A model of crack propagation in a 2D heterogeneous material

A continuous numerical model of pure mode I crack propagation in a bidimensional heterogeneous material is presented. This model describes the propagation of a macrocrack into a two-phases brittle material containing a finite density of second phase precipitates. The morphology of cracks produced for various mechanical and microstructural conditions is analysed. It is shown that the simulated cracks are self-affine with a roughness index similar or equal to 0.6 independent of the microstructure. Relevant length scales, on the contrary, strongly depend on the microstructural parameters, and indicate an optimum density leading to a maximum fracture toughness.