Elastic-Plastic Analyses of Surface Flaws in a Reactor Vessel

Abstract

Elastic-plastic analyses have been performed for the ASME Maximum Postulated Flaw and for three other semielliptical surface flaws in the beltline region of a nuclear reactor pressure vessel, with internal radius to thickness ratio, R /t , equal to 10, using nonlinear 3-D finite element methods based upon the deformation theory of plasticity. Three of the flaws had a maximum depth, a , equal to t /4, with aspect ratios, 2c /a , equal to 6 (the ASME Maximum Postulated Flaw), 4 and 3, respectively, where 2c is the surface length of the flaw. These flaws were analyzed for internal pressure varying from one to three times the design pressure, which is well into the fully plastic regime for the uncracked vessel. The fourth flaw had an aspect ratio, 2c /a , equal to 6, and its maximum depth, a , was equal to 3t /4. This deep flaw was analyzed for internal pressure varying from 60 percent of design pressure to twice the design pressure. The crack driving force was calculated as the energy release rate, J , using the virtual crack extension method. The results illustrate that, at the design pressure, plasticity near the crack front is so limited for the three flaws with a /t = 1/4 that an elastic analysis is adequate. At higher pressures, however, the elastic analyses become increasingly nonconservative and would grossly underestimate the severity of the flaws. The variation of both J and crack opening displacement, COD, along the crack front were studied. Generally, the values at the maximum depth location, denoted J * and COD*, respectively, were the maximum values, with minimum values occurring at the free surface. A simple normalization scheme was found which collapsed the J * versus pressure results for the four semielliptical flaws into a single curve. A similar normalization also collapsed the COD* versus pressure results for the four flaws into a single curve. In addition, a unique linear relationship between J * and COD* was found to apply for the results from all four sets of analyses for internal pressure levels up to at least 2.5 times the design pressure. The analyses therefore demonstrate that J and COD are equivalent measures of the crack driving force, and further demonstrate that a realistic 3-D elastic-plastic analysis is needed to properly assess the severity of surface flaws.