# Mechanical, Electrical and Fractural Characteristics of Carbon Nanomaterial-Added Cement Composites
## 2 Materials and Methods
In this dispersion method, CNMs were effectively distributed by maintaining a low fluidity of 120-160 mm (corresponding to 20% to 60%) in the freshly prepared cement composites Nam and Lee (2015 Nam). The testing methods are briefly described as follows. Three-point bending tests were performed to measure the flexural strength, fracture toughness, and fracture energy. Four specimens for each nanomaterial content ratio were subjected to the three-point bending test. All composite specimens were tested at 28 d of curing. A notch of 6 mm was made on the middle span using an electric saw in all cured samples. While measuring the flexural strength, a crack opening displacement (COD) gauge capable of measuring displacements with an accuracy of 0.01 mm was fixed at the notch to measure flexural displacement, as shown in Figure 2. A displacement-controlled universal testing machine (UTM) with a 5-t load cell was used at a loading rate of 0.002 mm/s. Figure 1: Fabrication procedure of CNM-added cement composites. Figure 2: Experimental setup for the three-point bending test. A three-point bending test was performed according to ASTM C 293 [64; 65] in an effort to evaluate flexural strength. \[\sigma_{t}=\frac{3 FL}{2b(h-a)^{2}} \tag{1}\]  
where \(\sigma_{t}\), \(F\), \(L\), \(b\), \(h\), and \(a\) represent flexural strength (MPa), maximum load (N), length of span (mm), width of the specimen (mm), height of the specimen (mm), and notch depth (mm), respectively [64; 65]. Fracture toughness and fracture energy were calculated using the following equations [66; 67]:  
\[G_{f}=\frac{0.75W_{0}+W_{1}}{A_{lig}} \tag{2}\]  
\[W_{0}=\int_{0}^{\delta 0}P(\delta)d\delta \tag{3}\]  
\[A_{lig}=(h-a)b \tag{4}\]  
\[W_{1}=0.75\bigg{(}\frac{SM_{1}}{L}+2M_{2}\bigg{)}gCMOD_{C} \tag{5}\]  
\[K_{ic}=\frac{FS}{bh^{\frac{3}{2}}}f\bigg{(}\frac{a}{h}\bigg{)} \tag{6}\]  
Figure 2.0  
Figure 2.1  
where \(G_{f}\) is the fracture energy of the composite (N/m), \(K_{ic}\) is the fracture toughness of the composite (MPa/m\({}^{1/2}\)), \(W_{0}\) is the area under the load-displacement curve, \(P(\delta)\) is the load-crack mouth opening displacement (CMOD) curve, \(\delta_{0}\) is the displacement at the times of failure, \(M_{1}\) is the mass of the composite between supports (\(Kg\)), and \(M_{2}\) is mass of the jig, which is not attached to a testing machine but placed on the specimen until rupture (\(Kg\)), \(g\) is the gravitational acceleration (m/s\({}^{2}\)), \(S\) is the loading span (mm), \(L\) is the total length of specimen (mm), \(CMOD_{C}\) is the crack mouth opening displacement at the time of rupture (mm), and \(F\) is the peak load (N). Note that the \(K_{ic}\) value can be deemed valid only when the condition stated in Equation (8) is satisfied. After performing the three-point bending test, a sample that was split into two was used for compressive strength tests by following ASTM C 349 [68], as shown in Figure 2.2 A UTM with a capacity of 300 t was used to conduct compressive strength tests. The measurements were taken at a constant head-loading rate of 0.02 mm/s using displacement control. Four specimens were evaluated for each nanomaterial content ratio; the average value was used as the representative compressive strength of each type [12]. The compressive strengths of the specimens were determined as follows:  
Figure 2.3  
where \(\sigma\) is the stress (N/mm\({}^{2}\)), \(P\) is the maximum load at the point of failure (N), and \(A\) is the cross-sectional area (mm\({}^{2}\))A porosity test was performed to analyze the changes occurring in the pore characteristics of cement composites when CNM was added and analyze the relationship between porosity and mechanical and fractural characteristics. Porosity can be defined as the volume of permeable space in the specimens. Generally, the porosity of cement composites decreases when CNM is added; this phenomenon occurs because CNM acts as a filler agent in the cement composite. Porosity tests were performed according to ASTM C 642 [69].