HIGHLY EFFICIENT COMPUTATIONAL MODELS FOR MICRO-MECHANICS OF POLYCRYSTALLINE MATERIALS IN THE PRESENCE OF LARGE STRAINS AND MICROSTRUCTURALLY SHORT CRACKS

Abstract

Accurately and efficiently predicting the mechanical behavior of structures made of polycrystalline materials presents many challenges and complications. Because of highly complex evolution laws that govern viscoplastic and failure processes of polycrystalline materials and complex microstructural morphologies, such as under large deformation or with short cracks, direct numerical simulations are typically computationally expensive. In this dissertation, novel and efficient reduced order computational frameworks are developed based on eigen-deformation-based mathematical homogenization method to resolve the computational cost issue, and they are applied to predict polycrystalline materials that exhibit large deformation - applicable in modeling the forming of highly anisotropic metals, or polycrystalline materials that contain short cracks - important for predicting the fatigue life of metallic materials. Specifically, the research contributes: (i) a finite strain formulation of a reduced order homogenization model for crystal plasticity; (ii) a short crack propagation framework based on crystal plasticity finite element method for three-dimensional polycrystalline microstructures, utilizing adaptive crack insertion; (iii) a reduced order framework based on eigen-deformation-based homogenization to integrate short cracks into quasi-two-dimensional microstructures; and (iv) a proper orthogonal decomposition-assisted reduced order homogenization model to handle complex three- dimensional microstructures with tortuous cracks.