On the computation of mixed-mode K-factors for a dynamically propagating crack, using path-independent integrals J'_k

The path-independent integral J'_k, which has the meaning of energy release rate in elastodynamic crack-propagation, is used to numerically obtain the mixed-mode dynamic stressintensity factors for a crack propagating in a prescribed direction with a prescribed velocity. Moving isoparametric (non-singular) elements are used to model crack propagation. Even though J' is a vector integral and hence is coordinate invariant, the desirability of using specific coordinate systems to improve the accuracies of the numerical solutions for K-factors is pointed out. Two procedures for extracting the mixed-mode K-factors from the J' integral for a propagating crack are given. It is found that the component of J' along the crack-axis, i.e. J'₁⁰, is always equal to or greater than the product of a crack-velocity-function and the component normal to the crack-axis, J'₂⁰. Several examples of a slanted crack are presented to demonstrate the practical utility of the J' integral. A discussion is also presented concerning the velocity factors for dynamic K-factors, and energy release rate, in a finite body.