Numerical and analytical study of the stress intensity factor in a mixed mode of isotropic fracture with a functionally graduated material

This study aims to present a finite element method for fractures analysis in a mixed mode of Functionally Graded Materials (FGM) in isotropic, under mechanical and thermal loading conditions. In this paper, the modeling accomplishes in a hull containing an inclined crack, provided by a fine mesh around these crack points due to the singularity elements. The stress intensity factors SIFs of modes I, II are determined by applying the two techniques: displacement extrapolation technique (DET), displacement Correlation technique (DCT) and J-integral method. We had used the ANSYS Parametric Design Language to prove the evolution. three numerical examples are presented to evaluate the accuracy of SIFs calculated by the proposed method. Comparisons have been made between the SIFs predicted by the DET, DCT, and the available reference solutions in the current literature. The results provided illustrate the influences of the inclination angle of the cracks on the transient behavior of the stress intensity factors in mixed mode. The numerical evaluation of this factor is determined using the Numerical code.