Combination of finite element and reliability methods in nonlinear fracture mechanics

This paper presents a probabilistic methodology for nonlinear fracture analysis in order to get decisive help for the reparation and functioning optimization of general cracked structures. It involves nonlinear finite element analysis. Two methods are studied for the coupling of finite element with reliability software: the direct method and the quadratic response surface method. To ensure the response surface efficiency, we introduce new quality measures in the convergence scheme. An example of a cracked pipe is presented to illustrate the proposed methodology. The results show that the methodology is able to give accurate probabilistic characterization of the J-integral in elastic–plastic fracture mechanics without obvious time consumption. By introducing an “analysis re-using” technique, we show how the response surface method becomes cost attractive in case of incremental finite element analysis.