A general approach for predicting the drawing fracture load and limit drawing ratio of an axisymmetric drawing process
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INTRODUCTION
SHEET metal deep-drawing processes are prevalently used to form a variety of parts that are used in the mass production of auto-body panels. One of the most difficult tasks of an analysis of such processes is to assess sheet metal formability. As shown in Figure 1, the most common failure mechanism encountered during sheet formation is wall fracture, which develops along the punch-profile region in an axisymmetric deep-drawing process. This failure is directly dependent on the loading capacity of the sheet material, which has been found to be a complex function of material properties, tool geometry, and process variables.[1] Under a given deep-drawing condition, the loading capacity of the sheet material specifies the forming limit of the sheets, which is represented by the limit drawing ratio (LDR). As a result, it is imperative to determine the LDR values of the sheet steels for designing deep-drawing dies and processes.[1] Due to the complexity of experimentally determining the LDR, the theoretical prediction of the LDR, which is directly associated with the determination of the loading capacity of the sheets, is of great significance. In fact, many endeavors have been made in the past years to directly model this failure mechanism.[2–6] Despite the merit of these works, there is little in the literature that takes into account three-dimensional stress states, bending, and tool geometry in the calculation of the LDR for various sheet steels. Hence, further work is necessary in this area, especially for the newly developed sheet steels that are currently used in the automotive industry. ZHI DENG, Postdoctoral Scholar, Center for Robotics and Manufacturing Systems, and M.R. LOVELL, Assistant Professor, Mechanical Engineering Department and Center for Robotics and Manufacturing Systems, are with the University of Kentucky, Lexington, KY 40506-0108. WOLFGANG BLECK, Director and Professor, and KOSTAS PAPAMANTELLOS, Researcher, are with the Institute of Ferrous Metallurgy, Aachen University of Technology, D-52072 Aachen, Germany. Manuscript submitted January 27, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
Herein lies the scope of this work: to develop an experimentally validated approach for determining an expression for the LDR, which takes diverse material, tooling, and process variables into account. Such an expression will allow the theoretical prediction of the drawing fracture load and LDR of sheet steels deformed in an axisymmetric deep-drawing process. In recent years, several new sheet steels have been developed to satisfy the requirements of increased safety, decreased weight reduction, and reduced mass-production costs in the automotive industry. In conjunction with the development of these new steel grades, applications for which they may be applied have become more diverse. Isotropic and multiphase steels, for example, have a higher yield point and considerably more strain-hardening ability. They may also be used for more-complex stamping processes. The fact that these newly developed s
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