"Butterfly Effect" in Shear-Banding Mediated Plasticity of Metallic Glasses

Abstract: Metallic glasses response to the mechanical stress in a complex and inhomogeneous manner with plastic strain highly localized into nanoscale shear bands. Contrary to the well-defined deformation mechanism in crystalline solids, understanding the mechanical response mechanism and its intrinsic correlation with the macroscopical plasticity in metallic glasses remains long-standing issues. Through a combination of experimental and theoretical analysis, we showed that the shear banding process in metallic glasses exhibits complex chaotic dynamics, which manifests as the existence of a torus destroyed phase diagram, a positive Lyapunov exponent and a fractional Lyapunov dimension. We also demonstrated that the experimentally observed large plasticity fluctuation of metallic glasses tested at the same conditions can be interpreted from the chaotic shear-band dynamics, which could leads to an uncertainty on the appearance of the critical condition for runaway shear banding. Physically, the chaotic shear-band dynamics arises from the interplay between structural disordering and temperature rise within the shear band. By tuning the deformation parameters, the chaotic dynamics can be transformed to a periodic orbit state corresponding to a smaller plasticity fluctuation in metallic glasses. Our results suggest that the plastic flow of metallic glasses is a complex dynamic process, which is highly sensitive to initial conditions and reminiscent of the "butterfly effect" as observed in many complex dynamic systems.