Limit load solutions for elbows with circumferential through-wall crack under the pressure-induced bending restraint effect

A typical pipe finite element model is made by assuming there is internal pressure with a single crack located in the middle of the pipe where both ends are constraint-free. In reality, however, both ends are constrained by their connections to components such as the pressure vessel or pump. Furthermore, due to the complexity of the pipe system, it also experiences a self-constraint effect. This is called the pressure-induced bending restraint effect, and is known to affect the fracture mechanics parameters at the crack tip. Some studies exist on the pressure-induced bending restraint effect of straight pipes, but none have focused on elbow pipe and junction between straight pipe and elbow. This study suggests limit load solutions for elbow and their jointing regions with circumferential through-wall cracks under the pressure-induced bending restraint effect. The relevant equations can be used to estimate the maximum withstand load evaluation of a highly ductile pipe, and can also be used to estimate the elasto-plastic fracture mechanics parameters using the reference stress method.