# Experimental Study on Properties of Ultrasonic Coupling Agent with Graphene in NDT
## 2 Principle and Performance Index of an Ultrasonic Coupling Agent  
### Principle of Acoustic Impedance  
The principle of application of ultrasonic coupling agent is the theory of acoustic impedance. When the acoustic impedance of the specimen matches the acoustic impedance of the coupling agent better, the smaller the sound energy loss is, and the more ultrasonic waves can enter the tested part successfully. The principle of acoustic impedance matching is shown in Figure 1.  
The acoustic impedance of the probe surfaces is \(Z_{1}\), the acoustic impedance of the coupling agent in thin layer medium is \(Z_{2}\), and the acoustic impedance of the tested part is \(Z_{3}\), and the corresponding wavelengths of ultrasonic waves in the three media are \(\lambda_{1},\lambda_{2},\lambda_{3}\) respectively. The transmission coefficient of ultrasonic intensity \(t_{I}\) is expressed by the ratio of transmitted ultrasonic intensity \(I_{T}\) to incident ultrasonic intensity \(I_{I}\):  
\[t_{I}=\frac{I_{I}}{I_{i}}=\frac{4Z_{1}Z_{3}}{\left(Z_{1}+Z_{3}\right)^{2}\cos^ {2}\left(\frac{2\pi}{\lambda_{2}}d\right)+\left(Z_{2}+\frac{Z_{1}Z_{3}}{Z_{2}} \right)^{2}\sin^{2}\left(\frac{2\pi}{\lambda_{2}}d\right)} \tag{1}\]  
In order to maximize \(t_{I}\), the derivative of Equation (1) with respect to \(Z_{2}\) was obtained, and set it as 0, and you get the following formula:  
\[Z_{2}=\sqrt{Z_{1}Z_{3}} \tag{2}\]  
The equations above indicate that the ultrasonic wave enters the tested part completely and there is no loss in the coupling agent thin layer medium. Therefore, the closer the square root value of the acoustic impedance product between the sensor and the specimens tested is to the acoustic impedance value of the coupling agent, the better the ultrasonic propagation efficiency will be. The corresponding acoustic impedance value \(Z\) is expressed as:  
\[Z=\rho C \tag{3}\]  
where \(\rho\) is the material density, while \(C\) is the speed of ultrasonic wave in material.  
Based on physical principles, the acoustic impedance value \(Z\) and the speed value \(C\) are determined by material properties, independent of other conditions. In this study, the experimental system established was employed to obtain the acoustic impedance values of the sensors and the specimens. According to Equation (2), it is necessary to change the acoustic impedance value of the coupling agent to approximate the square root of product of the acoustic impedance of the sensor and the specimens. Only in this way can the transmission coefficient of sound intensity be maximized. Corresponding high transmittance of ultrasonic wave was obtained in this way. In general, the acoustic impedance value of the coupling agent is changed by adding graphene into the coupling agent, in which Equation (2) was satisfied.  
Figure 1: Principle of acoustic impedance matching.  
Compared with the specimens tested, the density of the gel and glycerol coupling agents are relatively small, so the acoustic impedance value greatly differs from that of the specimens. Therefore, some energy will be reflected back in the ultrasonic propagation, resulting in a small transmission coefficient. When graphene powder is added to the coupling agent, the density of the composite coupling agent is increased; therefore, acoustic impedance matching between the coupling agent and the tested specimens was easy to satisfy Equation (2), so as to optimize the transmission effect of ultrasonic wave. In addition, the appropriate addition of graphene can increase the lubricity of the coupling agent [16], which can reduce the friction between the sensor and the specimen to increase the service life of the sensors.