On Stochastic Bifurcation Behavior of the Atom Movement at the Tip of a Crack in Fatigue Damage System

Abstract

By virtue of the stochastic bifurcation theory the transition of the atom moveme nt at a crack tip in fatigue damage system is investigated.Using the singular po int theory of one－dimensional diffusion process and the stochastic averaging ap proach of energy envelope a micro－model to describe the atom movement at the cr ack tip in homoclinic bifurcation fatigue damage system which is in the presence of stochastic perturbation is established.After the study on the characteristic of the diffusion exponent the drift exponent and the character exponent of the fatigue damage diffusion process on singular boundary the bifurcation behavior o f a homoclinic bifurcation fatigue damage system which is in the presence of par ametric white noise is examined.