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.