Nature of crack-tip plastic zone in metallic glasses

The fracture of metallic glasses(MGs) can be induced by shear banding in a ductile mode or by cavitation in a brittle way. Plastic zone in front of a crack tip, which is greatly involved with localized shear band, cavitation and the resultant fracture morphology, is a key clue to unveil the secrets of the intrinsic ductility and fracture. However, the characteristics of plastic zone, i.e., stress and strain distributions, size and shape, have not been clearly unraveled for MGs so far. In this paper, an analytical solution of the plastic zone for mode I crack under plane strain condition is derived through J-integral based on a slip line field analysis and shape approximation, by taking pressure-sensitivity, dilatancy, and structural evolution into account. Two length scales of the plastic zone, i.e. the maximum radius Rmax and the radius along the crack line direction Rx, are revealed to control shear flow instability and cavitation, and therefore failure modes. According to shear transformation zone (STZ) based free volume evolution dynamics, the critical values of the mode I stress intensity factor and the plastic zone size at crack initiation are obtained. The effects of Poisson's ratio, pressure sensitivity, and dilatancy on the stress/strain distributions, and the size of plastic zone are elucidated. It is found that larger Poisson's ratio and smaller dilatancy lead to higher fracture toughness and 'slender' critical plastic zone, facilitating a good ductility. The internal correlations of the fracture pattern (i.e. dimple structure) with the plastic zone are established, where the size of the fracture pattern is quantitatively characterized by the critical length of plastic zone. To be further, a shape change of the critical plastic zone from 'slender' (apt to shear plastic flow) to 'chubby' (inclined to cavitation) is revealed with increasing dilatancy or decreasing Poisson's ratio, which might shed light on the underlying mechanism of ductile-to-brittle transition in MGs.