Barry Marsden

A numerical study on the application of the Weibull theory to brittle materials

Abstract In this paper, the effects of assuming that a brittle material can be modelled by the two-parameter Weibull distribution, if the true representation of the material behaviour is actually a three-parameter distribution, are examined. It is shown that if data from a material characterisation test is used to predict the failure of a component and the stressed surface areas are very different, then this can lead to major discrepancies in the predicted failure stress. It is also shown that if the three-parameter model is a true representation of the material behaviour, then the Weibull modulus for the two-parameter approximation will vary with surface area.

X-ray tomography observation of crack propagation in nuclear graphite

Abstract X-ray microtomography has been used to investigate the mechanisms responsible for rising crack growth resistance with crack propagation (R curve behaviour) in polygranular nuclear graphite. Tomography can be used to observe changes in the crack shape with propagation, and a side grooved specimen has been developed to produce the planar straight fronted crack necessary for fracture toughness measurement. Crack bridging from frictional contact between the fracture surfaces is observed. A zone of reduced X-ray attenuation, attributed to microstructural damage, is also observed around the crack tip and in its wake. These are the first in situ observations of the mechanisms of the R curve behaviour in nuclear graphites.

The mechanical testing of nuclear graphite

Two billets of nuclear grade medium-grained semi-isotropic graphite were machined into rectangular 4-point bend and L-shaped specimens and tested to failure. The material was not irradiated. During the testing, as well as determining the failure load, the failure was monitored by a high speed camera. The results showed that: there was a difference in the failure loads both along a billet and between the billets, in the L-shaped specimens the cracks did not fail instantaneously but needed further movement of the testing machine’s crosshead before total failure, and the speed of the crack varied in the different specimens. The data were analysed and it was found that the Weibull theory does not predict the failure well but fracture mechanics does provide a way of correlating the data, particularly the crack propagation.

Graphite in Gas-Cooled Reactors

When graphite is used in a nuclear reactor, it will undergo dimensional and material properties changes due to the fast neutron irradiation and changes in temperature. These changes are further complicated in air and CO 2 cooled reactors due to the effect of radiolytic oxidation. This chapter draws upon the unique experiences in the UK of CO 2 cooled reactors and the behavior of graphite within such reactor environments. Examples of the observed changes in UK graphite grades as well as the current understanding of the mechanisms behind the changes are presented.

The relationship between irradiation induced dimensional change and the coefficient of thermal expansion: A modified Simmons relationship

Abstract In the 1960s, a theoretical relationship between the dimensional changes and the coefficient of thermal expansion of irradiated graphite was derived by J.H.W. Simmons. The theory was shown to be comparable with experimental observations at low irradiation doses, but shown to diverge at higher irradiation doses. However, various modified versions of this theory have been used as the foundation of design and life prediction calculations for graphite-moderated reactors. This paper re-examines the Simmons relationship, summarising its derivation and assumptions. The relationship was then modified to incorporate the high dose, high strain changes that were assumed to be represented in the changes in Young’s modulus with irradiation dose. By scrutinising the behaviour of finite element analyses, it was possible to use a modified Simmons relationship to predict the dimensional changes of an isotropic and anisotropic graphite to high irradiation doses. These issues are important to present high-temperature reactors (HTRs) as the life of HTR graphite components is dependent upon their dimensional change behaviour. A greater understanding of this behaviour will help in the selection and development of graphite materials.

The effect of the threshold stress on the determination of the Weibull parameters in probabilistic failure analysis

In the analysis of brittle materials and components the probability of failure is commonly modelled using a two-parameter Weibull distribution. Occasionally, a three-parameter model is used when the material shows significant threshold behaviour. In this paper two methods for determining the three-parameter constants are discussed. Two theoretical two- and three-parameter distributions are then analysed to examine the number of samples needed to determine the parameters accurately. The two-parameter models are the best fits of the three-parameter models and their failure distributions are very similar to the three-parameter distributions. It is concluded that far more specimens need to be tested than is usually the case to be confident that the correct distribution has been found.

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.

Stress concentrations due to axial loading applied to axisymmetric internal projections on hollow tubes

Abstract Stress concentration factors due to the axial loading applied to axisymmetric, internal projections on hollow tubes have been obtained by using the finite element method. A range of tube and projection dimensions and fillet radii have been covered by the investigation. It was found that all of the results could be presented on just two graphs. Hence the stress concentration factor, for any shape within the range investigated, can be quickly determined. A simple relationship between stress concentration factor and ‘load position’ was also found to exist.

Damage nucleation in nuclear graphite

Abstract This paper reports the use of advanced materials characterisation techniques, X-ray microtomography and surface strain mapping by electronic speckle pattern interferometry (ESPI), to study the mechanisms of damage nucleation in polygranular nuclear graphite. It is found that strain localisation occurs owing to the heterogeneous microstructure, giving rise to microcrack nucleation and coalescence before tensile failure. This produces a substantial damage zone at stress concentrations, such as notches and crack tips, which can be observed directly and in situ. Crack propagation occurs by the coalescence of microcracks in the damage zone. The measured R curve is a consequence of both frictional bridging in the crack wake and energy dissipation in the microcrack process zone.

CARBOWASTE: New EURATOM Project on ‘Treatment and Disposal of Irradiated Graphite and Other Carbonaceous Waste’

A new European Project has been launched in April 2008 under the 7th EURATOM Framework Programme (FP7-211333), with a duration of four years, addressing the ‘Treatment and Disposal of Irradiated Graphite and other Carbonaceous Waste (CARBOWASTE)’. The objective of this project is the development of best practices in the retrieval, treatment and disposal of irradiated graphite & carbonaceous waste-like structural material e.g. non-graphitised carbon bricks and fuel coatings (pyrocarbon, silicon carbide). It addresses both legacy waste as well as waste from future generations of graphite-based nuclear fuel. After defining the various targets for an integrated waste management, comprehensive analysis of the key stages from in-reactor storage to final disposal will then be undertaken with regard to the most economic, environmental and sustainable options. This will be supported by a characterisation programme to localize the contamination in the microstructure of the irradiated graphite and so more to better understand their origin and the release mechanisms during treatment and disposal. It has been discovered that a significant part of the contamination (including 14 C) can be removed by thermal, chemical or even microbiological treatment. The feasibility of the associated processes will be experimentally investigated to determine and optimise the decontamination factors. Reuse of the purified material will also be addressed to close the ‘Graphite Cycle’ for future graphite moderated reactors. The disposal behaviour of graphite and carbonaceous wastes and the improvement of suitable waste packages will be another focus of the programme. The CARBOWASTE project is of major importance for the deployment of HTR as each HTR module generates (during a 60 years operational lifetime) about 5,000 to 10,000 metric tonnes of contaminated graphite containing some Peta-Becquerel of radiocarbon. It is strongly recommended to take decommissioning and waste management issues of graphite-moderated reactors already into account when designing new HTR concepts.Copyright