13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- with a new stress state being obtained, and this peak temperature would hold a long time, where the thermal growth of TGO layer would occur. After that, the system is cooled to ambient again. The cyclic thermal load is obtained by repeating this sequence many times. 3. The simulation scheme 3.1. Description of model Due to the complexity of the morphology of interface and crack, the finite element method (FEM) is used to solve the problem. A conventional FEM model for the displacement instability is adapted in the calculations (Fig. 2) [13, 14]. The analysis is carried out by employing the computer program ABAQUS with the four-node, bi-liner plane strain elements. Geometric dimension of each layer is shown in the model and an initial instability zone with a depth 2 7.5 h m and radii of curvature 1 2 11.25 R R m is introduced. All the nodes at the right sides of the model are allowed to move with a limit of keeping an equal displacement in the X direction for them and a symmetric boundary condition is applied to the left side. The nodes on the bottom side are fixed in the Y direction to avoid rigid body motion. In the analysis, the initial static crack is not allowed to propagate, and the length L and the angle for both cracks are changed as variables. The crack behavior is achieved by using the extended finite element method (XFEM) [28-31], which can simulate the crack behavior without the crack tip conforming to any node point of the finite element mesh. In addition, in all calculations, only the case of single crack within the TC is simulated and the case of multi-crack is not considered in this paper. Figure 2. Finite element method model for the crack within the TC above the instability site.
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