fractal crack

This paper presents a stability analysis for fractal cracks. First, the Westergaard stress functions are proposed for semi-infinite and finite smooth cracks embedded in the stress fields associated with the corresponding self-affine fractal cracks. These new stress functions satisfy all the required boundary conditions and according to Wnuk and Yavari's embedded crack model they are used to derive the stress and displacement fields generated around a fractal crack.

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.

The fractal crack model described here incorporates the essential

features of the fractal view of fracture, the basic concepts of

the LEFM model, the concepts contained within the

Barenblatt-Dugdale cohesive crack model and the quantized

(discrete or finite) fracture mechanics assumptions. The

well-known entities such as the stress intensity factor and the

Barenblatt cohesion modulus, which is a measure of material

toughness, have been re-defined to accommodate the fractal view of

fracture.