Influence of limit stress states and yield criteria on the prediction of forming limit strains in sheet metals
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TRODUCTION
THE seminal concept of forming limits in sheetmetal working was first proposed by Gensamer[1] and brought to the fore by Keeler and Backofen.[2] Subsequently, it evolved into the present-day form of the so-called forming limit curve (FLC) by the pioneering experimental work of Keeler[3] and Goodwin.[4] An FLC basically gives an indication of the limiting principal surface strains for the onset of localized plastic flow which precedes eventual failure. The FLC has, since then, proven to be a useful diagnostic tool in the industrial shop floor for analysis of failures in sheetmetal stamping operations. Originally, an FLC was constructed by using various configurations of punch-die assemblies to simulate the different stress states that a sheet metal can possibly encounter in stamping operations. Hecker[5] successfully demonstrated the use of a path-breaking procedure for obtaining an FLC by using a single punch-die assembly, while the different stress states were simulated merely by varying the width of the sheetmetal blank and the lubrication conditions. Notwithstanding the universal acceptance of this vastly simplified technique, experimental construction of an FLC still remains too highly labor intensive, time and material consuming, and particularly monotonous for routine quality control, where a large number of heats of a given material grade must be speedily evaluated, on a tonnage basis, for forming worthiness. W.M. SING, Research Scholar, Department of Manufacturing Engineering, City University of Hong Kong, is also Lecturer, the Hong Kong Technical College, Chai Wan, Hong Kong, K.P. RAO, Associate Professor, is with the Department of Manufacturing Engineering, City University of Hong Kong, Kowloon, Hong Kong. K. SWAMINATHAN, formerly Research Fellow, Department of Manufacturing Engineering, City University of Hong Kong, is Assistant Professor, Department of Metallurgical Engineering, Indian Institute of Technology, Madras 600 036, India. Manuscript submitted August 15, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS A
Further, such conventional approaches have limitations, in terms of their applicability, in an integrated computer modeling environment which is progressively gaining greater acceptance in view of its superior accessibility and ease of application. Several theoretical approaches[6–12] have, therefore, been proposed for predicting the FLC analytically based on theories of flow localization. However, these have fetched only limited success and their validity and applicability is restricted to highly specific conditions. Despite this constraint, when an analytical approach can predict the appropriate FLC corresponding to a particular strain path based on easily measurable material properties, it can be linked with modeling software for sheetmetal processing so that the success or failure of a forming process can be predicted a priori. Figure 1 shows schematically such an integrated approach, which typically involves an analysis program, e.g., a finite-element method (FEM) analysis progra
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