Novel probabilistic crack growth assessment method: Based on the realised PDF law for growing cracks

Probabilistic fracture mechanics (PFM)-based crack growth assessment in load-bearing components has become a robust tool for reliability estimation for several decades. The PFM assessment considers at least one input parameter probabilistically distributed to estimate crack size probability over time. Nonlinear crack growth over time is primarily responsible for the high computational cost in PFM assessments. This paper establishes a novel probability density function (PDF) law for nonlinearly growing cracks. Furthermore, this law enables the development of the finite cell weight variation (FCWV) method as an efficient probabilistic crack growth procedure. The FCWV method discretises an input PDF parameter into a finite number of cells along the random variable axis and ties a crack size to every cell boundary. Consequently, the FCWV method determines the probability of crack size over time by computing the crack sizes at the cells’ boundaries. The crack size probability at every cell remains constant, whereas their PDFs vary over time because of non-linear crack growth. This paper considers a pipe susceptible to stress corrosion cracking with a circumferential semi-elliptical inner surface crack for validation. The initial crack length is postulated as the only probabilistically distributed input parameter. The FCWV with 20 cells and Latin hypercube sampling with 10,000 samples are applied to determine the probability of crack size over time. The results from both methods are in excellent agreement. Thus, such quantitative results prove the computational efficiency of the FCWV method, because the number of cells or samples is equivalent to the number of calculations a computer performs at a time step.