13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- The distribution of in-plane stress ( 11 ) in the intact TC is depicted in Fig. 4a. The compressive in-plane stress can induce the failure of the system by resulting in large-scale buckling [14]. Fig. 4a shows that the compressive 11 mainly occurs in the zones above the instability site and the tensile part distributes around the periphery of the instability zone. Fig. 5B presents the distribution of in-plane stress in TC along the TC-TGO interface under the case a crack existing within TC. The existing of crack within TC makes the stress state in the region above the instability site become tensile from compressive. Especially, when the crack is close to the base of instability site (crack “a”), the tensile stress is significant. Compared to the compressive state of in-plane stress, this tensile state may reduce the probability of buckling occurring. Therefore, the existing of the crack can partly prevent the failure mode caused by buckling. 4.2. The effect of crack length The influence of the normalized crack length max / L L on the instability amplitude defined by 0 1 1 / R R and 0 2 2 / R R is shown in Fig. 6, where max L is the maximum crack length used in the calculations, and 0 1R and 0 2R are the instability amplitudes when there is no crack within TC. It can be seen that both the magnitudes of the downward displacement 1R and the upward displacement 2R increase as the increase of crack length under both cracks case, and the increase rate also increase as the increase of crack length. It indicates that the crack extending would aggravate the instability and make the interface distortion be more significant. Inversely, the large interface distortion also can enhance the capacity of crack extending [3] and finally induce the failure of system. Note that the amplitude change of the displacement instability for the crack “a”, which is more close to the base of instability site, is always greater than that for crack “b”. This result shows that the crack close to the base of instability site has a greater enhancement on the instability. In addition, as the increase of crack length, the amplification of downward displacement 1R is always greater than that of upward displacement 2R . From max / 0.5 L L to max / 1.0 L L , the normalized amplification of 0 1 1 / R R is increased by more than 5 times, which can result in a markedly distortion at the interface. Therefore, the propagation of crack can significantly enhance the interface distortions as thermal cycling, especially that of the crack close to the base of instability site. 4.3. The effect of crack angle The effect of the crack angle ( 1 and 2) on the normalized instability amplitude 0 1 1 / R R and 0 2 2 / R R is shown in Fig. 7. Six different crack angles of 15 o, 30o, 45o, 60o, 75o and 90o are used in the calculations for both 1 and 2. It is demonstrated that the upward displacement 2R is insensitive to the crack angle. However, the crack angle has a great influence on the downward displacement 1R . When the angle is relatively small, the 1R increases as the increase of the crack angle. But when the crack angle makes the crack trend to be parallel the flat interface, 1R begins to decrease as the increase of the crack angle. From the previous analysis we can see that the propagation of crack within TC is preferential along the direction which is parallel to flat interface [33]. Therefore, when the crack direction is close to the preferential propagation direction, the crack propagation would play a dominant role and the instability of TGO can be restrained. However, even the extending of displacement amplitude begins to slow down when the crack trends to parallel to flat interface, the effect of the crack in this direction on the displacement instability is much greater than that of the crack in the direction which is perpendicular to the flat interface.
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