Elsevier

Carbon

Volume 163, 15 August 2020, Pages 308-323
Carbon

In situ measurement of elastic and total strains during ambient and high temperature deformation of a polygranular graphite

https://doi.org/10.1016/j.carbon.2020.03.020Get rights and content

Abstract

In situ neutron diffraction and synchrotron X-ray diffraction, combined with image correlation analysis of 2D optical and 3D X-ray tomography datasets, have been used to investigate the relationship between elastic lattice strain and total strain during deformation of Gilsocarbon (IM1-24) polygranular nuclear grade graphite. The specimens were flat-end Brazilian discs under diametral loading, such that a compressive-tensile biaxial stress state was developed in the central region. The X-ray study was at ambient temperature, and the neutron diffraction was conducted at temperatures from ambient to 850 °C. When under compression, there is a temperature-insensitive linear relationship between the total strain and the lattice strain that is measured perpendicular to the graphite basal planes. However, when under tensile stress, the total strain and elastic strain relationship is temperature sensitive: below 600 °C, the lattice tensile strain saturates with increasing total tensile strain; above 600 °C, significantly higher tensile lattice strains are sustained. The saturation in tensile lattice strain is attributed to microcracking in the graphite microstructure. Improved resistance to microcracking and damage tolerance at elevated temperature explains the increase in tensile strength of polygranular graphite.

Introduction

Nuclear graphite is an artificial polygranular material with broad applications in nuclear energy due to its thermal and neutronic properties. It was used to construct critical structural core components (e.g. neutron moderator, fuel element, reflectors and core support posts [1]) in the earliest reactors (e.g. the very first artificial nuclear reactor Chicago Pile-1 and the subsequent Clinton Pile) and it is a critical material in some operating reactors (e.g. the UK Advanced Gas Cooled reactors (AGRs) and Russian water-cooled RBMK reactors); a typical graphite moderated reactor may contain 2000 tonnes of graphite [2,3]. Nuclear graphite is also a key material for some future Gen IV high temperature gas-cooled reactor (HTGR) designs; prototype HTGRs have been built in China [4] (HTR-10 and HTR-PM) by licensing the German AVR design [5], and the Japanese HTTR [6], which has an outlet temperature of 950 °C, has operated since the mid-1990’s. The future potential for HTGRs is also demonstrated by ongoing national (e.g. India [7]) and international programmes (e.g. GEMINI and GEMINI + between EU and USA), with the latter focussed on the design and regulatory framework of the first modern HTGR [8]. Reliable structural integrity assessment of graphite components is critical for new build designs [9,10] and also for the safe operation and eventual decommissioning of the graphite cores in the current and retiring fleets [11]. This must be underpinned by a sound understanding of the deformation and fracture of graphite under conditions that represent its service in the reactor environment of a high temperature gaseous coolant and fast neutron irradiation [[12], [13], [14], [15]].

The structural integrity of graphite components is generally assessed using a maximum tensile stress criterion, such that failure is predicted to occur when the maximum principal stress exceeds an appropriate value. This is known to be simplistic and not fully satisfactory [[16], [17], [18]]; other approaches, such as strain energy density, have been proposed [19]. However, a major difficulty with applying or validating any fracture criterion, particularly at stress concentrations such as notches, is that one needs to know the distribution of both stresses and strains which are not linearly related for any type of material behaviour that includes damage. Polygranular graphite has non-linear and inelastic properties, particularly in the un-irradiated condition and also as it approaches failure [[20], [21], [22]]. To be able to reliably predict the structural integrity of graphite components, it is therefore necessary to have a detailed understanding of how stress causes strain, and how damage is accommodated by the graphite microstructure.

One of the most extensively studied polygranular graphite grades is Gilsocarbon (IMI-24). This was used to construct the UK AGRs and is typical of other medium/coarse-grained isotropic artificial graphites. Direct observations have demonstrated that its tensile strength is strongly related to pre-existing stress-concentrating defects in its microstructure [23,24]. At ambient room temperature, in situ neutron and X-ray strain measurements have shown that for unirradiated Gilsocarbon in compression there is a linear relationship between the elastic strains in the graphite crystals and the applied total strain, whereas in tension a non-linear behaviour occurs that is accompanied by a reduction in tensile elastic modulus and a relaxation of internal (i.e. thermally induced) stresses [25]. This behaviour has been attributed to tensile microcracking, and studies of a propagating macroscopic crack in Gilsocarbon have also detected a fracture process zone [26,27], the effects of which could be described by a non-linear damage model [28]. Similar modelling (traction-separation law-based maximum principal stress damage initiation and energy-based damage evolution with linear softening) has also been done for the modern fine-grained IG110 graphite [29,30]. Synchrotron X-ray diffraction and imaging have both been applied to map the crystal strains and total deformation in situ within the fracture process zone of a propagating crack in unirradiated Gilsocarbon [31]. By using the experimental data for the effect of tensile strain on elastic modulus to calibrate the material damage model, a very good agreement was found between the predicted and measured crack stress/strain fields. This showed that the non-linear deformation significantly reduced the stresses in the fracture process zone, and hence also reduced the elastic strain energy release rate available for crack propagation. The same behavior is reasonably expected to occur at stress concentrating notches, although this has not yet been demonstrated. An understanding of graphite non-linear behavior is therefore critical to the structural integrity assessment of graphite components.

The majority of studies of graphite deformation and fracture have been conducted at ambient room temperature, but graphite exhibits quite complex behaviour at elevated temperatures. For instance, the elastic modulus of unirradiated polygranular graphite varies significantly with the test temperature, and also the graphite processing conditions that affect the graphite microstructure [32,33]. At low temperatures, there is a negative temperature dependence of modulus that corresponds to the expected behaviour of its crystals but the temperature dependence of the elastic modulus can become positive at high temperatures (i.e. increasing stiffness with increasing temperature) [[34], [35], [36], [37], [38]]. This has been attributed to a void-filling effect from thermally-induced closure of the Mrozovski accommodation pores. These pores mainly lie between the graphite crystals, and form when cooling from graphitisation due to the crystal’s highly anisotropic thermal expansion coefficients and elastic properties [39]. In terms of strength and fracture toughness in graphite, Albers [40] reported increased tensile strength in three grades of nuclear graphite (PCEA, PPEA, and PCIB-SFG); Eto et al. [37] and Maruyam et al. [36] reported graphite flexural strength increased with temperature up to 1400 °C. Liu et al. [41], combining single-edge notched bending test with in situ X-ray computed tomography, reported the R-curve behaviour of Gilsocarbon graphite up to 1000 °C. It was found that the fracture toughness as well as crack propagation is also affected by temperature. Fast neutron irradiation further affects graphite behaviour in a complex manner through its influence on crystal dimensional change and other physical properties [42,43], but there are no data in the open literature for the elevated temperature mechanical properties of irradiated graphite.

To better understand how the graphite microstructure responds to stress and strain, in situ tests using neutron or X-ray diffraction can provide a “bridge” between the nano-scale characteristics of graphite, i.e. lattice strains in its network structure of fine crystals, and the macro-scale deformation of its heterogeneous porous microstructure. Our previous studies [25] have investigated unirradiated graphite at ambient temperature under flexural and tensile loading combined with diffraction methods. The present work sets out to quantify the relationships between elastic strains and total strains in an unirradiated graphite at ambient and high temperatures. The elastic strains, reflected as lattice spacing changes in the graphite crystals due to applied stresses, are measured using diffraction; the total strains are measured by image correlation methods applied to two-dimensional optical images and three-dimensional X-ray tomography datasets. A novel diametral compression setup using high temperature digital image correlation together with neutron diffraction has been adopted to investigate the effects of temperature. Additional insights and a validation of the neutron diffraction test methodology have been obtained by high resolution synchrotron X-ray diffraction and digital volume correlation of X-ray computed tomography scans at ambient room temperature. The methodology is suitable for examination of the behaviour of irradiated graphites at elevated temperatures, and these will be investigated in future studies.

The paper is structured as follows. The Gilsocarbon graphite material and disc compression specimen geometry are described, together with the various loading configurations that were employed for the different measurement techniques of neutron diffraction, X-ray computed tomography and X-ray diffraction. Together, these provide complementary datasets that describe the thermal expansion of the (0002) graphite basal planes, the effect of temperature on the load-displacement behaviour and strength of disc compression specimens, the evolution of total strains and elastic strains with loading and the relationships between these strains as a function of temperature. The observations obtained from these experiments provide new insights into the effects of temperature on the accommodation of strain in polygranular graphite.

Section snippets

Material and loading configuration

The material was nuclear grade (IMI-24) Gilsocarbon graphite from the same billet as previous studies by some of the authors of this article [25,[41], [44]]. This graphite, which is used in the UK AGRs, is an iso-moulded medium-grain polygranular artificial graphite with a nominal density [45] of 1.81 g/cm3 and total porosity [21] of ∼20 vol.%. It has weakly anisotropic properties, with a typical flexural strength ∼30 MPa [46], tensile strength ∼20 MPa and elastic modulus (both dynamic and

Reference (0002) plane spacing and thermal expansion coefficient

At ambient temperature, with a pre-load that was less than 1% of the failure load, the average (0002) plane spacing measured by neutron diffraction was 3.3754 ± 0.0003 Å (∼40 measurements, ± 1 sample standard deviation) and that measured by synchrotron X-ray diffraction was 3.3722 ± 0.0001 Å (961 measurements, ± 1 sample standard deviation). For reference, Nelson and Riley [62] first measured the c-dimension of the hexagonal lattice at room temperature in natural Ceylon graphite using powder

Discussion

The compressive elastic strains, measured by diffraction from the (0002) planes, increase in proportion with the compressive total strain (Fig. 14a). However, the magnitude of the elastic strains is only ∼20% of the applied total compressive strain. The discrepancy is attributed to both the macro-porosity and Mrozovski cracks [66] (Fig. 15a–c). As pointed out by Liu and Cherns [67], Mrozowski cracks and termination porosity are present between the crystal platelets due to crystallography

Conclusions

The polygranular synthetic nuclear graphite (Gilsocarbon, IM1-24) has been studied in situ by combined diffraction and imaging methods with X-rays at ambient temperature and neutrons at temperatures up to 850 °C. This allowed direct measurement of the elastic strains in the graphite crystals and the total applied strains as compressive and tensile strains develop simultaneously in the gauge volume at the centre of the disc compression specimens. It was found that the tensile strength of the

Acknowledgements

The authors gratefully acknowledge the award of beamtime at ENGIN-X ISIS (experiment RB1610238 and RB1710003), and the JEEP I12 beamline at the UK Diamond Light Source (experiment EE12585-2). DL acknowledges the support of EPSRC via Postdoctoral Fellowship Award (EP/N004493/1 and EP/N004493/2) and Royal Commission for the Exhibition of 1851 via 2015 Brunel Fellowship Award. The authors thank Drs Joe Kelleher and Tung-lik Lee for their assistance with the experiments at ENGIN-X, and Drs

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