Complex Dynamical Behavior in the Shear-Displacement Model for Bulk Metallic Glasses during Plastic Deformation

In this paper, a fresh shear-displacement model is developed for the plastic deformation of the bulk metallic glasses. The multiscale behavior in the shear banding process and the dynamics transition with the parameters are investigated in analytical form. We present a theoretical support for the transition from unstable states to stable states in the experiment by multiscale analysis and the stability analysis. With the small parameter increasing from negative to positive, the stability of the shear slipping displacement system changes, and there is a limit cycle at the transition stage. Meanwhile, the phase diagram and the power spectrum also suggest that there is dynamics transition with the parameter changing. Moreover, the complexity is analyzed for different disturbance parameters, and it is coincident with the fact that the solution is more irregular for larger disturbance. In addition, we find that the amplitude of solution decreases with the temperature decreasing, which is consistent with the experimental results that the amplitude of the serration is smaller and smaller as the temperature decreases.