Stress Intensity Factor Determination in Functionally Graded Materials, Considering Continuously Varying of Material Properties

In this paper, the plates made of functionally graded material (FGM) with and without a crack are numerically simulated, employing the finite element method (FEM). The material property variations are defined to be fully continuous; therefore, the elements can be as small as required. For this purpose, variations of the material properties are applied in both the integration points and in the nodes by implementing a subroutine in the ABAQUS software and hence, the stress field in the singular points such as crack tip is accurately achieved. First, the stresses in the plate without a crack are numerically determined and the accuracy of FGM behavior is validated. Then, the J-integral is investigated and the stress intensity factor (SIF) of the plate with a crack is calculated, using the strain energy release rate (SERR) and the J -integral. In the following, dependency of the J-integral on the path is studied and the results are compared with the contour independent J-integral. Finally, it is shown that if the selected path limits toward zero, the results of the J-integral, the SERR, and the contour independent J-integral are all the same. This is due to considering the continuously varying of material properties and the effect of fining the mesh at the crack tip.