SCALING PROPERTIES OF FRACTURE-TOUGHNESS IN RANDOM MATERIALS

We analyze the scaling properties of the average fracture toughness K1c, on the basis of a random elastic string network with a probability p. In the regime of p1, we study the problem with the stress intensity factor of a prefabricated crack and find that the average fracture toughness K1c is independent of the linear dimension of the system when the system size is large enough. This shows that the scaling form of K1c cannot be derived from that of the average fracture stress c and the linear relation between the fracture toughness and the fracture stress in terms of a Griffith-type crack. We also give an expression of K1c with p, demonstrating that the average fracture toughness decreases with decreasing p. In the regime of ppc, we obtain a standard scaling form of K1c, i.e., K1c (p-pc)(f+x)/2 from the energy consumed in the fracture process, where f and x are, respectively, the exponents of Youngs modulus and the order parameter defined by P. Duxbury et al. An interesting deduction is gained from our analyses and others research work: the less the average elastic fracture toughness, the larger the fractal dimension of the fractured surface. This may give us a clue to understanding the recent observations of the fractal dimensions of the fractured surfaces. © 1990 The American Physical Society.