Three reliability methods for fatigue crack growth

In this paper, three reliability methods (1) a first order reliability method (FORM) based on the total derivative method (TDM), (2) FORM based on the Lagrange multiplier formulation (LMF) and (3) a Monte Carlo Simulation (MCS) with pseudo-exact sampling technique are applied to curvilinear fatigue crack growth problems. The crack can follow an arbitrary path which is determined by a crack direction law. A boundary integral element method is used to determine the mechanical response. With the help of the pseudo-exact sampling technique used in MCS, we are able to determine an extremely low probability of failure as low as 10(-6) with high accuracy. A comparison of the three methods shows that the LMF is the most efficient method for the general fatigue crack growth reliability problems. For the class of problems we considered, LMF agrees very well with Monte Carlo simulation, indicating that it is quite accurate.