Multi scaling in fracture surfaces morphology

Full Text:Things fall apart via the propagation of cracks whose paths leave complex patterns behind. These fracture paths were shown to exhibit remarkable scaling properties that can be described by self-affine fractal geometry. In this framework, the fracture morphology is characterized by a single roughness exponent. We show, by analyzing higher order structure functions, that in 1+1 dimensions the fracture paths are actually multi scaling graphs, ruling out a the conjecture that two dimensional fracture belongs to the universality class of directed polymers in random media. We develop a model of two dimensional quasi-static fracture, based on the method of iterated conformal mappings for stochastic growth, reproducing the essential features of experimental fracture surfaces morphology