Multifractal fracture geometry and the scale effect

The effect of body dimensions on the material strength of the body is described by the equation sigma-p equals V exp -1/m, where sigma-p is the material strength; V is the characteristic fractured volume; and m is the scale effect. The latter can be directly related to fractal characteristics of the body and fracture by the relationship m = 6/3-D, where D is the fractal dimension of the crack surface. In this paper, the effect of inhomogeneity on the scale effect is reexamined, and a new equation relating the dimensions of the fracture to the dimensionality of the body is obtained.