Forming limit diagrams (FLDs) in simple and complex deformation paths are determined using a theoretical model of localized necking due to an initial heterogeneity of the sheet. The influence of the strain path upon the formability of the sheet is investigated using different types of FLDs under complex strain paths.
The effect of material strain hardening and strain-rate hardening is examined for several strain paths. The influence of the imperfection level on the FLDs is presented. Computer simulation of the evolution of rheological parameters during deformation and their dependence on the strain path is carried out.
The model is compared with previous experimental works, and a good agreement is obtained between theoretical results and experimental forming limit diagrams.
The mathematical model developed in this work is shown to be a powerful tool to understand and predict the plastic behaviour of metal under simple and complex strain paths.