Muhammad Treifi

Dimensional change, irradiation creep and thermal/mechanical property changes in nuclear graphite

Since the start of the ‘nuclear age’ graphite has been employed as a moderator in around 100 nuclear reactors, and today there are still some 30 graphite-moderated reactors operating and there are plans for new Generation IV high-temperature reactors. Many of the graphite moderator reactors now producing power are operating beyond their original design life. Therefore in some cases, to aid the reactor operators and designers, the existing graphite irradiation databases need to be extended either to a higher temperature or higher neutron fluence. Furthermore, data are needed for the different grades of graphite that are available at present. This can either be achieved by expensive, time consuming irradiation programmes or by improving the understanding of the mechanisms and processes which lead to irradiation-induced dimensional and property changes in the graphite core components. This review looks at three of the most important graphite properties which change with exposure to irradiation, namely dimensional change, irradiation creep and thermal expansion. The behaviour of UK AGR, Magnox and an experimental grade of German reactor graphite are explored in some detail. First graphite reactor core design is briefly discussed, giving examples of typical graphite components and core arrangements. Issues related to aging graphite component and core behaviour are illustrated through examples of component internal and thermal stress generation, and issues related to whole core behaviour are also outlined. Second the manufacture and microstructure of different nuclear graphite grades are discussed, highlighting how the choice of raw materials and manufacturing technique influences the graphite properties. Third the coefficient of thermal expansion, dimensional change and irradiation creep are analysed using microstructural and averaging methods which are used to relate crystal to bulk properties by accounting for graphite crystal orientation and porosity. These techniques, which were first applied to nuclear graphite in the 1960s, are extended and discussed with the aim of trying to lend some understanding to the role the microstructural crystallite and porosity distributions play in defining the dimensional stability and properties of virgin graphite, irradiated graphite and stressed graphite.

Applications of the fractal-like finite element method to sharp notched plates

The fractal-like finite element method (FFEM) has been proved to be an accurate and efficient method to analyse the stress singularity of crack tips. The FFEM is a semi-analytical method. It divides the cracked body into singular and regular regions. Conventional finite elements are used to model both near field and far field regions. However, a very fine mesh of conventional finite elements is used within the singular regions. This mesh is generated layer by layer in a self-similar fractal process. The corresponding large number of degrees of freedom in the singular region is reduced extremely to a small set of global variables, called generalised co-ordinates, after performing a global transformation. The global transformation is performed using global interpolation functions. The Concept of these functions is similar to that of local interpolation functions (i.e. element shape functions.) The stress intensity factors are directly related to the generalised co-ordinates, and therefore no post-processing is necessary to extract them. In this paper, we apply this method to analyse the singularity problems of sharp notched plates. Following the work of Williams, the exact stress and displacement fields of a plate with a notch of general angle are derived for plane stress and plane strain conditions. These exact solutions which are eigenfunction expansion series are used as the global interpolation functions to perform the global transformation of the large number of local variables in the singular region around the notch tip to a few set of global co-ordinates and in the determination of the stress intensity factors. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems.Copyright

Computations of SIFs for non-symmetric V-notched plates by the FFEM

The present paper further develops The Fractal-like Finite Element Method (FFEM) to compute the stress intensity factors (SIFs) for non-symmetrical configurations of sharp V-notched plates. The use of global interpolation functions (GIFs) in the FFEM significantly reduces the number of unknown variables (nodal displacements) in a singular region surrounding a singular point to a small set of generalised coordinates. The same exact analytical solutions of the notch tip asymptotic field derived for a symmetrical notch case can be used as GIFs when the notch is non-symmetrical. However, appropriate local coordinate transformation in the singular region is required to obtain the correct global stiffness matrix. Neither post-processing technique to extract SIFs nor special singular elements to model the singular region are required. Any conventional finite elements can be used to model the singular region. The SIFs are directly computed because of the use of exact analytical solutions as GIFs whose coefficients (generalised coordinates) are the unknowns in the singular region. To demonstrate the accuracy and efficiency of the FFEM to compute the SIFs and model the singularity at a notch tip of non-symmetrical configurations of notched plates, various numerical examples are presented and results are validated via available published data.Copyright

Graphite as a core material for Generation IV nuclear reactors

Graphite, an attractive moderating material due to its unique characteristics, has been used in different reactor generations and is currently a candidate for future Generation IV high-temperature reactors and molten salt-cooled reactors. The graphite material is complex and its properties are dependent on the length scale. Furthermore, the bulk graphite properties are dependent on many factors, such as manufacturing, grain size, and operational environment. These properties also change over time due to irradiation. Based on experience gained from different current graphite moderated reactors, referring to both past experience and data more recently obtained in various EU Framework projects, this chapter introduces the basics of graphite as a nuclear material for application to Generation IV reactors. Current procedures and understanding of graphite manufacturing, material properties models, component structural integrity assessment, and waste management are presented to help future reactor designers. Specific issues related to high-temperature nuclear graphite are also discussed.