13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- 3.2. Material properties All materials used in the calculations are assumed to be isotropic and all material properties are temperature-dependent, which are summarized in [32]. Both TC and substrate are linear elastic and BC is considered as elastic-perfectly plastic with a temperature-dependent yield strength. The user subroutine, uexpan, in ABAQUS is employed to simulate the thermal growth of TGO, which was introduced by Karlsson and Evans in [13]. The growth behavior is achieved by imposing a thermal strain at the holding time of high temperature. The thermal strain consists of two components: g , which is a lateral growth strain parallel to the TGO-BC interface, and t, which is a thickening strain. In this paper, a ratio of lateral growth strain to thickening strain, / 0.5 g t , is used with 3 1 10 g . Also, the TGO is allowed to yield at the peak temperature with a yield strength tgo Y =1 GPa and it is elastic in other temperature [13]. The sequence of thermal load is repeated 24 times with 3 hours hold time at peak temperature (1100℃) for each sequence [6, 13, 14]. 4. Results and discussions 4.1. General response Initial results are generated for an intact TC, a TC within a crack at location “a” and a TC within a crack at location “b” (Fig. 1b), respectively. Cracks in both cases have an initial length, 4 L m and 1= 2=90 o in this section. A synopsis of the major findings is presented in Figs. 3-5. Figure 3. The distortions of BC interface after 24 thermal cycles. Fig. 3 shows the morphology of BC-TGO interface after 24 thermal cycles. It can be seen that the interface is distorted significantly with large upward displacements around the periphery of the instability zone and large downward displacements at the base. This phenomenon is in accordance with the previous results found by experiments and simulations [5, 6]. The shape distortions at the interface are induced by the plastic deformation in BC directly, and thermal misfit stresses and thermal growth stresses are two main resources to cause the plastic deformation. From Fig. 3, we can see that all these distortions at BC-TGO interface can be represented by the change of R1 ( 1R ) and R2 ( 2R ). Therefore, in following discussions, we mainly focus on the parameters 1R and 2R . Fig. 3 also presents the change of R1 ( 1R ) and R2 ( 2R ) when an initial crack exists within TC. It clearly shows that the distortion of the interface is more significant when the microcrack exists within TC, especially the downward displacement 1R . In addition, the crack location also
RkJQdWJsaXNoZXIy MjM0NDE=