Abstract: According to the Williams series displacement field， only considering the elastic modulus E as a function of coordinate， a new format of Williams element with generalized degrees of freedom for the thin plane fracture analysis in a functionally graded material plate is derived by changing the integration mode of the overall stiffness of the crack tip in the singular region. Combined with a inclined crack and an edge crack contained in a functionally graded material plate， the influence of the distribution form of the elastic modulus E， the crack inclination angle and the crack length on the stress intensity factor at the crack tip is analysed. The results show that the method can directly and efficiently solve the crack tip stress intensity factor of the functionally graded material with cracks. When the elastic modulus E changes monotonically and its gradient is parallel to or vertical to the load direction， the stress intensity factors of mode I or mode II at the two crack-tips of the central inclined crack are different， and the distribution of stress intensity factors with the crack inclination angle is not affected by the distribution form of elastic modulus E.

Key words: functionally graded material, stress intensity factor, Williams element with generalized degrees of freedom, elastic modulus, singular region