Prediction of forming limits for anisotropic sheets containing prolate ellipsoidal voids

In sheet metal forming operations, the formability of sheet metals is limited by the occurrence of internal damage evolution that eventually yields a localized neck. Thus, designing and optimizing a sheet metal forming process, requires the precise prediction of the forming limits of the sheet materials. Accordingly, the current work attempts to theoretically predict the forming limit diagrams (FLDs) of voided anisotropic sheets using a new version of the Marciniak and Kuczynski (M–K) model. The analysis employs Gologanu–Leblond–Devauxʹs yield function for materials containing axisymmetric prolate ellipsoidal cavities with random orientations in conjunction with Barlat and Lianʹs 1989 anisotropic yield criterion. The effect of a void shape parameter on a ductile material under biaxial tensile loading is introduced and examined within the framework of the M–K model, along with the effect of including a first-order strain gradient term in the flow stress. To confirm the validity of the proposed M–K model, the predicted FLDs were compared with experimental results for steel sheets. The predicted forming limits for the voided sheets were found to agree well with the experimental data.