Linear and non-linear analyses for semi-elliptical surface cracks in pipes under bending

In this paper, the J integral was calculated for semi-elliptical surface cracks in pipes under bending using three-dimensional finite element analysis. The computations were performed for elastic and elastic-plastic behaviours. For the elastic case, the numerical results allowed the extrapolation of shape functions for analytical determination of the J integral. The results are in a good agreement with those in the literature if the ratio between the radius and the thickness of the pipe (R/t) is from 1 to 10. The analysis was extended to values of the ratio R/t higher than 10. For the elastic-plastic, the numerical results are in good agreement with the analytical solution found in the literature for thick pipes (R/t ≥ 10). The effect of the ratio R/t becomes sensible when the ratio of the applied moment to the moment of reference (M/Mor) exceeds 0.9.