Optimum designs for multi-layered film structures based on the knowledge on residual stresses

Residual stresses are inevitably generated within the multi-layered film structures due to the mismatches of material properties between the adjacent layers. Using the force and moment equilibrium conditions and beam bending theory, the residual stresses in each layer can be predicted and expressed as σi(z) = Ei[ɛ′ + K(z + δ)], where Ei is the elastic modulus of the layer, ɛ′ the strain due to the in-plane force resulting from the misfit strain, K(z + δ) characterizes the bending contribution. For a bilayer system, the expression of the residual stress in the film is relatively simple. If the each layer thickness is much less than the substrate thickness, Stoney's equation will be derived. The assumption of a constant elastic modulus throughout the system is only applicable when the film and the substrate thickness ratio is less than 0.1. Specific analyses are performed for the thermal stresses in ZrO2/NiCoCrAlY thermal barrier coatings (TBCs) to illustrate the implementation of the analytical model. Moreover, the effects of single interlayer and graded interlayer inserted between the metallic layer and the ceramic layer on the residual stress distributions in TBCs are investigated. Additionally, the zero-deflection design is also discussed for typically duplex-layer TBC system.