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Companion Guide to the ASME Boiler and Pressure Vessel Codes, Volume 2, Fifth Edition
K.R. Rao
K.R. Rao
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ASME Press
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The role of fracture mechanics in Section XI applications comes in the form of evaluation of indications or flaws detected during inservice inspection of nuclear components. The early ASME BPVC Section XI evaluation procedures have been typically based on linear elastic fracture mechanics (LEFM). For example, the vessel flaw evaluation procedure in IWB-3600 in the 1977 edition was based on the LEFM analyses described elsewhere. Appendix G of Section XI (essentially the same as Appendix G of Section III) also is an example of the first use of LEFM in Section XI applications. The background of Appendix G LEFM technology is provided in WRC-175. The current Section XI flaw evaluation procedures (Appendix A) have some provision for loading with limited plasticity in the form of plastic zone size correction. LEFM is limited by the small-scale yielding (SSY) condition that the plastic zone around the crack tip be small compared with the size of the K-dominant region and any relevant geometric dimension. It is virtually impossible to satisfy this condition for high-toughness, low-strength materials, which generally undergo extensive plastic deformation and crack tip blunting prior to the initiation of crack growth. Crack initiation in these materials is usually followed by stable crack growth or tearing. The need to include the influence of significant plastic deformation, which may accompany crack initiation and the subsequent stable growth, has been the main driving force for the development of the field of elastic-plastic fracture mechanics (EPFM). Furthermore, higher load capability (over that predicted by LEFM) can be demonstrated in ductile materials by allowing limited stable crack extension using EPFM techniques. Figure 33.1 shows the role of elastic-plastic or non-linear fracture mechanics; a center-cracked plate loaded to failure is considered. This figure shows a schematic plot of failure stress versus fracture toughness (KIc). For low toughness materials (such as ferritic steels at lower shelf), brittle fracture is the governing failure mechanism and the critical stress is predicted by the usual LEFM equations and the material KIc. At very high toughness values, LEFM is no longer valid and failure (or collapse by limit load) is governed by the flow properties of the material. Fracture mechanics ceases to be relevant to the problem because the failure stress is insensitive to toughness; a simple limit load analysis is all that is required to predict failure stress. The appropriate material property in this case is the flow stress that may be generally taken as the average of the material yield and ultimate stress or a suitable multiple (e.g., a factor of 3) of the Code allowable stress, Sm. At intermediate toughness levels, there is transition between brittle fracture under linear elastic conditions and ductile overload or collapse. Non-linear or EPFM bridges the gap between LEFM and collapse. When the plasticity is limited to a small zone surrounding the crack tip, an LEFM solution modified by a plastic zone size is adequate; this zone is called the SSY zone. Some of the ferritic materials used in the nuclear pressure vessel applications at the upper-shelf temperatures are analyzed using this approach with the material fracture resistance determined through appropriate J integral testing.

Early Progress in the Development of EPFM
Engineering Approach to EPFM and Piping Applications
Application to RPV Evaluation
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