Limit pressures of 90° elbows with circumferential surface cracks

This paper provides approximate limit pressure solutions for circumferential cracked elbows, resulting from small strain finite element limit analyses using elastic-perfectly plastic materials. Circumferential through-wall and constant-depth surface cracks of which the circumferential lengths are limited to 50% of the circumference are considered. Two locations along the longitudinal direction are considered; one in the centre of the elbow, and the other in the junction between the elbow and the attached straight pipe. Along the circumference, either extrados or intrados cracks are considered. It is found that limit pressures of circumferential cracked elbows are not affected by the presence of the circumferential surface crack, unless it is sufficiently deep and long. Moreover, normalized limit pressures with respect to un-cracked limit pressures decrease almost linearly with increasing the relative crack depth and length. Based on finite element results, approximate closed-form solutions for limit pressures are proposed.