Prediction of Forming Limit Curves from Hardness for Steels

This paper presents a method for predicting the strain-based forming limit curve (FLC) for steels using hardness. The stretching side (positive minor strain component) of the FLC was calculated by using a Marciniak-Kuczyński model with a non-quadratic yield function, while the drawing side (negative minor strain component) of the FLC was predicted based on the relationship between the major and minor critical strains, in accordance with the theory of maximum sheet tension for local necking. The requisite parameter that describes the plastic flow behavior (in this case, the strain hardening exponent) was calculated, based on correlations with the measured microhardness. Additionally, the strain rate sensitivity was considered in the model by using a newly developed empirical correlation between hardness and strain rate sensitivity. This hardness-based model was used to predict FLCs that demonstrate good agreement with experimental FLCs of a high-strength low-alloy steel and a dual-phase steel. Equations are provided that enable the calculation of the FLC from given hardness values for different severities of the material inhomogeneity.