Residual stress measurements in polycrystalline graphite with micro-Raman spectroscopy

Radiation Physics and Chemistry 111 (2015) 14–23

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Residual stress measurements in polycrystalline graphite with microRaman spectroscopy Ram Krishna a,n, Abbie N. Jones b, Ruth Edge a, Barry J. Marsden b a Dalton Nuclear Institute, Dalton Cumbrian Facility, University of Manchester, Westlakes Science & Technology Park, Moor Row, Whitehaven, Cumbria CA24 3HA, UK b Nuclear Graphite Research Group, School of Mechanical, Aerospace & Civil Engineering, University of Manchester, Manchester M13 9PL, UK

H I G H L I G H T S







Micro-Raman spectroscopy can measure significantly small residual stresses. Gilsocarbon, NBG-18 and PGA graphite were evaluated for residual stresses. Residual stresses in the constituents of graphite were evaluated. Binder and filler particles are often found under compressive and tensile stresses.

art ic l e i nf o

a b s t r a c t

Article history: Received 5 December 2014 Received in revised form 2 February 2015 Accepted 10 February 2015 Available online 11 February 2015

Micro-Raman microscopy technique is applied to evaluate unevenly distributed residual stresses in the various constituents of polygranular reactor grades graphite. The wavenumber based Raman shift (cm  1) corresponds to the local residual stress and measurements of stress dependent first order Raman spectra in graphite have enabled localized residual stress values to be determined. The bulk polygranular graphite of reactor grades – Gilsocarbon, NBG-18 and PGA – are examined to illustrate the residual stress variations in their constituents. Binder phase and filler particles have shown to be under compressive and tensile stresses, respectively. Among the studied graphite grades, the binder phase in Gilsocarbon has the highest residual stress and NBG-18 has the lowest value. Filler particles in Gilsocarbon have the highest residual stress and PGA showed the lowest, this is most likely due to the morphology of the coke particles used in the manufacturing and applied processing techniques for fabrications. Stresses have also been evaluated along the peripheral of pores and at the tips of the cracks. Cracks in filler and binder phases have shown mixed behaviour, compressive as well as tensile, whereas pores in binder and filler particles have shown compressive behaviour. The stresses in these graphitic constituents are of the order of MPa. Non-destructive analyses presented in this study make the current state-of-the-art technique a powerful method for the study of stress variations near the graphite surface and are expected to increase its use further in property determination analysis of low to highly fluence irradiated graphite samples from the material test reactors. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Residual stress Polycrystalline graphite PGA Gilsocarbon NBG-18 Raman micro-spectroscopy Binder Filler Cracks Pores

1. Introduction Graphite has a long and rich tradition of research and has widespread application as a neutron moderator and is used as a structural component in nuclear reactors (Fermi, 1952; Nightingale, 1962). In recent years, with interest in Gen-IV reactor design, graphite has attracted considerable attention as a potential

n

Corresponding author. E-mail address: [email protected] (R. Krishna).

http://dx.doi.org/10.1016/j.radphyschem.2015.02.007 0969-806X/& 2015 Elsevier Ltd. All rights reserved.

material, since it can be employed as a fast neutron moderator/ reflector structural component in Very High Temperature and Gascooled reactors (Bonal et al., 2009; Marsden and Hall, 2012). There are a variety of artificially produced polycrystalline graphite grades commercially available as reactor graphite and they are characterised by their: forming processes (extrusion, pressing, vibration and isostatic moulding, etc.), utilized source coke for manufacturing, their grain size, type of binder and filler particles, their randomly distributed multi-scaled porosities and nano-scale ‘Mrozowski’ cracks. Nuclear graphite grades are specifically manufactured for use within the nuclear reactors core to a specification

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–23

that is aimed at retaining its moderating, physical, and mechanical properties under nuclear radiation environment even at high temperatures (Simmons, 1965). However, reactor core graphite is subject to a hostile environment of fast neutrons and hot coolant gas in which it experiences irradiation-induced hardening and in some cases radiolytic oxidation during the exposure life. These irradiation-induced effects lead to progressive changes in the physical, mechanical properties and in particular, build-up of significant stresses and deformation in the graphite components (Marsden and Hall, 2012; Tsang and Marsden, 2006, 2007). During graphite manufacture, which involves several high temperature heating cycles (Marsden and Hall, 2012), internal stresses (Kuroda et al., 2005; Rand, 2012) are generated at the micro-scale in the constituent phases of graphite grades. The manufacturing stresses retained in bulk graphite billets as internal (residual) stresses and may cause cracking (Hodgkins et al., 2006; Kelly, 2000; Kuroda et al., 2005). In addition, such unintended residual stresses in artificially manufactured graphite grades may limit their service life depending up on the neutron irradiation temperature and doses. Therefore, it is important to characterise all grades of graphite to evaluate the irradiation material properties to understand the evolution of these properties and, hence predict component behaviour under the intended irradiation environment. Important reactor graphite grades are Gilsocarbon, Nuclear Block Graphite-18 (NBG-18) and Pile Grade-A (PGA) considered in the present study. These graphite grades are polycrystalline and heterogeneous; comprised of various carbonaceous phases such as coke filler particles, pitch binder phase, quinoline insoluble particles and graphitic and turbostratic graphite phases. The issues related with the build-up stresses in the constituent phases are significant. Internal stresses may possibly actuate the initiation and propagation of dislocations and nucleation of new cracks and voids. Stresses may also trigger swelling behaviour and dimensional change in graphite at low temperature under irradiation condition as observed in NBG-10 graphite (Burchell and Snead, 2007) and grade TSX graphite (Kennedy and Woodruff, 1989). Therefore, internal/residual stresses may play a significant role in explaining the failure of components. There are techniques available for measuring the distribution of internal strains/stresses in materials; however they are invasive, semi-invasive, require complex computer simulated modelling or may be applied to only a restricted class of materials. A few techniques such as X-ray diffraction, deep-hole-drilling (DHD), finite element simulations, micro-indentation and ultrasonic wave methods have been investigated for application in graphite (Nakhodchi et al., 2011; Shibata et al., 2008). In this paper, the internal (lock-in) stresses in various constituents of polycrystalline reactor grades graphite such as filler, binder, and along the peripheral of pores and at the tips of the cracks, have been evaluated using micro-Raman spectroscopy, a non-invasive analytic method for stress evaluation in near-surface submicrometer regions of reactor graphite. The applicability of this method to both non-irradiated and irradiated graphite is a promising method to access information on residual stresses effectively and non-invasively. Micro-Raman spectroscopy is a non-destructive technique and provides information on the microscopic state of stresses in the constituents of materials with up to a micrometre of lateral and depth spatial resolutions (Anastassakis et al., 1970; Wolf and Maes, 1998). The lateral and depth spatial resolution is along the XY and Z directions, respectively and the Z spatial resolution depends on the confocality of the spectroscope used. In particular, a spatial resolution in the order of 1 μm is effective for the local stress measurement and a better spatial resolution can be achieved with ‘polished’ samples (Wolf, 1996). An inelastic interaction of laser source with crystal lattice vibrations is employed for stress measurements with high lateral resolution and thus, the crystalline

15

Fig. 1. (a) Raman spectrum from HOPG taken with 532 nm laser excitation wavelength. The spectrum shows the presence of G-peak at 1580 cm  1 (E2g symmetry) and absence of D-peak. (b) A bright field TEM micrograph of HOPG shows layered structures of 20–200 nm thickness and a strong orientation [0002] along the stacking direction.

material can be probed non-destructively without the need for complex and time-consuming sample preparations (Wolf, 1996). The first-order stokes-Raman spectrum of Highly Ordered Pyrolytic Graphite (HOPG), with relatively near perfect graphite crystallographic geometry, exhibits a single G-peak, which corresponds to the k E0 vibrations of the doubly degenerate optical phonons (E2g symmetry) and the Raman G line represents almost negligible residual stresses (Ferrari, 2007). The Raman spectrum and bright field transmission electron (TEM) micrograph of HOPG are shown in Fig. 1. However, in artificially manufactured graphite, the constituent phases remain under residual stresses developed during fabrication process, which causes polarization dependent shifts which are observed to be dependent on the internal stress values (Mohr et al., 2010; Sakata et al., 1988). Thus, the Raman G line (optical phonons) in artificially manufactured graphite shifts due to the presence of internal stresses and the magnitude of this stress is directly proportional to the Raman line shift. A candid way to relate measured Raman shift to stress magnitude is the use of a stress model illustrating the stress state in the constituents or in the bulk sample within crystallites of arbitrary orientation. A linear relationship between Raman lineshift and stress has been previously applied to estimate the stress values in graphite fibre (Sakata et al., 1988), graphene based mechanical systems (Mohiuddin et al., 2009), quartz (Harker et al., 1970), polycrystalline Mn–Zn ferrite (Yamashita and Ikeda, 2004), polycrystalline silicon (Becker et al., 2007; Wolf and Maes, 1998) etc. It is well-known that compressive stress shifts the Raman line to a higher frequency, while tensile stress shifts it to a lower frequency, as shown in Fig. 2 (Wolf, 1996). The splitting of doubly degenerated E2g optical mode (G-band) into two components G þ and G  is due to the effect of anisotropic (deviatoric) stress that possibly changes the crystallographic symmetry and lifts the twofold degeneracy completely or partially (Mohiuddin et al., 2009; Sakata et al., 1988). However, hydrostatic stress within the constituents of graphite only produces a shift and the original symmetry remains intact (Frank et al., 2011; Ganesan et al., 1970; Tuinstra and Koenig, 1970). Therefore, in the present example, the graphene hexagonal symmetry – 2D building block of the graphite structure – remains preserved. The Raman line-shift is conditional on the material's property – phonon deformation potential – and corresponds to a change in

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R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–23

Fig. 2. Dispersive Raman spectra of filler–binder region in Gilsocarbon. The shifting of G peak towards left and right directions implies tensile and compressive residual stresses in the structure. The spectra show first order fundamental bands (D, G and D′) and their overtones (2D(G′), DþD′, 2D′(G′′)).

vibrational frequencies (Thomsen et al., 2002). In general, a stress of 1 GPa introduces a Raman line shift of about 2 cm  1 in polycrystalline silicon wafers, which appears large enough to cause cracking in the film (Sarau et al., 2012). Thus, the possibility of measuring residual stresses in the constituent phases of reactor grade graphite with a spatial resolution of less than 1 μm can be achieved using a Raman microscope. Few authors have also discussed the effects of external stresses on the Raman spectra (Anastassakis et al., 1993; Frank et al., 2011; Sakata et al., 1988). These studies demonstrate that stress affects the stacking order of pristine graphite and induces stress-induced symmetry breaking as splitting of G band into two distinct subbands (G þ , G  ) is observed. The experimental values for the phenomenological coefficients, which describe the changes in phonon deformation potentials under strains are specific to the materials properties, and can be obtained from the observed splitting of the G band (Huang et al., 2009). Taylor et al. (2003) presented a non-intrusive method for measuring residual surface stress in thin carbon films using Raman spectroscopy and nanoindentation. Therefore, in the present study the stress evaluation will lead to a better understanding of reactor grade graphite microstructure and its behaviour under the reactor operating conditions (i.e. interpresence of fast neutron irradiation and radiolytic oxidation).

2. Materials and experimental procedure The characteristics of graphite grades used in the present study are presented in Table 1 (Krishna et al., 2015). All graphite grades are polycrystalline and diverse in nature. Various carbonaceous phases such as filler particles, binder phase, quinolone insoluble (QI) particles, and turbostratic graphite make these grades complex and heterogeneous.

NBG-18 is polycrystalline and isotropic grade nuclear graphite manufactured by SGL Carbon Gmbh. The fabrication process utilizes vibration moulding (VM) based on isotropic pitch coke and coal-tar pitch. The spherical coke filler and isotropic structure is comparable with the near-to-isotropic Gilsocarbon graphite. Gilsocarbon is complex, heterogeneous and near-to-isotropic graphite with an anisotropy factor of 1.1. It is manufactured in the UK by AGL (now SGL) and BAEL (later UCAR now GrafTech) utilizing a coke manufactured from Gilsonite – a naturally occurring hydrocarbon. The Gilsocarbon billets were moulded in a press. Pile Grade-A (PGA) is a heterogeneous high purity graphite grade, employed in the early Magnox reactor design for neutron moderation, and is formed by extrusion. It was manufactured by BAEL and AGL and has needle-shaped petroleum coke particles. The extrusion process tends to align coke particles in the direction of extrusion and results in a highly anisotropic microstructure. Thus, the basal layers in extruded PGA tend to lie parallel to the extrusion axis and this is accompanied by a large difference in bulk properties parallel (With Grains – WG) and perpendicular (Against Grains – AG) to the extrusion direction. In this study, samples for characterization are taken Against Grain, AG direction, from a PGA graphite billet. Filler particles are mainly calcined pitch/Gilsonite coke, which has been calcined around 1200 °C. The binder is a thermoplastic material, with a high carbon content usually derived from the distillation of coal-tar pitch. Porosities and cracks are of different morphologies and observed randomly in the microstructure. These are one of the salient characteristics of microstructure depending upon graphitization/gas-evolution processes and exhibit a vital role in irradiation induced dimensional change, as this porosity type can accommodate crystallite expansion during irradiation (Hall et al., 2006; Jones et al., 2008). Micro-Raman Spectroscopy was conducted using a SENTERRA Raman microscope (Bruker Optics, Inc.). The Raman vibrational spectra were measured using a 532 nm wavelength excitation laser with a 10 s integration in the confocal mode of operation at a resolution of 3 cm  1. The spectrometer is equipped with Olympus BX51 reflected light and transmission light (R200-L) optical microscope with bright field (BF) illuminator consisting of universal condenser and illumination source for reflection and transmission (20  bright field, Olympus MPLN 20; NA ¼0.40; WD ¼1.30 mm and 50  bright field, Olympus MPLN 50; NA ¼0.75; WD ¼0.38 mm) objective lenses focus the 20 mW laser beam onto a 1 μm diameter spot on the graphite surface. Sample heating, heat transfer and dissipation to the graphite surface are negligible (Tsang et al., 2005). Spectra obtained from the Ramanscope are accurate to 71 cm  1. This equipment utilizes SENTERRA's patented Sure_Cals automatic laser and Raman frequency calibration method to produce reliable and reproducible measurements with excellent frequency accuracy and precision of about 0.1 cm  1. By measuring simultaneously each Raman spectrum from the excitation line of the laser and the emission lines from the laser/neon spectrum of a neon emission lamp and employing afterwards an integral transformation process on these spectra to correct automatically and continuously the Raman data for instrument instabilities. Due to this Sure_Cals method, the spectrometer is

Table 1 Characteristics of reactor grades graphite used in the present study. Graphite grade Manufacturer

Gilsocarbon NBG-18 PGA

Forming/moulding process

AGL, BAEL, UCAR Vibration SGL, Germany Vibration BAEL and AGL Extrusion

Bulk density (g/cm3) Particle grain size range (μm)

Source coke Porosity (%) Microstructure

1.92 1.85 1.74

Gilsonite Pitch Petroleum

1–300 1–300 1–800

16.2 17.8 18.3

Crystallite size (La) (nm)

Near-to-isotropic 62.5 Isotropic 35.4 Anisotropic 87.3

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–23

continuously calibrated and therefore, no routine calibration by external standard is required. The spectrometer is coupled with a computer controlled grating turrent monochromator with a grating of 1200 grooves/mm for high resolution and wide range and a CCD thermo-electrically cooled to 65 °C, 1024  256 pixels, filter changer consisting of Raleigh filter and ND filter wheel for changing the laser power, with a motorized aperture of slit type (25  1000 and 50  1000 μm2) and confocal pinhole type (25 and 50 μm) combination. A computer controlled motorized sampling stage connected to the device, to move the sample along X, Y and Z coordinates to control the measurement position in a region of the sample surface, with an accuracy of 0.1 μm and in this case, the repeatability was observed to be better than 1 μm. The dispersive Raman spectral information data acquisition, processing and evaluation were measured using 10 s measurement time with three accumulations using intuitive spectroscopic software – OPUS Version 7.5. Raman 2D chemical mapping is generated with the live OPUS video package. Spectral information computation was achieved using multivariate analysis tools available in the OPUS software navigation menu. All the measurements were conducted at the same sample height, z¼ 0 position. The Raman image/map produced was composed of 20  20 Raman spectra selected from the graphite surface region of range Y as  230 and X as  320 μm with an approximately 16 μm step size The maps illustrate the spectral information comprised of Raman data from the selected surface region. Raman imaging of graphite grades reveals the heterogeneity of the graphite structure and the spectral information, which is used to evaluate the magnitude of local stresses near to the surface regions. The Raman image is not self-interpreting. Rather, it requires a careful attention to the mathematical operations on the data and the interpretation of the results. Further, it must be noted here that the pristine HOPG is free from the defect D peak, at around 1350 cm  1. The obvious presence of G-peak, the E2g symmetry and absence of D-peak, A1g symmetry in Raman spectrum can be seen in Fig. 1. Fig. 1 also illustrates the bright field TEM micrograph of HOPG. The authors note the absence of defects in HOPG resulted in total disappearance of D-peak in the Raman spectrum. Therefore, in this research, the authors investigated the G-peak only. In a recent study, Peña-Álvarez et al. (2014) reported dispersive behaviour of strained HOPG as a result of compression characteristic to the resonant Raman features. The energy dispersion of first and second order Raman features at ambient conditions with a range of excitation energies (measured from 488.0 to 632.8 nm excitation wavelengths) under the strain conditions are evaluated and corroborated associated dispersion change to the electronic properties. Raman defect activated bands in nuclear graphite grades are observed and for a comparison, Raman shifts of various dispersive features are shown in Table 2. These Raman dispersive features behaviour changes with stress attributed to phonon dispersion evolution. In pristine graphite these dispersive features are mediated by the residual stress developed and retained during and Table 2 Raman features shifts for nuclear graphite grades measured with 532 nm excitation wavelength. Raman features

Gilsocarbon

NBG18

PGA

D D′ D þD′′ 2D(G′) D þD′ 2D′(G′′)

1350.93 1620.85 2456.94 2699.87 2945.00 3246.96

1350.71 1620.88 2454.61 2700.67 2945.11 3246.42

1352.34 1622.02 2452.85 2704.77 2946.28 3248.49

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after the manufacturing related processes.

3. Theoretical consideration Using the generalized Hooke's law which relates an arbitrary stress, sij, to an arbitrary strain, εij, via the compliance, Sij, in a coordinate system (x, y, and z) with x and y in the plane and z perpendicular to the graphite plane, as follows:

⎡S ⎡ εxx ⎤ ⎢ 11 ⎢ ε yy ⎥ ⎢ S12 ⎥ ⎢ ⎢ ⎢ εzz ⎥ ⎢ S13 ⎢ ε yz ⎥ = ⎢ ⎢ε ⎥ ⎢ 0 ⎢ zx ⎥ ⎢ 0 ⎢⎣ εxy ⎥⎦ ⎢ ⎣ 0

S12 S13

0 0 0

S11 S13 S13 S33 0 0 0 0 0 0

⎤ 0 ⎥ ⎡ σ xx ⎤ 0 ⎥ ⎢ σ yy ⎥ ⎥ ⎢ 0 ⎥ ⎢ σ zz ⎥ ⎥× ⎥ ⎢ σ yz ⎥ 0 ⎥ ⎢ σ zx ⎥ ⎥ 0 ⎥ ⎢ ⎥ ⎣ σ xy ⎦ 2(S11 − S12 ) ⎦ 0 0 0

S44

0

0

S44

0

0

The stress distribution in anisotropic grade graphite is described as σxx and σ yy in the x –y plane and for isotropic grade graphite σxx = σ yy stress distribution in the sample. In the present study, von Misses/average stresses are used for illustration and evaluation of the residual stresses in the sample, as follows:

σ=

2 2 σ xx + σ yy − σ xx σ yy

On considering the stress sensitivity under the stress/strain system, the resulting strain tensors are given by εxx = ε = S11σ and ε yy = − vε = S12 σ (v ¼0.16 has been assumed for Poisson ratio) or equivalently with all shears equal to zero:

εxx = ε = S11σ

(1)

ε yy = − vε = S12 σ

(2)

A phenomenological approach is used to analyse the Raman optical phonon mode in the presence of strain (Ganesan et al., 1970). The temporal equation for the E2g mode of graphite (under internal stresses) following the standard procedure is given as:

A (εxx + ε yy ) − λ

B (εxx − ε yy + 2iεxy )

B (εxx − ε yy − 2iεxy )

A (εxx + ε yy ) − λ

=0 (3)

where λ = ω2 − ω02 is the difference between the squared straindependent Raman line frequency ω , and the squared Raman line frequency in the absence of strain ω0 . ‘A’ and ‘B’ are the constants for phonon deformation potential coefficients, and εij is the strain tensor. The relationship can be approximated as

ω = ω0 +

λ 2ω 0

(4)

The phenomenological coefficients A and B describe the changes in the elastic constants of k E0 optical phonons (vibrations) with stresses/strains and their experimental values can be determined using the measured shifts in Raman line. Assuming shear component is absent, the temporal equation reduces to

A (εxx + ε yy ) − λ

B (εxx − ε yy )

B (εxx − ε yy )

A (εxx + ε yy ) − λ

=0 (5)

Solving Eq. (3) analytically, two solutions are obtained as follows:

λ1 = (A + B) εxx + (A − B) ε yy

(6)

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Table 3 Elastic compliances (  10  6 MPa  1) of reactor grades graphite (Kelly, 1981). Elastic compliances

S11 S12 S13 S33 S44

Anisotropic PGA

Isotropic Gilsocarbon and NBG-18

2150  140  162 1087 3230

1370  148 – – 3030

ω1 = ω 0 +

(A + B) S11σ + (A − B) S12 σ 2ω 0

(10)

ω2 = ω 0 +

(A − B) S11σ + (A + B) S12 σ 2ω 0

(11)

The Raman shifts in frequencies due to strains/stresses, Δω1 and Δω2, are

Δω1 = ω 0 − ω1 (A + B) S11σ + (A − B) S12 σ 2ω 0 σ =− [(A + B) S11 + (A − B) S12 ] 2ω 0 =−

Table 4 Correlation between the Raman shift and residual stresses in polycrystalline graphite structure. Isotropic

(12)

σ xx (MPa) = 0.3597Δω (cm−1)

Δω2 = ω 0 − ω2

σ yy (MPa) = 0.1198Δω (cm−1) Anisotropic

(A − B) S11σ + (A + B) S12 σ 2ω 0 σ =− [(A − B) S11 + (A + B) S12 ] 2ω 0

σ xx (MPa) = 0.2019Δω (cm−1)

=−

σ yy (MPa) = 0.0749Δω (cm−1)

Table 5 Raman shifts in binder and filler phases of three different grades of reactor graphite. Graphite grades

Binder phase Raman shift (cm  1)

Filler phase Raman shift (cm  1)

Gilsocarbon NBG-18 PGA

 1.9047 0.227  0.905 7 0.264  1.842 7 0.175

1.30 70.758 0.57070.269 1.019 70.876

Table 6 Compressive and tensile stresses in binder and filler phases of three different grades of reactor graphite. Graphite grades

Binder phase Compressive stresses (MPa)

Filler phase Tensile stresses (MPa)

Gilsocarbon NBG-18 PGA

0.526 70.072 0.287 70.084 0.326 70.031

0.258 7 0.103 0.1397 0.035 0.1247 0.075

(13)

The experimental data for the phenomenological coefficients A and B were taken from Sakata et al. (1988), which are consistent with values reported in Frank et al. (2011) and Mohiuddin et al. (2009). For the backscattering from the (0001) surface, a doubly generated Raman phonon mode is observed. Using the values given in Table 3 and the experimental values for A and B, Table 4 outlines the relation between wavenumber based Raman shift, Δω (cm−1) and the residual stress in graphite samples. The correlation in Table 4 illustrates that a negative Raman shift indicates compressive residual stress, and a positive Raman shift indicates a tensile residual stress. The doubly degenerate Raman phonon mode at 1581.118 cm  1 corresponds to Raman allowed E2g mode in HOPG, which having no stress/strain in the structure, was used to characterise the Raman line shift associated with residual stress/strain in the reactor grade graphite.

4. Experimental results and discussion Microscopic graphite surface characteristics of assorted reactor

Table 7 An averaged residual (compressive) stress distribution at different locations in crack tips and pore peripheries of the reactor graphite grades. Graphite grades

Residual (compressive stresses (MPa) Crack

Gilsocarbon NBG-18 PGA

Pore

Edge (crack tip) 1

Centre

Edge (crack tip) 2

End 1

Centre

Edge 2

0.8157 0.113 0.081 7 0.017 0.1127 0.067

0.208 7 0.010 0.028 7 0.025 0.059 7 0.064

0.839 7 0.178 0.284 7 0.114 0.290 7 0.084

0.706 7 0.151 0.1397 0.103 0.254 7 0.104

0.4937 0.174 0.0457 0.051 0.1147 0.138

0.6337 0.029 0.3677 0.163 0.3587 0.154

λ 2 = (A − B) εxx + (A + B) ε yy

(7)

where S11 and S12 are the elastic compliances. For each of the reactor graphite grades elastic compliances for isotropic and anisotropic structures are tabulated in Table 3. Substituting the stress–strain relations in (3) into the two solutions given by Eqs. (6) and (7) and using the Eq. (4), the stress dependent Raman frequencies now can be represented as

λ1 = (A + B) S11σ + (A − B) S12 σ

(8)

λ 2 = (A − B) S11σ + (A + B) S12 σ

(9)

grades graphite are investigated by Raman spectroscope. The residual stress distribution in the region of binder phase, filler particles and multi-scaled cracks and pores of sizes up to 300 μm is evaluated using Raman spectra. A total of 400 spectra are used to illustrate the Raman image(s) from the different region of the graphite structure. The averaged Raman shifts in binder and filler phases for all three grades graphite are illustrated in Table 5. Here, the binder and filler particles are representing negative and positive Raman shifts for compressive and tensile residual stresses, respectively. Table 6 demonstrates the averaged values of compressive stresses (MPa) in binder phase and tensile stresses in filler

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–23

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Fig. 3. The average residual stress (MPa) values of binder (compressive) phase and filler (tensile) particle region in reactor grades graphite evaluated from Raman spectra. The average residual values are from the 20 different locations in binder and filler particle regions.

Fig. 4. The averaged residual stress at the measured points (tips and the centre for cracks and diametrically end points and the centre for pores) in the cracks and pores of reactor graphite grades.

particles extracted from the Raman spectra of reactor grades graphite. It is noted that there are very limited published studies available on stress evaluation in graphite under strained conditions, and it is difficult to compare the present results as it is evaluating the stress already present under the pristine condition and no external stress has been applied to the graphite samples. Tsang and Marsden (2006) studied the stress analysis in nuclear graphite bricks subjected to both fast neutron irradiation and radiolytic oxidation, using material model subroutine called MAN UMAT (Tsang and Marsden, 2006). The stress values reported in Tsang and Marsden (2006) nuclear graphite bricks under irradiation condition are typically several orders of magnitude higher than the stress evaluated in the present study, which is expected as the samples were radiation damaged. Complex stress fields within the nuclear graphite bricks are expected to develop under radiation environment. Table 7

shows the averaged values of compressive stresses in crack and pore periphery of reactor grades graphite. The averaged values of the stresses are true representation of Raman spectral information and the averaged data of stresses are from both the tips of crack, diametrically opposite ends of the pore and centre periphery of the pore and the crack. Multi-scaled pores and cracks are characteristics to graphite structures and attributed to the manufacturing and forming operations. It is interesting to compare the residual stress values obtained here with that expected for isotropic (Gilsocarbon and NBG-18) and anisotropic (PGA) graphite grades. The shift in phonon frequencies is due to changes in the phonon deformation potential induced by the residual strain. The sign of compressive stresses and tensile stresses are negative and positive, respectively and now onwards tensile and compressive stresses will be referred without their respective

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Fig. 5. Optical micrographs and Raman mappings (230 μm  320 μm) which were created across the regions on polycrystalline Gilsocarbon graphite (a) filler region, (b) binder region, and (c) cracks in the binder phase.

signs. Typical Raman spectra from the region of filler particle and binder phase in Gilsocarbon are shown in Fig. 2. Fig. 2 also illustrates residual stress nature in the structure; such as compressive stress exists if G peak shifts towards right or tensile stress exists if G peak shifts towards left. Fig. 3 illustrates the average residual stress (MPa) values of binder and filler particle regions in reactor grades graphite – Gilsocarbon, NBG-18 and PGA. The results showed that compressive residual stress in binder phase is the highest for Gilsocarbon and

lowest for NBG-18, although, in filler particles stress is highest for Gilsocarbon, but lowest for PGA among the reactor grades graphite. The reason for this is probably due to morphology of the coke particles used in the manufacturing and applied techniques for fabrication. The dimensions of filler particles in all reactor grades graphite (PGA, Gilsocarbon and NBG-18) are typically in the range 0.10–1 mm (Hodgkins et al., 2010). However, Gilsocarbon and NBG-18 graphite filler particles are spherical in shape, particularly

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Fig. 6. Optical micrographs and Raman mappings (230 μm  320 μm) which were created across the regions on polycrystalline NBG-18 graphite (a) filler region, (b) binder region, and (c) cracks in the binder phase.

in the case of Gilsocarbon, whereas the PGA graphite contains filler particles in the form of laths/needles. The filler particles in PGA graphite are aligned in the extrusion direction, so properties and microstructure are different from the isotropic graphite grades (Mostafavi et al., 2012). HOPG (SPI-1 grade) sample was employed as a model material in the present study to evaluate the residual stress values in the artificial reactor graphite grades, as it has no residual stresses due to the absence of defect volume and constituents phases. Fig. 4 details the residual stress values of cracks tips and at pore

peripheries in reactor grades graphite. The residual stresses are measured at the tips and centres in cracks and in micro-pores at the diametrically end points and their centres. The nature of residual stresses at the tips of the cracks is mixed – tensile and compressive. Pores in binder and filler particles have compressive stresses, both at the ends and the centre of the pores. However, centres of cracks and pores have lower stress values than their ends. Gilsocarbon has higher compressive stresses in pores and cracks than the other graphite grades. These stress values are in the range of several MPa.

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Fig. 7. Optical micrographs and Raman mappings (230 μm  320 μm) which were created across the regions on polycrystalline PGA graphite (a) filler region, (b) binder region, and (c) cracks in the binder phase.

The stress values observed in different constituents of the graphite are small, but these values are critical in graphite bricks for applications in nuclear reactor. During reactor operation graphite brick structures are exposed to gradients of temperature and neutron radiation, which results in significant changes in graphite brick properties, and develop a complex stress fields within the brick (Tsang and Marsden, 2006). Figs. 5–7 present 2D contour plots and optical micrographs of the analysed area where these results are spectroscopically analysed the local information along x–y coordinates of the

measurement points. The trace values representing the spectral data in x- and y-coordinates system from the sample surface region of interest. The z-dimension (trace values) is visualized by means of colour-coded contour levels. For this purpose, the range of the z-values – trace values – is subdivided into several contour levels and each contour level is assigned to a certain colour code. This colour-coded contour plot is projected on the two-dimensional area of the xy-coordinate system. The map contours show the Raman spectra featuring the local regions characteristics in the Raman maps. These spectra provide

R. Krishna et al. / Radiation Physics and Chemistry 111 (2015) 14–23

information on Raman shift, which are used to measure the corresponding residual stresses. The maps show the blue colour has the lowest value of stress and the white has the highest value of stress. Also, the compressive stress would lead to a shift towards higher wavenumber, which is in contrast to the findings observed for polycrystalline silicon (Kang et al., 2005). Stress measurement in polycrystalline graphite is an important aspect in understanding fracture mechanism under graphite technology (Hodgkins et al., 2010). Measurement of stress dependence of Raman active vibrations is notable for both applied and fundamental studies and can be used to verify the theoretical models (Tsang and Marsden, 2006). Thus, the Raman microscopy has been evolved as a fast, relatively easy to use and non-destructive examination technique for potentially useful information source concerning the structure of graphite such as the residual stresses developed before and after irradiation and can be applied to examine the induced internal stresses in low to high dose radioactive graphite samples.

5. Conclusions Micro-Raman spectroscopy is an analytical method that can be rapidly applied to evaluate internal stresses distribution in the constituents of polycrystalline graphite. It is sensitive enough to measure low stress concentration in constituent phases of graphite grades. Three different grades of reactor graphite are considered namely Gilsocarbon, NBG-18, and PGA for the analysis and evaluation. Graphite structural constituents such as filler particles, binder phase, cracks and pores are the salient consideration for residual stress estimation study and the results revealed that stresses in filler particles are tensile in nature, and stresses in the binder phases are compressive in nature. It was found that the binder phase in Gilsocarbon has the highest residual stress and NBG-18 has the lowest value. Filler particles in Gilsocarbon have the highest residual stress and PGA has the lowest. Stresses at pore peripheries and cracks tips in the binder and filler particles are also evaluated and these stresses were found to lie in the range of several orders of MPa. Compressive stresses in binder were in the range of 0.29–0.53 MPa and tensile stresses in filler were in the range of 0.12–0.26 MPa. Stresses in cracks present in binder and filler particles were of mixed nature, compressive and tensile and their values were in the range of 0.11–0.84 MPa. Stresses in pores were in the range of 0.14–0.71 MPa.

Acknowledgement The authors would like to thank Prof. Simon M. Pimblott, Director, Dalton Cumbrian Facility (DCF), Dalton Nuclear Institute for access to the-state-of-art facilities at Cumbrian site.

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