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In this article, a J-integral estimation scheme of circumferential through-wall cracked pipe welds under pure bending is introduced. Three-dimensional elasto-plastic finite element computations are carried out, as pipe materials usually have a yielding plateau. Compared with the solution of the finite element method, the results indicate that the LBB.ENG3 scheme is easy to use and can give a satisfactory and reasonable J-integral estimation solution. Finally, the effect of mismatching on the J-integral for pipe-welded joints is discussed in detail.