Analytical modelling of forming limit curves and the Lankford coefficients of anisotropy, r-values, using the non-associated Barlat´s Yld 2000-2d plastic potential

The aims of present work are to apply the Bressan-Barlat mathematical model to predict the FLC curve and the proposed new equations of r-values to accurately predict the Lankford and the equal biaxial stress coefficients of anisotropy in sheet metal forming operations, using the non-associated Barlat´s Yld 2000-2d plastic potential. The Forming Limit Curve by shear stress fracture, FLC-S, was predicted employing Bressan-Barlat critical shear stress criterion combined with the non-associated Barlat´s Yld 2000-2D plastic potential. The predicted coefficients of anisotropy were calculated and validated by the new Bressan´s anisotropy equations in conjunction with the Lankford and equal biaxial stress material anisotropy parameters, r-values, and the non-associated Barlat´s Yld 2000-2d plastic potential. New Barlat´s coefficients of anisotropy a_i were defined and calibrated from material experimental data of r-values for specimens under simple uniaxial tension and equal biaxial stress tests. The examined distinct metal alloys were the highly anisotropic AISI 439 steel sheets and AA 6016-T4 aluminium sheets presented in the ESAFORM 2021 cup drawing benchmark articles obtained from published literature. In the results analysis and discussion, the new coefficients of anisotropy of the Barlat´s non-associated plastic flow rule were calculated and validated by plotting on the same graph the predicted r-value and s-value curves and experimental data for the anisotropic steel sheets. Correlation analyses have revealed that the Barlat´s yield criterion and the plastic flow stress potential were not coincident. Prediction of FLC-S of AISI 439 steel was quite good, when using the Bressan-Barlat shear stress fracture criterion combined with the non-associated Barlat´s Yld 2000-2d plastic stress potential. For both AISI 439 and AA 6014-T4, the non-associated Barlat´s Yld 2000-2d flow rule, calibrated by 7 r-values, provided a better fit to the experimental Lankford and equal biaxial coefficients of anisotropy. Exponent m = 10 was excellent and improved prediction accuracy over m = 8 for the AA 6014-T4.