Ginzburg-Landau equation for steps on creep curve

Bekele, M. ; Ananthakrishna, G. (1997) Ginzburg-Landau equation for steps on creep curve International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 8 (1). pp. 141-156. ISSN 0218-1274

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We consider a model proposed by us earlier for describing a form of plastic instability found in creep experiments. The model consists of three types of dislocations and some transformations between them. The model is known to reproduce a number of experimentally observed features. The mechanism for the phenomenon has been shown to be Hopf bifurcation with respect to physically relevant drive parameters. Here, we present a mathematical analysis of adiabatically eliminating the fast mode and obtaining a Ginzburg-Landau equation for the slow modes associated with the steps on creep curve. The transition to the instability region is found to be one of subcritical bifurcation over a major part of the interval of one of the parameters while supercritical bifurcation is found in a narrow mid-range of the parameter. This result is consistent with experiments. The dependence of the amplitude and the period of strain jumps on stress and temperature derived from the Ginzburg-Landau equation are also consistent with experiments. On the basis of detailed numerical solution via power series expansion, we show that high order nonlinearities control a large portion of the subcritical domain.

Item Type:Article
Source:Copyright of this article belongs to World Scientific Publishing Company.
ID Code:91341
Deposited On:18 May 2012 07:25
Last Modified:18 May 2012 07:25

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