13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- The research of Chao and Zhu [20] on 2D plane strain models shows that the size requirement for ductile fracture initiation under J-A2 dominant conditions is aσ0/J >6 for the shallow cracked cases or bσ0/J >11 for deep cracked cases, where a is the crack length and b is the remaining ligament. In the present finite element analyses (FEA), the highest load levels are those corresponding to the values mentioned above. In addition, Chao and Zhu [20] also argue that, for deep crack cases, a value of bσ0/J around 30 corresponds to fully plastic condition, while for shallow cracks, values of aσ0/J ≤ 50 already nearly correspond to the fully plastic deformation. Table 2. FEA results for SECP 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 0.250 0.91524 0.55153 0.38552 0.25194 0.18600 0.150 0.91848 0.55422 0.38785 0.25432 0.18828 0.500 0.92583 0.55861 0.39022 0.25514 0.18820 0.250 0.92787 0.56120 0.39339 0.25847 0.19307 0.750 0.93635 0.56870 0.39808 0.25894 0.18998 0.350 0.93984 0.57046 0.40079 0.26298 0.19567 0.900 0.93816 0.57312 0.40230 0.26189 0.19169 0.450 0.95082 0.58010 0.40830 0.26851 0.19989 1.000 0.93815 0.57465 0.40464 0.26473 0.19350 0.550 0.96266 0.59058 0.41728 0.27570 0.20481 1.100 0.93624 0.57543 0.40646 0.26701 0.19586 0.650 0.97216 0.60094 0.42667 0.28420 0.21255 1.200 0.93422 0.57461 0.40738 0.26909 0.19841 0.750 0.98224 0.61135 0.43656 0.29347 0.22260 1.300 0.92749 0.57367 0.40708 0.27057 0.20102 0.760 0.98243 0.61224 0.43751 0.29452 0.22376 1.400 0.92144 0.57114 0.40649 0.27139 0.20346 0.780 0.98498 0.61374 0.43951 0.29626 0.22521 1.450 0.91770 0.56776 0.40569 0.27165 0.20471 0.800 0.98738 0.61595 0.44135 0.29836 0.22766 1.500 0.91686 0.56569 0.40371 0.27184 0.20520 0.810 0.98750 0.61664 0.44223 0.29939 0.22884 1.600 0.90796 0.56079 0.40124 0.27086 0.20712 0.850 0.98972 0.62004 0.44594 0.30331 0.23291 1.700 0.89741 0.55511 0.39682 0.26981 0.20857 0.900 0.99387 0.62480 0.45027 0.30814 0.23877 1.800 0.89022 0.54923 0.39370 0.26909 0.21073 0.950 0.99752 0.62919 0.45497 0.31297 0.24481 1.900 0.88251 0.54524 0.39123 0.26969 1.000 1.00097 0.63260 0.45915 0.31797 0.25032 2.000 0.87144 0.54097 0.39000 0.27253 1.050 1.00410 0.63700 0.46394 0.32345 0.25702 2.100 0.86730 0.53830 0.39109 1.100 1.00960 0.64135 0.46831 0.32895 0.26489 2.200 0.85850 0.53831 0.39465 1.150 1.01256 0.64566 0.47320 0.33449 0.27227 2.300 0.85574 0.53960 0.40008 1.200 1.01744 0.64968 0.47739 0.34043 2.400 0.85089 0.54220 0.40819 1.250 1.02045 0.65409 0.48381 2.500 0.84605 0.54595 0.40777 1.300 1.02606 0.66051 1.400 1.03790 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 0.050 0.90776 0.54631 0.38146 0.24915 0.18447 0.010 0.89720 0.53809 0.37467 0.24350 0.17829 0.100 0.91152 0.54799 0.38246 0.25035 0.18470 0.020 0.89423 0.53474 0.37177 0.23876 0.17434 0.150 0.91955 0.55268 0.38576 0.25173 0.18561 0.030 0.89173 0.53033 0.36724 0.23706 0.17199 0.200 0.93053 0.56034 0.39127 0.25422 0.18691 0.040 0.89061 0.52866 0.36531 0.23293 0.16760 0.250 0.94523 0.57130 0.39853 0.25971 0.18961 0.050 0.89235 0.52783 0.36371 0.23065 0.16503 0.290 0.95976 0.58280 0.40750 0.26493 0.19437 0.060 0.89697 0.52928 0.36403 0.22991 0.16382 0.320 0.97212 0.59245 0.41527 0.27163 0.20003 0.070 0.90474 0.53483 0.36613 0.23019 0.16289 0.350 0.98591 0.60372 0.42555 0.28017 0.20751 0.080 0.91638 0.54304 0.37198 0.23524 0.16446 0.380 1.00133 0.61660 0.43649 0.29048 0.21678 0.085 0.92330 0.54792 0.37719 0.23715 0.16544 0.400 1.01265 0.62591 0.44562 0.29848 0.22604 0.090 0.93138 0.55575 0.38172 0.24035 0.16915 0.420 1.02430 0.63620 0.45449 0.30771 0.23951 0.095 0.94057 0.56281 0.38760 0.24638 0.17440 0.440 1.03745 0.64737 0.46606 0.32072 0.100 0.95116 0.57116 0.39635 0.25400 0.18140 0.450 1.04403 0.65423 0.47252 0.32716 0.105 0.96122 0.58068 0.40441 0.26322 0.19312 0.460 1.05195 0.66160 0.47764 0.33425 0.110 0.97422 0.59175 0.41412 0.27427 0.20781 0.470 1.05901 0.66752 0.48483 0.34231 0.115 0.98931 0.60421 0.42753 0.28745 0.480 1.06637 0.67394 0.49279 0.120 1.00308 0.61856 0.44058 0.490 1.07404 0.68244 0.50135 0.500 1.08353 0.69169 0.50789 0.510 1.09180 0.69890 0.51741 According to the above criteria, the external load ratios (σ/σ0) used here to determine numerical solutions for parameter A from FEA for the three specimens cover the deformation range from small-scale yielding (SSY) to large-scale yielding (LSY). For example, for SECP with a/W=0.7
RkJQdWJsaXNoZXIy MjM0NDE=