Issue 39

S. K. Kudari et alii, Frattura ed Integrità Strutturale, 39 (2017) 216-225; DOI: 10.3221/IGF-ESIS.39.21 223 The variation of T 33-max /  against B/W for various a/W is shown in Fig.9. This figure indicates that, T 33 strongly depend on B/W. It is observed that the magnitude of T 33 is negative for all cases that were considered in this analysis, and approached to zero as B/W increased to 1. For B/W=0.5, ASTM requirement for K IC test specimen [15], it is seen that T 33 /  is negative indicating loss of out-of-plane constraint. T 33 also showed dependence on a/W, for B/W<0.7, T 33 is found to be maximum for thinner specimens (B/W=0.1) with higher a/W =0.7. As T 33 strongly depends on the specimen thickness, it is not possible to get a simple relation between T 33 and specimen geometry as obtained in case of K I and T 11 . To obtain expressions between T 33 , specimen geometry and the applied load, the results in Fig.9 are given a polynomial fit to suit the 3D FEA results. In this exercise, it is found that the 5 th order polynomial fits the data with least error. A typical equation for estimation of T 33–max is given by Eq. (13). The equations for the 3D geometric factors (C 3 ) to compute T 33-max for various a/W obtained by fitting 5 th order polynomial are tabulated in Tab.3. T C 33-max 3   (13) The computed values of C 3 for various a/W are given in Tab.4. The maximum percentage of error in the use of equations given in Tab.3 for various B, a/W and  is found to be < 7.8%. Table 3 : Polynomial equations for T 33 . a/W B/W 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.45 -1.7789 -1.1638 -0.8782 -0.7333 -0.6288 -0.5279 -0.4316 -0.3537 -0.2952 -0.2187 0.50 -1.9659 -1.2962 -0.9818 -0.8167 -0.6934 -0.5739 -0.4618 -0.3735 -0.3097 -0.2271 0.55 -2.3066 -1.5136 -1.1231 -0.9112 -0.7573 -0.6148 -0.4825 -0.3758 -0.2971 -0.2078 0.60 -2.6057 -1.6969 -1.2512 -1.0063 -0.8239 -0.6545 -0.5012 -0.3831 -0.3003 -0.1970 0.65 -3.2337 -2.0548 -1.4816 -1.1664 -0.9288 -0.7066 -0.5075 -0.3600 -0.2647 -0.1457 0.70 -3.7325 -2.3393 -1.6366 -1.2367 -0.9384 -0.6721 -0.4449 -0.2855 -0.1895 -0.0644 Table 4 : Values of C 3 computed from formulations given in Tab.3. a/W Polynomial Equations 0.45 T B B B B B W W W W W 2 3 4 5 33 max 3.02667 16.98748 53.07517 86.44814 68.70629 21.15385                                        0.50 T B B B B B W W W W W 2 3 4 5 33 max 3.32333 18.49597 58.0134 95.41084 76.51515 23.71795                                        0.55 T B B B B B W W W W W 2 3 4 5 33 max 3.858 20.88005 62.97348 100.77273 79.1317 24.10256                                        0.60 T B B B B B W W W W W 2 3 4 5 33 max 4.40067 24.26372 74.31294 121.11772 96.8648 30                                        0.65 T B B B B B W W W W W 2 3 4 5 33 max 5.582 31.84602 98.58275 162.16142 130.62937 40.64103                                        0.70 T B B B B B W W W W W 2 3 4 5 33 max 6.44533 36.53654 110.79021 181.22902 146.36364 45.76923                                       