13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- 0 z ij ij J T Tij Q (θ=0º and r=2J/σ0) (17) Combining Eq.(9), the relationship between QTij and Qij is 0 z ij HRR ij J T Tij Q Q (18) The comparisons of the three-parameter solution J–QT–Tz with the solutions of J-Q and HRR are shown in Fig.5. It is shown that the three-parameter approach J–QT–Tz can describe the 3D stress fields effectively. 0 5 10 15 2 3 4 5 (a) n=13 a/c=0.5 =47.970 FE J-Q HRR J-QT-Tz r/(J/ ) m/ 0 0 2 4 6 8 10 0 1 2 3 4 (b) e/ 0 r/(J/ ) n=3, a/c=0.5 =8.330 =53.630 FE FE J-Q J-Q J-QT-Tz J-QT-Tz 0 2 4 6 8 10 1.5 2.0 2.5 3.0 3.5 4.0 (c) n=13 a/c=0.5 FE J-Q HRR J-QT-Tz r/(J/ ) m/ 0 Fig.5 The radial distributions of the stress components. (a) Mean stress for a semi-elliptical surface crack, (b) Von Mises equivalent stress σe for a quarter elliptical corner crack, (c) Mean stress for an embedded elliptical crack.
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