On crack path stability in a finite body

Theoretical and numerical investigations are made for crack path stability in a finite brittle solid under a predominantly Mode I loading condition. Based upon a first order perturbation solution, an"intermediate" range of stability (as compared with the "local" and "global" ranges) is introduced for the crack growth path. This theory is an extension of the stability concept proposed by Cotterell and Rice, but includes the effect of the change of the stability with increasing crack length along the curved trajectory. Four kinds of crack paths are identified: (i) stable, (ii) initially unstable but intermediately stable, (iii) initially stable but intermediately unstable, and (iv) unstable ones. The first two conditions may lead to stable (i.e. straight) crack growth, while the remaining conditions may lead to an unstable (i.e. sharply curved) crack path. Crack path stability is examined for a biaxially stressed Griffith crack. Then numerical results are given for compact tension and double-cantilever beam specimens for various initial crack lengths. In the numerical examples of compact tension specimens, crack paths are sometimes predicted as unstable by the Cotterell-Rice theory, while stable crack paths are always obtained by using the present theory. On the other hand. unstable crack paths are predicted for double-cantilever beam specimens, except for the eases with extremely long initial cracks. The numerical estimates of crack path stability presented here are in good agreement with experimental observations.