Invariance of safety factor in probabilistic fracture mechanics analysis

摘要

Probability of failure (p_f) and reliability (safety) index (beta) were calculated for edge and surface cracks loaded under linear-elastic conditions. Probabilistic fracture mechanics calculations were performed using the first-order reliability method. The calculations were repeated several thousand times using randomly selected mean values and coefficient of variations (COV = standard deviation/mean) of the fracture mechanics parameters (fracture toughness, crack depth, crack aspect ratio, tensile and bending stresses). Multiple linear regression analyses of the results were performed with p_f and beta as dependent variables and expressions for p_f and beta were obtained as a function of key variables of interest. Safety factor expressed as a ratio of mean values of fracture toughness and stress intensity factor is close to be an invariant relative to p_f and beta for surface cracks with a lognormal distribution of the crack depth. The safety factor invariance for edge crack is marginal or relatively weak depending on the crack depth probability distribution. The results of the calculation indicated that the variations in COV had a relatively small effect on p_f and beta.