Extension of Non-Associated Hill48 Model for Characterizing Dynamic Mechanical Behavior of a Typical High-Strength Steel Sheet

Sheet metals usually exhibit a certain degree of plastic anisotropy because of the rolling effect. To characterize the anisotropic behavior in simulations related to large deformation, strain-rate independent phenomenological models are frequently used in quasi-static conditions. Two functions are generally included in such a model, i.e. the yield function and the plastic potential. The former limits the stress state within the yield surface while the latter determines the direction of the plastic strain increment. Traditional plasticity models mostly assume associated flow rule, in which the two functions mentioned above are identical. With the enhanced demand of accuracy, the forms of the associated models become too complex with more and more parameters to achieve an easy calibration procedure. Alternatively, in the past decade the non-associated models were increasingly used for sheet metals. Separate functions for the two aspects of plasticity lead to efficient characterization and convenient calibration. In numerical study of dynamic loading cases, how to characterize strain-rate dependence of plasticity is an important issue. Some visco-plastic models were developed to take the rate effect into account, e.g. Johnson-Cook and Cowper-Symonds models, where the isotropic J2 flow theory was commonly used. However, when the material is severely anisotropic, this approach is very likely to be insufficient, and a model including both anisotropy and rate dependence would be needed. Extending a non-associated anisotropic model to be rate-dependent is a promising approach which has not been published in open literature to the best knowledge of the authors. Objective of the present study is to develop an applicable model for characterizing dynamic mechanical behavior of a typical high-strength steel sheet. Two steps are performed. The material is investigated under quasi-static loading firstly. Tensile test results show an obvious anisotropy which cannot be described by traditional associated models. So the non-associated Hill48 model is chosen and calibrated. Accuracy of the model is verified by a quasi-static punching test. Thereafter the dynamic material properties are obtained by conducting tensile tests at quite a few strain-rate levels covering 0.0004–1200s−1. To characterize the positive strain-rate effect in strength, the non-associated Hill48 model is extended to be visco-plastic after checking two rate-dependence formulations in existing isotropic models. With implementing the extended model into a user subroutine of ABAQUS/explicit, simulations of the dynamic tension tests are run and compared to the real experiments. A good agreement between the simulated and the experimental result is achieved using the VUMAT.