A UNIFIED DAMAGE APPROACH FOR PREDICTING FORMING LIMIT DIAGRAMS

Plastic deformation in sheet metal consists of four distinct phases, n amely, uniform deformation diffuse necking, localized necking, and fin al rupture. The last three phases are commonly known as nonuniform def ormation. A proper forming limit diagram (FLD) should include all thre e phases of the nonuniform deformation. This paper presents the develo pment of a unified approach to the prediction of FLD to include all th ree phases of nonuniform deformation. The conventional method for pred icting FLD is based on localized necking and adopts two fundamentally different approaches. Under biaxial loading, the Hill's plasticity met hod is often chosen when alpha (=epsilon(2)/epsilon(1)) < 0 On the oth er hand, the M-K method is typically used for the prediction of locali zed necking when alpha > 0 or when the biaxial stretching of sheet met al is significant. The M-K method, however suffers from the arbitrary selection of the imperfection size, thus resulting in inconsistent pre dictions. The unified approach takes into account the effects of micro -cracks/voids on the FLD. All real-life materials contain varying size s and degrees of micro-cracks/voids which can be characterized by the theory of damage mechanics. The theory is extended to include orthotro pic damage, which is often observed in extensive plastic deformation d uring sheet metal forming. The orthotropic FLD model is based on an an isotropic damage model proposed recently by Chow and Wang (1993). Coup ling the incremental theory of plasticity with damage, the new model c an be used to predict not only the forming limit diagram but also the fracture limit diagram under proportional or nonproportional loading. In view of the two distinct physical phenomena governing the cases whe n alpha (=epsilon(2)/epsilon(1)) < or alpha > 0, a set of instability criteria is proposed to characterize all three phases of nonuniform de formation. The orthotropic damage model has been employed to predict t he FLD of VDIF steel (Chow et al, 1996) and excellent agreement betwee n the predicted and measured results has been achieved as shown in Fig . 1. The damage model is extended in this paper to examine its applica bility and validity for another important engineering material, namely aluminum alloy 6111-T4.