Influence of fractality of fracture surfaces on stress and displacement fields at crack tips

In the classic theory of fracture mechanics, expressions for calculating the stresses and displacements in the vicinity of the crack tip are deduced on the basis of the assumption that a fracture surface is a smooth surface or that a crack is a smooth crack. In fact, the surface of a crack formed during the fracture is usually very irregular. So the real asymptotic form of the stress and displacement fields at the crack tip is different from the classic one. Considering the irregularity of a real fracture surface or a real crack profile, the crack is taken as a fractal one, and then the real asymptotic form at the crack tip is developed by applying Griffith’s energy balance principle and fractal geometry. Through the developed asymptotic form, it is discovered that the fractality of the crack reduces the stress singularity at the crack tip.