A SIMPLE CRITERION FOR THE ONSET OF DISCONTINUOUS PLASTIC-DEFORMATIONIN METALS AT VERY-LOW TEMPERATURES

THE METHOD of small strain-rate-sensitivity asymptotics, which is the analogue of high-activation-energy asymptotics in the mathematical the ory of combustion, is used to simplify a model of discontinuous plasti c deformation in metals during tensile loading at cryogenic temperatur es. The procedure is analogous to what has been used to derive the ign ition problem in combustion theory. It is shown that a degenerate Poin care-Andronov-Hopf bifurcation occurs in the simplified model as a con trol parameter which is proportional to the applied strain rate is inc reased. The bifurcation point is shown to correspond closely to the on set of ''serrations'' in the load-displacement response predicted by t he original model.