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A simple criterion for the onset of discontinuous plastic deformation in metals at very low temperatures

Authors
Journal
Journal of the Mechanics and Physics of Solids
0022-5096
Publisher
Elsevier
Publication Date
Volume
42
Issue
5
Identifiers
DOI: 10.1016/0022-5096(94)90043-4
Disciplines
  • Mathematics

Abstract

Abstract The method of small strain-rate-sensitivity asymptotics, which is the analogue of high-activation-energy asymptotics in the mathematical theory of combustion, is used to simplify a model of discontinuous plastic deformation in metals during tensile loading at cryogenic temperatures. The procedure is analogous to what has been used to derive the ignition problem in combustion theory. It is shown that a degenerate Poincaré-Andronov-Hopf bifurcation occurs in the simplified model as a control parameter which is proportional to the applied strain rate is increased. The bifurcation point is shown to correspond closely to the onset of “ serrations” in the load-displacement response predicted by the original model.

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