Shear bands in metallic glasses subject to uniaxial loading such as tension and compression exhibit the inclination angle different from $45°$ on the maximum resolved shear stress plane with respect to the loading axis. The cause is often attributed to the effective normal stress acting on the shear plane, which also suggests Coulomb–Mohr yield criterion for metallic glasses. We show here that this argument is conceptually ill justified. Instead, shear band inclination angle can be described by a simple model taking into consideration the volume dilatation and the pressure effects.

We present and compare three elastoplastic models currently used for deformation of metallic glasses, namely, a von Mises model, a modified von Mises model with hydrostatic stress effect included, and a Drucker-Prager model. The constitutive models are formulated in conjunction with the free volume theory for plastic deformation and are implemented numerically with finite element method. We show through a series of case studies that by considering explicitly the volume dilatation during plastic deformation, the Drucker-Prager model can produce the two salient features widely observed in experiments, namely, the strength differential effect and deviation of the shear band inclination angle under tension and compression, whereas the von Mises and modified von Mises models are unable to. We also explore shear band formation using the three constitutive models. Based on the study, we discuss the free volume theory and its possible limitations in the constitutive models for metallic glasses.

Shear band (SB) velocity is a key parameter in assessing the dynamic behavior and also deformation mechanisms of metallic glasses. Using a coupled thermo-mechanical model, we calculated the speed of SB propagation in Vitreloy 1 (Zr_41.25Ti_13.75Ni₁₀Cu_12.5Be_22.5) under compression at a strain rate of 10 s⁻¹. The propagation of the SB exhibits a non-uniform speed: a rather slow stage followed by a rapid propagation when the SB is close to the sample surface or at failure. The average speed is estimated to be about 100 m/s, while the maximum speed could reach 1400 m/s. The impact of the varying SB velocity on measurement relying on surface detection such as thermographic images, strain gauge, and surface offsets is discussed.