PSI - Issue 26

E. Solfiti et al. / Procedia Structural Integrity 26 (2020) 187–198 E. Solfiti and F. Berto / Structural Integrity Procedia 00 (2019) 000–000

195

9

3.4. Other relevant properties

As suggested in the previous sections, electrical and thermal conductivity have a strong relationship. For metals this is usually described by the well-known Wiedemann-Franz law: λ = LT σ (7) where σ is the electrical conductivity and L the Lorentz number whose values for metals is equal to 2.44 · 10 − 8 W Ω/ K 2 . Similar relations have been carried out for di ff erent types of graphites, for example λ − 1 = 2 . 93 · 10 − 3 σ − 1 + 0 . 34 (8) that works for graphitised coked based materials and PG [Kelly (1981) and Mason and Knibbs (1962)]. Typical value of L for polycrystalline graphites is 1.2 · 10 − 6 W Ω/ K 2 [Powell (1937)] whereas for PG in the in-plane and out-of-plane directions is respectively 2.9 · 10 − 6 W Ω/ K 2 and 5.4 · 10 − 5 W Ω/ K 2 [Chen and Chung (2014)]. With regard to FG, results in Wei et al. (2010) gave L values from 5.6 to 6.2 · 10 − 6 W Ω/ K 2 and a final fit in the shape of a sigmoidal regression at room temperature as follow λ = 1168 . 4 e − 1 / (3 . 5 σ ) + 102 . 2 . (9) Chen and Chung (2014) finally found a linear relation among the electrical and thermal conductivity in the out of-plane direction corresponding to L = 7.3 · 10 − 6 W Ω/ K 2 . Typical values for the electrical conductivity are reported in figure 8, both against density and temperature. As expected, the values of σ in the in-plane direction increase together with the compaction pressure i.e. the density, in the same monotonical manner as the thermal conductivity does (figure 4a). The e ff ect of temperature instead seems to be more e ff ective, making the conductivity to increase for a larger range of temperature. Despite e ff ects due to di ff erent intercalant species were not found [Ionov et al. (2000)], other e ff ects can take action and give quite di ff erent values that remains anyway in the same order of magnitude. Theoretically, both the thermal and electrical conductivity do not depend on the thickness of the specimen tested but actually a slight di ff erence is found in the σ results from Chugh and Chung (2002) at very low thicknesses (0.13 - 0.38mm). FG also inherits from graphite properties both a certain degree of thermoelectric power and piezoresistivity.

0.35

0.18

0.3

0.16

0.25

0.14

0.2

0.12

0.15

0.1

0.1

0.08

0.05

0.06

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0

0.04

0

500 1000 1500 2000 2500 3000

(a)

(b)

Fig. 8: (a) Density and (b) temperature dependence of FG electrical conductivity: 1. Wei et al. (2010), 2. Sigraflex ® , ρ = 1 g / cm 3 , 3. Ionov et al. (2000), ρ = 1 g / cm 3 , 4. Chugh and Chung (2002), ρ = 1.1 g / cm 3 .

The first was quantified by Hoi and Chung (2002) in the out-of-plane direction. The voltage at the outer surfaces raises approximately in a linear manner with a slope equal to -2.6 µ V / ◦ C when reported to the absolute scale. The second instead were investigated recently from Xi and Chung (2019) who pointed out an increment of electrical resistivity over 30% when the material is stressed up to 3.18 MPa. In the latter work moreover the behavior of FG as electret and piezoelectret element has been studied for the first time. Finally, due to good compliance that stems from the porous