Abstract: In this paper,the constitutive equation of isotropic plate with variable thickness is derived under straight normal assumption and it is equivalent to that of anisotropic material,Then,by introducing free energy and entropy function and all of basis equations of solid mechanics, a path-independent generalized .J-integral is derived.Finally, this generalized J-integral is used to calculate the stress intensity factor kI of a turbine disk by means of finite element method and satisfactory results are obtained.