The Role of Damage in Fracture Dynamics

A propagating crack tip in a medium poses immense intellectual challenges. Despite the apparent simplicity by which the tip moves, the underlying mechanisms are not at all trivial. In fact only the simplest configurations with a moving crack tip have to t his date been solved. An important aspect of crack propagation is how the tip interacts with the medium. In general the medium is damaged in the vicinity of a moving crack tip and depending on the material, one typically sees in front of the tip a formati on of small separations. The nature of the separations ranges from small micro cracks to large voids. The damage separations are known to influence the dynamics but so far studies have only with limited success described how. We shall here develop techniq ues to analyze the interaction between a moving crack tip and nearby damage cavities. Inspired by the recent succes of iterated conformal mappings in fracture problems we shall endeavor to do conformal mappings of 2D cracks surrounded by small voids. For this purpose we shall devise a general approach to the non trivial problem of mapping multi connected domains. Fracture surfaces in various materials reveal self-affine structures which can be characterized by a scaling exponent, the roughness exponent . The presence of micro-separations may affect this exponent, which for a broad range of materials is believed to be universal. We shall propose simple dynamical rules including elements of plasticity theory to put the universality to a test, and more imp ortantly uncover the physical mechanisms leading to the non-triviality of the experimentally observed scaling exponents.