Issue34

Y. Sumi, Frattura ed Integrità Strutturale, 34 (2015) 42-58; DOI: 10.3221/IGF-ESIS.34.04 48   2 4 6 12 2 4 2 3 10 3 10 133 59 ' ( ). 2 16 36 256 F O                             (33) In order to examine the similarity of the criteria given by Eqs. (31) and (26), we again calculate the determinant D 2 of the coefficients of k I and k II , which is given by         5 7 2 21 12 11 21 2 2 ' ' ( ). 45 D F F F F O            (34) It is interesting to note that these two criteria are identical up to the 4th order with respect to the kink angle  . Also, from the above discussions, the direction which maximizes the Mode-I stress intensity factor is another distinct criterion. In Fig. 3, one may compare the difference or similarity of kink angles predicted by these criteria. It is rather difficult to numerically distinguish the difference of the local symmetry and maximum energy release rate criteria. We shall discuss the local symmetry criterion in the following discussions, because it may lead to slightly kinked and curved crack propagation in a relatively simple way by using the perturbation solution. Figure 3 : Comparison of the kink angles under mixed mode conditions [16]. C RACK PATH PREDICTION AND ITS STABILITY Crack Path Prediction Based on the Local Symmetry Criterion ince a smooth path can be obtained by the local symmetry criterion and the equivalence of the maximum energy release rate may be expected within a small kink angle, discussions are made based on this criterion. We shall consider the prediction of a kinked and curved crack path based on the first order perturbation solution (15) and (16) at an arbitrarily extended crack tip from a straight crack, so that the crack path is obtained by substituting Eq. (16) into the local symmetry criterion (26), and the shape parameters of the crack path are obtained as [6-8] II I 2 , k k    (35) I 8 2 , 3 T k     (36) S