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The nuclear task in fracture mechanics is to determine the stress intensity factor. According to the crack mouth widening energy release rate based on the principle of virtual work and bending theory,respectively, i.e. J₂ integral theory is proposed to solve the stress intensity factor expression of D-shape cross section cracked pipe under tension and bending loads. The results show application of this method not only can give closed-form solution, but also extremely simple.Comparing the proposed method with the finite element method to show the feasibility of the proposed method.