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

Abstract

The path-independent integral , 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 is pointed out. Two procedures for extracting the mixed-mode from the J' integral for a propagating crack are given. It is found that the component of J' along the crack-axis, i.e. , is always equal to or greater than the product of a crack-velocity-function and the component normal to the crack-axis, . 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 , and energy release rate, in a finite body.