| Abstract | Analytical formability models based upon in-plane proportional plane stress loading such as the Marciniak–Kuczynski (MK) model are commonly evaluated against forming limit curves (FLCs) obtained using Nakazima tests with out-of-plane deformation, non-linear strain paths and tool contact. The present study has conducted a comprehensive experimental characterization of a DP1180 advanced high strength steel with relatively low formability to demonstrate that the use of Nakazima FLC data can lead to a physically inconsistent MK model. Although good agreement can be obtained using the MK model with Nakazima data, it is attributed to calibration bias in the hardening model and selection of the imperfection factor. Marciniak tests should be performed to characterize the FLC or process-corrections be applied to the Nakazima FLC to then calibrate the MK imperfection factor. An analysis of the MK framework reveals a false dependence of the imperfection factor on the hardening model due to artefacts in the hardening model calibration. When the Considère constraint for the uniform elongation is imposed during the hardening model calibration, the MK imperfection factor becomes nearly independent of the choice of hardening model. The accuracy of the FLC predicted by the MK model, when appropriately constrained and calibrated in a deterministic manner, was in a reasonable agreement with the experimental data only after accounting for material anisotropy. In contrast, the deterministic Modified Maximum Force Criterion (MMFC) model provided a very close estimate of the experimental forming limit strains of the mildly anisotropic DP1180 using both isotropic and anisotropic yield functions. |
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