A Unified Damage Approach for Predicting Forming Limit Diagrams

Plastic deformation in sheet metal consists of four distinct phases, namely, uniform deformation, diffuse necking, localized necking, and final rupture. The last three phases are commonly known as nonuniform deformation. A proper forming limit diagram (FLD) should include all three phases of the nonuniform deformation. This paper presents the development of a unified approach to the prediction of FLD to include all three phases of nonuniform deformation. The conventional method for predicting FLD is based on localized necking and 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 typically used for the prediction of localized necking when α > 0 or when the biaxial stretching of sheet metal is significant. The M-K method, however, suffers from the arbitrary selection of the imperfection size, thus resulting in inconsistent predictions. The unified approach takes into account the effects of micro-cracks/voids on the FLD. All real-life materials contain varying sizes and degrees of micro-cracks/voids which can be characterized by the theory of damage mechanics. The theory is extended to include orthotropic damage, which is often observed in extensive plastic deformation during sheet metal forming. The orthotropic FLD model is based on an anisotropic damage model proposed recently by Chow and Wang (1993). Coupling the incremental theory of plasticity with damage, the new model can 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 when α(=ε₂/ε₁) < or α > 0, a set of instability criteria is proposed to characterize all three phases of nonuniform deformation. The orthotropic damage model has been employed to predict the FLD of VDIF steel (Chow et al, 1996) and excellent agreement between the predicted and measured results has been achieved as shown in Fig. 1. The damage model is extended in this paper to examine its applicability and validity for another important engineering material, namely aluminum alloy 6111-T4.