Proper orthogonal decomposition assisted eigendeformation-based mathematical homogenization method for modeling cracks in 3D polycrystalline microstructures

Abstract

In this manuscript, a reduced order model (ROM) is proposed for full three-dimensional (3D) polycrystalline microstructures with tortuous short cracks. The model reformulates eigendeformation-based homogenization method (EHM) assisted with the proper orthogonal decomposition (POD) method to account for local plastic deformation and crack separation fields. A constrained optimization problem is formulated with reduced order objective functions and un-reduced constraints to solve for the separation. To make the optimization process more feasible, an integrated form of the constraint is introduced, enabling the use of only one constraint regardless of the crack morphology. The model is verified against direct numerical simulations (DNS) with crystal plasticity as the constitutive relation. The use of priori knowledge in building crack separation field basis functions as well as sampling strategies in the absence of prior knowledge are discussed. The performance and accuracy of the ROM are assessed under various loading conditions and different crack configurations.