On the use of vector J-integral in crack growth criteria for brittle solids

In this paper the criterion for crack-growth in solids is investigated on the basis of the concept of potential energy release rate. The expressions for path-independent vector integral J_i (i = 1, 2) are derived for brittle crack growth. The relationship is then established between the value of the path-independent vector integral J_i and the potential energy release rate for crack growth in an arbitrary orientation. This allows the prediction of crack re-orientation angles on the basis of the maximum energy release rate (MERR) criterion. The crack growth angle is determined analytically as a function of J_i (i = 1, 2). This result is compared with other theoretical formulations of crack growth criteria, as well as with experimental results reported in the literature, and good agreement is found. The formulation provides a rigorous basis for numerical modelling of the processes of crack initiation and propagation.