13th International Conference on Fracture June 16–21, 2013, Beijing, China 4. Effects of confining pressure on pure mode II crack loading condition According to the definition of the pure mode I loading and pure mode II loading, the pure mode II crack can be determined from the conditions that 0= ΙK , 0≠ ΙΙ K . By letting 0= ΙK in Eq.(14), we get 0 (1 ) 2 2( 1) 1 1 1 11 = − + − = ∑ i i n i i A f t f α （16） It’s not easy to directly achieve the closed-form solutions from Eq. (16), but the solution is ( , )α θ θ t = which means that the pure mode II loading angle is the function of αand t. According to Eq. (16), we develop a small program to compute the critical loading angle cθ for various α and different coefficientst , the results are listed in Table 1. Tab.1 the critical loading angles cθ(°) for pure mode II crack with different confining pressures cθ(°) α t=0[2] t=0.1 t=0.3 t=0.5 t=0.7 t=1.0 t>1 0 30.00 28.32 24.73 20.70 15.89 0 No real solution 0.1 29.67 28.00 24.43 20.44 15.67 0 No real solution 0.2 28.72 27.06 23.56 19.66 15.05 0 No real solution 0.3 27.23 25.60 22.20 18.45 14.07 0 No real solution 0.4 25.27 23.70 20.43 16.89 12.81 0 No real solution 0.5 22.93 21.40 18.30 15.02 11.31 0 No real solution 0.6 20.18 18.72 15.82 12.84 9.58 0 No real solution 0.7 16.96 15.57 12.92 10.33 7.60 0 No real solution 0.8 13.07 11.79 9.49 7.41 5.35 0 No real solution 0.9 8.17 7.05 5.32 3.99 2.81 0 No real solution From Table 1 we can know that the confining pressure significantly influences the loading condition of pure mode II crack. As the confining pressure increases, the critical loading angle for pure mode II crack decreases gradually to 0 degree. 5. Discussion 5.1 Mode I fracture toughness under confining pressure According to the experiment results in the literature [8], the fracture toughness increases with the increasing confining pressure (Fig.6). Al-Shayea et al.[8] used the five-term approximation formula proposed by Atkinson et al.[1] to calculate the mode I stress intensity factors, which is equivalently letting n=5 in Eq.(11). They ignored the effects of confining pressure on stress intensity factors; therefore, the failure load max P increased with the increasing confining pressure and thus the test values of the fracture toughness increased with the confining pressure. However, according to Eq.(14) presented in this paper, mode I stress intensity factors decrease with the increasing confining pressure. Under confining pressure loading condition, though the test values of the failure load increase, but part of the load has to offset the‘negative effect’caused by confining pressure on IK . So according to Eq.(14), though the failure load show an increase with the increasing confining pressure, the fracture toughness may be unchanged actually.
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