Plastic flow localization analysis of heterogeneous materials using homogenization-based finite element method

• A novel framework to predict the onset of plastic flow localization is presented.
• A plastic flow localization analysis can be performed taking only one or two material points in macroscopic scale.
• Materials involving very complex microstructures can be taken into account with a reasonable computational cost.
• We perform sheet necking analysis for FCC polycrystal as an example.

A novel framework to predict the onset of plastic flow localization is presented. The proposed framework combines a classical strain localization analysis with a homogenization-based finite element method, and has high applicability to various types of material with a characteristic microstructure that may have significant heterogeneity as long as its representative volume element can be represented by a finite element discretization. According to the proposed method, a plastic flow localization analysis can be performed taking only one or two material points in macroscopic analysis. This means that localization analysis of materials involving very complex microstructures, which is hard to be satisfactorily treated in a fully micro-macro-coupled finite element analysis with the homogenization approach, can be carried out with a reasonable computational cost. As a practical application of the proposed general framework, a plane stress version, that is, a Marciniak–Kuczyński-type (M–K) approach, is considered, then the forming limit strains of FCC polycrystalline sheets are evaluated. Crystal plasticity theory is adopted as a constitutive model for each crystal grain, and the homogenization-based finite element method is used to evaluate the average material response to be used in M–K-type sheet necking analysis. A numerical convergence analysis is conducted to determine the appropriate size of the representative volume element in the homogenization, and the effect of the geometrical configuration of crystal grains is studied. Then, the forming limit strains of a textured material are evaluated. The computational results are compared with those obtained using the conventional Taylor-type polycrystalline model.