Understanding Through-Thickness Integration in Springback Simulation

The “adequate” number of integration points (NIP) required to achieve accurate springback simulation results is studied in this paper in an effort to clarify confusions reported in the literature and shed light on the origin of the confusion. A bending-under-tension model is adopted where springback solution can be obtained with analytical integration through metal thickness. Numerical integrations are then performed and compared with analytical solution to assess associated errors. A crucial distinction is made in the paper that, the model can be posed either as a displacement-value problem where both tension strain and bending radius are prescribed or as a mixed-value problem where the tension force and bending radius are prescribed. Although they are physically equivalent due to the uniqueness of solution, the numerical solutions are different. The associated errors in springback respond differently to the number of integration points employed. It is found that the mixed-value problem gives much smaller errors in springback than the displacement-value problem for the same numbers of integration points. The origin of the difference is examined in detail by analyzing requirements for stress distribution across thickness. Influence of tension force and bending radius is also investigated.