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Based on the theory of damage mechanics, an orthotropic damage model for the prediction of forming limit diagram (FLD) is developed. The conventional method of FLD used to predict localized necking adopts two fundamentally different approaches. Under biaxial loading, the Hill's plasticity method is often chosen when α (= ε2/ε1) < 0. On the other hand, the M-K method is adopted for the prediction of localized necking when α > 0 or the biaxial stretching of sheet metal is pronounced. The M-K method however suffers from the arbitrary selection of the imperfection size, thus resulting in inconsistent predictions. The orthotropic damage model developed for predicting the FLD is based on the anisotropic damage model recently proposed by Chow et al (1993). The model is extended to take into account, during the sheet forming process, orthotropic plasticity and damage. The orthotropic FLD model consists of the constitutive equations of elasticity and plasticity coupled with damage.

Strains in most stamped parts are produced under non-proportional loading. Limit strains induced during forming are, therefore, path dependent. Experimental Forming Limit Diagrams (FLDs) are usually determined under proportional loading and are not applicable to most forming operations. Experimental results have shown that path dependent FLDs are different from those determined under proportional loading. A number of analytical methods have been used to predict FLDs under proportional loading. The authors have recently introduced a new method for predicting FLDs based on the theory of damage mechanics. The damage model was used successfully to predict proportional FLDs for VDIF steel and Al6111-T4. In this paper, the anisotropic damage model was used to predict non-proportional FLDs for VDIF steel. Experiments were conducted to validate model predictions by applying pre-stretch in plane strain followed by uniaxial and balanced biaxial tension.