Thermal barrier coatings are of growing importance in high temperature applications, but their use is hindered by an insufficient understanding of their failure mechanisms. A detailed analysis of the stress state in these coatings is necessary to determine stress conditions leading to cracking in the thermal barrier coating and subsequent spallation.
The stress state in a thermal barrier coating is strongly dependent not only on the different thermal properties of the coating materials, but also on their creep behaviour. The creep rate of the thermally grown oxide (TGO) is especially important as it determines whether the stresses caused by TGO growth and swelling can be relaxed within the TGO.
To study the influence of the creep rates in detail, a finite element model of the thermal barrier coating is used. Material data and a detailed description of the model can be found in .
To show the influence of the growing TGO and its creep behaviour, three different simulations are compared: In the first model, no TGO formation is assumed, in the second model, a 1 micrometer thick purely elastic TGO layer grows, in the third model, the TGO is assumed to creep with a high creep rate. As the creep of the TGO is determined by its grain size, the second model corresponds to a large-grained TGO with grain size of the order 1 micrometer, whereas the TGO in the third model has a very small grain size of the order 10nm.
Fig.1: Stress state in the TBC system after cooling. The left figure shows the case of no TGO formation, the second figure the case of an elastic TGO and the third figure the case of strongly creeping TGO. 
Figure 1 shows the stress state for the three cases after cooling of the system. In the first case, the thermal barrier coating (TBC) is in a state of tensile stress in the peak region of the asperity and in a state of compressive stress in the valley region. The reason for this is that creep in the TBC and the bond coat (BC) is so fast that all stresses are fully relaxed at high temperatures and so on cooling the smaller coefficient of thermal expansion (CTE) of the TGO determines the stress field. If a growing TGO is introduced into the system which is purely elastic, the stresses in the TBC at high temperature can only relax if the growth rate is small. For the parameters considered, this is not the case, so that the TBC cannot relax the stresses at high temperature. The strong swelling of the TGO leads to a region of large tensile stresses in the valley region of the TBC and to large compressive stresses in the peak region.
Fig 2: Failure mechanisms of the TBC for the case of very fast swelling of the TGO (no relaxation in TBC and bond coat), moderately fast swelling (relaxation in bond coat, but not TBC) and slow swelling. In the latter case, cracks will form at the peak position but will propagate during TGO growth. 
If fast creep is assumed within the TGO, the stresses in the system can again completely relax at high temperatures, as in the first case. On cooling, the resulting stress state is then again determined by the CTEs of the different materials and is similar to that of the first case. The region of tensile stress in the TBC is slightly shifted from the peak to an off-peak position, as the thermal shrinking of the bond coat is hindered by the high elastic modulus of the TGO.
These results show that the creep properties of the TGO are important in determining the stress state of the TBC and thus in understanding possible failure mechanisms. If the loading caused by swelling of the TGO is fast compared to stress relaxation by creep, large tensile stresses occur in TBC and bond coat, with cracks forming in the valley region of the TBC and the peak region of the bond coat (see figure 2).
When the swelling rate decreases, the bond coat will be the first component able to relax the stresses during the high temperature phase as its creep rate is higher than that of the TBC (see figure 2). In this case, no damage in the bond coat will occur. However, during the thermal cycle, damage accumulation not simulated here may begin to play a role and lead to failure also in the bond coat.
If the swelling rate is decreased further, the peak region of the TBC will be the first to fail as tensile stresses here are above the TBC fracture strength. These microcracks will expand when the TGO thickness grows, as the cooling stresses in the TBC are determined by the slightly larger CTE of the TBC compared to the TGO.
From these considerations it can be concluded that the CTE of the TGO should preferredly not be smaller than that of the TBC in order to reduce tensile stresses caused by the CTE mismatch for large TGO thickness. To achieve this is, however, not easy. More importantly, the TGO and the TBC should be sufficiently soft at high temperatures to allow relaxation of the swelling induced stresses. Thus, tayloring the TGO creep properties by reducing its grain size may be an important method of increasing the lifetime of thermal barrier coatings.
 J. Rösler, M. Bäker, M. Volgmann
The Role of TGO Creep on Stress State and Failure Mechanisms of Thermal Barrier Coatings,