# Dynamic Response of Electro-Mechanical Properties of Cement-Based Piezoelectric Composites
## 3 Results and Discussion
### Impact Compression Test  
The impact compression test was performed on the type 1-3 and type 2-2 cement-based piezoelectric composite samples, and the dynamic mechanical properties of the two samples under different strain rates were obtained. The original waveforms of the electrical signals associated with the strain gauges on the incident and transmission bars were recorded by the oscilloscope (Figure 5). In the figure, Figure 5a,b represent the waveform without and with the waveform shaper, respectively; the waveform effectively prolongs the rising time of the incident wave. The penetration depth of the bullet inside the ballistic is 300 mm, and the strike pressure is 0.2, 0.4, 0.6, 0.8, and 1.0 MPa.  
According to the test results, the stress-strain curves of the samples under different strain rates are obtained using Formulas (1)-(4), as shown in Figure 6. With the continuous increase in the strain rate, the stress values of type 1-3 and type 2-2 specimens increase under the same strain. This result indicated that both the cement-based piezoelectric composites exhibit evident strain rate effects and can be regarded as strain rate sensitive materials.  
This study refers to the Maxwell model used by [PERSON] [28] to characterize the stress relaxation effect of cement-based piezoelectric composites. The stress relaxation effect of type 1-3 and type 2-2 samples under impact compression has also been characterized. The differential equation used in the Maxwell model can be expressed as Formula (5):  
\[\frac{\mathrm{d}\sigma}{dt}+\frac{\sigma}{\tau}=E_{1}\dot{\varepsilon} \tag{5}\]  
where \(E_{1}\) is the Young's modulus of the spring, \(\tau\) is the stress relaxation time of the viscous pot, and \(\dot{\varepsilon}\) is the total strain rate of the model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter**Sample & **Linearity Range/MPa** & **Fitting Function** & **Correlation Coefficient R2** & **Sensitivity/(pC\(\cdot\)N\({}^{-1}\))** \\ \hline
1-3 & 0–21.7 & \(D=0.000157\sigma-0.43533\) & 99.88\% & 157 \\
2-2 & 0–35.0 & \(D=0.000169\sigma+0.00052\) & 99.49\% & 169 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Linear fitting parameters of quasi-static sensitivity.  
Figure 4: Calibration of quasi-static sensitivity.  
For the constant strain rate process, the differential equation of the Maxwell model can be expressed by Formula (6), where \(\varepsilon\) is the total strain of the model.  
\[\sigma=E_{1}\tau\dot{\varepsilon}(1-e^{-\frac{\varepsilon}{\tau\varepsilon}}) \tag{6}\]  
According to Formula (6), the data on the stress-strain curves of type 1-3 and type 2-2 composites under different strain rates are fitted. Figure 7 shows the stress relaxation time \(\tau\) of the viscous pot under different strain rates. The stress relaxation time and strain rate show an approximately negative linear relationship, regardless of the type of cement-based piezoelectric composite; that is, the relaxation time decreases monotonously with an increase in strain rate. However, under the same strain rate, the relaxation time of type 2-2 is lower than that of type 1-3, indicating that the time required for type 2-2 to return to its normal state is lower after the external force is released. This feature is more advantageous in the application of engineering sensors.  
Figure 5: Original waveform of the sample under impact loading. (**a**) Original waveform without the waveform shaper; (**b**) Original waveform with waveform shaper.  
Figure 6: Stress-strain curves of the sample under different strain rates.