THE SHAPE OF SLOWLY GROWING CRACKS

We present a theory for the shape of the fracture surface left behind by a slowly propagating crack in a linear, isotropic and homogeneous three-dimensional elastic medium. We find that sinusoidal currugations decay exponentially, and that the roughness of any section of the surface, induced by fluctuations in the material, has a 1/f spatial power spectrum. We also present the results of simple experiments which confirm the theoretically predicted evolution of shape corrugations and the spatial power spectrum of the crack roughness.