13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- ݔ ൌோయ యോమ൫௨బమ,బି ௨బమ,య൯ି ோమ యോమ൫௨బయ,బି ௨బయ,య൯ ඥோమඥோయሺோయି ோమሻ (Eq. 7) ݇ పప ൌ √ ሺଵି ଶ ఔ ⋅ா଼మሻ ⋅ܺ (Eq. 8) KIII can be calculated by the tangential displacement component at point P on the crack front. The tangential displacement component at this point is ݑ ሺ ߠ,ݎ ሻൌ2ቀଵା ா ఔቁටଶ ݇ ሺ ݏ ሻsinቀఏ ଶቁ (Eq. 9) For r=R2 →௨ሺோమ,ሻି ௨ሺோమ,ି ሻ ඥோమ ൌ௨మ,బି ௨మ,య ඥோమ ൌ ݔ ܻܴ ଶ And For r=R3 →௨ሺோయ,ሻି ௨ሺோయ,ି ሻ ඥோయ ൌ௨య,బି ௨య,య ඥோయ ൌ ݔ ܻܴ ଷ ݔ ൌோయ యോమ൫௨మ,బି ௨మ,య൯ି ோమ యോమ൫௨య,బି ௨య,య൯ ඥோమඥோయሺோయି ோమሻ (Eq. 10) ݇ పపప ൌ √ ሺଵି ଶ ఔ ⋅ா଼మሻ ⋅ܺ (Eq. 11) ߤ ൌଶሺଵ ா ାఔሻ (Eq. 12) Therefore, the total strain energy release rate under mixed mode loading is ்ܩ ൌ ܩ ଵ ܩ పప ܩ పపప ൌ൫ଵି ఔమ ா ൯ ቄ݇ ଵଶ ݇ ప ଶ ప ഢమ ഢഢ ଵି ఔቅ (Eq. 13) After the accuracy of the finite element model is checked out, the same model is used for the analyses of semi-elliptic inclined surface crack embedded in the FGM coating of composite structure. The finite element analyses of FGM coating- bond coat-substrate structure are carried out and the numerical results are calculated for various inclinations of three dimensional semielliptic surface crack, coating types, crack front angles and relative dimension of the crack with respect to FGM coating thickness. 4. Numerical results There is a semi-elliptic inclined surface crack which has a length of 2c and a depth of a. The semielliptic crack has an inclination angle α, on the surface of the FGM at x=0. In the numerical analysis conducted, crack depth/ FGM thickness ܽ ݐ ൗ ratios and aspect ratio are used. These are as follows: ܽ ݐ ൗ ൌ0.2 ܽ݊݀ ܽܿ⁄ ൌ 1ൗ 2 (Eq. 14) In this analysis, the stress intensity factors are normalized by, ݇ ோ ൌ ߪ ට ொ (Eq. 15)
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