Randomness and fuzziness of mesco ductile fracture for metallic materials

Based on the macro-and mesco-experimental results of four steels, 30CrMnSiA, 40CrNiMoA, No.45 and No.20,the random and fuzzy properties of fracture are studied. The isolated void model is used as an example, and the fracture occures as the void radius R is greater than the critical R_c. The void radius can be expressed as R = R₀exp[C₁exp(C₂R_σ)ε _p](R₀ is the initial void radius, R_σ the stress triaxiality, ε_p the plastic strain, C₁ and C₂ are model parameters). The initial and critical radii of voids are in lognormal distributions and the other parametrs in normal distributions. The calculated fracture characteristics of the four steels in different stress states and strains are more near to the experimental results taking the random fracture model than the deterministic fracture model. The illustrative calculation shows that fuzziness is the nature of fracture state, and with appropriate values the fuzzy model can agree well with the experimental results.