An analytical model for predicting residual stresses in progressively deposited coatings Part 2: Cylindrical geometry

An analytical model is presented to predict the residual stress distributions in progressively deposited coatings with cylindrical substrates. Misfit strains, due either to the deposition stress or to differential thermal contraction, set up axial forces in the longitudinal direction and interfacial pressures in the radial direction. Use of stress-strain relationships in the longitudinal and hoop directions allows these forces and pressures to be evaluated. A layer-by-layer approach is employed to determine the stresses set up in the coatings during deposition. Predicted stress distributions are presented for three plasma sprayed systems. Comparisons with a numerical model, of the type presented in Part 1 for planar systems, have not been made, but the behaviour predicted is intuitively as expected. In addition, the model has been applied to predict the through-thickness stresses in specimens with planar substrates for the case when bending is not allowed, by artificially assigning a large inner radius to the substrate.