4.1.2. Viscosity

Plastic viscosity represents the deformation of cement pastes due to external loading [7]. Plastic viscosities were calculated from the flow curve using the Bingham, Modified Bingham and Casson models. The results are presented in Figure 3. Generally, for control sample (M0), Bingham model showed the highest value of plastic viscosity followed by the Casson and Modified Bingham (Figure 3a). However, for the GM3 sample, Modified Bingham showed the highest value of plastic viscosities followed by the Casson and Bingham model (Figure 3a). Furthermore, direct relationship between graphene and plastic viscosity was observed, as plastic viscosity increased with the increase in the amount of graphene in cement composite. These results are in line with Shang et al. [6], who found that the plastic viscosity values increased by 78% with the addition of 0.04% graphene oxide in plain cement mix. When samples were subjected to high shear rate cycle, the plastic viscosity reduced as shown in Figure 3b. Shang et al. [6] reported that the apparent viscosities are dependent on the shear rate, i.e., at low shear rate, the values of apparent viscosities would be higher while at high shear rate, the values of viscosities would be lower. A possible reason for this may be due to the breaking of the agglomerates of cement paste which in turn resulted in lower apparent viscosity. It was noticed that the values of plastic viscosity increased with the increase in resting time as shown in Figure 3c. It might be related to the hydration of cement particles and the fractional resistance between cement and graphene sheets. The influence of hydration of cement particles and fractional resistance was dominant for the resting time of 60 min, in which plastic viscosity was very high.

**Figure 3.** *Cont*.

**Figure 3.** Plastic viscosity values (Pa.s) for different mixes calculated by Bingham, Modified Bingham and Casson models using smooth parallel plate: (**a**) effect of graphene percentage; (**b**) effect of shear rate cycle range; and (**c**) effect of resting time.

#### 4.1.3. Consistency and Power Rate Index

The trend of the viscosity data was determined using Herschel–Bulkley (HB) model, which considers two factors, i.e., consistency (K) and the power rate index (n). By considering these factors, the relationship between viscosity trend and the shear rate of the flow curve can be determined [9]. Based on power rate index values "n", it also provides the information about the shear deformation, i.e., shear thickening (n > 1) or shear thinning (n < 1) [7] The consistency (K) has no physical meaning and difficult to compare because of its dimension (Pa.sn) which is dependent on "n" [34]. Wang et al. [7] studied the shear deformation for graphene oxide in cement paste and found that cement paste curve can be divided into shear thinning and shear thickening stage based on the inflection point. They suggested that cement paste with higher graphene oxide content shows the shear thinning effect at high shear rates. The values of the consistency and power rate index for various samples are given in Table 5. It can be seen that the "n" values are less than one and hence cement paste behaves as shear thinning. However, for 60 min resting, the value of "n" for samples M0–60 and GM3-60 exceeded 1, indicating shear thickening behavior. When cement paste comes in contact with water then coagulations and links are formed between two cement particles. With the increase in resting time, these links become strong and provide resistance to flow of cement paste [35]. Therefore, hydration reactions and presence of permanent links between cement particles will result in high resistance to flow.


**Table 5.** Consistency and rate index values calculated by Herschel–Bulkley model.
