Bekele, Mulugeta and Ananthakrishna, G (1998) Ginzburg-Landau equation for steps on creep curve. In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 08 (01). pp. 141-156.
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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:||Journal Article|
|Additional Information:||Copyright of this article belongs to World Scientific Publishing Company.|
|Department/Centre:||Division of Chemical Sciences > Materials Research Centre
Division of Physical & Mathematical Sciences > Physics
|Date Deposited:||23 Jul 2009 04:54|
|Last Modified:||19 Sep 2010 05:24|
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