An improved Marciniak-Kuczynski approach for predicting sheet metal formability

Abstract

The Marciniak-Kuczynski (M-K) approach is the most renowned numerical method for forming limit strain curve (FLC) determination. In the commonly used M-K model, the thickness imperfection orientation (ψ) in the sheet plane is variable and the analysis is looped for different initial imperfection orientations (ψ0) for each strain route (ρ), which causes enormous computational waste. In addition, the predicted necking angle may obviously deviate from the theoretical one. This paper investigates the initial imperfection orientation and the necking angles (ψ*) of the AA5182-O sheet by both Nakazima experiments and M-K analysis. The effects of anisotropy on the necking angles and forming limit strains are investigated numerically. The results indicate that the necking orientation at equibiaxial stretching corresponds to the direction of the maximum r-value. The reason of necking angle deviation is well explained. Furthermore, the theoretical equation of necking angle is modified by an empirical formula, which is related to the ratio of r0 to rmax near the equibiaxial expansion. In light of the constant orientation of the imperfection deformation band during stretching, an improved M-K method is proposed based on the pre-assigned and non-evolving groove orientation. Compared with the modified M-K approach, this improved method achieves a higher calculation efficiency with a 97.7% reduction in computing time while maintaining the same level of accuracy.