KIC ¼A E H 1 2 P C 2 3 ð 21:1Þ where A is a geometric constant (0.016), E is the elastic modulus, H is the hardness value, P is the load, and C is the length of the radial crack from the center of the impression of the indent. In this method, toughness value is a function of radial crack length, elastic modulus and hardness. Since, elastic modulus can be a function of porosity, the following equation proposed by Snead et al. was used for calculating elastic modulus, E [25]. E¼E0expð CVpÞ ð21:2Þ Where E0 ¼460 GPa is the modulus of non-porous SiC, and C ¼3.57 is a constant. 21.4 Experimental Results 21.4.1 Relative Density and Densification Variation of relative density as a function of sintering temperature and graphene content is presented in Table 21.1. It is interesting to note that graphene content influence densification along with sintering temperature. Moreover, different dispersion routes also have effect on evolution of porosity in the bulk compact. Absolute density was calculated using rule of mixture as shown in equation (21.3). ρc ¼ 1 ðWf =ρf ÞþðWm=ρmÞ ð 21:3Þ Where, ρc ¼Density of the composite, Wf and Wm are weight fractions of graphene nanoplatelets and SiC, respectively, ρf ¼2. 2 g/cc is density of xGnP platelets and ρm ¼3. 21 g/cc is density of SiC. From Table 21.1 it can be clearly seen that temperature plays an important role in densification with graphene addition. Specially in case of separate graphene addition in SiC matrix using IPA, even at 2,000 ∘ C SPS temperature the relative densities are 85 % for 2 wt% C and 88 % for 5 wt% C addition. Moreover, open porosities are much higher compared to other samples. However, at 2,100 ∘ C density improves for both samples. It is believed that addition of carbon during sintering of SiC activates the sintering process. Furthermore, carbon helps in eliminating the oxide impurities residing at the grain boundaries [26]. At higher sintering temperature the following reaction takes place when there is no excess carbon [27]. SiO2 þnSiC¼Si"þSiO"þCO"þ ðn 1ÞSiC Table 21.1 Density and open porosity of graphene reinforced SiC samples at 2,000 and 2,100 ∘ C sintering temperature Sintering temperature ( ∘ C) Sample Density(g/cc) Relative density (%) Open porosity (%) 2,000 SiC 2.95 0.02 92 1.11 2,100 SiC 3.05 0.03 95 0.77 2,000 AHPCS-2 wt% C 2.92 0.09 92 1.70 2,100 AHPCS-2 wt% C 2.98 0.04 94 0.92 2,000 AHPCS-5 wt% C 2.87 0.05 92 4.27 2,100 AHPCS-5 wt% C 2.90 0.05 93 1.66 2,000 SiC-2 wt%C 2.70 0.05 85 11.83 2,100 SiC-2 wt%C 2.91 0.07 92 2.42 2,000 SiC-5 wt%C 2.77 0.03 88 8.73 2,100 SiC-5 wt%C 2.82 0.11 90 4.34 168 A. Rahman et al.
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