Crack propagation in heterogeneous media

We assume that an infinite material contains a point inhomogeneity which ha s slightly different elastic constants from the rest of the otherwise isotr opic and homogeneous elastic material. We evaluate the path of a three-dime nsional semi-infinite quasi static crack propagating near this point inhomo geneity. The real space crack path is evaluated as well as the power spectr um of the crack surface. The latter enables us to calculate the roughness e xponent for quasi-static fracture. It is also shown how the real space crac k surface and its power spectrum can be obtained for an arbitrary distribut ion of inhomogeneities. (C) 1999 Elsevier Science Ltd. All rights reserved.