# Dynamic Response of Electro-Mechanical Properties of Cement-Based Piezoelectric Composites
## 3 Results and Discussion
### Electro-Mechanical Response Analysis  
Because the sample generates a larger voltage at the time of impact loading, a current mode circuit is used to measure the electrical signal output by the sample in order to better protect the circuit. The oscilloscope collects the voltage across the resistor in real time. The voltage recorded by the oscilloscope is \(V(t)\) and the current in the circuit is \(I(t)\).  
The discharge at both ends of the sample is calculated as Formulas (7) and (8):  
\[Q(t)=\int_{0}^{t}I(t)dt=\int_{0}^{t}\frac{V(t)}{R}dt \tag{7}\]  
The electric displacement of the sample is expressed as:  
\[D(t)=\frac{Q(t)}{A_{0}} \tag{8}\]  
where \(A_{0}\) is the cross-sectional area of the sample.  
The ratio of \(D(t)\) to \(\sigma(t)\) represents the dynamic sensitivity \(K\) of the sample.  
Based on Formulas (7) and (8) and the definition of sensitivity, the stress and electric displacement time curves of type 1-3 and type 2-2 samples are shown in Figure 8. The stress-time curves of type 1-3 (Figure 8a) and type 2-2 (Figure 8b) composites are highly similar to their output electric displacement time curves, indicating that the output electric displacement of the sample can accurately respond to the impact loading of the sample; this implies that type 1-3 and type 2-2 composites are good electro-mechanical sensing materials, rendering them applicable in the production of engineering sensors.  
Figure 9 shows the electric displacement-time curves of the composites under different strain rates. At lower strain rates, an increase in the loading strain rate causes the peak values of the output electric displacements corresponding to type 1-3 (Figure 9a) and type 2-2 (Figure 9b) samples to show an increasing trend. At higher strain rates, an increase in the loading strain rate causes the growth rate associated with the amplitude of output electric displacement to decrease.  
Figure 7: Relationship between relaxation time and strain rate.  
Based on Figures 6, 9 and 10 shows the variation in the stress peak value and output electric displacement of the samples under different strain rates. MATLAB is used to linearly fit the test data, and the slope of the straight line represents the dynamic sensitivity of the cement-based piezoelectric composite. The relevant parameters obtained by linear fitting are shown in Table 2.  
By combining Figure 10 and Table 2, results similar to those obtained under quasi-static compression are obtained; that is, the dynamic sensitivity of type 1-3 and type 2-2 composites also exhibits electrical domain switching points, namely: 70.5 and 88.0 MPa. When the applied load is less than the domain switching point (first yielding point), the electro-mechanical response of type 1-3 and type 2-2 exhibits a good linear relationship. In the linear range, the dynamic sensitivity of type 1-3 and type 2-2 is 323 and 296 pC/N, respectively. When the applied load exceeds the domain switching point, the increase in the output electric displacement is attenuated. Subsequently, the output electric displacement and the stress of the sample no longer show a linear relationship because the piezoelectric ceramics eventuate domain change, which reduces the piezoelectric performance of the sample.  
Overall, the difference in the sensitivity of type 1-3 and type 2-2 is observed to be minor; however, the linear range of type 2-2 is significantly greater than that of type 1-3 (by 24.8%).  
Figure 8: Time curves of the stress and electric displacement of the composite.  
Figure 9: Electrical displacement-time curves of the composite.