A model based on nonlinear oscillations to explain jumps on creep curves

Abstract

A dislocation transformation model with three types of dislocations-namely the mobile, the immobile and those with clouds of solute atoms-is considered. Some physically reasonably reactions are postulated, leading to a coupled set of nonlinear differential equations for the rate of change of their densities. The basic idea of Cottrell's mechanism has been incorporated. It is shown that these equations admit a class of periodic solutions called limit cycles which are typical of nonlinear systems, suggesting that nonlinearity plays a fundamental role in the model. The rate equations are solved on a computer to obtain the oscillatory behaviour of the densities and hence leading to steps on the creep curve. The theory predicts that there is a range of temperature over which the phenomenon can occur, in agreement with the experiment of L.N. Zagorukuyko et al. (1977). The theory also reproduces other normal forms of creep curves.