Probability of a ductile fracture

The present paper studies ductile fracture by a random fractal and calculates the fracture probability q of a ductile fracture. The fracture probability q is sensitive to the number n (microvoid size) and the probability p of forming microvoids. There are two critical probabilities p c1 and p c2. When p⩾ p c2 = 1-1/ n 2, the fracture probability q is 100%, the ductile fracture occurs with probability 1; when p c2 > p> p c1, there is a positive probability q (1> q>0), the fracture probability q increases with increasing probability p and/or decreasing number n; when p< p c1, the fracture probability q is zero (in fact less than 0.00001), the fracture does not occur. The critical probabilities p c1 and p c2 increase with increasing n. When 1-1/ n 2> p>1-1/ n, though a ductile fracture does not occur, there is at least a macrovoid which passes through the transverse plane of the specimen.