Surrogate modeling of 3D crack growth

Abstract

This paper presents the development of a surrogate modeling technique for efficient non-planar fatigue crack growth analysis in mechanical components under multi-axial loading. Non-planar crack fronts are freely deformable space curves and require a high-dimensional representation. The large number of Cartesian co-ordinate variables involved in crack front representation makes it prohibitively expensive to train surrogate models for crack growth. Therefore, in our previous work, the crack shape was approximated using a planar parametrized representation. However, the parametrized representation limits the choice of crack shapes that can be considered. This paper presents the development of a non-parametric crack shape representation that allows for construction of a surrogate model for non-planar crack growth with complex crack shapes. The surrogate model is trained using a few runs of high-fidelity 3D simulations and predicts the evolution of a non-planar crack front under a given multi-axial, variable amplitude load history. We first parametrize the crack fronts as 3D spline curves with a fixed number of nodes. Instead of modeling the crack growth in this high dimensional data space, we project the data to a lower dimensional space using Principal Component Analysis (PCA) and then model the crack growth in this lower dimensional space. Finally, the predicted crack fronts are recovered using PCA back to the original data space. The proposed crack representation, growth modeling and recovery are illustrated using training points gathered from high-fidelity 3-D finite element simulations of non-planar crack growth in a cylindrical component similar to a rotorcraft mast, and the ability of the surrogate model to accurately predict the evolution of the crack growth over entire load histories is demonstrated.