Hidden spatiotemporal sequence in transition to shear band in amorphous solids

Abstract

Localization of plastic flow into a narrow shear band is a fundamental and ubiquitous nonequilibrium phenomenon in amorphous solids. Because of the intrinsic entangling of three types of elementary local atomic motion—shear, dilatation, and rotation—the precise physical process of shear band emergence is still an enigma. Here, to unveil this mystery, we formulate a theoretical protocol covering both affine and nonaffine components of deformation, to decode these three highly entangled local atomic-scale events. In contrast to the broad concept of the shear transformation zone, the plastic behavior can be demonstrated comprehensively as the operative manipulation of more exact shear-dominated zones, dilatation-dominated zones, and rotation-dominated zones. Their spatiotemporal evolution exhibits a transition from synchronous motion to separate distribution at the onset of the shear band. The hidden mechanism is then revealed with the help of extreme value theory and percolation analysis. Numerical evidence from extreme value theory indicates that dilatation is the dominant mode at the embryonic stage of the initial plastic units, as evidenced through the larger degree of dilatation localization compared with shear and rotation. The percolation analysis points towards the critical power-law scaling nature at the transition from stochastic activation to percolation of plastic regions. Then the comprehensive picture underlying shear banding emergence is uncovered. Firstly, dilatation triggers initial shear and rotation in soft regions, leading to the embryos of the initial flow units, which are followed by the secondary activation of rotation in neighboring hard material, thus causing an alternating distribution of rotation and shear-dilatation regions. Such rotation activation contributes to further perturbation in these regions and ultimately leads to percolation transition and shear band formation. Our findings also reinforce that the discussion of plastic behavior in disordered materials must take into account both affine and nonaffine component deformation.