Formation and growth of shear bands in glasses: existence of an underlying directed percolation transition
The response of glasses to mechanical loading often leads to the formation of inhomogeneous flow patterns that strongly affect materials properties. Among them, shear bands are ubiquitous in a wide variety of materials, ranging from soft matter systems to metallic alloys. Shear banding is associated with strain localization, i.e. the deformation of the sheared glassy solid is localized in space in form of band-like structures. These structures are often precursors to catastrophic failure, implying that a proper understanding of the underlying mechanisms could lead to the design of smarter materials. However, despite its importance in material science, the microscopic origin of shear banding in glassy materials is only poorly understood. Here, the formation of shear banding in glassy systems is revealed by non-equilibrium molecular dynamics simulations (NEMD) of a binary Lennard-Jones mixture, subject to a constant strain rate. In its glass state, this system exhibits for all considered strain rates the formation of a percolating cluster of mobile regions at a critical strain. We show that this percolation transition belongs to the universality class of directed percolation. Only at low shear rates, where the steady-state stress is close to the yielding threshold, the percolating cluster evolves into a transient (but long-lived) shear band with a diffusive growth of its width.