Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Plastic flow in a deeply notched bar with semi-circular root


Author: Alexander J. Wang
Journal: Quart. Appl. Math. 11 (1954), 427-438
MSC: Primary 73.2X
DOI: https://doi.org/10.1090/qam/58437
MathSciNet review: 58437
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Abstract: The unsteady motion problem of a circular-notched bar pulled in tension in plane strain is considered. The theory of perfectly plastic solids is used. Large strains are analyzed so that the material can also be considered as plastic-rigid. The basic equations governing stress and velocity are integrated independently in the characteristic plane. The results are used to construct the boundary change in a step-by-step manner. The problem is greatly simplified because at each step the new free boundary of the plastic region can be approximated by a circle. The final shape of the boundary of an initially semi-circular notch is presented when plastic flow has reduced the initial connection at the root to a line contact between the shanks.


References [Enhancements On Off] (What's this?)

  • [1] E. H. Lee, Plastic flow in a V-notched bar pulled in tension, J. Appl. Mech. 19, 331-336 (1952).
  • [2] E. H. Lee, The deformation of a bar with rectangular notch, Report written for Watertown Arsenal under P.O. No. ORDEB 52-988, Brown University, June 1952.
  • [3] R. Hill, The Mathematical Theory of Plasticity, Oxford, at the Clarendon Press, 1950. MR 0037721
  • [4] William Prager and Philip G. Hodge Jr., Theory of perfectly plastic solids, John Wiley & Sons, Inc., New York, N. Y.; Chapman & Hall, Ltd., London, 1951. MR 0051118
  • [5] E. H. Lee, The theoretical analysis of metal forming problems in plane strain, J. Appl. Mech. 19, 97-103, (1952).
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  • [7] Whitaker and Watson, Modern analysis, 4th ed. Cambridge, p. 377.

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DOI: https://doi.org/10.1090/qam/58437
Article copyright: © Copyright 1954 American Mathematical Society


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