13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- not only appear in the cases of uniaxial loading and external loading ratio σ/σL (σL, limit load of specimen) but also in the cases of biaxial loading and loading normalization, σ/σ0, see Figure 4-7 for example. Table 4. FEA results for CCP specimen under λ=0.5 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 0.500 1.03293 0.64948 0.46887 0.32352 0.25390 0.250 0.98134 0.60644 0.43267 0.29277 0.22469 0.700 1.07906 0.68806 0.50129 0.34936 0.27751 0.500 1.05796 0.66917 0.48450 0.33539 0.26464 0.900 1.11904 0.71974 0.52744 0.36991 0.29557 0.750 1.12909 0.73037 0.53563 0.37581 0.30014 1.000 1.13527 0.73370 0.53894 0.37836 0.30237 0.900 1.16595 0.76170 0.56335 0.39798 0.31924 1.200 1.15529 0.75361 0.55608 0.39210 0.31170 1.000 1.18836 0.77990 0.58012 0.41203 0.33108 1.500 1.16895 0.76686 0.56621 0.39975 0.31748 1.100 1.20084 0.79773 0.59419 0.42491 0.34168 1.800 1.16139 0.75712 0.56246 0.39239 0.31165 1.200 1.21286 0.80829 0.60522 0.43449 0.35199 2.000 1.13246 0.74272 0.54581 0.38135 0.30277 1.300 1.22667 0.81872 0.61313 0.44234 0.36159 2.100 1.11699 0.73432 0.53681 0.37501 0.29808 1.400 1.22663 0.82549 0.62225 0.44924 0.37116 2.200 1.09825 0.71748 0.52619 0.36777 0.29321 1.450 1.22873 0.82394 0.62381 0.45351 0.37509 2.300 1.08745 0.70466 0.51373 0.35901 0.28309 1.500 1.22943 0.82773 0.62419 0.45429 0.37893 2.400 1.06267 0.68221 0.49896 0.34764 0.27633 1.550 1.22865 0.83059 0.62359 0.45407 0.37497 2.450 1.04035 0.67860 0.49075 0.34698 1.600 1.22625 0.82498 0.62134 0.45371 0.38314 2.500 1.03254 0.66464 0.48187 0.33447 1.650 1.22214 0.82517 0.62323 0.45807 0.39281 2.600 1.01409 0.64474 0.46421 1.700 1.21616 0.82321 0.62016 0.44720 0.39826 2.700 0.97462 0.62172 1.750 1.20833 0.81313 0.61771 0.46113 0.40449 1.800 1.21234 0.81012 0.59436 0.45637 0.41530 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 0.100 0.94657 0.57838 0.40893 0.27252 0.20548 0.050 0.94003 0.57410 0.40565 0.27004 0.20336 0.150 0.96767 0.59526 0.42335 0.28498 0.21745 0.100 0.97886 0.60394 0.43006 0.28991 0.22255 0.250 1.01066 0.63010 0.45229 0.30762 0.23933 0.150 1.01980 0.63643 0.45724 0.31137 0.24264 0.350 1.05770 0.66699 0.48260 0.33321 0.26171 0.250 1.11106 0.71061 0.51835 0.36082 0.28602 0.450 1.10582 0.70680 0.51559 0.35931 0.28520 0.350 1.19965 0.79269 0.59128 0.42146 0.34039 0.550 1.15103 0.74722 0.55041 0.38757 0.31005 0.400 1.24116 0.83100 0.62637 0.45712 0.37568 0.650 1.19119 0.78594 0.58557 0.41778 0.33689 0.450 1.28136 0.86873 0.66098 0.49110 0.41489 0.750 1.23122 0.82265 0.61827 0.44734 0.36587 0.460 1.28455 0.87745 0.66976 0.49773 0.42362 0.850 1.25716 0.85287 0.64612 0.47604 0.39809 0.470 1.29303 0.88141 0.67470 0.50429 0.43117 0.900 1.27272 0.86516 0.65953 0.48757 0.41343 0.480 1.30103 0.89001 0.68317 0.51077 0.43860 0.950 1.28575 0.87540 0.66842 0.49850 0.42643 0.490 1.30828 0.89773 0.68769 0.51719 0.44600 1.000 1.29677 0.88340 0.67961 0.50783 0.44074 0.500 1.31593 0.90135 0.69194 0.52353 0.45333 1.050 1.30484 0.89560 0.68895 0.51551 0.45175 0.510 1.31719 0.90949 0.70028 0.52982 0.45925 1.100 1.31050 0.89834 0.69041 0.51172 0.46758 0.550 1.34438 0.93362 0.72286 0.55120 0.48569 1.150 1.31258 0.90536 0.69556 0.53219 0.48279 0.580 1.36147 0.94855 0.73659 0.56478 0.50540 1.200 1.32147 0.90225 0.70169 0.54275 0.600 1.37217 0.95601 0.74623 0.57506 0.50833 0.620 1.37384 0.96127 0.75475 0.58194 0.640 1.38217 0.97261 0.75650 0.57980 0.660 1.39806 0.98232 0.76824 0.59876 By analyzing the numerical solutions of parameter A for three cracked specimens (see Tables 2-7, Figures 4-11), several dependencies have been found. First, it is found that, for any specific specimen geometry (a/W) of some cracked body (SECP, CCP or DECP), generally the maximum external loading ratios (σ/σ0), which are determined by the criteria suggested by Chao and Zhu [20], increase with decreasing of hardening coefficient n. In addition, the effects of crack geometry, hardening exponent (n) and biaxial loading ratio (λ) on parameter A (constraint level) are also observed. For uniaxial loading cases (λ=0.0) investigated in a previous work of authors [13], it has been shown that A values gradually increase with external loading. The results in the current work show that, with smaller biaxial loading ratio (λ=0.5), the parameter A follows a general decreasing trend with increasing external loading for shallow crack geometries (e.g. a/W=0.1 for SECP and CCP, a/W=0.1, 0.3 for DECP). Decreased values for parameter A indicate the increasing constraint level. For the cases with bigger biaxial loading ratio (λ=1.0), a decreasing trend of parameter A appears not only for those shallowest cracks but also for cracks with larger depth and even fairly deep cracks (e.g. a/W=0.3 for SECP, 0.3, 0.5 for CCP, 0.5,
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