Bending of beams with elastically non-linear coatings

Young's moduli of thermally sprayed materials are known to be substantially lower than those of well-sintered materials, due to elastic openings and partial closings of microcracks. Under compressive stresses some microcrack faces come into contact, which leads to the increase of Young's moduli and to non-linear elastic behavior. The bending of beams with elastically non-linear coatings on the compression face caused by external moments or residual stresses is analyzed theoretically. Examples of stress distributions are given for a model ceramic coating. Different coating and substrate elastic properties and thicknesses are considered. The difference between the presented non-linear and previously used linear solutions is shown to be important at high compressive stresses, especially in ceramic coatings with high densities of microcracks.