-2- stress in the process of thermal spraying[16-18]. The defects near the interface may coalesce during the service, leading to the interface cracks[19, 20]. The original motivate of present work is the author's experiment observations to TBCs that the surface cracks intensively appears in some areas of the ceramic coating of TBCs. Generally, one reason for the phenomenon is that, after air plasma spraying, as previous mentions, the ceramic/bond coat interface usually contains numbers of small scale delamination, which may promote the surface crack emerging above it. Another one is that the facilitation of the interfacial delamination induced by TGO growth or material property mismatch to the surface cracks. In general, the interaction between the interface defect and surface rupture make a great contribution to the experiment observations. In order to understand the fracture mechanisms of the TBCs clearly, the analyses of the mutual effects between the interface defect and surface rupture should be extremely necessary. More recently, investigations focus on the interaction of interfacial delamination and surface cracks[21, 22]. Among these studies, much attention has been paid on the effect of the surface cracks on the interfacial delamination, the basic assumption of which is that the interfacial delamination initiated from roots of surface channel cracks. However, for most cases, the interface cracks exist before the top ceramic coating starts to failure. Therefore, it is important to investigate the effect of the pre-existing interfacial defect on the ceramic failure especially on the initiation and propagation of the surface vertical crack. Zhou and Kokini[21] investigated the effect of pre-existing surface crack morphology on the interfacial thermal fracture and demonstrated that the large density of the period surface cracks can postpone the interfacial delamination, Fan et al. [22] used FEM to obtain the critical spacing of the periodic surface cracking below which the surface channel cracks have a dramatic effect on the interfacial delamination. However, much less attention has been paid directly to the effect of interface defect on the coating rupturing. In practice, actual spalling failure of TBC is followed by multiple surface cracks that propagate through the top coat and coalesce with interfacial crack between the top coat and the bond coat[22]. Therefore, to design excellent TBCs with high durability, it is necessary to study the effect of the interface cracks on the surface cracks which determines the coalescent of the surface cracks and interface cracks. In this paper, we build a multiple-layers TBCs model which contains pre-existing interfacial defect to investigate the effect of pre-existing interfacial defect on surface cracking. In Section 2, we firstly descript the numerical model for the problem of surface cracks and interfacial defect in TBCs. In Section 3, the crack driving forces for surface cracks are calculated, and moreover the effect of interfacial defect on surface cracks is discussed in detail. Section 4 summarizes the concluding remarks and emphasizes the effect of interfacial cracks on the durability of TBC system. 2. Statement of the problem Due to the pre-existing interfacial defect after air plasma spraying or the interface cracks induced by thermal stress, the interfacial delamination probably emerges in some small areas, which effects the inevitable following surface cracks and the subsequent coalescent of the surface cracks and interface cracks. A steady state concept for cracks in multilayer structure is essential for many situations, where the crack driving force of surface crack is independent of the tunnel length if the length is enough long. Once the steady state is reached, the crack driving force can be calculated by using a two-dimensional (2D) plane strain model[23]. As a result, a three-dimensional TBCs model with surface cracks and interface defects is reduced to a 2D plane stain model. Fig. 1 shows the 2D plane strain model of steady state multiple surface cracks accompanied with interfacial cracks, in which h, a and W are the ceramic coating thickness, the surface crack length, and the cell model width, respectively. Based on our experimental observation[22], when the distance between adjacent surface cracks is large enough (about ten to twenty times the film thickness), the interaction between neighboring surface cracks can be ignored. Therefore, a unit cell model with single surface crack and interfacial defect can be constructed to simulate the actual TBCs with multiple cracks by setting the W equal twenty times the ceramic coating thickness.
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