Generalized criteria for localized necking in sheet metal forming

Sheet metal forming is an important engineering field in manufacturing industries. The formability of a sheet metal in a stamping process is often limited by localized necking. The primary objective of the thesis is to develop generalized criteria for localized necking, which are capable of predicting limit strains for sheet metal components subjected to stamping operations. The criteria are engineering oriented and ready for application in practical sheet metal forming processes.; The theoretical foundation of the localized necking criteria used here for strain-hardening materials is the vertex theory, which assumes that localized necking is caused by a vertex developed on the yield surface. A generalized deformation theory for materials with anisotropic plasticity is developed based on a general form of high-order yield criterion. By coupling the new deformation theory with the vertex theory, a generalized criterion of localized necking to predict forming limit strains is proposed. Closed-form expressions of critical hardening modulus over the entire range of forming limit diagram are deduced. For power-law strain hardening, the corresponding limit strains are explicitly derived. The theoretical results are validated by previous experiments and it is found that higher-order yield criterion is preferable in prediction of limit strains.; For strain-softening materials, the singularity of acoustic tensor is taken as the criterion, which treats localized necking as a consequence of plasticity instability. The acoustic tensor is deployed to get closed—form expressions of localized necking criteria for both the positive and the negative strain ratio regions, together with the inclination angle of localized band within the negative strain ratio region. For a special case of isotropic plasticity following von Mises yield criterion, analytically expressions of critical hardening modulus are derived, based on which the limit strains of strain-softening materials can be determined. Forming limit diagrams (FLDs) are computed for A6061 sheets at 4000 and three levels of strain rate.; A unique consideration of this investigation is material inhomogeneity, which is described by an anisotropic damage model within the framework of Continuum Damage Mechanics (CDM). Critical hardening modulus for localized necking is analytically presented for strain-hardening materials based on the vertex theory and for strain-softening materials based on the singular of acoustic tensor, respectively, with involvement of anisotropic damage of materials. It is observed that the critical damage value at localized necking is not a constant. (Abstract shortened by UMI.)...