## 2 Methods
### Measuring Principle
#### 2.2.1 Acoustic Evaluation Model  
In the offline ultrasonic measurement experiment, the fluororubber specimen was immersed in an ultrasonic couplant, and the ultrasonic propagation within the specimen can be described using a simple layered structure. As shown in Figure 2, both the probe and the specimen were immersed in the couplant. The couplant above the fluororubber layer was treated as a separate layer and labeled as L0, the fluororubber layer was labeled as L1, and the couplant below the fluororubber layer was labeled as L2. The corresponding interfaces were labeled as IFO, IF1, and IF2. A series of convolutions was used here to describe the ultrasonic echo signals received by the probe from each layer. The specific description is as follows:  
\[f(t,0)=E(t)*h_{0}^{a}(t)*[h_{0}^{r}(t)+h_{0}^{s}(t)]*h_{0}^{a}(t)*h_{0}^{s}(t)*R (t)*A\delta(t) \tag{8}\]  
\[f(t,1)=E(t)*h_{0}^{a}(t)*[h_{0}^{r}(t)+h_{0}^{s}(t)]*h_{1}^{a}(t)*[h_{1}^{r}(t )+h_{1}^{s}(t)]*h_{1}^{a}(t)*[u_{0}^{r}(t)+h_{1}^{s}(t)]*h_{0}^{a}(t)*h_{0}^{s} (t)*R(t)*A\delta(t) \tag{9}\]  
Equation (8) represents the echo signal from the couplant-fluororubber interface (the 0 th interface), while Equation (9) represents the echo signal from the fluororubber-couplant interface (the 1 st interface). In the two equations, \(E(t)\) represents the impulse response of the ultrasound probe to an electrical pulse, \(R(t)\) is the impulse response of the ultrasound probe to an acoustic pulse, \(h_{n}^{a}(t)\) denotes the one-way attenuation factor of the \(n\)-th layer to the ultrasound, \(h_{n}^{r}(t)\) represents the reflection impulse response at the \(n\)-th interface,  
Figure 2: Ultrasonic layered propagation model in fluororubber experiment. (**a**) The model for fluororubber sheet specimen, and (**b**) the model for fluororubber column specimen. To ensure that the meas-urement area of the ring is straight, its axis must be aligned parallel to the axis of the linear focused transducer. \(h_{n}^{s}(t)\) represents the one-way scattering response of the \(n\)-th layer to the ultrasound, and \(u_{n}^{r}(t)\) and \(u_{n}^{r}(t)\) are the return reflection impulse response at the interface and an impulse function with an amplitude of \(A\), respectively. In Equation (8), first, the signal is transmitted through the couplant layer \(h_{0}^{a}(t)\). Then, the signal is reflected back from the probe-couplant interface \(h_{0}^{r}(t)\) and passed through the layer again \(h_{0}^{s}(t)\), interacting with the interface IF1. Finally, the reflection and scattering terms combine with the reflection coefficient \(R(t)\), representing the echo signal at the probe. In Equation (9), the signal is transmitted through the couplant layer L0, reflected at the probe-couplant interface. Then, the signal passes through the fluororubber layer (L1), where it is reflected and transmitted at the couplant-fluororubber interface (IF1) and the fluororubber-couplant interface (IF2). The multiple convolutions describe the complex interactions of the wave as it passes through the different layers and interfaces including scattering, reflection, and transmission. Taking the Fourier transform of both sides of Equation (8), we obtain:  
\[F(\omega,0)=E(\omega)H_{0}^{a}(\omega)[H_{0}^{r}(\omega)+H_{0}^{s}(\omega)]H_ {0}^{a}(\omega)H_{0}^{s}(\omega)R(\omega)A\Delta(\omega) \tag{10}\]  
When using a couplant with known properties (typically water), \(H_{0}^{a}(\omega)\) and \(H_{0}^{s}(\omega)\) are known quantities. When the experimental parameters and conditions of use are constant, \(E(\omega)\), \(R(\omega)\), and \(A\Delta(\omega)\) are then invariant. In the above equation, \(H_{0}^{r}(\omega)\) is the reflection coefficient spectrum of fluororubber with respect to the couplant, which is related to the material and acoustic properties of fluororubber.