A numerical spectral model for shear transformation zone dynamics in heterogeneous metallic glasses

A shear transformation zone dynamics numerical model using a spectral micromechanical solver based on fast Fourier transform algorithms is developed to study the effects of elastic stiffness spatial heterogeneities and/or porosity on shear localization and mechanical response of metallic glasses. The model is applied to Vitreloy 1 material system. In the model, the activation rate for individual shear events depends on the local stress field, while the nucleation time and the selection of the shear direction and nuclei positions are determined using a kinetic Monte-Carlo algorithm. A small strain framework with heterogeneous elasticity is used to predict strain localization at low temperatures and strain rates. Similar to existing finite element implementations, the shear transformation volumes are introduced as plastic eigenstrains within the spectral micromechanical solver and stress equilibrium is enforced. The effects of local elastic stiffness heterogeneity and porosity on shear band activity and mechanical response are first analyzed by performing 2D simulations. Results show that the spatial heterogeneity of elastic stiffness and/or porosity can significantly affect strain localization and maintain high mechanical strength; their combined action is further beneficial to the overall response of the system. Next, 3D microstructures with homogeneous/heterogeneous elasticity are simulated. As in 2D, the formation of multiple STZ clusters in soft regions produces a smoother elastoplastic transition in 3D volumes. However, unlike the 2D case, the 3D simulations ultimately develop an intense, locally wavy shear band, enabled by the fully three-dimensional internal stress state and the greater freedom in shear orientations. The 3D results thus show that local heterogeneity in elastic stiffness delays the onset of shear localization and enhances the overall plasticity of metallic glasses.