On the strain-path dependence of forming limit curves

Strain-path effects strongly influence the formability of sheet metals, limiting the applicability of standard forming limit curves (FLCs) under non-proportional loading conditions typical of industrial processes. This study provides a comprehensive evaluation of the main approaches proposed to achieve strain-path independent FLCs, including equivalent-strain-based diagrams, stress-based representations, and interpolation methods. Their theoretical foundations are discussed and their practical relevance is assessed through experimental data and predictive model comparisons. The analysis shows that, under isotropic hardening assumptions, equivalent-strain-based and stress-based approaches are mathematically equivalent, with the former being more straightforward and equally accurate. The equivalent-strain correction was further validated using established theoretical criteria and extensive experimental evidence, demonstrating that it offers a simpler but fully consistent framework for formability assessment under complex loading paths. Moreover, although the equivalent-strain and interpolation methods converge when sufficient experimental FLCs are available, this study quantitatively identifies and analyses the differences between them. These findings provide new insight into the limitations and applicability of each approach and establish a robust foundation for future experimental and modelling developments.