Application of Barlat’s Yld 2000-2d Yield Stress Function for Modeling the Anisotropic Plastic Behaviour and the Forming Limit Strain Curve

Abstract

The objective of present paper is to examine the plastic anisotropy behaviour of steel sheet, employing the Barlat´s Yld 2000-2d yield stress criterion and the corresponding non-associated plastic flow rule. New Barlat´s coefficients of anisotropy were defined and calibrated from material experimental data of simple uniaxial tension and equal biaxial stress tests. The new set of coefficients calculated from the experimental Lankford anisotropy coefficients (r-values), normalized yield stress (s-values), equal biaxial stress parameters (r_b and σ_b) were numerically obtained using the Newton-Raphson method. The investigated metal was the highly anisotropic AISI 439 steel sheets found in the 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 the experimental data for the anisotropic steel sheets. The correlations have revealed that the Barlat´s yield criterion and the plastic flow stress potential were not coincident. Furthermore, the predicted limit strain curve of 439 steel correlated better with the experimental FLC_TD transverse curve when using the shear stress fracture criterion and the non-associated plastic potential than the associated flow rule. Therefore, the Barlat´s Yld 2000-2d non-associated plastic flow rule provides a better fit with the experimental Lankford and equal biaxial coefficients of anisotropy and the FLC_TD curve results of AISI 439 steel sheets.