A user-friendly 3D yield function to describe anisotropy of steel sheets

A sixth-order polynomial type 3D yield function, which has a high flexibility of describing anisotropic behavior of steel sheet, is proposed. The yield function is constructed as a sum of several components of the which was derived as an extension of the J2–J3 Drucker yield criterion () to orthotropy using the linear transformation of the stress deviator, so that the convexity of the yield locus is perfectly guaranteed. The model was validated by comparing the numerical predictions of planar anisotropy of r-values and flow stress directionality, as well as the shape of yield loci, with the corresponding experimental data on several types of steel sheets (high r-valued IF steel and SPCE, and high strength steel sheets of 440–980 MPa TS grades). For most of steel sheets, the model using the sum of two J2 components, which involve eight anisotropic coefficients, is sufficient for the description of their anisotropies. Further it was found that the consideration of J3 effect improves the description of anisotropy for some steel sheets (e.g., high r-valued IF steel and 980 MPa grade dual phase HSS).