A moment quadrature method for uncertainty quantification of three-dimensional crack propagation via extremely few model runs

Abstract

The finite element-based three-dimensional crack propagation analysis has increasingly been used in many design assessment applications, particularly those high reliability-demanding structures subject to complex multi-axial fatigue loading. Such analysis is computationally intensive and poses a great challenge to current uncertainty quantification methods, which normally require a substantial number of finite element model runs. This study proposes a new method for uncertainty quantification of finite element-based three-dimensional crack propagation analysis under material uncertainty via extremely few, normally 2d, model runs, and d is the number of uncertain variables. When the classical two-parameter Paris’ equation is employed as the fatigue crack growth rate model, a total number of 4 model runs are sufficient. The method employs the Hankel matrix of moments associated with the uncertainty variables to determine the optimal nodes and weights in the variable space for Gauss quadrature under prescribed distributions. A two-step time integration scheme is employed to further reduce the number of propagation steps within an individual finite element model run. The accuracy of the proposed method is validated using a practical case with realistic fatigue testing data and analytical solutions. The holistic method is applied to two three-dimensional crack propagation problems to demonstrate the effectiveness. It is shown that using 4 model runs the mean and variance of the crack front can be accurately captured under material uncertainty.