An inverse approach for material parameter identification in a cyclic bending test using LS-DYNA and LS-OPT

The residual stresses in the blank after forming are the main cause for the subsequent springback in a sheet forming operation. The accuracy of the predicted springback in a Finite Element simulation of the forming operation is very much determined by the quality of the material modeling. Those parts of the workpiece, which in particular contribute to the global springback, have usually been subjected to a bending/unbending deformation mode, when the sheet material has slipped over a tool radius. It is thus of utmost importance that the material model can accurately describe the material response, when it is subjected to such a deformation mode. This is considered by the so-called "hardening law" of the material model. In this context the terms "kinematic" or "mixed" hardening are frequently employed. There are numerous such hardening models described in the literature. Common for them all is that they involve material parameters, which have to be determined from some kind of cyclic test. In theory, the most simple and straight forward test is a tensile/compression test of a sheet strip. In practice, however, such a test is very difficult to perform, due to the tendency of the strip to buckle in compression. In spite of these difficulties some successful attempts to perform cyclic tension/compression tests have been reported in the literature. However, common for these tests has been that rather complicated test rigs have been designed and used in the experiments, in order to prevent the sheet strip from buckling. Another method that frequently has been used for the determination of material hardening parameters is the three-point bending test. The advantage of this test is that it is simple to perform, and standard test equipments can be used. The disadvantage is that the material parameters have to be determined by some kind of inverse approach. The current authors have previously, successfully been utilizing this method. In the test the applied force and the corresponding displacement are recorded. The test has then been simulated by means of the Finite Element code LS-DYNA, and the material parameters have been determined by finding a best fit to the experimental force-displacement curve by means of the optimization code LS-OPT, based on a Response Surface Methodology. A problem is, however, that such simulations can be quite time consuming, since the same Finite Element model has to be analyzed numerous times. In the current paper an alternative numerical methodology is described, in which the Finite Element problem only has to be solved a limited number of times, and, thus, considerably reducing the computational cost. In this new methodology a computed moment-curvature curve is fitted to an experimental one. A complicating factor is, however, that all information to determine a moment- curvature relation is not available directly from the experiment. Therefore, the problem has to be solved in two nested iteration loops, where the optimization loop is contained within an outer loop, in which the FE-analysis is performed. It is demonstrated that the parameters determined by this new method correspond excellent to the ones determined by the conventional method.