Gradient-enhanced modelling of deformation-induced anisotropic damage in metallic glasses

Abstract

Recent experimental and computational studies at different scales reveal an apparent flow-induced anisotropy of the inelastic deformation behaviour in metallic glasses (MGs). However, the anisotropic damage behaviour accompanied by the formation of shear bands is not adequately described in the previous constitutive modelling work. In this study, we develop a thermodynamically-consistent, anisotropic damage model incorporating tension–compression asymmetry (TCA) to describe the unique deformation and damage behaviours. The elastic–plastic response, including the normal stress sensitivity and the plastic dilatancy, is captured by the extended Mohr–Coulomb criterion. A second-order damage tensor is adopted for describing the anisotropic damage behaviour of MGs. By augmenting the Helmholtz free energy function to be dependent on the gradient of the free volume concentration and the gradient of the nonlocal damage parameter, the kinetic equations for the corresponding internal variables are derived within the framework of finite deformation continuum thermodynamics. Different material degradations under tension and compression are considered by decomposing the elastic strain tensor into a positive mode and a negative mode in the free energy function, where the tension-strain-induced damage is fully switched on while the compression-strain-induced damage is only partially activated. The influence of the TCA parameter on the damage initiation, crack propagation and shear bands density, as well as the influence of the gradient regularisation parameter on the width of the damage zone, are systematically studied. The proposed damage model is validated by experiments carried on unnotched and notched microcantilever beams. The simulation results show that both the displacement–load curves and the shear band patterns are in good agreement with the experimental observations.