Role of yield criteria and hardening laws in the prediction of forming limit diagrams
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I. INTRODUCTION
THE forming limit diagram (FLD), first proposed by Keeler[4] and Goodwin,[5] indicates the relationship between major and minor principal strains under diffuse or localized instability in a plane-stress condition for different strain paths. The FLD is a useful diagnostic tool for trouble shooting in sheet metal forming operations and is also an assessment method for determining the formability of different sheet materials.[6] Because of practical difficulties associated with the experimental determination of the FLD, a number of theoretical predictive models have been developed on the basis of continuum theory of plasticity and different yield and instability criteria and flow or hardening rules.[7] Among the earliest theories for the analysis of FLD, that of Marciniac and Kuczynski[8] has probably been the most influential on subsequent developments. They postulated the existence of an initial imperfection in the sheet material in the form of a line of slightly reduced thickness, or groove, across the test specimen. The model was later developed by Hutchinson and Neal[9] and Barlat et al.,[10] who considered the imperfection band angles with the orientation of the metal sheet, the anisotropy of the sheet, and the complex strain paths involved in the deformation process. A quite different approach has been taken by the development of the Jones–Gilliss (JG) theory,[11] which eliminates the necessity for the determination of the initial heterogeneity coefficient by calculation of the forming limit diagram for complex strain paths. The JG criterion for plastic instability is based on three easily observable features from a tensile test of a typical sheet metal. The plastic deformation process is approximated by three phases: (I) homogeneous deformation up to maximum load; (II) deformation localization under constant load; and (III) local necking with a precipitous drop in load.
M. AGHAIE-KHAFRI, Postdoctoral Student, R. MAHMUDI, Professor, and H. PISHBIN, Assistant Professor, are with the Department of Metallurgy and Materials Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran. Contact e-mail: [email protected] Manuscript submitted August 21, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS A
The transition point between phases I and II is denoted as point H and that between phases II and III as point J, as shown in Figure 1. The JG theory was originally applied to the tension test of a round bar and then to the right-hand side (RHS) of the FLD, where the limiting principal strains are positive. The JG analysis was improved by Choie et al.,[12] who extended the theory to the left-hand side (LHS) of the FLD. Later, Pishbin[13] developed the model using Hill’s nonquadratic flow law for sheets having in-plane isotropy and applying a kinematic condition for the LHS that was not recognized by Choi. The main concern of the present work is to extend the model using Hosford’s yield criterion and the Voce hardening law. II. GENERAL DESCRIPTION Hosford’s yield criterion[14] has been used in
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