Elastic-Plastic Analysis of the Maximum Postulated Flaw in the Beltline Region of a Reactor Vessel

A maximum postulated surface flaw in the beltline region of a PWR pressure vessel has been analyzed under elastic-plastic conditions. The analysis was performed using 3-D finite element methods, and the deformation theory of plasticity was used to describe the plastic flow of the material. The calculations were carried out for the internal pressure varying from the design pressure up to approximately twice the design pressure. The results show that at the design pressure the plastic flow of the material around the crack front is so small that an elastic analysis is adequate. However, the commonly used approach of treating the flaw in the vessel as a surface flaw in a flat plate under far field tension loading is nonconservative. At a pressure of approximately 50 percent over the design pressure the energy release rate derived from an elastic analysis starts to deviate from the value obtained from an elastic-plastic calculation. The elastic result now starts to be nonconservative and at twice the design pressure the elastic analysis will clearly underestimate the severity of the crack. A 2-D elastic-plastic plane strain approximation will on the other hand grossly overestimate the severity of the crack. A realistic 3-D elastic-plastic analysis is, therefore, needed to estimate the safety factors of surface flaws and to serve as benchmarks for the development of simpler design calculations.