In-situ neutron diffraction measurements have been performed on IMI-24 grade (20% porosity) and PG25 (48% porosity) graphite subjected to external uni-axial compression loading. The ‘pore free’ matrix properties such as modulus of elasticity of about 72 GPa and 46 GPa were measured for the IMI-24 and PG25, respectively, and were higher than those measured at the macro-length-scale. The elastic modulus of each crystal plane, hkl, is reported ranging from about 48–145 GPa and Poisson ratio ranging from 0.08–0.28 for IMI-24 graphite. With the proposed method, the pore morphology factor ‘m’ was independently evaluated to be 10.8 and 4.8 for IMI-24 and PG25, respectively. It has been demonstrated from that the micro-diffraction the Young modulus is not dependent on the pore morphology factor. We consider and discuss the experimental plus modelling approach to provide a new perspective on the micro-mechanics of porous graphites.
McEnaneyB.Chapter 1 – structure and bonding in carbon materials A2. In: BurchellTD, editor. Carbon materials for advanced technologies. Oxford: Elsevier Science; 1999. p. 1–33.
2.
SakaiMUrashimaKInagakiM.Energy principle of elastic-plastic fracture and its application to the fracture mechanics of a polycrystalline graphite. J Am Ceram Soc. 1983; 66:868–874. doi: 10.1111/j.1151-2916.1983.tb11003.x
3.
HolmesC.The mechanical behaviour and ultrasonic measurement of graphite joints [PhD thesis]. University of Bristol; 2003.
4.
NakhodchiS.Prediction and measurement of strains and stresses in metallic and non-metallic materials. Bristol, UK: University of Bristol; 2009.
5.
NakhodchiSHodgkinsAMoskovicRFracture process zones in polygranular graphite in bending. Key Eng Mater. 2011; 452–453:93–96. doi: 10.4028/www.scientific.net/KEM.452-453.93
6.
NakhodchiSSmithDFlewittP.The formation of fracture process zones in polygranular graphite as a precursor to fracture. J Mater Sci. 2013; 48:720–732. doi: 10.1007/s10853-012-6785-4
7.
MostafaviMBaimpasNTarletonEThree-dimensional crack observation, quantification and simulation in a quasi-brittle material. Acta Mater. 2013; 61:6276–6289. doi: 10.1016/j.actamat.2013.07.011
8.
HodgkinsAMarrowTJWoottonMRFracture behaviour of radiolytically oxidised reactor core graphites: a view. Mater Sci Technol. 2010; 26:899–907. doi: 10.1179/026708309X12526555493477
9.
MoskovicRFlewittPEJSchlangenEUnderstanding fracture behaviour of PGA reactor core graphite: perspective. Mater Sci Technol. 2014; 30:129–145. doi: 10.1179/1743284713Y.0000000354
10.
KellyBT.Graphite – the most fascinating nuclear material. Carbon. 1982; 20:3–11. doi: 10.1016/0008-6223(82)90066-5
11.
LaudoneGMGribbleCMMatthewsGP.Characterisation of the porous structure of gilsocarbon graphite using pycnometry, cyclic porosimetry and void-network modeling. Carbon. 2014; 73:61–70. doi: 10.1016/j.carbon.2014.02.037
12.
MarsdenBJHavertyMBodelWDimensional change, irradiation creep and thermal/mechanical property changes in nuclear graphite. Int Mater Rev. 2016; 61:155–182. doi: 10.1080/09506608.2015.1136460
13.
BrunoGEfremovAMLevandovskyiANConnecting the macro- and microstrain responses in technical porous ceramics: modeling and experimental validations. J Mater Sci. 2011; 46:161–173. doi: 10.1007/s10853-010-4899-0
14.
MunroRG.Effective medium theory of the porosity dependence of bulk moduli. J Am Ceram Soc. 2001; 84:1190–1192. doi: 10.1111/j.1151-2916.2001.tb00815.x
15.
RobertsAPGarbocziEJ.Elastic properties of model porous ceramics. J Am Ceram Soc. 2000; 83:3041–3048. doi: 10.1111/j.1151-2916.2000.tb01680.x
16.
MostafaviMMcDonaldSAÇetinelHFlexural strength and defect behaviour of polygranular graphite under different states of stress. Carbon2013; 59:325–336. doi: 10.1016/j.carbon.2013.03.025
17.
JoyceMRMarrowTJMummeryPObservation of microstructure deformation and damage in nuclear graphite. Eng Fract Mech. 2008; 75:3633–3645. doi: 10.1016/j.engfracmech.2007.11.003
18.
MostafaviMSchmidtMJJMarsdenBJFracture behaviour of an anisotropic polygranular graphite (PGA). Mater Sci Eng A. 2012; 558:265–277. doi: 10.1016/j.msea.2012.08.001
19.
NakhodchiSFlewittPSmithD.A method of measuring through-thickness internal strains and stresses in graphite. Strain. 2011; 47:37–48. doi: 10.1111/j.1475-1305.2008.00588.x
20.
NakhodchiSFlewittPETrumanCMeasurement of internal strains in graphite using the deep hole drilling technique. In ASME 2008 Pressure Vessels and Piping Conference, Chicago, Illinois, USA; 2008. p. 821–828.
21.
NakhodchiSHilsonGSmithDJA consideration of the measurement of macro-stresses in non-metallic materials. Key Eng Mater. 2010; 417–418:221–224.
22.
KrishnaRJonesANEdgeRResidual stress measurements in polycrystalline graphite with micro-Raman spectroscopy. Radiat Phys Chem. 2015; 111:14–23. doi: 10.1016/j.radphyschem.2015.02.007
23.
BertoFLazzarinPAyatollahiMR.Brittle fracture of sharp and blunt V-notches in isostatic graphite under pure compression loading. Carbon. 2013; 63:101–116. doi: 10.1016/j.carbon.2013.06.045
24.
AyatollahiMRAkbardoostJBertoF.Size effects on mixed-mode fracture behavior of polygranular graphite. Carbon. 2016; 103:394–403. doi: 10.1016/j.carbon.2016.03.030
BarhliSMSaucedo-MoraLJordanMSLSynchrotron X-ray characterization of crack strain fields in polygranular graphite. Carbon. 2017; 124:357–371. doi: 10.1016/j.carbon.2017.08.075
27.
LiuDGludovatzBBarnardHSDamage tolerance of nuclear graphite at elevated temperatures. Nat Commun. 2017; 8:15942. doi: 10.1038/ncomms15942
28.
LiuDHeardPNakhodchiSSmall-scale approaches to evaluate the mechanical properties of quasi-brittle reactor core graphite. In Graphite testing for nuclear applications: the significance of test specimen volume and geometry and the statistical significance of test specimen population. ASTM International; 2014.
29.
LiuDFlewittPEJ.Deformation and fracture of carbonaceous materials using in situ micro-mechanical testing. Carbon. 2017; 114:261–274. doi: 10.1016/j.carbon.2016.11.084
30.
FitzpatrickMELodiniA.Analysis of residual stress by diffraction using neutron and synchrotron radiation. London and New York: Taylor & Francis; 2003.
31.
WithersPBhadeshiaH.Residual stress. Part 1 – measurement techniques. Mater Sci Technol. 2001; 17:355–365. doi: 10.1179/026708301101509980
32.
DowlingNE.Mechanical behavior of materials: engineering methods for deformation, fracture, and fatigue. Upper Saddle River, United States: Pearson; 2013.
33.
MouhatFCoudertF-X.Necessary and sufficient elastic stability conditions in various crystal systems. Phys Rev B. 2014; 90:224104. doi: 10.1103/PhysRevB.90.224104
BrunoGKachanovM.Porous microcracked ceramics under compression: micromechanical model of non-linear behavior. J Eur Ceram Soc. 2013; 33:2073–2085. doi: 10.1016/j.jeurceramsoc.2013.03.012
36.
ŠavijaBSmithGELiuDModelling of deformation and fracture for a model quasi-brittle material with controlled porosity: synthetic versus real microstructure. Eng Fract Mech. 2019; 205:399–417. doi: 10.1016/j.engfracmech.2018.11.008
