Analysis on spherical cavity expansion in gradient elastic media

Abstract

Abstracth In this paper, an analysis for spherical cavity expansion in elastic media is presented. In order to account for the long-range interactions among microstructures undergoing elastic deformation, a simplified strain gradient elasticity constitutive model, including only one extra internal length scale, is invoked. Analytical solutions of stresses, strains and displacement, containing the length scales of cavity and microstructures explicitly, are given. The influence of underlying microstructure on the macroscopic behavior of the material is investigated. The results show that gradient-dependent stresses components are smaller than their classical counterparts, indicating that the strength of material seems to be higher by considering the influence of microstructures. It is noted that the gradient-dependent maximum hoop stress does not occur at the inner surface in contrast with Lame solution. When the length scale is trivial to cavity size, the gradient-dependent solutions reduce to conventional ones. The improved cavity expansion model can be used to improve the design of spherical pressure vessel and interpret indentation size effect.