Brittle fracture and fatigue propagation paths of 3D plane cracks under uniform remote tensile loading

Fatigue and brittle fracture propagation paths of arbitrary plane cracks, loaded in mode I, embedded in an infinite isotropic elastic body, are investigated. The crack advance is supposed to be governed by the stress intensity factor, for instance through Paris' law in fatigue or Irwin's criterion in brittle fracture. The method used is based on successive iterations of the three-dimensional weight-function theory of Bueckner-Rice, that gives the variation of the stress intensity factor along the crack front arising from some small arbitrary coplanar perturbation of the front. Its main advantage is that only one dimensional integrals along the crack front are involved so that only the one dimensional meshing of the crack front is needed, and not the 3D meshing of the whole body as in the finite-element method. It is closely linked to previous works of Bower and Ortiz (1990, 1991, 1993). The differences lie on the one hand, in the simplified numerical implementation; on the other hand, in the simplified treatment of brittle fracture, Irwin's criterion being regularized by Paris' law by a procedure analogous to the `viscoplastic regularization' in plasticity; and finally in the applications studied: propagation paths of an initially elliptical, rectangular or heart shaped crack in an homogeneous media and of a penny shape crack in an heterogeneous one.