An image-based model for the sintering of air plasma sprayed thermal barrier coatings

A micromechanical model is developed to predict microstructure evolution and the resultant in-plane modulus increase in a thermal barrier coating (TBC) manufactured by air plasma spray (APS). The model is based on the experimental observation that the main sintering events include the progressive healing of the inter-splat cracks and the coarsening of the columnar grains within the splats. During sintering, the splats undergo Coble creep, which relaxes the constraint on crack healing and therefore sintering. Given its columnar structure, the creep response of the splats is taken to be transversely isotropic. The proposed model is implemented numerically using finite element (FE) meshes that have been developed from cross-sectional micrographs of an as-deposited coating. This allows the evolution of microstructural features directly relevant to the performance of TBCs to be modelled, from which the overall elastic response can also be determined. The curvy nature of the nearly horizontal inter-splat cracks and the intersecting vertical intra-splat cracks explain the low in-plane modulus of the as-deposited TBC and their healing explains the evolution of in-plane modulus during sintering. The model results are validated by comparison with sintering experiments, in terms of the evolution of crack patterns and in-plane modulus. The sensitivity of the model results to the major geometrical parameters is explored and summarised in the form of a sintering map, which identifies the controlling processes as a function of the microstructural and kinetic properties. Finally, the effect of constraint on the overall sintering response is investigated.