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In this paper we first obtain the order of stress singularity for adynamically propagating self-affine fractal crack. We then show that there isalways an upper bound to roughness, i.e. a propagating fractal crack reaches aterminal roughness. We then study the phenomenon of reaching a terminalvelocity. Assuming that propagation of a fractal crack is discrete, we predictits terminal velocity using an asymptotic energy balance argument. Inparticular, we show that the limiting crack speed is a material-dependentfraction of the corresponding Rayleigh wave speed.

Estimating Terminal Velocity of Rough Cracks in the Framework of Discrete Fractal Fracture Mechanics