Integrating multiple samples into full-field optimization of yield criteria

Abstract

Describing the anisotropic yielding behavior of sheet metal requires the determination of a yield criterion along with its model parameters. A method often used for this task is inverse full-field optimization. The method is typically combined with either multiaxial experiments or complex-shaped specimens to cover various stress states, over which the parameters of the yield criterion are optimized. This study investigates the feasibility of replacing the complex experiments with multiple simpler ones simultaneously. As material, the aluminum alloy AA6014-T4 is used. The yield criterion considered is YLD2000 2D, assuming both the associated and non-associated flow rules. Firstly, it is demonstrated through identifiability analysis that the model parameters, although often attempted in the literature, cannot be uniquely identified using only conventional experiments if non-associated flow is assumed. Secondly, it is shown that parameter identifiability in the latter case is achieved by combining multiple specimen geometries and orientations to rolling direction simultaneously. Thirdly, it is quantitatively shown that the use of multiple specimens simultaneously generally enhances the identifiability of model parameters due to an increase in the aggregated stress heterogeneity. Furthermore, the result indicates that while the full-field optimization of yield criteria assuming the associated flow rule can rely on force–displacement or direction of plastic strain increment alone, yield criteria assuming the non-associated flow rule require both. All yield criteria are benchmarked based on the strain distribution of Nakazima experiments, demonstrating comparable or higher accuracy compared to conventionally derived models.