Uncertainty quantification of the stochastic process “crack size” for the Forman model using the “fast crack bounds” method

Abstract

This study presents the use of a crack propagation model under constant amplitude loading, proposed by Forman, admitting the existence of uncertainty in the definition parameters of the model and considering the uncertainty quantification of the crack propagation phenomenon as an objective. For this purpose, uncertainty modeling is performed using random variables. Thereafter, the Monte Carlo simulation and fast crack bound methods are used to estimate the statistical moments of the stochastic process “crack size.” The performance of the proposed method is measured by combining the Monte Carlo and Runge–Kutta methods. Two unpublished theoretical results related to the existence of bounds for the realizations of the “crack size” stochastic process and those for the estimators of their statistical moments are presented. The classic “finite width plate with central crack” example is used to explore the accuracy and efficiency of the proposed solution for the problem of the initial value of crack growth. This study identifies the computational gains obtained by the fast crack bound method to be at least 396.92% more efficient than that obtained by Monte Carlo simulation and relative deviations of at most 4.60% for the first statistical moment, demonstrating the applicability and accuracy of the fast crack bounds method.