13th International Conference on Fracture June 16–21, 2013, Beijing, China -12- Table 7. FEA results for DECP specimens under λ=1.0 a/W 0.1 0.3 σ/σ0 n=3 n=4 n=5 n=7 n=10 σ/σ0 n=3 n=4 n=5 n=7 n=10 0.150 0.86925 0.51533 0.35529 0.22685 0.16266 0.150 0.87254 0.51647 0.35567 0.22672 0.16228 0.250 0.84806 0.49772 0.34026 0.21168 0.14827 0.250 0.84930 0.49767 0.33986 0.21364 0.15104 0.500 0.78679 0.44669 0.29733 0.17643 0.11728 0.500 0.78991 0.44755 0.29760 0.17940 0.12105 0.650 0.74962 0.41600 0.27248 0.15509 0.09888 0.650 0.75172 0.41771 0.27370 0.15879 0.10214 0.750 0.72289 0.39416 0.25184 0.14370 0.08746 0.750 0.72614 0.39540 0.25541 0.14475 0.09047 0.900 0.68110 0.35892 0.22231 0.12096 0.06931 0.900 0.68443 0.36244 0.22572 0.12207 0.07298 1.000 0.65233 0.33357 0.20057 0.10054 0.05484 1.000 0.65589 0.33742 0.20404 0.10436 0.05877 1.100 0.62156 0.30469 0.17667 0.07855 1.100 0.62717 0.31193 0.18046 0.08248 1.150 0.60835 0.29324 0.16211 1.150 0.61160 0.29698 0.16595 1.200 0.59283 0.27797 0.14712 1.200 0.59593 0.28166 0.15098 1.250 0.57732 0.26237 0.13066 1.250 0.58020 0.26597 0.13868 1.300 0.56184 0.24644 1.300 0.56443 0.24989 0.12144 1.350 0.54324 0.23021 1.350 0.54865 0.23344 1.400 0.52774 0.21371 1.400 0.53291 0.21662 1.450 0.51192 0.19698 1.450 0.51725 1.500 0.49678 1.500 0.49766 1.800 0.40071 1.600 0.46654 1.900 0.36851 1.700 0.43085 1.800 0.39539 a/W 0.5 0.7 σ/σ0 n=3 n=4 n=5 n=7 n=10 σ/σ0 n=3 n=4 n=5 n=7 n=10 0.150 0.87424 0.51821 0.35734 0.22834 0.16451 0.100 0.88853 0.52789 0.36562 0.23577 0.17097 0.250 0.85134 0.49955 0.34149 0.21579 0.15266 0.150 0.87517 0.51917 0.35853 0.23019 0.16620 0.350 0.82888 0.48056 0.32587 0.20241 0.14183 0.250 0.85440 0.49999 0.34298 0.21630 0.15487 0.500 0.79558 0.45179 0.30169 0.18284 0.12336 0.350 0.83843 0.48690 0.32904 0.20342 0.14223 0.650 0.76040 0.42457 0.27963 0.16356 0.10690 0.450 0.82472 0.47563 0.31904 0.19605 0.13322 0.750 0.73700 0.40661 0.26290 0.15092 0.09652 0.550 0.81355 0.47025 0.31567 0.19398 0.13129 0.850 0.71251 0.38709 0.24703 0.13889 0.08753 0.650 0.80264 0.46755 0.31802 0.19668 0.13503 0.950 0.68765 0.36495 0.23096 0.12676 0.07590 0.750 0.79021 0.46407 0.31850 0.20183 0.14366 1.000 0.67356 0.35483 0.21976 0.12006 0.07036 0.850 0.77393 0.45752 0.31708 0.20500 0.14922 1.050 0.65937 0.34459 0.21074 0.10979 0.860 0.77172 0.45652 0.31663 0.20504 0.15020 1.100 0.64599 0.33115 0.20129 0.10092 0.870 0.76927 0.45543 0.31606 0.20495 0.15023 1.150 0.63102 0.32000 0.18807 0.09070 0.880 0.76820 0.45447 0.31541 0.20483 0.15019 1.200 0.61733 0.30549 0.17686 0.07515 0.890 0.76556 0.45323 0.31467 0.20457 0.15003 1.300 0.58549 0.27751 0.14798 0.900 0.76281 0.45187 0.31387 0.20437 0.15008 1.400 0.55166 0.24273 0.950 0.75103 0.44386 0.30871 0.19984 0.14562 1.500 0.51534 0.20277 1.000 0.73702 0.43410 0.29979 0.19153 0.13142 1.600 0.47414 1.050 0.72000 0.42111 0.28561 0.17653 1.700 0.43161 1.100 0.70436 0.40281 Through analyzing numerical solutions of constraint parameter A, several dependencies (mainly on the constraint effect) for 2D cracked models under biaxial loading are founded. They are: (1) generally, the maximum external loading ratio (σ/σ0) for which a valid solution can be obtained increases with decreasing hardening coefficient n; (2) in general, the constraint level in crack-tip fields increases with an increase of biaxial loading ratio, λ; (3) the constraint level for materials with smaller values of hardening exponent n rises more with increased biaxial loading ratio; (4) the constraint level for shallow cracks increases more than for deep cracks with an increase of biaxial loading ratio; (5) compared with SECP and CCP specimens, a higher biaxial loading ratio increases the constraint level of DECP more. All numerical solutions for constraint parameter A under biaxial loading obtained in this work can be utilized to predict corresponding values for other two commonly-used constraint parameters A2 and Q by the relationships between A and A2, Q presented in an previous paper of authors [13].
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