Fractals and fracture

The relation between quantities resulting from fracture energetics and thos e describing the geometrical structure of a surface is of fundamental impor tance in investigating the physical nature of a fracture. Since the Mandelb rot's works, fractal geometry has been extensively applied to characterize the roughness of fracture surfaces and to correlate it with mechanical prop erties. We will first make a survey of several experimental methods to dete rmine the fractal dimension, D-f, according to the roughness of fracture su rfaces. Then we will discuss the experimental results reported in the bibli ography and the relations inferred to correlate the fractal dimension of fr acture surfaces with mechanical properties, These results show that a gener al conclusion cannot easily be drawn. Some works report a positive variatio n 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 fract ure surface is a universal constant. The discrepancy between these results is related to the methods used to calculate the fractal dimension. Theoreti cal and experimental problems exist and have to be solved before correlatin g the fractal dimension to mechanical behaviour. (C) 1998 Elsevier Science Ltd. All rights reserved.