Fractals and fracture

Abstract

The relation between quantities resulting from fracture energetics and those describing the geometrical structure of a surface is of fundamental importance in investigating the physical nature of a fracture. Since the Mandelbrot’s works, fractal geometry has been extensively applied to characterize the roughness of fracture surfaces and to correlate it with mechanical properties. We will first make a survey of several experimental methods to determine the fractal dimension, D f, according to the roughness of fracture surfaces. Then we will discuss the experimental results reported in the bibliography and the relations inferred to correlate the fractal dimension of fracture surfaces with mechanical properties. These results show that a general conclusion cannot easily be drawn. Some works report a positive variation of fracture toughness along with D f and others a negative one. To other researchers, there is no correlation and the fractal dimension of the fracture surface is a universal constant. The discrepancy between these results is related to the methods used to calculate the fractal dimension. Theoretical and experimental problems exist and have to be solved before correlating the fractal dimension to mechanical behaviour.