Inhomogeneous deformation in metallic glasses

The present study provides a theoretical framework for the inhomogeneous deformation in metallic glasses. The free volume concentration is adopted as the order parameter, which is a function of position and time. The three processes that can change the local free volume concentration are diffusion, annihilation, and stress-driven creation. The rate functions for free volume generation and plastic flow depend on the underlying microscopic model, but the framework is generally valid for different models. A simple shear problem is solved as an example. A linear stability analysis is performed on the basis of the homogeneous solution. An inhomogeneous solution is obtained with a finite amplitude disturbance to the initial free volume distribution. Numerical simulation shows the development of the inhomogeneous deformation and strain localization.