Probabilistic fracture mechanics analysis of three-dimensional cracked structures considering random field fracture property

Abstract This paper presents a probabilistic fracture mechanics approach to evaluate the reliability of three-dimensional (3D) cracked structures considering spatially varying random fracture property. The applied loads and initial crack length are modeled as random variables, and the fracture toughness is modeled as a spatially-varying random field. Based on the weakest link model, a system reliability model for 3D cracked structures is constructed through discretizing the crack front into a finite number of elements. The dimensional reduction integration approach is then modified to calculate the reliabilities of elements in the crack front as well as the correlations among them simultaneously, such that the system reliability model can be efficiently solved. Numerical examples are presented to illustrate the validity of the proposed method, and the thickness and size effects on the results are discussed. The results show that the predicted probabilities of fracture based on the proposed method are very consistent with the Monte Carlo simulation results, and in the meanwhile, it has a satisfactory computational efficiency. In addition, it is found that the fracture probability increases with the increasing of the thickness and size due to the existing of more possible effective failure elements or the larger stress intensity factors.