Issue34

Y. Sumi, Frattura ed Integrità Strutturale, 34 (2015) 42-58; DOI: 10.3221/IGF-ESIS.34.04 46 1/2 II II II I I I I I 21 3/2 I 11 22 II 22 II 12 21 3 2 3 2 2 2 4 2 4 4 1 1 ( ). 2 2 b K k k k T h b T k k k k k k k k k k k h O h                                                       (16) C RACK PATH CRITERIA aving obtained the stress intensity factors of a slightly kinked and curved crack, investigations are made for possible crack paths along which fracture takes place. Several aspects should be taken into account, such as the stress state prior to crack extension, geometrical continuity of a crack path, and the change of energy along different crack paths. The stress field ahead of a crack tip has been obtained for Mode-I and Mode-II, respectively, and the corresponding hoop stress component of is expressed by 3 1 3 3 3 3 I II cos cos sin sin . 4 2 4 2 4 2 4 2 2 2 k k r r                         (17) The solution of a straight kink of a finite kink angle was obtained by Bilby and Cardew [20], Bilby et al . [21], Hayashi and Nemat-Nasser [22], Leblond [23], and Amestoy and Leblond [10], where the analytical expression of the stress intensity factors ahead of the kinked tip was obtained by Amestoy and Leblond [10] in the following form:       I 11 I 12 II , K F k F k      (18)       II 21 I 22 II , K F k F k      (19) where k I and k II are the stress intensity factors at the original crack tip, and K I and K II are those at the extended crack tip, respectively. F pq ( p , q =1,2) which are functions of the kink angle  , are given by   2 4 6 8 11 2 4 2 3 1 5 1 11 119 1 ( ), 8 128 9 72 15360 F O                             (20)   3 5 7 12 2 4 2 3 10 1 2 133 59 ( ), 2 3 16 180 1280 F O                              (21)   3 5 7 21 2 4 2 1 4 1 2 13 59 ( ), 2 3 48 3 30 3840 F O                             (22)   2 4 6 8 22 2 4 2 6 4 2 4 3 8 29 5 32 4 1159 119 1 ( ). 8 3 18 128 15 9 7200 15360 F O                                          (23) Using these equations, the energy release rate along the kink can be calculated by   2 2 I II 1 , 8 G K K      (24) in which   is a function of Poisson’s ratio and  is the shear modulus. The crack path criterion based on the stress distribution prior to crack extension was proposed by Erdogan and Sih [11], where they assumed that a crack would propagate in the direction normal to the maximum hoop stress. By differentiating H