Implementation of the extended maximum force criterion (EMFC) for evaluating the pressure-dependent forming limit diagrams (PD-FLD) in the tube bulging process

The contact pressure in rubber pad forming (RPF) processes contributes to increased formability under the influence of normal stress. In this study, the extended maximum force criterion (EMFC) based on the Swift neck theory is introduced to provide a novel 3D analytical solution for assessing the impact of through-thickness normal stress on plastic instability. Assumptions include rigid-plastic behavior, a power-law hardening model, and the normal plastic anisotropy of the metallic sheet. The plastic flow rule is utilized to incorporate five different forms of non-quadratic Hill yield criterion, including the consideration of normal stress. Initially, the constants of the yield criterion are calculated based on the anisotropy coefficients of the sheet. Subsequently, the critical stress and strain at the onset of diffuse necking are extracted. The most suitable form and exponent of the yield criterion are selected by comparing theoretical results with experimental data. Following this, the pressure-dependent forming limit diagram (PD-FLD) associated with the actual normal stress of the rubber pad forming process for both the safe and seam-welded zones of the stainless steel (SS304) tube is derived. Finally, the tearing of the seam-welded tube is predicted using this modified FLD and compared with experimental data. Findings indicate a significant increase in the accuracy of damage estimation by incorporating the impact of normal stress on the tube FLD.