Calibration of anisotropic Yld2000-2d model and implementation in finite element simulation for formability analyses: Various sheet forming case studies

Abstract

In this study, an experimental and numerical investigation was conducted to analyze the formability of extra-deep drawing steel sheets of 1 mm thickness during different sheet metal forming case studies, including stretch forming (SF), square cup deep drawing (SDD), and single-point incremental forming (SPIF) processes. Three various sample geometries and two different tool paths were used to induce diversity of deformation paths during SF and SPIF tests, respectively. Whereas, a combination of square blank with square tooling was adopted to promote nonuniform material flow during SDD tests. In the numerical approach, finite element (FE) simulations of all the forming experiments were conducted using the advanced Barlat Yld2000-2d anisotropic material model. In this regard, the Yld2000-2d model was calibrated using four distinct approaches by evaluating the normalized stress ratios at various anisotropic orientations in four different methods. The first (M1) and second (M2) methods were based on the minimum plastic work till the fracture and the ultimate tensile strength (UTS) point, respectively. In contrast, the third (M3) and fourth (M4) methods were based on the stress values corresponding to the UTS and yield point, respectively. Accordingly, four distinct sets of normalized stress ratios and plastic strain ratios were evaluated from mechanical tests and used to calibrate the Yld2000-2d model. The prediction capabilities of the Yld2000-2d model calibrated through different methods were estimated in terms of various formability assessment parameters, including dome heights, limiting draw ratio, and thickness distributions. It was found that the Yld2000-2d model calibrated through the M1, M2, and M3 methods exhibited encouraging prediction capabilities, with the overall average prediction errors of 3.05%, 2.85%, and 3.96%, respectively, compared to a noticeably higher error of 8.27% when calibrated through the M4 method combining all the samples.