Nonlinear diffusion-induced stresses in a long bar of square cross section

Abstract

This paper is to investigate the nonlinear effect of the self-induced electric field on the diffusion-induced stresses in a long bar. We first approximate the nonlinear concentration-dependent diffusivity as a series of third-degree polynomials by the least-squares curve-fitting techniques, and then calculate the distributions of concentration by the Galerkin method. Afterwards, the diffusion-induced stresses inside the bar are determined analytically by introducing the Goodier displacement potential and Airy stress function. It is found that the nonlinear self-induced electric fields can depress both the concentration gradient and the maximum diffusion-induced stresses apparently, and these effects are more significant at short times than at long times.