Issue 49

B. El-Hadi et alii, Frattura ed Integrità Strutturale, 49 (2019) 547-556; DOI: 10.3221/IGF-ESIS.49.51 551 0 ij ij ij w d      (5) where, σ ij and ε ij are the stress and strain tensors, respectively. The traction is a stress vector normal to the contour. To evaluate these integrals, ABAQUS defines the domain in terms of rings of elements surrounding the crack tip. Figure 4 : Definition of the J-integral: a contour integral along the path Γ [y]. The Von-Mises stress used in the analysis of stress distribution along the crack front can be written in terms of stress components as [30]:         2 2 2 2 2 2 6 2 xx yy yy zz zz xx xy yz zx VM                   (6) where, xx  , yy  and zz  are the normal stresses according to x, y and z direction respectively and xy  , yz  and zx  are shear stresses in the yz, xz and xy planes respectively (Fig. 5). Figure 5: Stresses on a cubical element in equilibrium V ALIDATION OF THE MODEL he validation of the present model is presented in fig.6.a and 6.b, where a comparison with the results of Hossieni & all [21] is made. The figures show a comparison of the fatigue life of thin and thick panels respectively. Moreover, it can be seen from the figures that present results are in good agreement with the literature. Figure gives the fatigue life of plate after repair. T