A dislocation-based solution for stress introduced by arbitrary volume expansion in cylinders

A cylindrical structure undergoing volume expansion and contraction is common in engineering practice. For example, the charging (discharging) process of axisymmetrical batteries will give rise to volume expansion (shrinkage). The nitriding process of axles for better fatigue performance also introduces volume expansion. Here, by taking the equivalence of volume expansion (or shrinkage) as continuous insertion (or distraction) of infinitesimal dislocations, we supply a framework to solve the stress field of a cylinder with arbitrary insertion (distraction) profile of materials along the radial direction. Under the assumptions that the volume expansion profile along the axis of a cylinder is uniform and the deformation is small so that the current configuration is regarded as the original, we supply analytical solutions of stress fields to several typical volume expansion or shrinkage profiles. Our analysis shows that different volume variation gives rise to either high tensile stress in the surface or hydrostatic tension in the core, and supplies distinct failure mechanisms in cylindrical batteries.