Prediction of springback in sheet metal forming: with emphasis on material modeling
Licentiatavhandling, 2009

The prediction of springback is probably the area in sheet metal forming simulation, where the least success has been achieved in terms solution accuracy. The springback is caused by the release of the residual stresses in the work piece after the forming stage. An accurate prediction of residual stresses puts, in turn, high demands on the material modeling during the forming simulation. Among the various ingredients that make up a reliable material model, the hardening law is one of the most important ones for an accurate springback prediction. The hardening law should be able to consider some, or all, of the phenomena that occurs during bending and unbending of metal sheets, such as the Bauschinger effect, the transient behavior, and permanent softening. The complexities of existing hardening laws do of course vary within quite wide ranges. One purpose of the present study has been to try to identify a model of reasonable complexity, which at the same time can fulfill the requirements concerning accuracy. Five different hardening models have been evaluated in the present investigation. The simplest model, the isotropic hardening one, involves only one history variable, while the most advanced model involves ten history variables and four additional material parameters. The unknown material parameters used in the description of the hardening behavior is determined by inverse modeling of a three point bending test. A new effective optimization technique based on Response Surface Methodology is presented for this purpose. Furthermore, the unloading behavior is investigated in detail. It is shown that the elastic stiffness is decreasing with increased effective plastic strain. Since the springback deformation is an elastic recovery process, the elastic stiffness has a large influence on the final amount of springback. Thus, the degradation of elastic stiffness has to be considered for an accurate springback prediction. Four different materials, frequently used in the car manufacturing industry, were considered in this study: Two DP600 steels from two different suppliers and with different thicknesses, a mild DX56 steel and, finally, a 220IF steel, classified somewhere in between the two latter material classes. For all these materials the springback for the well known U-bend benchmark problem from the NUMISHEET’93 conference has been calculated. From the results of these simulations some conclusions regarding the appearance of a proper material model are drawn.


Hardening law

Elastic degradation

Yield surface


Bauschinger effect

Omega 2, Chalmers södra, Eklandagatan 86
Opponent: Mats Oldenburg, Luleå tekniska universitet


Per-Anders Eggertsen

Chalmers, Tillämpad mekanik, Material- och beräkningsmekanik


Teknisk mekanik



Omega 2, Chalmers södra, Eklandagatan 86

Opponent: Mats Oldenburg, Luleå tekniska universitet