Abstract
Much of the development of a statistical energy-based theory of fragmentation of stretching ductile metals has been restricted to one-dimensional geometries such as expanding rings or, at best, a uniformly expanding cylinder where the theory is intended to describe the average and statistical spacing of axial fractures. In this chapter an analysis will be extended to describe the breakup of a biaxial expanding shell or membrane of ductile metal in which stretching rates in mutually orthogonal directions are each nonzero and are, in general, different. A specific case of interest, of course, is that of a stretching spherical shell segment in which the orthogonal stretching rates are the same.
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References
Abramowitz, M. and I. A. Stegun, eds. (1954), Handbook of Mathematical Function, No. 55, National Bureau of Standards Applied Mathematics Series, U. S. Government Printing Office.
Barlat, F. (1989), Forming Limit Diagrams – Predictions Based on Some Microstructural Aspects of Materials, in Form Limit Diagrams: Concepts, Methods and Applications, R. H. Wagner, K. S. Chang, S. P. Keeler, eds., The Minerals, Metals & Materials Society.
Buck, R. C. (1965), Advanced Calculus, McGraw-Hill, New York.
Grady, D. E. and Olsen, M. L. (2003), A Statistical and Energy Based Theory of Dynamic Fragmentation, Int. J. Eng. Mech., 29, 293–306.
Gurney, R. W. (1943), The Initial Velocity of Fragments from Bombs, Shells and Grenades, Army Ballistic Research Laboratory Report BRL 405.
Hancock, J. W., and Mackenzie, A. C. (1976), On the Mechanisms of Ductile Failure in High-Strength Steels Subjected to Multi-Axial Stress States, J. Mech. Phys. Solids, 24, 147–169.
Needlemann, A., and V. Tvergaard (1992), Analysis of Plastic Flow Localization in Metals, Applied Mechanics Review, 45, s3–s18.
Mott, N. F. (1948), Fracture of Metals: Theoretical Considerations, Engineering, 165, 16–18.
Romero, L. A. (1991), The Stability of Stretching and Accelerating Plastic Sheets I & II, J. Appl. Phys. 69, 7474–7486, 7487–7499.
Storen, S. and J. R. Rice (1975), Localized Necking in Thin Sheets, J. Mech. Phys. Solids, 23, 421–441.
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Grady, D. (2006). Application to the Biaxial Fragmentation of Shells. In: Fragmentation of Rings and Shells. Shock Wave and High Pressure Phenomena. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27145-1_6
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DOI: https://doi.org/10.1007/978-3-540-27145-1_6
Publisher Name: Springer, Berlin, Heidelberg
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