The J-integral solutions for cracked pipes are important in crack growth calculation and failure evaluation based on the elastic-plastic fracture mechanics. One of the most important crack types in structural integrity assessment for nuclear piping systems is circumferential semi-elliptical surface crack on the inside of the pipes. Although several J-integral solutions have been provided, no solutions were developed at both the deepest and the surface points of circumferential semi-elliptical surface cracks in pipes. In this study, with backgrounds described above, the J-integral solutions of circumferential semi-elliptical surface cracks on the inside of the pipe were developed by numerical finite element analyses. Three dimensional elastic-plastic analyses were performed considering different material properties, pipe sizes, crack dimensions and, especially, combined loading condition of internal pressure and bending moment which is a typical loading condition for nuclear piping systems. The J values at both the deepest and the surface points were extracted from finite element analysis results. Moreover, in order to benefit users in practical applications, a pair of convenient J-integral estimation equations were developed based on the calculated J values at the deepest and the surface points. Finally, the accuracy and applicability of the convenient equations were confirmed by comparing with the provided stress intensity factor solutions in elastic region and with finite element analysis results in elastic-plastic region.

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