applied fracture mechanics

370Applied Fracture MechanicsIinJi , ,012 / / 1.5 4A A a w A a w0 1 2 F F n 221 a/w2 3 2 3 2 3 A 0.79 0.07 b/ a 0.04 b/ a 0.011 b/aA 1.74 2.84 b/ a 1.44 b/ a 0.206 b/aA 6.02 2.19 b/ a 3.26 b/ a 0.828 b/aand analytical single edge crack SIF reference by (Brown & Strawley, 1966),KKI,refI,ref 0 0I , ref , BS 2 3 4 a 1.12 0.23 a/ W 10.6 a/ W 21.7 a/ W 30.4 a/W a f(15)(16)4.1. Crack interaction factor I , in,Dcomparison with analytical data, ,The mode I fracture of the elastic interaction factorsI , in, D( I , in, D, ct1 ,I , in, D, ct2)I in Ji for crackinterval ratio b/ a 1.5 3.0 and a/ W 0.05 0.5 are shown in Fig. 3-6. Overall, it can beseen that the interaction factor varies with the different a/W values where the crackinteraction factor increases as the a/W increases and vice versa. The point of intersectionalso observed occurred for all the b/a values. For example, the plot of ( , ) against a/W at b/ a 3.0 are illustrated in Fig. 3.I , in, D I , in, D, ct1 I , in, D, ct2The I , in,Dprediction line is compared with the predicted result of single edge crackfI , ref , BS. A general good agreement can be observed with a minimum difference 0.6% ata/ W 0.1 and maximum difference 5.39 % difference a/ W 0.15 . In comparison, thepresent I , in,Dhas demonstrated more accurate prediction compared with I , in,Jiresults.For example, in reference to f I , ref , BS, at a/ W 0.5 , the present prediction I , in,Dis indifference of I , in, D, ct10.85 % and I , in, D, ct20.4%, while I , in,Jiis at 2.15% difference. In termsof the CIL point, the closer the crack interaction to fI , ref , BSof single crack, a more accurateCIL prediction can be achieved. It is noted that the I , in,Jianalytical expression wasformulated using the numerical results of J-integral analysis. The formulation is unable tocalculate the crack interaction factor for both crack tips and become the weakness of I , in,Ji.Therefore, the present work of DEM has improved the existing J-integral analysis byimproving the accuracy of CIL to predict fracture due to crack interaction.Theoretically, the study of intersection point is most significant in identification of crackinteraction limit (CIL) and crack unification limit (CUL). The intersection point of two cracks with single crack fI , ref , BSjustifies the realization of CIL at higher a/W and CUL atI , in,D