Prediction of Forming Limit Diagram with Damage Analysis
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.