GINZBURG-LANDAU EQUATION FOR STEPS ON CREEP CURVE

We consider a model proposed by us earlier for describing a form of pl astic instability found in creep experiments. The model consists of th ree types of dislocations and some transformations between, them. The model is known to reproduce a number of experimentally observed featur es. The mechanism for the phenomenon has been shown to be Hopf bifurca tion with respect to physically relevant drive parameters. Here, we pr esent a mathematical analysis of adiabatically eliminating the fast mo de and obtaining a Ginzburg-Landau equation for the slow modes associa ted with the steps on creep curve. The transition to the instability r egion is found to be one of subcritical bifurcation over a major part of the interval of one of the parameters while supercritical bifurcati on is found in a narrow mid-range of the parameter. This result is con sistent with experiments. The dependence of the amplitude and the peri od 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 d omain.