Effect of diffusion-induced bending on diffusion-induced stress near the end faces of an elastic hollow cylinder

Diffusion-induced stress plays an important role in determining structural integrity of mechanical structures used in lithium-ion batteries and microelectromechanical devices. Incorporating the diffusion-induced bending in the analysis of the diffusion-induced stress in an elastic hollow cylinder, analytical forms of the diffusion-induced resultant axial stress and hoop stress have been formulated for the traction-free condition and the built-in condition at the end faces of the cylinder. Using these results, the evolution of the diffusion-induced stress at the end faces of a hollow, elastic electrode due to the insertion of lithium is discussed under the potentiostatic operation. The end faces of the electrode experience compressive hoop stress through the thickness in contrast to the stress state in the hollow cylinder far away from the end faces. The magnitude of the resultant hoop stress decreases with increasing the diffusion time for the traction-free end faces; it increases with increasing the diffusion time near the inner surface for the built-in end faces.