Issue 47

V. Rizov, Frattura ed Integrità Strutturale, (2047) 468-481; DOI: 10.3221/IGF-ESIS.47.37 477 i xRi R p   (43) 0 yRi p  (44) 2 R ds dy   (45) cos 1 R   (46) 2 2 R u z x     (47) Formula (16) is applied to calculate the stress, i R  , in (43). For this purpose, 1 i  , 2 i  , 3 i  , 4 i  , 5 i  , 6 i  , 1 y and 1 z are replaced with 1 Ri  , 2 Ri  , 3 Ri  , 4 Ri  , 5 Ri  , 6 Ri  , 2 y and 2 z , respectively. The average value of the J -integral along the delamination crack front is written as 2 1 2 1 h av h J J dz h    (48) By substituting of (33), (34) and (42) in (48), one arrives at 1 1 1 2 1 2 2 0 1 2 2 0 1 2 2 cos cos i L i i i i i h y i n av L xi yi i h y h y i n R R xRi yRi R i h R R y u v J u p p ds h x x u v u p p ds x x                                                              (49) where 0 i L u , 0 i R u , xi p and xRi p are obtained by (16), (19), (20), (23), (25) – (28), (31), (36), (37) and (43) at 1 x a  . The integration in (49) should be carried-out by the MatLab computer program. The J -integral value obtained by (49) matches exactly the strain energy release rate determined by (32). This fact is a verification of the delamination fracture analysis developed in the present paper. It should be mentioned that the delamination fracture is analyzed also by keeping more than six members in the in series of Taylor (15). The results obtained are very close to these derived by keeping six members (the difference is less than 2 %). P ARAMETRIC STUDY ffects of material inhomogeneity in width and length directions, crack location along the beam width, non-linear mechanical behavior of the material and crack length on the delamination fracture in the multilayered four-point bending beam are investigated by applying the solution to the strain energy release rate (32). The results obtained are presented in non-dimensional form by using the formula   1 / N g G G E b  . Two three-layered four-point bending beam configurations are considered in order to evaluate the influence of the delamination crack location along the beam width on the fracture behavior (Fig. 3). A beam configuration with a delamination crack located between layers 2 and 3 is shown in Fig. 3a. A beam with a delamination crack between layers 1 and 2 is also considered (Fig. 3b). The width of each layer is t . It is assumed that 0.004 t  m, 0.016 h  m, 1 0.100 l  m, 2 0.150 l  m and 15 F  N. E