Graphite Specimens Research Articles

Studies of irradiation creep on core graphite by thermal annealing

The mechanism of irradiation creep and its effect on the internal stresses of reactor core graphite components are not well understood. Historical studies on Materials Test Reactor creep specimens have shown that thermal annealing can lead to recovery of creep strain. By selecting appropriate sets of trepanned graphite specimens for the AGR cores, the thermal annealing programme in this work uses the findings of these historical studies in order to investigate irradiation creep and importantly, the stress state of AGR core bricks. Changes in dimensions, Coefficient of Thermal Expansion and Young’s modulus after each annealing step are reported. Laser Raman spectroscopy is used to investigate the effect of thermal annealing on irradiated graphite. The results are combined with core inspection data and demonstrate the complexity of estimating irradiation creep in different parts of reactor graphite components.

Scaling effects on notch fracture toughness of graphite specimens under mode I loading

In this paper, the mode I notch fracture toughness of graphite specimens weakened by notches of different shapes is investigated experimentally and theoretically. For this purpose, first, by conducting experiments, the apparent fracture toughness values of cracked semi-circular bending (SCB) graphite specimens with four various radii are determined. Next, numerous fracture experiments are performed on the notched SCB graphite specimens in four various scales. Then, the critical radius of the fracture process zone (FPZ) for the notched graphite specimens is obtained using two various equations already proposed in literature for cracked bodies. A well-known stress-based failure model, namely the point stress (PS) criterion, is employed for estimating the notch fracture toughness values of the specimens tested at different scales, taking advantages of two different critical distance formulas. The results show that the fracture toughness values of various notches obtained from PS criterion are in good agreement with the experimental results. Also, found in this research that the notch fracture toughness is considerably dependent on the nominal dimension (radius) of the specimen, such that, as the specimen radius increases, the mode I notch fracture toughness increases. Furthermore, it is revealed that for the present specimens tested, both the critical distance formulas provide almost identical predictions, suggesting that each of them can be arbitrarily selected for prediction.

Design, construction and operation of a graphite irradiation creep facility

Representative irradiated graphite properties are essential for the successful design, licensing and long term operation of a graphite moderated reactor. These properties are acquired from irradiation programs that are executed in different Materials Test Reactors around the world. Recently, the Nuclear Research and consultancy Group (NRG) has completed a graphite irradiation creep program by the name ACCENT to support long term operation of Advanced Gas-cooled Reactors in the UK.In a series of 4 irradiation steps, paired graphite specimens are irradiated at a temperature of 440 °C under loaded and non-loaded conditions. By using a modular design with pressurized bellows, a load of 5 or 10 MPa is applied to the specimens. Characterization of the graphite specimens is performed before, between and after the irradiation steps to generate graphite property curves in a range of 0 to 14 DPA.This paper describes the different design, construction and operational aspects of graphite irradiation (creep) facilities that are fundamental to successfully acquire representative irradiation data. It will be demonstrated how these different aspects are controlled for the ACCENT graphite irradiation creep facility.

A 3D benchmark problem for crack propagation in brittle fracture

We propose a full 3D benchmark problem for brittle fracture based on experiments as well as a validation in the context of phase-field models. The example consists of a series of four-point bending tests on graphite specimens with sharp V-notches at different inclination angles. This simple setup leads to a mixed mode (I + II + III) loading which results in complex yet stably reproducible crack surfaces. The proposed problem is well suited for benchmarking numerical methods for brittle fracture and allows for a quantitative comparison of failure loads and propagation paths as well as initiation angles and the fracture surface. For evaluation of the crack surfaces image-based 3D models of the fractured specimen are provided along with experimental and numerical results. In addition, measured failure loads and computed load–displacement curves are given. To demonstrate the applicability of the benchmark problem, we show that for a phase-field model based on the Finite Cell Method and multi-level hp-refinement the complex crack surface as well as the failure loads can be well reproduced.

Study of heat transfer in the boundary layer in a nitrogen flow past a catalytic graphite wall

The results of investigating the physical and chemical processes in the wall boundary layer on graphite specimens in a nitrogen flow are reported. The effect of the catalytic wall on the heat flux is considered. The emphasis is on analyzing the distribution of the chemical species concentrations across the boundary layer based on a detailed consideration of the mechanism of heterogeneous catalytic reactions under the surface mass flux conditions. The distributions of the chemical species concentrations over the boundary layer thickness at the stagnation point of a blunted graphite body for a particular flight path segment are presented.

Fracture assessment of U-notched graphite specimens by means of cohesive zone model

Various types of graphite have gained interest in many industrial applications due to their high strength and excellent heat tolerance. However, due to the brittle nature of this material, presence of stress concentrators such as notches and geometrical discontinuities considerably re-duces the overall loading bearing of the graphite components. Here we evaluate the applicability of the Cohesive Zone Model (CZM) for the assessment of the fracture strength of experimentally tested U-notched specimens subject to mode I loading. The fracture loads of U-notched components with different notch tip radii can be predicted with an average discrepancy of ±7%.

Brittle fracture prediction of key-hole notched specimens by means of J-integral expression

The main goal of the present research is to check if J-integral criterion is capable of predicting the onset of brittle fracture in key-hole notched isostatic poly-granular graphite plates. In this way, this article provides the prediction of fracture loads in several key-hole notched rectangular graphite specimens with five different notch tip radii subjected to pure mode I loading condition, which has been previously reported in the literature by Lazzarin et al. (2013). The fracture load predictions for five dimensional cases were obtained through the J-integral calculations. It is revealed that the J-integral criterion is capable of predicting well the fracture loads of graphite key-hole notched specimens, independent of the size of key-hole notch.

Investigating the effects of confining pressure on graphite material failure modes and strength criteria

As a critical material in very/high-temperature gas-cooled reactors, graphite material directly affects the safety of the reactor core structures. Owing to the complex structures of graphite material in reactors, the material typically undergoes complex stress states. It is, therefore, necessary to study its mechanical properties, failure modes, and strength criteria under complex stress states so as to provide guidance for the core structure design. In this study, compressive failure tests were performed for graphite material under the condition of different confining pressures, and the effects of confining pressure on the triaxial compressive strength and Young's modulus of graphite material were studied. More specifically, graphite material based on the fracture surfaces and fracture angles, the graphite specimens were found to exhibit four types of failure modes, i.e., tension failure, shear-tension failure, tension-shear failure and shear failure, with increasing confining pressure. In addition, the Mohr strength envelope of the graphite material was obtained, and different strength criteria were compared. It showed that the parabolic Mohr-Coulomb criterion is more suitable for the strength evaluation for the graphite material.

3D fracture behaviour of graphite specimens weakened by V- notches with end holes under mixed mode (I+II) loading

In the present contribution, the static strength of isostatic graphite using V-notched specimens with end holes under mixed mode loading is investigated considering 3D simulation. An experimental program was performed and in total, 14 new experimental data are provided in the paper for the first time. The criterion based on the averaged value of the strain energy density over a control volume which has been applied to assess the static strength of the different 2D specimens, is developed in the current work by modification of the control volume to assess the thickness effect on the static strength of graphite specimens. A sound agreement is found between the experimental data and the results obtained from the strain energy density criterion.

Evidence of diamond-like carbon phase formation due to 80 keV Xe+ ion impact on pencil-lead graphitic systems with oblique angle incidence

We report on the effect of 80 keV Xe+ ion irradiation on the commercially available, sectioned 10B pencil-graphite specimens subjected to normal and oblique angle incidence of ions (θi = 0°–70°) and considering a fixed ion fluence of . The pristine and irradiated samples were characterized by powder x-ray diffraction, atomic force microscopy and Raman spectroscopy studies. Unlike pristine graphite and normal incidence cases, several ripple patterns can be visualized in the atomic force micrographs of the specimens irradiated with an oblique angle incidence. Moreover, apart from conventional G-band located at , a distinct diamond-like carbon (DLC) phase has been witnessed at in the Raman spectra of the graphitic specimens subjected to ion impact and for values of 50° and 70°. The formation of the DLC phase along with surface ripple formation would find numerous scopes while dealing with properties such as surface transport, field emission and mechanically hard coating in miniaturized devices.

Experimental and simulation study on stress concentration of graphite components in tension

Nuclear graphite is a typical quasi-brittle material used in nuclear reactors. Damage can easily generate and accumulate under loads due to widespread defects (such as cracks or holes) inside the material and thereby cause the degradation of material properties. Studies have shown that nuclear graphite exhibits different damage evolution behaviours under tensile and compressive loading. In this paper, experiments were first carried out to measure the stress concentration factors of L-shaped graphite specimens with different corner radii subjected to tension. Subsequently, finite element models with and without damage evolution were established, and different damage evolution laws were considered for tension and compression in the damage model. The importance of damage on stress concentration prediction of graphite components was emphasized by comparing the experimental and numerical simulation results.

Fracture study in notched graphite specimens subjected to mixed mode I/II loading: Application of XFEM based on the cohesive zone model

The aim of the present research is to predict the fracture load of key-hole and U-notched graphite components under mixed mode I/II loading by means of the extended finite element method (XFEM) based on the linear cohesive zone model (CZM). For this purpose, two series of fracture experiment conducted on several key-hole notched rectangular graphite plates, and also U-notched Brazilian disk graphite specimens and reported previously in the literature are presented. Then, the experimentally obtained fracture loads of the tested graphite specimens for both fracture test series are theoretically estimated by means of XFEM in combination with CZM. Since the graphite specimens have perfectly brittle behavior, the linear elastic notch fracture mechanics (LENFM) assumption is utilized. For different notch geometries, the experimental and theoretical results are plotted in the form of the variations of the fracture load versus the notch tip radius. Finally, it is shown that XFEM-CZM approach could successfully predict the experimentally obtained fracture loads of the tested specimens.

Measuring the fracture properties of irradiated reactor core graphite

The assessment of the post-cracking behaviour of the reactor core components requires knowledge of the fracture properties, such as the fracture toughness, KIC, and work of fracture, γf, of irradiated graphite. The measurement of these properties is a proven technique for linearly elastic materials but application on small nuclear graphite specimens demands further consideration. The purpose of this work is to develop this technique for use on irradiated graphite specimens whose size and geometry are restricted by the reactor core trepanning or Materials Test Reactor experiments. This paper describes the theoretical basis of the method, the work undertaken to prove the measurement technique and demonstrate its applicability to small irradiated and oxidised graphite specimens. Finally, the paper presents work of fracture values of irradiated graphite trepanned from AGR core bricks; for the first time, the relationship between work of fracture and other graphite properties, such as density, modulus and strength is experimentally demonstrated.

Non-Eulerian behavior of graphitic materials under compression

The mechanical behavior of graphitic materials is greatly affected by the weak interlayer bonding with van der Waals forces for a range of thickness from nano to macroscale. Herein, we present a comprehensive study of the effect of layer thickness on the compression behavior of graphitic materials such as graphene which are fully embedded in polymer matrices. Raman Spectroscopy was employed to identify experimentally the critical strain to failure of the graphitic specimens. The most striking finding is that, contrary to what would be expected from Eulerian mechanics, the critical compressive strain to failure decreases with increase of flake thickness. This is due to the layered structure of the material and in particular the weak cohesive forces that hold the layers together. The plate phenomenology breaks down for the case of multi-layer graphene, which can be approached as discrete single layers weakly bonded to each other. This behavior is modelled here by considering the interlayer bonding (van der Waals forces) as springs in series, and very good agreement was found between theory and experiment. Finally, it will be shown that in the post failure regime multi-layer graphenes exhibit negative stiffness and thus behave as mechanical metamaterials.

Effective gaseous diffusion coefficients of select ultra-fine, super-fine and medium grain nuclear graphite

Understanding “Where?” and “How much?” oxidation has occurred in a nuclear graphite component is critical to predicting any deleterious effects to physical, mechanical, and thermal properties. A key factor in answering these questions is characterizing the effective mass transport rates of gas species in nuclear graphites. Effective gas diffusion coefficients were determined for twenty-six graphite specimens spanning six modern grades of nuclear graphite. A correlation was established for the majority of grades examined allowing a reasonable estimate of the effective diffusion coefficient to be determined purely from an estimate of total porosity. The importance of Knudsen diffusion to the measured diffusion coefficients is also shown for modern grades. Knudsen diffusion has not historically been considered to contribute to measured diffusion coefficients of nuclear graphite.

A new oxidation based technique for artifact free TEM specimen preparation of nuclear graphite

Graphite is a key component in designs of current and future nuclear reactors whose in-service lifetimes are dependent upon the mechanical performance of the graphite. Irradiation damage from fast neutrons creates lattice defects which have a dynamic effect on the microstructure and mechanical properties of graphite. Transmission electron microscopy (TEM) can offer real-time monitoring of the dynamic atomic-level response of graphite subjected to irradiation; however, conventional TEM specimen-preparation techniques, such as argon ion milling itself, damage the graphite specimen and introduce lattice defects. It is impossible to distinguish these defects from the ones created by electron or neutron irradiation. To ensure that TEM specimens are artifact-free, a new oxidation-based technique has been developed. Bulk nuclear grades of graphite (IG-110 and NBG-18) and highly oriented pyrolytic graphite (HOPG) were initially mechanically thinned to ∼60 μm. Discs 3 mm in diameter were then oxidized at temperatures between 575 °C and 625 °C in oxidizing gasses using a new jet-polisher-like set-up in order to achieve optimal oxidation conditions to create self-supporting electron-transparent TEM specimens. The quality of these oxidized specimens were established using optical and electron microscopy. Samples oxidized at 575 °C exhibited large areas of electron transparency and the corresponding lattice imaging showed no apparent damage to the graphite lattice.

Experimental and computational correlation of fracture parameters KIc, JIc, and GIc for unimodular and bimodular graphite components

The influence of bimodularity (different stress ∼ strain behaviour in tension and compression) on fracture behaviour of graphite specimens has been studied with fracture toughness (KIc), critical J-integral (JIc) and critical strain energy release rate (GIc) as the characterizing parameter. Bimodularity index (ratio of tensile Young's modulus to compression Young's modulus) of graphite specimens has been obtained from the normalized test data of tensile and compression experimentation. Single edge notch bend (SENB) testing of pre-cracked specimens from the same lot have been carried out as per ASTM standard D7779-11 to determine the peak load and critical fracture parameters KIc, GIc and JIc using digital image correlation technology of crack opening displacements. Weibull weakest link theory has been used to evaluate the mean peak load, Weibull modulus and goodness of fit employing two parameter least square method (LIN2), biased (MLE2-B) and unbiased (MLE2-U) maximum likelihood estimator. The stress dependent elasticity problem of three-dimensional crack progression behaviour for the bimodular graphite components has been solved as an iterative finite element procedure. The crack characterizing parameters critical stress intensity factor and critical strain energy release rate have been estimated with the help of Weibull distribution plot between peak loads versus cumulative probability of failure. Experimental and Computational fracture parameters have been compared qualitatively to describe the significance of bimodularity. The bimodular influence on fracture behaviour of SENB graphite has been reflected on the experimental evaluation of GIc values only, which has been found to be different from the calculated JIc values. Numerical evaluation of bimodular 3D J-integral value is found to be close to the GIc value whereas the unimodular 3D J-value is nearer to the JIc value. The significant difference between the unimodular JIc and bimodular GIc indicates that GIc should be considered as the standard fracture parameter for bimodular brittle specimens.

The first irradiation testing and PIE or TRISO-coated particle fuel in Korea

The first irradiation testing of TRISO-coated particle fuel to demonstrate and qualify its use in a VHTR was finished at the beginning of 2014 in HANARO, Korea. A PIE (post-irradiation examination) of the irradiated TRISO-coated particle fuel was then performed. The irradiation device contained two kinds of test rods: one containing nine fuel compacts, and the other five compacts and eight graphite specimens between the fuel compacts. The irradiation testing was carried out under the condition of filled with an inert gas atmosphere and being sealed (no sweep gas). After irradiation testing, the maximum power of the fuel compact was estimated to be around 56 W at 25 EFPD, and the maximum power of the particle was calculated to be 215.4 mW. And, the maximum discharged burn-up was evaluated to be about 37,344 MWD/MTU (3.99% FIMA). The estimated maximum fast fluence of the graphite specimen was 2.99 × 1020 n/cm2 (E > 0.18 MeV). In this paper, the characteristics of TRISO-coated particle fuels, the estimated thermal power, fuel temperature, burnup, fluence, and some PIE results were described.

Analytical solution for a flexural bimodulus beam

Formulations for the deformed shape of a simply supported, uniformly loaded bimodulus beam and the location of the neutral axis have been developed. A theoretical model for bimodulus and unimodular beams has been developed to calculate the maximum deflection considering the neutral axis shift in the case of a bimodulus beam. The finite-element technique is used for the evaluation using the concept of the Ambartsumyan bimodular model for simply supported and cantilever bimodulus and unimodular beams with centrally pointed load, uniformly distributed load and gradually varying load. It is found that the value of the maximum deflection is large for a bimodular beam in comparison to that for a unimodular beam for all types of loading. Shifting of neutral axis has been correlated with three point bend testing of graphite specimens. Qualitative comparison for uniformly distributed load and centrally pointed load has been carried out to demonstrate the influence of bimodularity for both cantilever and simply supported numerical specimens based on finite element procedures.

Self-heating effect at graphite ohmic heating

We present the numerical modeling results of an experiment where the self-heating process was observed. The results confirm the supposition (put forward earlier) that self-heating occurs during the transmission of an electric current through a graphite specimen at temperatures above 3000 K and is the consequence of a combination of low thermal conductivity values and strong temperature dependence of specific electrical resistivity.