13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- Fig 1- Deformed shape of the crack surface (non-symmetric) The displacement component, which is required to calculate KI, at point P on the crack front can be expressed as ݑ ௱ሺ ߠ,ݎ ሻൌ൬ 1 ߥ ܧ ൰ඨ 2 ݎ ߎ ൜݇ పሺ ݏ ሻsin൬ ߠ 2 ൰2ሺ1െ ߥ ሻെcosଶ ൬ ߠ 2 ൰൨ െ݇ పపሺܵ ሻcos൬ ߠ 2 ൰ሺ1െ2 ߥ ሻെsinଶ൬ ߠ 2 ൰൨ൠ ሺEq.1ሻ ݑ ௱ሺ ߎ,ݎ ሻis calculated by using equation (4.1). For the non-symmetric crack model, ݑ ௱ሺ ,ݎ െ ߎ ሻ is also required. Thus, substituting ߠ ൌെ ߎ into equation: ݑ ௱ሺ ,ݎ െ ߎ ሻൌെቀଵା ா ఔቁටଶ ݇ ଵ2ሺ1െ ߥ ሻ (Eq. 2) Kı can be obtained as ݇ ଵ ൌ √ ሺଵି ଶ ఔ ⋅ா଼మሻ ⋅ ቂ݈݅݉→ ቄ௨೩ሺ,ሻି ௨೩ √ ሺ,ି ሻ ష ቅቃ (Eq. 3) At the crach tip (i.e. ݎ →0) , ݈݅݉→ ቄ௨೩ሺ,ሻି ௨೩ √ ሺ,ି ሻ ష ቅൌܺ .Hence, equation ݇ ଵ ൌ √ ሺଵି ଶ ఔ ⋅ா଼మሻ ⋅ܺ (Eq. 4) ݔ ൌோయ యോమ൫௨೩మ,బି ௨೩మ,య൯ି ோమ యോమ൫௨೩య,బି ௨೩య,య൯ ඥோమඥோయሺோయି ோమሻ (Eq. 5) For r=R2 →௨೩ሺோమ,ሻି ௨೩ሺோమ,ି ሻ ඥோమ ൌ௨೩మ,బି ௨೩మ,య ඥோమ ൌ ݔ ܻܴ ଶ And For r=R3 →௨೩ሺோయ,ሻି ௨೩ሺோయ,ି ሻ ඥோయ ൌ௨೩య,బି ௨೩య,బ ඥோయ ൌ ݔ ܻܴ ଷ ݇ పప ൌ √ ሺଵି ଶ ఔ ⋅ா଼మሻ ⋅ ቂ݈݅݉→ ቄ௨బሺ,ሻି ௨బ √ ሺ,ି ሻቅቃ (Eq. 6) For r=R2 →௨బሺோమ,ሻି ௨బሺோమ,ି ሻ ඥோమ ൌ௨బమ,బି ௨బమ,య ඥோమ ൌ ݔ ܻܴ ଶ And For r=R3 →௨బሺோయ,ሻି ௨బሺோయ,ି ሻ ඥோయ ൌ௨బయ,బି ௨బయ,య ඥோయ ൌ ݔ ܻܴ ଷ
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