Efficient probabilistic fracture mechanics analysis

A systematic and efficient method for probabilistic fracture mechanics analysis is proposed. The method is based on a most-probable-point-locus concept. The locus is obtained iteratively where the initial locus is determined using the linear approximation of the service life N(X) function about the mean values of the random variables X. Linear and quadratic approximations of N(X) are established locally at the most probable points, and the reliability analysis methods are used to compute the cumulative probabilities. By using two examples, the proposed method is demonstrated to be efficient and accurate. One example involved a random loading and N(X) was computed using cycle-by-cycle integration. The method is general and can be applied to other performance functions. It is particularly suitable when the computation of the performance function is time consuming such that Monte Carlo simulation is prohibitively costly.