Macro- and Mesoscopic Finite Element Analysis of Strain Path-Induced Plastic Anisotropy Evolution in Steel Sheet

Abstract

In this study, the influence of the strain path on the evolution of plastic anisotropy was analyzed through macro- and mesoscopic finite element (FE) modeling. The macroscopic FE analysis focused on the evaluation of an advanced constitutive model, which accounts for non-proportional strain path. Continuous strain path change was applied on a mild steel from plane strain tension to simple shear, i.e., cross-loading, with six different transition rates between the two deformation states. The test was modeled with the homogeneous yield function–based anisotropic hardening (HAH) model, which was applied for both rigid- and elastoplastic conditions. Stress overshooting and Bauschinger-like behaviors, observed with abrupt and very gradual strain path changes, respectively, were well predicted. The other four responses were reasonably well described in between these two extremes. The results were explained based on the different proportions of plastic work in the tensile and shear directions and ultimately resulted in different stress evolution paths in the tensile–shear stress space. At a lower scale, the mesoscopic FE analysis focused on the understanding of the anisotropic mechanical behavior of ferrite-martensite dual-phase materials. Two models were constructed using the microstructure representative volume element (RVE) concept: simplified models with idealized martensitic inclusion shapes and a more realistic model that was reconstructed using microstructure images collected after serial sectioning. With the simplified models, the Bauschinger effect was specifically investigated focusing on the martensite particles of three ideal shapes, i.e., elongated, large spherical and small spherical configurations, and two volume fractions, i.e., 10 % and 30 %, embedded in a ferritic matrix. The simulation results pointed out a higher influence of the martensite volume fraction on the resulting properties compared to that of the particle shape. The Bauschinger effect was notably higher with 30 % volume fraction of martensite particles, irrespective of their shapes. A simple one-dimensional analysis based on an elasto-plastic theory successfully explained the Bauschinger effect considering only the strength differences of the constituents and the dual-phase structure. As an extension, the realistic model was applied to a micromechanical analysis for the plastic strain dependent r-value (Lankford coefficient) evolution. This analysis was performed on a DP780 steel subjected to three boundary conditions: monotonic tension (T), compression–tension (CT), and tension–orthogonal tension (TO). To examine the sensitivity of the r-value evolution to the r-values of the individual phases, four combinations of Hill 48 and von-Mises yield functions were assigned. The results showed a qualitative good description in that the plastic strain dependent r-value changes, including a sharp decrease of the initial value of this property just after reloading and its downward transition before saturation. The results were analyzed to determine the relative contribution of the r-value difference between ferrite and martensite, martensite configuration-induced stress state inside a RVE with a multiphase structure, and the distinct stress partitioning and its evolution when the strain path changed. The following general conclusions were derived: (1) plastic anisotropy and its evolution should be modeled with an appropriate constitutive model; (2) a constitutive model needs to be evaluated under extensive test conditions; and (3) the strength heterogeneity has a strong influence on both macro- and mesoscopic mechanical behaviors.