Adaptive Hierarchical-Concurrent Multiscale Modeling of Ductile Failure in Heterogeneous Metallic Materials

Abstract

This article addresses two topics on multiscale modeling of heterogeneous metals and alloys. The first topic focuses on developing an adaptive hierarchical-concurrent multilevel modeling framework for ductile fracture. The microstructure of aluminum alloys, for example, is characterized by a dispersion of heterogeneities such as silicon and intermetallics in a ductile aluminum matrix. The multilevel model invokes two-way coupling, viz. hierarchical models for homogenized constitutive modeling and concurrent models with scale transition in regions of localization and damage. Adaptivity is necessary for evolving microstructural deformation and damage. A macroscopic analysis in regions homogeneity incorporates homogenization-based continuum plasticity-damage models. A microscopic analysis using locally enhanced-Voronoi cell finite-element method is required for regions of high macroscopic gradients caused by underlying localized plasticity and damage. Coupled macroscopic and microscopic analysis is conducted concurrently. Physics-based level change criteria are developed to improve accuracy and efficiency. The second topic discusses a nested dual-stage homogenization method for microstructure-based homogenized continuum plasticity models for cast aluminum alloys with large secondary dendrite arm spacing. Two distinct statistically equivalent representative volume elements are identified and used in the asymptotic expansion-based homogenization and self-consistent homogenization processes, respectively. The two-stage homogenization enables an evaluation of the overall homogenized model of a cast alloy from limited experimental data, as well as material properties of constituents like interdendritic phase and pure aluminum matrix.