Forming limit curves determined in high-speed Nakajima tests and predicted by a strain rate sensitive model

Abstract

Material characteristics such as yield strength and failure strain are affected by the loading speed. Even the start of instability and necking depends not only on the strain hardening coefficient but also on the strain rate sensitivity parameter. Therefore, the strain rate dependence of materials for both plasticity and the failure behavior is taken into account in crash simulations for strain rates up to 1,000 s−1. The current standard experiment for investigation of strain rate dependence is the high speed tensile test as described in a FAT guideline. Moreover, the need of material characterization at multi-axial loadings and high strain rates is pointed out in FAT guideline. Forming limit diagrams (FLD) can be used for the description of the material`s instability behavior at multi-axial loading. Usually, the FLD are determined quasi-statically at 1.5 mm/s. The usage of experimentally determined, quasi-static FLD also at high strain rates leads to great uncertainties and thus can be hardly used in crash simulations. A possibility for experimentally recording FLD at high forming rates > 100 s−1 offers the present described high speed Nakajima test. The results for the deep drawing steel DC01 illustrate the need of the determination of dynamic FLD. In this context, due to the strain rate dependence of the material behavior an extrapolation of quasi-static FLD is not feasible. Alternatively, the prediction of forming limit curves (FLC) at high strain rates is possible with the extended modified maximum force criterion. This new and extended model includes the strain rate dependence and therefore predicting forming limits at dynamic forming gets possible. The new approach is described and the accordance of experimental determined and predicted results for the begin of instability is presented.