Determination of forming limit diagrams of sheet materials with a hybrid experimental–numerical approach

A new methodology is proposed to obtain the forming limit diagram (FLD) of sheet materials by utilizing routinely obtained experimental punch load versus displacement traces from hemispherical punch stretching experiments and by analyzing strain history of the test samples from finite element simulations of the experiments. The simulations based characteristic points of diffuse and localized necking are utilized to obtain the limit strains. The proposed method for FLD determination considers out-of-plane displacement, punch–sheet contact and friction, and avoids using experimental strain measurement in the vicinity of the neck on the dome specimens and the rather arbitrary inhomogeneity factor to trigger localization such as in the commonly used Marciniak–Kuczynski method. A criterion of maximum in the ‘pseudo’ major strain acceleration for the onset of localized necking, proposed earlier by the present authors, is utilized to determine the limit strain in FE simulations as well as in FLD verification experiments. The proposed overall approach for obtaining FLD is rapid and accurate and could be implemented for routine FLD generation in a laboratory setting with significant reduction in cost, effort and subjectivity.