Evaluation of associated and non-associated quadratic plasticity models for advanced high strength steel sheets under multi-axial loading

The accuracy of quadratic plane stress plasticity models is evaluated for a dual phase and a TRIP-assisted steel. Both sheet materials exhibit a considerable direction-dependence of the r-ratio while the uniaxial stress–strain curves are approximately the same irrespective of the specimen direction. Isotropic and anisotropic associated as well as non-associated quadratic plasticity models are considered to describe this behavior. Using a newly-developed dual-actuator system, combinations of normal and tangential loads are applied to a flat specimen in order to characterize the sheet material response under more than 20 distinct multi-axial loading states. The comparison of the experimental results with the plasticity model predictions reveals that both the associated and non-associated quadratic formulations provide good estimates of the stress–strain response under multi-axial loading. However, the non-associated model is recommended when an accurate description of the thinning behavior is important. Moreover, a structural validation example is presented that demonstrates the higher prediction accuracy of the non-associated plasticity model.