An Analytical Model for the Generation of Residual Stresses in Sprayed Coatings Deposited Progressively onto Planar Substrates

Abstract

Abstract An analytical model has been developed to predict the residual stress distributions in thermal spray coatings on substrates of finite thickness. This is based on the concept of a misfit strain, caused by either the quenching of splats or by differential thermal contraction during cooling. During spraying, the coatings are asssumed to deposit on the substrate in a progressive (layer-by-layer) manner. Although the misfit strain ("the quenching strain") is the same for each successive incremental layer of deposit, this is imposed each time on a "substrate" of changing thickness. The final stress distribution will in general differ from that which would result if the coating were imposed on the substrate (with the same misfit strain) in a single operation. The model is straightforward to apply: for example, it can be implemented using a standard spreadsheet program. The required input data are the quenching strain (or stress), the spraying temperature, material properties and specimen dimensions. Comparisons have been made between the predictions from this model and from a numerical model for two plasma sprayed systems. Good agreement is observed. The effects of varying certain parameters, such as coating thickness, substrate thickness, coating stiffness, etc, are readily explored, so that the model provides a useful tool for controlling residual stress levels. Application of the model to determine the quenching stress, in conjunction with the use of a curvature monitoring technique, is briefly outlined. In addition, an analysis is made of the errors introduced by using Stoney's equation to deduce stress levels from curvature measurements.