A model of one-surface cyclic plasticity with Lemaitre damage criterion for plastic instability prediction in the incremental forming process

• We propose a one-surface plastic constitutive model that integrates the damage accumulation into hardening model, so it could predict the deformation accurately under complex and large-strain paths.
• Constitutive model are implemented with simple expressions in FE analysis. So the expressions can be easily transplanted to other forming process.
• The profile and thickness of metal sheet after incremental forming obtained by numerical analysis is highly consistent with experimental results. The proposed model is quite suitable to predict the deformation under complex loading conditions.
• Forming instability (local necking position) in incremental forming process is predicted by numerical analysis is highly consistent with experimental results.

The precise prediction of plastic deformation instabilities during the incremental forming process is quite complex because of the complex stress state and extremely large plastic strain. Until now, most elasto-plastic constitutive models are only suitable within a small strain range and describe the isotropic behavior. However, for extremely large plastic deformation under complex loading processes such as an incremental forming process, these models are ineffective and ill-conceived. This paper presents an elasto-plastic constitutive model which combines a mixed isotropic-kinematic hardening model with the Lemaitre damage model. This model can predict the Bauschinger effect, transient behavior, permanent softening and fractures over a large plastic strain range. By using explicit integration schemes, an integration algorithm of numerical implementation is proposed using simple expressions. A cyclic loading test comparison between experiments and numerical analysis is carried out to validate these models. The model is also applied to FE analysis of incremental forming. The deformation and the prediction of thickness are consistent with experimental results and thus verify the accuracy of the model.