Elastic stress–strain analysis of an infinite cylindrical inclusion with eigenstrain

TL;DR: In this article, a complete set of analytical expressions for the eigenstress state inside and outside of a cylindrical volume element along the dislocation line is presented, and the resultant stress field is then given by superposition, which allows also to determine the interaction energy between the Cottrell cloud and the dislocations.

Abstract: The ensemble of interstitial atoms as C attracted to a dislocation is well established as “Cottrell cloud” phenomenon. The deposition of the interstitial atoms in octahedral or tetrahedral positions in a bcc lattice may yield a remarkable internal stress state according to their anisotropic misfit eigenstrains. The stress fields of the atoms may then lead to a significant change in the stress field, e.g., around a dislocation. In such a case, the interstitial atoms are situated near the dislocation core in cylindrical volume elements along the dislocation line. As the occupancy of the sites in each cylinder by interstitial atoms can be considered as constant, also the eigenstrain state tensor is constant in the cylinder. A complete set of analytical expressions for the eigenstress state inside and outside of the cylinder is presented. The resultant stress field is then given by superposition, which allows also the determination of the interaction energy between the Cottrell cloud and the dislocation.