Issue 41

V. Rizov, Frattura ed Integrità Strutturale, 41 (2017) 491-503; DOI: 10.3221/IGF-ESIS.41.61 499 where 1 y varies in the interval   / 2, / 2 b b  . The J -integral solution in segment, 2  , of the integration contour (Fig. 1) can be determined by (30). For this purpose, r , 1 1 n z , 1  , 2  and 1  have to be replaced with 0 , 2 2 n z , 1 u  , 2 u  and 2  , respectively. Besides, the sign of (30) must be set to „minus” because the integration contour is directed upwards in segment, 2  . The J -integral final solution is found by substituting of 1 J  and 2 J  in (25)         2 2 1 1 1 0 1 1 2 1 1 2 2 2 4 1 1 1 1 m m m u u u u u B y B B r m J m m b m h m                               1 2 2 1 1 2 1 1 2 1 2 2 2 1 2 1 n m m m m u u u u u u z B r m m h                      3 3 2 2 1 2 1 1 2 1 2 2 2 1 3 2 f q f q f q f q u u u u u u u u n q q q q u u u u u u u u u z B q f q f q h                                     2 1 1 1 2 f q f q u u u u n q q u u u z f q                     (31)       2 1 1 1 0 1 1 2 1 2 2 4 1 1 1 m m m u u u u u u B y B m m m b m                         3 3 2 2 2 2 2 1 2 1 2 2 2 1 3 2 f q f q f q f q u u u u u u u u n q q q q u u u u u u u u u u u u u z B q f q f q h                                     2 2 2 1 2 f q f q u u u u n q q u u u u u z f q                     Formula (31) describes the distribution of the J -integral value along the crack front. The average value of the J -integral along the crack front is written as 2 1 2 1 b AV b J J dy b    (32) It should be noted that the J -integral solution derived by substituting of (31) in (32) is exact match of the strain energy release rate (22). This fact verifies the fracture analysis developed in the present paper. R ESULTS he distribution of J -integral value along the crack front is analyzed. For this purpose, calculations are performed by using formula (31). It is assumed that b =0.020 m, h =0.004 m, m =0.7, f =7, q =10, 1.7 u m  , 17 u f  , 10 u q  and 20 y M  Nm. The J -integral value is presented in non-dimensional form by using the formula,   0 / N J J B b  . The material gradient along the beam width is characterized by 1 0 / B B ratio. Fig. 5 shows the distribution of the J -integral value in non- T