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Ginzburg-Landau equation for steps on creep curve

We consider a model proposed earlier by us 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 most 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.