A dimensional decomposition method for stochastic fracture mechanics

This paper presents a new dimensional decomposition method for obtaining probabilistic characteristics of crack-driving forces and reliability analysis of general cracked structures subject to random loads, material properties, and crack geometry. The method involves a novel function decomposition permitting lower-variate approximations of a crack-driving force or a performance function, Lagrange interpolations for representing lower-variate component functions, and Monte Carlo simulation. The effort required by the proposed method can be viewed as performing deterministic fracture analyses at selected input defined by sample points. Compared with commonly-used first- and second-order reliability methods, no derivatives of fracture response are required by the new method developed. Results of three numerical examples involving both linear-elastic and nonlinear fracture mechanics of cracked structures indicate that the decomposition method provides accurate and computationally efficient estimates of probability density of the J-integral and probability of fracture initiation for various cases including material gradation characteristics and magnitudes of applied stresses and loads.