Forming Limits

Abstract

Fracture and localized instability are two important modes of failure in the cold working of metals. In cold forging operations, axial surface cracks result at a critical value of circumferential tensile strain (ε2 ) that is dependent on the magnitude of the corresponding axial strain (ε1 ). In the stretching and drawing of sheet metal, initial failure involves visible localized necking instead of fracture, and forming limit diagrams give combinations of biaxial strain that do not lead to failure. Since strains are involved in both of these situations, it is convenient to adopt a fracture criterion based on strain instead of stress. A maximum active tensile strain (MATS) criterion is such a criterion used in this paper to explain forming limits in cold forging and sheet forming operations.