Abstract: The elbow is an important component in nuclear piping system,and also is the location where crack easily occurrs.To ensure the structural integrity of the nuclear piping system,a fracture mechanics analysis for the cracked elbows will be necessarily performed.In this paper,the 3-D elastic-plastic fracture mechanics methodology is used to study the elbows with a through-wall circumferential crack by using of ABAQUS software,and some numerical results for J-integral are obtained.The calculated results show that the influence of bending radius on J-integral is not associated with locations of the cracks.It is,however,intimate to sizes of the cracks.The effects on the J-integral for elbows with small size of cracks are insignificant.As to the J-integral for elbows with large size of cracks,the value of the J-integral is reduced as the R_b/R ratio of bending radii increases.In the case that the end rotating angle is kept unchanged,the relation between R/t ratio and J-integral is approximately linear,i.e.,a linear interpolation can be used.