Crack propagation in solids and crack-surface roughness

It is seen from extensive computer simulation results and some experimental observations that for inhomogenous solids with moving cracks, the surface roughness exponent ζ crosses over from a low value ζ∼0.42 to a higher value ζ∼0.8, as the crack-tip velocity increases above a certain threshold. In this paper we extend a simple phenomenological model and a scaling analysis for the growth of crack surfaces in inhomogenous solids by introducing explicitly the effects of the stress rate. We find that the stress rate is indeed a relevant parameter and its consideration leads to a qualitative understanding of the phenomena described above.