Prediction of Forming Limit Diagrams in Sheet Metals Using Different Yield Criteria

Abstract

Based on the analysis proposed by Jones and Gillis (JG), forming limit diagrams (FLDs) are calculated from idealization of the sheet deformation into three stages: (I) homogenous deformation up to maximum load, (II) deformation localization under constant load, and (III) local necking with a precipitous drop in load. A constant cross-head speed is assumed in the deformation program for the first time. This means that the logarithmic strain rate varies during deformation, while in all previous works, the strain rate is assumed to be constant. In the calculation, three yield criteria including HillÕs 1948 quadratic criterion, HillÕs 1979 nonquadratic criterion, and HosfordÕs 1979 criterion are used. Using these yield criteria and the JG model, the effects of material parameters such as strain hardening, strain-rate sensitivity, and plastic anisotropy on the shape and level of the forming limit curves are studied. In addition, the capability of the JG model to predict the limit strains is demonstrated through comparison of calculated results with experimental data for interstitial-free (IF) steel and aluminum alloys 2036-T4, 3003-O, 5052-O, and 8014-O. It is observed that while the model predicts the FLDs of 2036-T4 and 5052-O more closely, it overestimates the forming limit strains for IF steel, 3003-O, and 8014-O aluminum alloys. It is concluded that the accuracy of the prediction depends on the measured mechanical properties of the material, the applied yield criterion, and the method of strain measurement, which determines how the FLDs are passed through different points. For those cases in which the predicted FLD is above the experimental one, care must be taken not to use the models for industrial purposes.

Effects of Microstructural Morphology on Formability, Strain Localization, and Damage of Ferrite-Pearlite Steels: Experimental and Micromechanical Approaches

“…On the other hand, it is necessary to evaluate the forming limit diagram (FLD), which reveals details on the ability of metal sheets to undergo plastic deformation into the desired shape without failure. [20,21] A variety of experimental investigations and numerical simulations based on the micromechanical modeling have been developed to study the forming limits by incorporating underlying microstructural effects. [22][23][24][25] Furthermore, various constitutive laws have been reported in the literature about the accurate measurement of stress-strain relation of single phases involved in steels, and among them, the physically based plasticity model is the most commonly used.…”

Improved predictability of forming limit curves through microstructural inputs

“…Therefore, it is useful to predict the FLCs. Advanced finite element (FE) packages [5][6][7][8][9][10][11] and availability of accurate material models [10][11][12][13][14][15][16][17][18][19][20][21] has made simulations of even most complex geometries [22,23] a practical choice for today's metal forming industries. The quest for better forming predictability is an area of significant technological importance [24][25].…”

Effect of necking types of sheet metal on the left-hand side of forming limit diagram

“…Since it is difficult to obtain FLD directly from tests, more and more scholars focused on the investigations of predicting FLD based on forming limit theories. Noori and Mahmud (2007) theoretically predicted the FLDs of IF steel and some aluminum alloys based on the analysis proposed by Jones and Gillis by applying different yield criterion, and the FLDs were demonstrated by experiments. Giuliano (2006) investigated the FLD of superplastic materials from the aspects of theory and numerical simulation.…”