On constitutive modeling for springback analysis
Artikel i vetenskaplig tidskrift, 2010

The springback phenomenon that occurs in thin metal sheets after forming is mainly a stress driven problem, and the magnitude is roughly proportional to the ratio between residual stresses and Young's modulus. An accurate prediction of residual stresses puts, in turn, high demands on the material modeling during the forming simulation. A phenomenological plasticity model is made up of several ingredients, such as a yield condition, a plastic hardening curve, a hardening law, and a model for the degradation of elastic stiffness due to plastic straining. The authors of this paper have recently, [1], showed the importance of a correct modeling of a cyclic stress-strain behavior via a phenomenological hardening law, in order to obtain an accurate stress prediction. The main purposes of the present study are to study the influence of two other constitutive ingredients: the yield criterion and the material behavior during unloading. Three different yield criteria of different complexity are evaluated in the present investigation: the Hill'48 criterion, the Barlat-Lian Y1d89 criterion, and the 8-parameter criterion by Banabic/Aretz/Barlat. The material behavior during unloading is evaluated by loading/unloading tension tests, where the material is unloaded/reloaded at specified plastic strain levels. The slope of the unloading curve is measured and a relation between the "unloading modulus" and the plastic stain is established. In the current study, results for four different materials are accounted for. The springback of a simple U-bend is calculated for all the materials in the rolling-, transverse- and diagonal directions. From the results of these simulations, some conclusions regarding constitutive modeling for springback simulations are drawn. (C) 2010 Elsevier Ltd. All rights reserved.


Hardening law

Bauschinger effect

stress yield function

Yield function


sheet metals



Constitutive modeling





Per-Anders Eggertsen

Chalmers, Tillämpad mekanik, Material- och beräkningsmekanik

Kjell Mattiasson

Chalmers, Tillämpad mekanik, Material- och beräkningsmekanik

International Journal of Mechanical Sciences

0020-7403 (ISSN)

Vol. 52 6 804-818





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