In the late 1970s and early 1980s the use of computer-aided techniques (computer-aided engineering, design, and manufacturing) in the metal-forming industry increased considerably. The trend seems to be toward ever wider application of this technology for process simulation and process design. A goal in manufacturing research and development is to determine the optimum means of producing sound products. The optimization criteria may vary, depending on product requirements, but establishing an appropriate criterion requires thorough understanding of manufacturing processes. In metal-forming technology, proper design and control requires, among other things, the determination of deformation mechanics involved in the processes. Without the knowledge of the influences of variables such as friction conditions, material properties, and workpiece geometry on the process mechanics, it would not be possible to design the dies and the equipment adequately, or to predict and prevent the occurrence of defects. Thus, process modeling for computer simulation has been a major concern in modern metal-forming technology. Figure 1.1. indicates the role of process modeling in some detail. In the past a number of approximate methods of analysis have been developed and applied to various forming processes. The methods most well known are the slab method, the slip-line field method, the visioplasticity method, upper- (and lower-) bound techniques, Hill’s general method, and, more recently, the finite-element method (FEM). In the slab method, the workpiece being deformed is decomposed in several slabs. For each slab, simplifying assumptions are made mainly with respect to stress distributions. The resulting approximate equilibrium equations are solved with imposition of stress compatibility between slabs and boundary tractions. The final result is a reasonable load prediction with an approximate stress distribution. The slip-line field method is used in plane strain for perfectly plastic materials (constant yield stress) and uses the hyperbolic properties that the stress equations have in such cases. The construction of slip-line fields, although producing an “exact” stress distribution, is still quite limited in predicting results that give good correlations with experimental work. From the stress distributions, velocity fields can be calculated through plasticity equations.
Solution of the problem of sheet bending by the slip line field method
