Formability assessment during square cup drawing of anisotropic sheets using associated and non-associated flow rules

In the present study, the experimental and numerical analyses during cup drawing using a square deep drawing setup were conducted with extra deep drawing (EDD) steel sheets. Circular blanks of 120 mm diameter of 1.0 mm and 1.5 mm thicknesses were taken as the input blanks for deformation using a square die-punch setup. Experimental results showed a strong non-uniformity of the cup heights at the cup edge periphery, and the maximum differences between the maximum and minimum cup height were recorded as 4.63 mm and 7.85 mm for 1 mm and 1.5 mm sheets, respectively. Subsequently, surface strain and thickness distributions were investigated along the rolling direction (RD) and diagonal direction (DD) of the formed cups. For numerical analyses, three different material models were used based on the associated flow rule (AFR) and non-associated flow rule (NAFR) of metal plasticity. In the context of AFR, the classical Hill48 and the advanced Yld2000 yield models were used to formulate the material models. Whereas in the NAFR model, the stress-based Hill48 was used to define the yield function, and the strain-based Hill48 was used as the potential function, and the NAFR formulation was termed as the N-Hill48 model. Furthermore, the predictive accuracy of the material models was investigated in terms of estimation of the cup heights, surface strain distributions, and thickness distributions along the RD and DD of the sheets. An average cup height prediction error of 3.5 % and 4.3 % was obtained when estimated through the N-Hill48 and Yld2000 AFR material models, respectively. On the contrary, the Hill48 AFR material model yields a significant error of 7.7 % for the same. All the prediction results indicated the encouraging accuracy of the N-Hill48 and Yld2000 AFR models over the Hill48 AFR models during the square cup drawing process.