A New Approach to Obtain Forming Limits of Sheet Materials

Abstract

A new methodology is proposed to obtain the forming limit diagram (or FLD) of sheet materials by utilizing routinely obtained experimental load versus displacement traces and incorporating finite element (FE) analysis of strain history to extract the characteristic points of diffuse and localized necking and further the limit strains. The experimental data from hemispherical punch stretching test such as limit dome height, maximum load and location of inflection point are utilized to adjust the load curves in the FE simulations. An optimization procedure to obtain various parameters in material definition has been established to obtain a good agreement between the FE-based and experimental punch load versus displacement curves. An analysis of FE model based strain history is then carried out to determine the limit strains. This approach avoids using experimental strain measurement in the vicinity of the neck on the dome specimens. The materials tested with the new methodology include automotive sheets AA6111-T4, AA6181-T4 and DP600. The one utilized for optimization of FE inputs was AA6111-T4. The proposed method for FLD determination considers out-of-plane displacement, punch-sheet contact and friction, and avoids the use of a rather arbitrary inhomogeneity factor to trigger localization such as in the Marciniak-Kuczynski method. A new criterion to determine the localized necking is proposed by seeking an inflection point m the major strain rate curve, or, maximum point in the second order of derivative of major strain, (ε1)max. The proposed localized necking criterion is compared with other two methods to determine the onset of localized necking. These are (i) Bragard criterion for post-test of deformation, and (ii) critical major strain (ε1)cr based on comparison of strain of material inside the localized site and its vicinity in the un-necked site. The new criterion of (ε1)max exhibits a more definite physical meaning towards developing an understanding of flow localization, formability and fracture. This new approach for obtaining FLDs is rapid and accurate and could be implemented easily for routine FLO generation in a lab setting with little user input and subjectivity.