Sensitivity of probabilistic fracture mechanics analysis to variations in statistical parameters

Probability of failure (pf) of a structure is usually calculated for a specified set of statistical parameters (mean, standard deviation, and probability distribution) that characterize random variables. This approach may not be efficient in cases where one would like to know the effect of variations in statistical parameters on the probability of failure. A method based on generating and analyzing randomly selected statistical parameters is proposed. The method consists of generating databases of mean and coefficient of variation (COV = mean/standard deviation) values of relevant fracture mechanics variables through a random process. The method was applied to surface cracks in a flat wide plate loaded under elastic conditions. Probability of failure was calculated for each database record using the first-order reliability method (FORM). Multiple linear regression analyses of the database records were performed with pf as dependent variable and statistical parameters as independent variables. The predicted pf values were in very good agreement with the directly calculated pf values for the specified variations of statistical parameters (±10%, ±15%, and ±20%), except those for fracture toughness and tensile stress, where variations should be limited to ±10% and ±15% ranges.