Collective evolution dynamics of multiple shear bands in bulk metallic glasses

• Multiple shear banding of BMGs is examined over a wide range of sample scales.
• A theoretical model is developed for the dynamic evolution of multiple shear bands.
• Analytical solutions of shear band spacing, offset and failure strain are obtained.
• Notable scaling laws and size effect of multiple shear banding are uncovered.
• Energy competing map is proposed for shear band nucleation and propagation.

The collective behavior of multiple shear bands was investigated under in situ four-point bending tests of a Zr-based bulk metallic glass (BMG) over a wide range of sample scales. The self-organization of shear band pattern, characterized by shear band spacing and shear offset, is observed with the variation of sample size and bend curvature, which presents significant size effect and tension–compression asymmetry. To unveil these fundamental behaviors, an analytical model for the evolution dynamics of multiple shear banding is developed for BMGs. In this model, both micro-structural evolution and pressure sensitivity are taken into account by introducing a new law for the stress softening of BMGs within the framework of continuum mechanics; the collective evolution of shear bands is regarded as the coupling result of the structural softening, the momentum diffusion, and the energy conservation. Applying the proposed theoretical model to the bending deformation of BMGs, the analytical solutions of shear band spacing, shear offset and failure strain are obtained. The fundamental behaviors of multiple shear bands are uncovered, in line with the experimental observations: notable scaling laws are found in the evolution of shear band spacing and shear offset, and the inhomogeneous size effect of plasticity is revealed by a transition from weak to strong size-dependence of failure strain with decreasing sample thickness. To be further, a competing map of shear band nucleation and propagation is established based on energy dissipation. The underlying mechanism of these size dependent behaviors of multiple shear bands in BMGs is found to be ascribed to the energy dissipation competition between the nucleation and propagation of shear bands.