Accuracy analysis of anisotropic yield functions based on the root-mean square error

This paper evaluates the accuracy of popular anisotropic yield functions based on the root-mean square error (RMSE) of the yield stresses and the R-values. The yield functions include Hill48, Yld89, Yld91, Yld96, Yld2000-2d, BBC2000 and Yld2000-18p yield criteria. Two kind steels and five kind aluminum alloys are selected for the accuracy evaluation. The anisotropic coefficients in yield functions are computed from the experimental data. The downhill simplex method is utilized for the parameter evaluation for the yield function except Hill48 and Yld89 yield functions after the error functions are constructed. The yield stresses and the R-values at every 15°from the rolling direction (RD) and the yield stress and R-value at equibiaxial tension conditions are predicted from each yield function. The predicted yield stresses and R-values are then compared with the experimental data. The root-mean square errors (RMSE) are computed to quantitatively evaluate the yield function. The RMSEs are calculated for the yield stresses and the R-values separately because the yield stress difference is much smaller that the difference in the R-values. The RMSEs of different yield functions are compared for each material. The Hill48 and Yld89 yield functions are the worst choices for the anisotropic description of the yield stress anisotropy while Yld91 yield function is the last choice for the modeling of the R-value directionality. Yld2000-2d and BBC2000 yield function have the same accuracy on the modeling of both the yield stress anisotropy and the R-value anisotropy. The best choice is Yld2000-18 yield function to accurately describe the yield tress and R-value directionalities of sheet metals.