On the shear-band direction in metallic glasses

Abstract

This paper shows that it is inappropriate to relate the angle between the loading axis and the shear-band (or fracture) plane in metallic glasses under uniaxial loading conditions to the coefficient of internal friction in the Mohr–Coulomb model. Shear bands in metallic glasses are a result of material instability (which can be predicted from constitutive parameters and loading conditions), which does not correspond to the material yield condition. Specifically, the shear-band directions depend on the Poisson’s ratio, the ratios of three deviatoric principal stresses to the von Mises stress, the coefficient of internal friction, and the dilatancy factor. The last parameter describes whether the plastic flow is associative or non-associative. Theoretical predictions based on the classic Rudnicki–Rice model agree well with a compilation of observations in uniaxial mechanical tests. Furthermore, using the elastic contact solutions and the Rudnicki–Rice model, we identify three (two) regimes under the two-dimensional cylindrical (three-dimensional spherical) contact where different shear-band directions may occur. When using a bonded-interface technique to visualize shear bands under three-dimensional contacts, it should be noted that the stress component normal to the bonded interface is released, resulting in the commonly observed semicircular shear bands whose directions are predicted to follow the larger in-plane principal stress.