Crack Fronts Trapped by Arrays of Obstacles: Numerical Solutions Based on Surface Integral Representation

This paper addresses the trapping of the front of a planar crack as it impinges upon a row of periodically-emplaced tough obstacles. The initial penetration of the crack between obstacles, under increasing load, as well as the ultimate unstable joining of penetrating segments so as to surround and by-pass the obstacles, are analyzed. The formulation used for the associated three-dimensional elasticity problems of half-plane cracks with nonuniform, curved fronts is a Boundary Element Method (BEM). This incorporates a specialized fundamental solution for an opening (prismatic) dislocation source ahead of a half-plane crack with a straight front (Rice, 1985a). The implementation of this BEM and associated mesh moving with the front is first discussed after which a series of case studies are carried out. The first two case studies evaluate the accuracy of previously obtained linear perturbation results (Rice (1985b), Gao and Rice (1988)). The last study is a crack growth simulation around a periodic array of circular obstacles with a particle size to spacing ratio of 0.5. The simulation shows in that case that crack trapping achieves an effective toughening ratio of 2.35 when the particle-to-matrix-toughness ratio (K-cp/K-c) is greater than 3.52. The simulation also gives lower bounds on the net toughening when K-cp/K-c < 3.52.