Parametric study of the reliability of a cracked pipe using non-linear finite element analysis

Reliability analyses of structural components aim at estimating the probability that the external loading exceeds the structures resistance. In some industrial cases, the failure of the structure cannot be defined by an:explicit function of the random variables and only an implicit definition of the limit state function is available. It is the case when finite element calculations are used. This paper deals with the calculation of the failure probability of an axisymmetrically cracked pipe under pressure and tension using a finite element code with incremental non linear plasticity. The failure criteria corresponds to the crack initiation that is to say when the Rice's integral reaches the material fracture toughness. Six random variables are considered : the crack size, the material fracture toughness and the parameters describing the material stress strain curve (the Young's modulus, the yield strength, the strain hardening exponent and the Ramberg-Osgood coefficient alpha). The different reliability codes and finite element codes combined using different methods (Direct method and quadratic response surface method) give very similar results on this problem.