2003 Volume 44 Issue 1 Pages 28-33
In order to reveal the microscopical mechanism which causes the plastic deformation induced by the vacancy diffusion process, we model and analyze mathematically the motion of the atom with the vacancy in an atomic chain. We describe the dynamics of the atom with the vacancy by a kind of the diffusion equation which includes the essential effects on the plastic deformation, namely, the thermal effect, the interactions of atoms, the friction of the environment and the external force. Stripping off the fluctuation of the prime motion by the perturbation expansion, we can get the situation where the essential motion of the atom with the vacancy is represented by the propagation of the kink wave which responds to the external force and the temperature, though the system is described by the diffusion process. Then deriving the strain of the atomic chain, we show the strain against time behaves viscoelastically like the typical response, for instance, that of the Voigt model. The properties of the temperature and the applied stress coincide with the well-known results of the primary creep phenomenon.