13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- ܧ ∗ ൌቐ ܧ 1െ ߥ ଶ ; plane strain ܧ ; plane stress ;݅ ൌ1,2 ሺ4ሻ Using the general fracture-mechanical solution for an interface crack, ߜ ଵ ൌ ݑ ଵ ሺ௨ሻ െ ݑ ଵ ሺሻ and ߜ ଶ ൌ ݑ ଶ ሺ௨ሻ െ ݑ ଶ ሺሻ (where superscripts (u) and (l) stand for upper and lower crack flanks, respectively) are then given by ߜ ଵ ߜ ଶ൨ൌΨ⋅sinሺ߳ ln ݎ ሻെ2߳ cosሺ߳ ln ݎ ሻ 2߳ sinሺ߳ ln ݎ ሻcosሺ߳ ln ݎ ሻ 2߳ sinሺ߳ ln ݎ ሻcosሺ߳ ln ݎ ሻ െsinሺ߳ ln ݎ ሻ2߳ cosሺ߳ ln ݎ ሻ ൨ ܭ ூ ܭ ூூ൨ ሺ5ሻ where Ψൌ 1 2 ቆ 1 ܧ ଵ ∗ 1 ܧ ଶ ∗ቇ ⋅ 8 ሺ14߳ ଶሻcoshሺ ߳ߨ ሻ ⋅ ቀ ݎ 2 ߨ ቁ ଵ ଶ ሺ6ሻ Eq. (6) is only used for establishing an expression for ߚ ൌ ܭ ூ ܭ ூூ ⁄ : ߚ ൌ ܭ ூ ܭ ூூ ൌ െሾsinሺ߳ ln ݎ ሻെ2߳ cosሺ߳ ln ݎ ሻሿ ⋅ ߜ ଵ െሾ2߳ sinሺ߳ ln ݎ ሻcosሺ߳ ln ݎ ሻሿ ⋅ ߜ ଶ െሾ2߳ sinሺ߳ ln ݎ ሻcosሺ߳ ln ݎ ሻሿ ⋅ ߜ ଵ ሾsinሺ߳ ln ݎ ሻെ2߳ cosሺ߳ ln ݎ ሻሿ ⋅ ߜ ଶ ሺ7ሻ In order to improve numerical performance, this computation of ߚ is done for a number of positions along the crack, and the average of these is used together with Eq. (1) for the final computation of ܭ ூ and ܭ ூூ: ۖۖە ۔ۖۖ ܭ ۓ ூ ൌ ඩ ܪܩ 1 1 ߚ ଶ ܭ ூூ ൌඨ ܪܩ 1 ߚ ଶ ሺ8ሻ
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