Multirange fractal analysis on the negative correlation between fractal dimension of fractured surface and toughness of materials

Applying the concept of multirange fractals, a new explanation to the Williford's multifractal curve on the relationship of fractal dimension with fracture properties in materials has been given. It shows the importance of factorizing out the effect of fractal structure from other physical causes and separating the appropriate range of scale from multirange fractals.