Springback compensation for an analytical elasto-plastic stretch-bending model: Milestone Report M3

Especially when modern materials like high-strength steels and aluminium are used, springback compensation algorithms can help to shorten the products development time and cost. The two algorithms, Displacement Adjustment (DA) and SpringForward (SF) that were introduced in literature have been tested extensively but some basic questions and problems remain. An analytical model for a stretch-bending process provides many possibilities to gain more insight in those problems. Furthermore, the calculation of the forming process is much faster and doesn’t suffer from stability problems. In the stretch-bending model a rectangular bar is bent to a certain radius after which the load is removed and the bar recovers elastically. To model the influence of a blankholder force, the bar can also be loaded with a tension force. An elasto-plastic material model was used. The model assumes that the stress-profile is equal along the entire bar. If the DA method is used in one step, a compensation factor is required to obtain an accurate tool geometry. The optimal compensation factor can be directly calculated for the analytical model. It was shown that this factor varies heavily with increasing tension force. When the tension force is zero, or when the force is so large that the bar is deformed entirely in the plastic region, the compensation factor is close to 1.0. When an elastic band is still present in the bar, the ideal compensation factor rises from around 1 to a value of 1.5 or 2.0 depending on the material. Iterative DA was also implemented for the analytical model. With this method no knowledge about the ideal compensation factor is required, the tool shape converges to its optimal shape with each iteration. As expected the convergence depends also heavily on the tension force in the bar, in the case of pure bending (zero tension force) or fully plastic deformation (large tension force) convergence is very fast, when an elastic band is present, convergence becomes a bit slower. Although there is no straightforward mathematical or physical proof, the iterative SF method also converges for the analytical model. Interestingly, the SF method is faster than DA, and the difference is considerable in the pure bending case. The type of material also has an influence, higher strength steels require a higher compensation factor. In order to check whether the conclusions also hold for industrial forming processes, the stretch bending process was transformed to an FE model. The loading was now carried out with ’real’ tools. Opposed to the analytical model, now the DA method performs much better, especially when the tension force is raised. In that case the SF method leads to very low improvements in shape accuracy. It was shown that SF already proposes a worse tool shape in the first iteratio