This study has been made to determine the performance of the (Ti-TiB) FGM plate to reduce the J-integral calculated for the crack tip emanating from the semicircular notch root in mode I and mixed mode, when the crack is propagated from the notch root. In this paper, 3D finite element method is applied to analyze the behavior of a crack emanating from semicircular notch root growing from the metal (Ti) and is oriented perpendicularly in direction of ceramic (TiB). The J-integral has been found for several combinations laws of FGM plates with respect to the variable combination of the crack length, the plate thickness, the notch radius, Young modulus of FGM plate constituents and the crack orientation. These parameters must be optimized in order to improve the best performances.