Modelling of anelastic deformation in dual-phase steel for improved springback simulation

Classical elasto-plastic models assume linear elastic stress-strain relations for all stresses within the yield surface. Closer examination discloses a nonlinear relation in the elastic domain that is dependent on the prior plastic deformation. The 'unloading strain' can be decomposed in a linear elastic contribution and an anelastic contribution that is related to reversible dislocation movement in the crystal lattice. The anelastic contribution in the total recovered strain upon unloading is significant and therefore should be considered in accurate springback predictions. Modelling of this phenomenon with E-modulus degradation is fundamentally incorrect and only gives a fair strain prediction after completely unloading the material. In springback situations, inner fibres of the sheet material are partly unloaded and outer fibres are even reloaded in compression. Therefore, a model is required that includes the amount of plastic pre-loading and the amount of unloading separately. For implementation of the model in a finite element code, it needs to be formulated in the complete 6-dimensional stress space and not only for uniaxial stresses. A model is presented that can be applied for arbitrary strain paths and that is consistent with the main observations in uniaxial loading-unloading-reloading experiments.