13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- also widely exist within the TC. Experimental investigations have shown that when these microcracks appear in the region near the site of displacement instability, they would nucleate and extend as thermal cycling under the large tensile stress [5], and finally cause large scale delamination and spallation at the interface of TC-TGO [3, 4]. Based on Mumm's experiment results, Karlsson [14] modeled these cracks as traction-free internal planes and found that these cracks also can significantly promote the extending of the instability. Therefore, the existing of microcracks near the instability site would affect the durability of the system. Similarly to the surface cracks, there would be an optimal direction for the internal cracks, in which the effect of these cracks on the instability extending is weakest. However, in all of the previous studies focusing on the displacement instability, the effect of the geometric parameters of pre-existing cracks within the TC on the instability was not considered [2, 5-7, 13-15, 19, 27] and the optimal direction is still not obtained. Hence, the objective of this paper is to explore the effect of pre-existing cracks within TC of varying length, location and direction on the displacement instability of TGO under thermal cycling and try to obtain the optimal crack direction, in which the instability development is weakest. The results may be helpful in controlling the instability and providing the probability to design a longer life TBC. Figure 1. Schematic for (a) the multi-layer TBC system with TGO displacement instability, and (b) the microcracks within TC above the instability site. 2. Statement of the problem Due to the microcracks appearing in the region near the site of TGO displacement instability can significantly promote the extending of instability and induce the final failure of TBC system, we only consider the case where the initial crack exists above the instability site in this problem. As shown in Fig. 1b, two different cracks are introduced in this problem: crack “a”, which is at a distance h away from the base of instability region extending from the symmetry axis to the inward of TC, and crack “b”, which is at a distance h2 from the base with the same morphology as crack a. Each of these two cracks is defined by the included angle 1 and 2 (Fig. 1b), respectively. It must be noted that these two cracks are not considered in this problem together and only a single static crack problem is solved. In this problem, all materials are assumed to be isotropic (the detailed material properties are described below) and the plane strain condition exists. In order to investigate the extending of instability zone under thermal cycling when the crack exists above the instability site, cyclic thermal load is applied. In each thermal cycle, the system is cooled to ambient temperature from an initial peak temperature firstly and a thermal stress analysis is carried out associated with this temperature change. Then, the temperature rises to the initial state
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