Issue 48

A. S. Bouchikhi et al., Frattura ed Integrità Strutturale, 48 (2019) 174-192; DOI: 10.3221/IGF-ESIS.48.20 180 J-integral % error becomes less than 2%. As the refinement increases, the error decreases and the result converges to the exact solution. This is advantageous especially for modeling the crack propagation through non-homogenous materials because this eliminates the need of enrichment functions. 1000 2000 3000 4000 5000 6000 7000 8000 -2,5 -2,0 -1,5 -1,0 -0,5 0,0 J-Integral % error Reffinement FEM-Reffinement Figure 7 : % error in J-integral with refinement in the region around the crack tip, using the proposed method. R ESULTS AND D ISCUSSIONS n this study the numerical calculation is based on FE using ABAQUS software. The direction of variation of the Young's modulus of the FGM is according to r-FGM [17, 18]. Effect of crack-crack interaction according to their position on J-Integral In this Section, we studied the influence of the interaction between two cracks AB et CD according to their position on the J-Integral. Figure 8 : Interaction between two cracks for different positions. Five different geometric configurations between two cracks AB and CD are studied, their interaction effects are analyzed and compared. Fig. 8 shows the details and designation of the geometrical shapes under consideration (a) Two cracks (AB) and (CD) are parallel (it is perpendicular to the applied load), and the transversal interdistance L between is assumed variable of these two cracks. (b) Two cracks (AB) and (CD) are parallel (it is perpendicular to the applied load), and the longitudinal interdistance d between is assumed variable of these two cracks. I