Lattice theory of three-dimensional cracks

The problem of the stability of a three-dimensional crack is analyzed within a lattice-statics approximation. The consequence of introducing a jog into the crack face as well as the effects of various nonlinear-force laws are studied. The phenomenon of lattice trapping (upper and lower bounds on the applied stress for an equilibrium crack of given length) is again obtained. It is possible to obtain some physical insight into which aspects of the force law are critical for crack stability. In particular, the inadequacy of a thermodynamic approach - which relates the critical stress to a surface energy corresponding to the area under the cohesive-force-vs-displacement curve - is demonstrated. Surface energy is a global property of the cohesive-force law. Crack stability is sensitive to much more refined aspects of the cohesive-force law. Crack healing is sensitive to the long-range portion of the cohesive force. Crack expansion is sensitive to the position of the maximum in the cohesive-force relation.