Model of crack propagation in heterogeneous materials

A continuous numerical model of crack propagation in a bidimensional heterogeneous material is presented. This model describes the propagation of a macrocrack into a two-phase brittle material with a finite density of inclusions. The morphology of the cracks produced for various mechanical and microstructural conditions is analysed. The simulated cracks are self-affine and there exist two fracture regimes, each of them being characterized by a roughness index independent of the microstructure. Relevant length scales, on the contrary, depend on the microstructural parameters. It is shown that there exists a microstructure leading to an optimal fracture toughness.