SHEET METAL FORMING: ANALYSIS AND MODELING

Plastic instabilities occurring during sheet metal forming and the determination of the forming limit were studied. The theories of necking and plastic instability according to Swift, Hill and Marcinaik-Kuczunski were discussed. The conventional theory of plasticity for isotropic work-hardening material was adopted to reformulate the three models (Swift, Hill, Marciniak). This new analysis was used to calculate the theoretical forming limit according to each model. Since this reformulation of the three models was based on the same assumption (the same yield function and the power law (sigma) = K(epsilon)('n)). It was easy to compare the results and discuss the limitations of each model. To overcome the limitations of these models, a simple theoretical model was introduced. This model based on the idea that necking develops from a local region of initial nonuniformity in the sheet metal. This simple model has the capability to prodict the limit strains in the entire range of the forming limit without solving a very complicated differential equations and consuming long periods of computer time. Many criterion were introduced in this analysis to define the limiting strains. The constant thickness strain criterion was found to be the most appropriate one to construct the forming limit. This simple analytical model was used to develop a computer program which predicts the development of nonuniform flow in sheet metals under various plane-stress loading conditions. The specimen was assumed to have an initial nonuniformity in the form of a band of reduced section. This band has an angle with respect to the directions of the principal stresses. This angle also changes when the state of strain inside the material changes.; A complete experimental program was conducted to determine the forming limit based on a new definition for the limit strain. The fracture limit strain was also determined. The experimental data presented in this work were limited only to the left side fo the forming limit. On the left side of the forming limit, many test specimens with different geometries were designed to cover the forming limit from unaxial tension to plane strain tension. The reasons we did not extend this work to cover the entire range of the forming limit is the requirement for a very lengthy experimental program by which we can eliminate the uncertainty was found in previous investigators' experimental programs.