The investigation of multiple crack interactions in fracture mechanics is important to predict the safety and reliability of structures. This paper introduces a numerical investigation used to calculate the J-integral of the main crack behaviour emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) FGM plate subjected to tensile mechanical load. Young’s modulus of the functionally graded material plate varies along the specimen width (notch radius direction r-FGM) with exponential-law (E-FGM) function. Further, the Poisson’s ratio is taken as a constant in normal direction. For this purpose the variations of the material properties are applied at the integration points and at the nodes by implementing a subroutine USDFLD in the ABAQUS software. The variation of the J-integral according to the position, the length, and the angle of rotation of cracks is demonstrated. The variation of the J-integral according to the position, the length, and the angle of rotation of cracks are examined; also the effect of different parameters for double notch FGM plate is investigated as well as the effect of band of FGM within the ceramic plate to reduce J-integral. According to the numerical analysis, all parameters above played an important role in determining the J-integral.