Study on the Influence of the Refinement of a 3‐D Finite Element Mesh in Springback Evaluation of Plane‐Strain Channel Sections

Springback phenomenon associated with the elastic properties of sheet metals makes the design of forming dies a complex task. Thus, to develop consistent algorithms for springback compensation an accurate prediction of the amount of springback is mandatory. The numerical simulation using the finite element method is consensually the only feasible method to predict springback. However, springback prediction is a very complicated task and highly sensitive to various numerical parameters of finite elements (FE), such as: type, order, integration scheme, shape and size, as well the time integration formulae and the unloading strategy. All these numerical parameters make numerical simulation of springback more sensitive to numerical tolerances than the forming operation. In case of an unconstrained cylindrical bending, the in‐plane to thickness FE size ratio is more relevant than the number of FE layers through‐thickness, for the numerical prediction of final stress and strain states, variables of paramount importance for an accurate springback prediction. The aim of the present work is to evaluate the influence of the refinement of a 3‐D FE mesh, namely the in‐plane mesh refinement and the number of through‐thickness FE layers, in springback prediction. The selected example corresponds to the first stage of the “Numisheet’05 Benchmark♯3”, which consists basically in the sheet forming of a channel section in an industrial‐scale channel draw die. The physical drawbeads are accurately taken into account in the numerical model in order to accurately reproduce its influence during the forming process simulation. FEM simulations were carried out with the in‐house code DD3IMP. Solid finite elements were used. They are recommended for accuracy in FE springback simulation when the ratio between the tool radius and blank thickness is lower than 5–6. In the selected example the drawbead radius is 4.0 mm. The influence of the FE mesh refinement in springback prediction is discussed, for this example where the drawbead restraining force results in a non‐symmetrical through‐thickness stress gradient.