EIGENSTRESSES GENERATED BY DIFFUSION IN A SPHERICAL-PARTICLE EMBEDDED IN AN ELASTIC MEDIUM

Diffusion governed by the Fourier parabolic heat equation for a sphere embedded in a continuum with elastic properties is studied as a mechanism of generating eigenstresses in the sphere and in the surrounding continuum. The problem studied is related to the phenomenon of thermal eigenstresses first acknowledged by Fourier's student Duhamel more than 150 years ago. The physical model presented in this paper is investigated in the context of the deleterious crack generating alkali-silica reactions observed in cement based materials. The model seems to be capable of supporting the notion that cracks associated with alkali-silica reactions are caused by diffusion generated eigenstresses. Quantified results are derived from the physical model and it is demonstrated that the development in time of eigenstresses can be expressed by one material parameter describing the relation between the elasticity constants of the sphere and the continuum and two functions describing concentration and saturation in the sphere. The results might be useful for the interpretation of related phenomena.