Multiscale modelling of sintering in thermal barrier coatings - Shanmugam, K (2010)
Multiscale (analytical and computational) models have been developed based on a thermodynamic variational principle (TVP) to model sintering and eventual mudcracking in thermal barrier coatings (TBCs) made using the electron beam physical vapour deposition (EB-PVD) process. It is assumed that the sintering occurs by interfacial diffusion at local contacts between columns and driven by changes in interface free energy and elastic stored energy of the coating. The models link diffusional processes at the scale of contacting feathery columns with the macroscopic deformation and sintering response. In service, the columns can come into contact and sinter together. As sintering progresses there is a build up of strain energy in the system which reduces the driving force for sintering and leads to either complete or incomplete sintering of the TBC depending on the magnitude of effective modulus (E) of the coating. By seeding the coating with initial imperfections, different types of behaviour are observed depending on the value of E and the spacing between imperfections. For compliant coatings, the response is insensitive to the presence of imperfections and the coating fully sinters. At higher values of E, strain energy is released by the development of intercolumnar cracks in the coating, which can propagate to the interface with the TGO (thermally grown oxide), deflect into the interface and propagate, leading to spallation of regions of the coating and loss of thermal protection. It is observed that cracks develop at initial imperfections in the structure. The greater the spacing between imperfections the faster the development of cracks at these locations. If a TBC contains a distribution of imperfections there is progressive formation of cracks, with the average spacing decreasing with time, after an initial incubation period. The crack density eventually saturates to a constant value, which depends on the mechanical properties of the TBC. Initially, a crack spacing, CS, in the range 1.5H ≤ CS ≤ 3H has been predicted based on trapezoidal contact models. Here H is the thickness of the coating. Crack spacing predicted using this model is consistent in the lower range of experimentally observed crack spacing. However, axisymmetric contact models predict a crack spacing, CS, in the range 4H ≤ CS ≤ 8H, which is in good agreement with experimentally observed crack spacing range 3H ≤ CS ≤ 10H reported in the literature. Compared to the trapezoidal contact models, axisymmetric contact models more accurately predict the sintering response.