Characterization and modeling of biaxial plastic anisotropy in metallic sheets

Abstract

The anisotropic behavior of cold-rolled sheet metals has been extensively studied, typically characterized by uniaxial loading tests in different directions to determine yield strengths and plastic flow (Lankford r-values). However, biaxial principal stress states often focus solely on yield loci in the RD/TD (rolling/transverse) directions, with limited studies on other loading directions. This study analyzes the relationship between the principal stress yield loci and the material principal anisotropic stress directions based on the Hill48 yield function. Biaxial tensile tests are conducted on DP590 high-strength steel using cruciform specimens cut in various directions different from the sheet RD/TD directions. The evolution of the anisotropic yield locus and plastic flow of DP590 under biaxial tensile directions beyond the traditional RD/TD anisotropic directions is revealed. Furthermore, a modified Hill48 model that considers any principal stress direction of loading is proposed, accurately describing the continuous evolution of equi-biaxial tension stress, near-plane strain stress, and plastic flow direction for different principal stress directions of loading. The issues of failing to predict plastic flow under biaxial loadings in the original Hill48 model, and the degraded representation of existing constitutive models when accounting for out-of-plane anisotropy are addressed by decoupling the relationship between anisotropic parameters and stress state. In addition, the proposed calibration strategy of anisotropic parameters, using experimental data from various principal stress directions of loading, effectively captures the anisotropic evolution caused by changes in principal stress directions. Comprehensive evaluation and verification of the plasticity model should consider yield locus for any principal stress directions of loading, and also the normal and shear planes.