An implicit finite element method for simulating inhomogeneous deformation and shear bands of amorphous alloys based on the free-volume model

Inhomogeneous deformation of amorphous alloys is caused by the initiation, multiplication and interaction of shear bands (i.e. narrow bands with large plastic deformation). Based on the free-volume model under the generalized multiaxial stress state, this work develops a finite element scheme to model the individual processes of shear bands that contribute to the macroscopic plasticity behaviour. In this model, the stress-driven increase in the free volume reduces the viscosity and thus leads to the strain localization in the shear band. Using the small-strain and rate-dependent plasticity framework, the plastic strain is assumed to be proportional to the deviatoric stress, and the flow stress is a function of the free volume, while the temporal change in the free volume is also coupled with the stress state. Nonlinear equations from the incremental finite element formulation are solved by the Newton-Raphson method, in which the corresponding material tangent is obtained by simultaneously and implicitly integrating the plastic flow equation and the evolution equation of the free-volume field. This micromechanical model allows us to study the interaction between individual shear bands and between the shear bands and the background stress fields. To illustrate its capabilities, the method is used to solve representative boundary value problems.