PSI - Issue 26

E. Solfiti et al. / Procedia Structural Integrity 26 (2020) 187–198

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E. Solfiti and F. Berto / Structural Integrity Procedia 00 (2019) 000–000

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Dowell and Howard (1986) reported a reduction on the ultimate tensile strain after heat treatment at 1750 ◦ C by a factor of 2 whereas strength increases by 1.2. It is also worth to be reported the attempt to fit the stress-strain curve with Jenkins (1962) relation used for polycrystalline graphite, that is ε = A σ + B σ 2 (1) where A and B are two fitting coe ffi cients. Such fitting model is found to be valid up to a half of the tensile strength. Due to its low mechanical strength FG is quite complicated to test and some attempts of nanoindentation has been carried out first from Chen and Chung (2015) and then from Khelifa et al. (2018) with good results. In the following sections the thermal conductivity, the coe ffi cient of thermal expansion and the specific heat ca pacity of FG will be reviewed. Data from literature result limited and sometimes absent especially when dependence on temperature is observed. Polycrystalline graphite and pyrolytic graphite without any additive will be the main ref erence for FG comparison due to their particular structure: pyrolytic graphite indeed have highly oriented graphite crystals and due to its grade of purity it can be considered as the most similar material to pure cystalline graphite [Kelly (1981)]. Data from commercial FG datasheet will be shown as well, in particular Sigraflex ® , Grafoil ® and Papyex ® . 3. Thermophysical properties

3.1. Thermal conductivity

Thermal conductivity has been employed to describe the material compression mechanism during density growth and thus the microstructure modeling. In the first section, the anisotropy has been introduced but there is not a unique definition of it since depends on the property observed. In such sense, the thermal conductivity can be a good indicator of the thermal response of the material:

λ λ ⊥

Conductivity anisotropy =

(2)

where λ and λ ⊥ are the thermal conductivities in the in-plane and out-of-plane directions respectively. The electrical conductivity can be employed as well, since it is strictly related to the thermal conductivity, often holding the same trend against density increasing. Celzard et al. (2005) measured values for the electrical conductivity anisotropy up to ≈ 70 around the conductivity threshold and for elasticity anisotropy (dynamic elastic modulus) beyond 10. In figure 4, the behavior of the thermal conductivity with the bulk density increase is displayed. The dashed lines indicate data from commercial FG datasheets. At low density, all the materials tested are graphite compacts, whereas at high density are either compacts or rolled foils. In figure 4a the thermal conductivity in the in-plane direction increases in a pretty linear manner all along the wide density range as expected by the gradual orientation of the structural units along the plane directions. Figure 4b instead deserves more discussion: almost all the data, except Chen and Chung (2014), increase at the early density but decrease when overcome a certain value oscillating within 0.4 - 0.6 g / cm 3 interval. Such fact can be attributed to a still random orientation of the units whose interlocking enhances the conductivity in both in-plane and out-of-plane direction indistinctly. After this region the conductivity decreases, as expected, being hindered from already oriented particles. It is underlined that data from Chen and Chung (2014) seems to follow a quite di ff erent trend in the first interval, that is decreasing with density, probably due to a di ff erent measurement technique. Value of thermal conductivity anisotropy are calculated up to ≈ 32 - 35 at 1 g / cm 3 , around a half of the electrical conductivity anisotropy. If the same approach is used in order to calculate the tensile strength anisotropy, one can obtain values beyond ≈ 100 at 1 g / cm 3 [out-of-plane tensile data from Gu et al. (2002)]. The thermal conductivity, moreover, is temperature dependent and despite FG can reach high working temperature in absence of oxygen, data from literature are not available except those ones from datasheets of commercial FG. In figure 5 the comparison is shown among various graphitic materials. It should be noticed that commercial FG fall in the range delimited by the pyrolytic graphite (PG) thermal con ductivity in-plane and out-of-plane, which can be viewed as the upper and lower bounds of graphite-based material Conductivity anisotropy for PG shows values above 300. FG conductivity in the in-plane direction also fits very well