HIGH-ORDER AMPLITUDE EQUATION FOR STEPS ON THE CREEP CURVE

We consider a model proposed by one of the authors for a type of plast ic instability found in creep experiments which reproduces a number of experimentally observed features. The model consists of three coupled nonlinear differential equations describing the evolution of three ty pes of dislocations. The transition to the instability has been shown to be via Hopf bifurcation, leading to limit cycle solutions with resp ect to physically relevant drive parameters. Here we use a reductive p erturbative method to extract an amplitude equation of up to seventh o rder to obtain an approximate analytic expression for the order parame ter. The analysis also enables us to obtain the bifurcation (phase) di agram of the instability. We find that while supercritical bifurcation dominates the major part of the instability region, subcritical bifur cation gradually takes over at one end of the region. These results ar e compared with the known experimental results. Approximate analytic e xpressions for the limit cycles for different types of bifurcations ar e shown to agree with their corresponding numerical solutions of the e quations describing the model. The analysis also shows that high order nonlinearities are important in the problem. This approach further al lows us to map the theoretical parameters to the experimentally observ ed macroscopic quantities.