Peter E J Flewitt

Computational modelling of fracture in polycrystalline materials

Abstract This review provides a brief survey of the computational methods which have been adopted to model fracture in materials, particularly polycrystalline metals and alloys, and considers in greater detail the use of geometrical modelling. The different modes of fracture, transgranular and intergranular brittle and ductile, are discussed, together with the modelling tools adopted for macroscale, microscale and nanoscale applications. The procedures which have been used for creating computer models of two– and three–dimensional polycrystalline materials and for propagating cracks through them are then outlined. Applications of these methods to investigate the propagation of cleavage cracks across grain boundaries, to study the influence of texture, grain shape, impurity segregation and prior creep cavitation, to examine the ductile–to–brittle transition region in ferritic steels and to consider the influence of work hardening on ductile fracture are then presented. The predictions are compared with experimental results and proposals for future studies are discussed.

Fracture behaviour of radiolytically oxidised reactor core graphites: a view

Abstract This paper provides a view on the fracture behaviour of polygranular graphites, used to moderate gas cooled nuclear reactors. Graphite is often cited as a classic example of a brittle material because failure, in tension, is associated with small strains. However, attempts to characterise the fracture behaviour of graphite by linear elastic fracture mechanics methods have been largely unsuccessful. Observations of graphite fracture show that elastic strain energy may be dissipated by the formation of distributed microcracks, and their formation may be responsible for non-linearity in the rising load–displacement curve. Progressive softening behaviour may also be observed in some specimens after the peak load. This type of load–displacement behaviour is a characteristic of quasi-brittle materials. Radiolytic oxidation increases the proportion of porosity within reactor core graphite so that the microstructure becomes increasingly skeletal. Consideration is given to the fracture of radiolytically oxidised graphite to support an argument for quasi-brittle behaviour.

Grain boundary impurity segregation and neutron irradiation effects in ferritic alloys

Segregation of alloying and impurity elements to grain boundaries in ferritic steels and alloys is known to modify the mechanical properties. This paper considers segregation of such elements, in particular phosphorus and carbon, that occur in ferritic nuclear pressure vessel steels subject to neutron irradiation and temperature typical of that encountered in service. Models are presented that allow the prediction of equilibrium and non-equilibrium segregation of phosphorus to grain boundaries and also take into account synergistic interaction with carbon under various combinations of neutron-irradiation temperature. These are related to a wide range of experimental observations compiled from data in the literature for mainly phosphorus and carbon measured at grain boundaries in neutron-irradiated ferritic vessel steels and alloys. The predictions from the segregation models are compared with these experimental data. The discussion provides a rationalization for the apparent variability in the measured grain boundary phosphorus compositions and thereby fracture susceptibility for various nuclear pressure vessel ferritic steels.

An examination of the linkage of cleavage cracks at grain boundaries

Abstract Grain boundaries resist the propagation of cleavage cracks in polycrystalline materials, and 3D geometrical models have been used to predict the accommodation required at a grain boundary as a crack propagates from grain to grain. This paper describes how focused ion beam (FIB) microscopy, which provides topographic and crystallographic contrast imaging and allows ion milling to be undertaken at selected areas of interest, can be used to investigate these local fracture events. Results of low temperature fracture of polycrystalline bcc Fe–3%Si and hcp zinc are presented. The interactions between these results and the geometrical modelling are briefly discussed.

A review of the changes of internal state related to high temperature creep of polycrystalline metals and alloys

Abstract When polycrystalline metals and their alloys are used at high temperature, creep deformation leads to changes in their internal state. The change in internal state manifests itself in many ways, but the two ways that concern us in this review are (i) the creation of internal stress arising from the strain incompatibility between grains and/or the formation of cell/sub-grain structures and (ii) a change in the material resistance. This review aims to provide a clear separation of these two concepts by exploring the origin of each term and how it is associated with the creep deformation mechanism. Experimental techniques used to measure the internal stress and internal resistance over different length-scales are critically reviewed. It is demonstrated that the interpretation of the measured values requires knowledge of the dominant creep deformation mechanism. Finally, the concluding comments provide a summary of the key messages delivered in this review and highlight the challenges that remain to be addressed.

Calibration of Raman Spectroscopy in the Stress Measurement of Air-Plasma-Sprayed Yttria-Stabilized Zirconia

Thermal barrier coatings (TBC) are used widely on a range of components that operate at high temperatures. We report measurement of the factor that is required to convert the Raman shift to stress for air plasma sprayed yttria (7 wt %) stabilized tetragonal zirconia (ZrO2) (YSZ) thermal barrier coatings. The factor is evaluated for the as-coated condition and also following a heat treatment at 1000 °C for 1050 h. Two Raman bands at 608 cm−1 and 640 cm−1 have been investigated in a diamond anvil cell under hydrostatic pressure up to ~24 GPa. In the range of zero to ~1.6 GPa, a linear behavior was observed in terms of the shifts of these two Raman bands with a gradient similar to dense bulk tetragonal ZrO2. From these measurements the factors to convert wavenumber shift to stress have been derived. The application of these conversion factors to stress measurement in TBC coated test specimens and components is discussed.

An improved method to identify grain boundary creep cavitation in 316H austenitic stainless steel

Inter-granular creep cavitation damage has been observed in an ex-service 316H austenitic stainless steel thick section weldment. Focused ion beam cross-section milling combined with ion channelling contrast imaging is used to identify the cavitation damage, which is usually associated with the grain boundary carbide precipitates in this material. The results demonstrate that this technique can identify, in particular, the early stage of grain boundary creep cavitation unambiguously in materials with complex phase constituents.

Contribution of multiscale materials modelling for underwriting nuclear pressure vessel integrity

Abstract The continued safe operation of high integrity structures such as Magnox steel reactor pressure vessels is assured by using arguments which are usually based upon deterministic methodologies. These require models to provide the input parameters together with the necessary mechanistic understanding of the changes in mechanical or physical properties of the steels with service life. The use of modelling to provide key parameters for input to the fracture mechanics assessments is discussed, in particular, the application of statistical procedures to describe the required materials mechanical property data. However, there is a need to underwrite these data with an understanding of the underlying physical mechanisms. Here mechanistic models have been derived which span many orders of magnitude of length scale. At the atomic scale these provide an insight into the production of point defect damage in steels as a result of exposure to a neutron spectrum at various temperature and neutron doses. In addition, equilibrium and nonequilibrium segregation of alloying and impurity atom species to grain boundaries is modelled. Both are necessary for understanding the changes in the fracture mode and the mechanical properties for these steels after extended periods of service mode. At the microscale, models are adopted to develop insights into the fracture processes. The benefits of these models to the arguments developed within safety cases which underwrite safe continued operation of these reactor pressure vessels are described.

Effect of boron on phosphorus-induced temper embrittlement

Combined equilibrium and non-equilibrium grain boundary segregation of solute atoms in dilute ternary alloys is modelled through consideration of site competition between two solutes. Model predictions are made for a low-alloy steel containing boron. The predicted results indicate that the kinetics of phosphorus segregation are dramatically facilitated by quenched-in vacancies, and the magnitude of the segregation, however, is substantially suppressed by the competition of boron with phosphorus for segregation sites, and in turn the phosphorus-induced embrittlement may be alleviated.

Micro-scale testing of ductile and brittle cantilever beam specimens in situ with a dual beam workstation

Micro-scale cantilever beam specimens created by focused ion beam milling have been mechanically loaded in situ at room temperature to observe the deformation and fracture of single crystal silicon, nanocrystalline nickel and thermal barrier coatings with a multilayer structure. The micro-scale preparation technique allows cantilever beams to be selected from preferred positions in the samples so that specific mechanical properties can be evaluated. As a consequence these microstructural specific properties can be combined with direct observation of the response of the test specimen throughout the period of the test. The measured mechanical properties and response for the materials given above are discussed and compared with previously published data.