A sintering model for thermal barrier coatings

A mathematical model is developed for the progressive sintering of ceramic columns in a thermal barrier coating made using the electron beam-physical vapour deposition route. The model assumes that inter-columnar sintering is driven by changes in the interface energy and elastic stored energy of the columns. The analysis reveals the sensitivity of the sintering rate to the in-plane elastic modulus as well as to an imposed thermal mismatch strain, interfacial energies and diffusivities. It is shown that mud-cracking of the coating leads to a drop in in-plane stress within the coating and thereby to accelerated sintering. Explicit calculations are reported for the evolution of sintering within an array of mud-cracked columns, and for the density of mud cracks.