Per-Anders Eggertsen

A Phenomenological Model for the Hysteresis Behavior of Metal Sheets Subjected to Unloading/Reloading Cycles

The springback phenomenon is defined as elastic recovery of the stresses produced during the forming of a material. An accurate prediction of the springback puts high demands on the material modeling during the forming simulation, as well as during the unloading simulation. In classic plasticity theory, the unloading of a material after plastic deformation is assumed to be linearly elastic with the stiffness equal to Youngs modulus. However, several experimental investigations have revealed that this is an incorrect assumption. The unloading and reloading stress-strain curves are in fact not even linear, but slightly curved, and the secant modulus of this nonlinear curve deviates from the initial Youngs modulus. More precisely, the secant modulus is degraded with increased plastic straining of the material. The main purpose of the present work has been to formulate a constitutive model that can accurately predict the unloading of a material. The new model is based on the classic elastic-plastic framework, and works together with any yield criterion and hardening evolution law. To determine the parameters of the new model, two different tests have been performed: unloading/reloading tests of uniaxially stretched specimens, and vibrometric tests of prestrained sheet strips. The performance of the model has been evaluated in simulations of the springback of simple U-bends and a drawbead example. Four different steel grades have been studied in the present investigation.

An efficient inverse approach for material hardening parameter identification from a three-point bending test

The cyclic three-point bending test has been frequently used for the determination of material hardening parameters. The advantage of this test is that it is simple to perform, and standard test equipment can be used. The disadvantage is that the material parameter identification requires some kind of inverse approach. The current authors have previously, successfully been utilizing a method, in which computed force–displacement relations have been fitted to corresponding experimental results. The test has 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 results by means of the optimization tool LS-OPT, based on a response surface methodology. A problem is, however, that such simulations can be quite time consuming, since the Finite Element model has to be analyzed numerous times. In the current paper, an alternative numerical methodology will be described, in which instead calculated moment–curvature relations are fitted to experimental ones. This optimization procedure does not involve any solution of the FE problem. The Finite Element problem needs only to be solved a limited number of times in an outer iteration loop. This fact results in a considerable reduced computational cost. It is also demonstrated that the parameters determined by this new method correspond excellently to the ones determined by the conventional method.