  In this paper we first obtain the order of stress singularity for a
dynamically propagating self-affine fractal crack. We then show that there is
always an upper bound to roughness, i.e. a propagating fractal crack reaches a
terminal roughness. We then study the phenomenon of reaching a terminal
velocity. Assuming that propagation of a fractal crack is discrete, we predict
its terminal velocity using an asymptotic energy balance argument. In
particular, we show that the limiting crack speed is a material-dependent
fraction of the corresponding Rayleigh wave speed.
