-6- asymptotic to 1. Therefore, ( , , , , ) Z L a c α β seems to approach to ( , , ) Z a α β which indicates the influence of interface can be ignored. In present model, the critical offset value is about 0.15 above which the interaction between surface crack and interface defect can be ignored. Moreover, a interesting finding in Fig.2 is that the ( , , ) L a c κ for / a h= 0.8 and 0.9 exhibits an irregular convex at 0.05 c =± . This irregular effect on surface cracking behavior is related to the extra deviating driving force induced by an asymmetric loading and restraint which are a result of the offsetting interface defect. Next part we will discuss this irregular behavior. Figure 2. The reduced revised function ( , , ) L a c κ as a function of interface defect location for different surface crack length. Figure 3. The SERR as a function of surface crack length for different interface defect offset. Figure 3 shows the variations of SERR with normalized crack length a/h for the different offset of the interfacial defect. Moreover, SERR for the TBCs model with perfect interface is also plotted in Figure 3 for comparing. It is seen that the SERR for perfect interface rises to the maximum value as surface crack propagates and then drops as the crack approaches to interface, which coincides with the results obtained by Beuth[24]. Moreover, it is interesting to find that the overall trend of SERR curve in Figure 3 would change as the offset decrease. For the remote defect (e.g. 0.15 c = ), the curve of is much similar to the solution for perfect interface which, as previous described, rises to the maximum value as surface crack propagates and then drops as the crack approaches to interface. However, when the defect offset diminishes to 0.05, the SERR curve turns to monotonously ascend (e.g. 0.05 c = ). Then, Continue to decrease the offset of the defect, the
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