A correspondence principle for fractal and classical cracks

In this paper we introduce a correspondence principle between fractal cracks and notches. This correspondence principle defines an equivalent smooth blunt crack for a fractal crack. Once this transformation is accomplished, the laws of linear elastic fracture mechanics apply. Since the root radius of the equivalent crack is finite, the crack may be further reduced to a notch visualized as an elongated elliptical void. Therefore, the laws of the LEFM and those of Neuber’s ‘notch mechanics’ coincide, and they can be used interchangeably. In other words, we have shown that the three mathematical representations of discontinuities in the displacement field, a notch, a classic Griffith crack and a fractal crack, are related, and the pertinent relationships are determined by the proposed correspondence principle. We also give an estimation of the size of the plastic region ahead of a self-similar (or self-affine) fractal crack tip.