Energy release rate and crack kinking

A closed form solution is presented for the energy release rate at the onset of kinking of a straight crack in an infinite elastic medium subjected to a predominantly Mode I loading. The solution is accurate to the second order of kink angle and is carried out by the method which models the kink as a continuous distribution of infinitesimal edge dislocations. On the basis of the maximum energy release rate criterion, simple expressions are obtained for the critical kink angle and the critical applied stress. The examination of the results shows that the second order solutions are in very good agreement, up to fairly large kink angles, with numerical results reported by others. It is also analytically established that the Irwin formula for the energy release rate remains valid under the predominantly Mode I loading, provided that the stress intensity factors in the formula are appropriately interpreted.