the shear band spacing varies linearly with the thickness; and (iv) failure strain (bend ductility) decreases with increasing thickness.