Stress Measurements of GIS Epoxy Composite with Transverse Waves Based on the Ultrasonic Pulse-Echo Method

Abstract

The mechanical reliability of the gas-insulated metal-enclosed switchgear (GIS) is critical to the safe and stable operation of a power system. The internal stress induced in GIS insulators, which typically lead to cracking, can degrade the mechanical properties and compromise the reliability of the GIS. In this work, ultrasonic nondestructive measurements of the internal stress in a GIS 126 kV epoxy composite with the transverse waves are demonstrated for the first time. Our results show that the velocities of ultrasonic transverse waves increase linearly with the compressive stress and decrease linearly with the tensile stress. The acoustoelastic coefficients are −1.18 × 10⁻⁴/MPa and −1.96 × 10⁻⁴/MPa for measurements with transverse waves polarized vertically and parallelly to stress, respectively. Based on these acoustoelastic coefficients, the internal stresses are calculated, and the maximum absolute values of relative errors are 35.4% and 26.3% for measurements with the transverse wave polarized vertically and parallelly to stress, respectively.

1. Introduction

A gas-insulated metal-enclosed switchgear (GIS) fully or partially uses insulating gas instead of atmospheric air as the insulation medium in an electrical substation. With the increasing power demand and the elevation of voltage levels, the GIS is increasingly used in power grids. The basin insulators are significant components in the GIS, and they consist of epoxy insulation, metal inserts, and flange rings. They function as supporting conductors, electrical insulation, and isolation of gas chambers. Thus, their performance is crucial to the safe operation of GIS [1].

The stresses inside basin insulators include residual stress, generated during the manufacturing process, as well as the stress caused by the external loads during installation and operation, as well as during transportation [2].

The GIS basin-type insulators are made through high-temperature curing of integrally poured mixtures of liquid epoxy resin, curing agent, and inorganic powder filler with an aluminum central conductor insert [1]. The origins of residual stress in the pouring and curing process include (1) the curing shrinkage of epoxy resin [3]; (2) different thermal expansion and contraction values between the epoxy composite and metal inters in the case of temperature changing in the curing process [4]; (3) uneven pouring and curing, such as non-uniform mixing of the epoxy resin, inorganic filler particles, and curing agent, or non-uniform sedimentation distribution of the filler material [5].

External loads include jostling and vibration during transportation, mechanical friction, tilted installation of conductor, and an uneven bolt fastening force that can produce stretch or compression in GIS basin-type insulators. In addition, the insulators are also subjected to forces caused by their weight and the weight of conductors during their operation, the pressure difference of SF₆ on two sides [6], mechanical vibration from the switch action [7], and the electrodynamic forces exerted on the conductor by the electromagnetic field of the short circuit alternating current [8], and so on.

The stress gradually accumulates under the action of external loads during the operation of the basin insulators. When the stress exceeds the mechanical strength, cracks will easily form and lead to air leakage, partial discharge, insulation ablation, and flashover [9,10]. The failure rate of GIS due to the insulation problem reached 69%, in a certain region in China from 2010 to 2018 [11]. The internal stress will degrade the insulation mechanical properties. Thus, its measurement is critical for ensuring the mechanical reliability of the insulator [12].

Currently, researchers have used stress–strain sensors such as strain gauges [13] and fiber sensors [14] on insulators to measure the surface stress in hydraulic testing. The Xi’an Jiaotong University group analyzed the failure mode of the basin insulator after the hydraulic testing and simulated the stress field using the finite element method. They found that the tangential stress was the main cause for peeling at the interface [15]. However, there are a limited number of reports on the internal stress measurement in the GIS insulation.

Typically, there are two ways of measuring internal stress: destructive testing methods and non-destructive testing methods [16]. Magnetic tests, X-ray imaging, photoelastic methods, and ultrasonic methods are non-destructive testing methods. Only the ultrasonic method, based on the acoustoelastic effect (correlation between wave velocity and stress), is applicable to composite materials [16,17,18].

The ultrasonic stress measurement methods, according to the types of ultrasonic waves applied, can be divided into Rayleigh waves, LCR (longitudinal critically refracted) waves, longitudinal waves, combined longitudinal and transverse waves, and transverse waves methods. The Rayleigh waves and LCR waves are typically for subsurface stress testing (within a limited depth of area beneath the surface) [19,20]. The longitudinal wave, combined longitudinal and transverse wave, and transverse wave methods have been investigated for measuring the internal stress in materials, such as bolts and concrete [21,22]. The longitudinal wave method and the combined longitudinal and transverse wave method work effectively in the condition that the stress direction is along, with wave propagation due to the high sensitivity of the wave velocity to the stress in this case [2,23]. The combined longitudinal and transverse wave method can eliminate the influence of thickness and deformation on test results, but the required probe must be specifically manufactured [22]. As for the transverse wave method, some researchers have investigated the acoustoelastic effect of transverse waves and measured the internal stress in wood, patch-welded disks, concrete prisms, and so on. Fukuoka found that the transverse wave velocity linearly changed with stress in mild steel using the transverse waves with polarization parallel or vertical to stress and thus verified the acoustoelastic effect. Then, they measured the residual stress in a patch-welded plate and found that the results obtained using the ultrasonic stress method agreed well with the conventional destructive method [21]. M. Hirao applied the transverse-wave electromagnetic acoustic transducer to measure the axial stress in bolts. They applied the pulse-echo method, in which two reflection echoes from the bottom are selected to determine the propagation time in bolts. The accuracy in this research is high (approximately 5% at 5 tons) [24]. Yuri Kudryavtsev verified the acoustoelastic effect in railway wheel by using the transverse waves with polarization parallel or normal to stress, based on the pulsed-echo method. Then, they obtained the corresponding acoustoelastic coefficients and measured the biaxial residual stress in a railway wheel [25].

Currently, most ultrasonic stress measurements are focused on metals, like bolts [20], patch-welded plates [21], and non-metallic materials, like concrete [22] and wood [26]. Research on stress measurements in epoxy composite materials is still needed. Santos et al. investigated the acoustoelastic effect of carbon fiber composites with an epoxy matrix using the LCR wave. They found that the stress varies linearly with the ultrasonic transmitting time and calculated the acoustoelastic coefficients [16]. Based on the acoustoelastic effect, Tianjin University applied the longitudinal wave pulse-echo method to measure the residual stress, induced in the curing process, in aramid reinforced epoxy composites of GIS pull rods [27]. So far to date, the ultrasonic testing method had been applied to investigate the density uniformity or stress condition of a GIS basin insulator. The density uniformity was detected using the longitudinal wave pulse-echo method [11]. The internal stress, caused by a temperature gradient in the working conditions, was calculated based on the relationship between the transmitting time and temperature. The maximum relative error was 28.7%, compared with simulation results [11]. In the previous work, 0–50 MPa subsurface stress of GIS composite was calculated based on the acoustoelastic effect by applying the LCR waves. However, the LCR waves are applied to measure the sub-surface stress, not the internal stress [28]. The 0–70 MPa compressive internal stress in GIS composites was measured with the longitudinal waves, based on the acoustoelastic effect. In this research, due to the applied through-transmission method, the effect of coupling agent thickness had to be eliminated. The relative errors are relatively high in a low-stress state, reaching 55–85% below 25 MPa [2]. The relative high error was due to the fact that the ultrasonic longitudinal wave is insensitive to the stress, if the longitudinal waves propagate normally to the stress, i.e., the tangential stress. Thus, it is necessary to seek a more accurate method to measure the tangential internal stress inside a GIS composite.

In this work, an ultrasonic testing system for measuring the internal stress in GIS basin-type insulators was proposed by applying the 0.5 MHz ultrasonic transverse waves with polarization vertical or parallel to stress. The acoustoelastic coefficients were measured, under 0–100 MPa compressive stress state and 0–50 MPa tensile stress state. Then, the internal stresses were calculated with relative errors.

2. Detection Principle

2.1. Acoustoelastic Effect

The acoustoelastic effect is widely used for ultrasonic stress measurements. In a solid, the ultrasonic velocity varies due to the applied stress, within the elastic limits of the material [21].

The uniaxial stress and the ultrasonic velocity in a solid have a linear relationship as shown in the expression of Equation (1) [23]. This equation is applicable to uniaxial stress in isotropic materials [2]. South China University of Technology group applied Equation (1) in internal stress measurements for a GIS epoxy composite with the longitudinal wave detection technique [2].

$$\frac{V-V_0}{V_0}=K(\sigma -{\sigma }_0)$$

(1)

where $V$ refers to ultrasonic wave velocity under a stressed state (unit of m/s), $V_0$ refers to ultrasonic wave velocity under the initial stress, σ is stress under a stressed state (unit of MPa),${ \sigma }_0$ is internal stress under the initial stress, and $K$ refers to the acoustoelastic coefficient (unit of MPa⁻¹) [2]. For basin insulators, differences in the manufacturing technique and material can affect the acoustoelastic coefficient.

$K$ can be calculated from $k,$ the slope of $V–\sigma$ linear equation, and $V_0$ as shown in Equation (2) below [2].

$$K=\frac{k_0}{V_0}$$

(2)

The internal stress σ is derived as the following Equation (3), according to Equations (1) and (2) [2].

$$\sigma =\frac{V-V_0}{K{V}_0}$$

(3)

2.2. Propagation Model of Pulse-Echo Method

In this study, a pulse-echo method was used with one ultrasonic probe. The piezoelectric chip of the probe converts electric waves into ultrasonic waves. When the ultrasonic wave encounters the back wall of the sample, the wave is reflected and received by the probe. The ultrasonic wave is then converted back into an electric wave by the piezoelectric chip. The propagation time of the ultrasound is measured using the time difference of the back wall echoes, which eliminates the influence of the coupling agent thickness [11,24].

The ultrasonic propagation path of the ultrasonic reflection and the diagram of the detected waveform are schemed in Figure 1a,b.

The piezoelectric chip of the probe emits the ultrasonic wave $E$. When the wave $E$ reaches the surface of the sample, a portion of the ultrasonic wave is reflected and returns along the same path to be detected by the probe (indicated as wave $F$ in Figure 1). The other part of the wave $E$ continues into the sample (of a thickness H) and propagates until reflected by the back wall surface. The reflected wave travels to the sample–probe interface where it is again transmitted and reflected. The transmitted ultrasonic wave is detected by the probe as wave $B_{S1}$, and the reflected part of the ultrasonic wave continues to propagate in the sample. It is reflected at the back wall surface for the second time. The secondary reflected wave is detected at the sample–probe interface and is detected by the probe as wave $B_{S2}$. The $T$ is the time difference between the first wave peak of the reflected wave $B_{S1}$ from the back wall of the epoxy sample and the first wave peak of the second reflected wave $B_{S2}$, as shown in Figure 1b [11,24].

2.3. Ultrasonic Propagation Velocity

The wave velocity $V$ is derived from Equation (4) below:

$$V=\frac{L}{T}$$

(4)

In this study, a 0.5 MHz ultrasonic transverse wave was applied to internal stress measurements. The velocity of a 0.5 MHz transverse wave with polarization vertical to the stress direction is noted as $V_v$, and the velocity of a 0.5 MHz transverse wave with polarization parallel to the stress direction is noted as $V_p$. This way of notation is the same as for the acoustoelastic coefficient $K$. In Equation (4), $T$ denotes to the propagation time of the ultrasonic wave, with $T_v$ and $T_p$ corresponding to the transverse waves polarized vertically and parallelly to the stress. $L$ is the ultrasonic path length in the sample, which is two-fold the thickness of the epoxy sample $H$. $L$ can be written as

$$L=2H=2(H_0+\mathrm{d}h)$$

(5)

where $H_0$ is the sample thickness at zero stress in the ultrasonic wave propagating direction, and dh is the amount of deformation along the ultrasonic propagation direction, which can be calculated from $H_0$ and strain $\epsilon$:

$$\mathrm{d}h=H_0\epsilon$$

(6)

3. Experiment

3.1. Specimen

The GIS epoxy composite specimen tested in this research is the same as the 126 kV three-phase-in-one-tank GIS basin insulator, with an elastic modulus of 12.25 GPa, a density of 2.23 g/cm³, and a Poisson’s ratio of 0.32.

In the vertical compressive stress test, a cuboid specimen A was fabricated with the size of 20 mm × 25 mm × 60 mm. The ultrasonic propagation direction is along the 20 mm side. Six specimens of A were labelled as #A-1, #A-2, #A-3, #A-4, #A-5, and #A-6. To ensure the ultrasonic wave propagates in a uniform uniaxial stress field, a dumbbell-type tensile standard specimen B was made [29] (as shown in Figure 2a). Six specimens of B were marked as #B-1, #B-2, #B-3, #B-4, #B-5, and #B-6. The fabricated specimen A and B are shown in Figure 2b.

3.2. Acoustoelastic Coefficient Measurement System

The acoustoelastic coefficient of the epoxy composite is measured using the compressive stress acoustoelastic effect test system and the tensile stress acoustoelastic effect test system, as shown in Figure 3. The compressive stress acoustoelastic effect test system consists of a universal testing machine, an ultrasonic pulser/receiver, an ultrasonic transverse wave probe, a strain instrument, strain gages, a computer, an oscilloscope, and a cuboid sample [2], as shown in Figure 3a. The tensile stress acoustoelastic effect test system is similar to the compressive stress system, but the difference is that the sample is a dumbbell-type tensile sample, and a tensile fixture in a universal testing machine is used, as shown in Figure 3b. The experimental set-up is shown in Figure 4.

During the test, a CTS-23 ultrasonic pulser/receiver is used to emit ultrasonic waves. The main properties of the CTS-23 ultrasonic pulser/receiver include 0.5–3 MHz bandwidth, A-scan mode, about 30 ns transmitted pulse rising time, and the reflective mode selected to connect one probe. The original unprocessed ultrasonic signal that contains the largest amount of information can be acquired by connecting the oscilloscope to the point in front of the rectification mode in the internal circuit of the ultrasonic pulser/receiver [2].

A transverse wave probe (model 0.5C14S) was used in the experiment, with 0.5 MHz center frequency and 14 mm diameter. Considering the high attenuation of ultrasonic waves in the epoxy composite, composite probes with less clutter and better waveform were used. The piezoelectric wafer of the probe is made of lead zirconate titanate (PZT) and epoxy resin composite material. The probe is connected to the ultrasonic pulser/receiver system with Q9Q6 wires, where the Q9 connector is attached to the ultrasonic pulser/receiver system and the Q6 connector is attached to the probe. The coupling agent is applied between the probe and the sample [2].

A digital oscilloscope (Tektronix, model DPO3102) is used, with 2.5 GS/s sampling rate (0.4 ns sampling period) and 20 MHz bandwidth.

For compressive stress test, the compressing device is a computer-controlled universal testing machine with 100 kN capacity and level 1 accuracy. A level 1 accuracy means that the maximum absolute error is 1 kN within the 100 kN range [30]. Since the epoxy sample would crack under 130 MPa compressive loading, the compressive stress test was carried to 100 MPa. It corresponds to an area of 5 × 10⁻⁴ m² (a cross-section of 20 mm × 25 mm) at a load of 50 kN. For tensile stress tests, the tensile strength of the GIS composite is 70 MPa. The maximum tensile stress load applied is 50 MPa [2]. This corresponds to a load of 12.5 kN on a cross-sectional area of 2.5 × 10⁻⁴ m² (10 mm × 25 mm). For both the compressive stress test and the tensile stress test, the stress load is applied to the samples at an increment speed of 0.5 mm/min and a constant stress gradient of ∆σ = 5 MPa (stress is the ratio of pressure to cross-sectional area).

The ultrasonic propagation time and strain were tested at every 10 MPa of increase in compressive stress in the 0–100 MPa range for a total of 11 tests, while the ultrasonic propagation time and strain were tested for every 5 MPa of increase in tensile stress in the 0–50 MPa range for a total of 11 times. When the transverse wave probe was tested, two types of measurement were made, polarization direction parallel to the stress and polarization direction normal to the stress, as shown in Figure 5 [21].

Strain occurs when the specimen is loaded by force, which was measured with a high-performance static strain test instrument and the associated strain gage. A caliper micrometer (0.001 mm error) was used in measuring the sizes of the samples.

3.3. Mechanical Simulation

The stress in the epoxy sample was simulated using the finite element method to investigate the stress distribution in the ultrasonic propagation region. The results are demonstrated in Figures S1 and S2 in the Supplementary Information.

4. Results and Discussion

4.1. Ultrasonic Testing

During the test, the attenuation setting of the ultrasonic instrument was set to 48 dB. The compressive stress specimen A and the tensile stress specimen B were tested using 0.5 MHz transverse ultrasonic waves polarized perpendicularly to the stress, and 0.5 MHz transverse ultrasonic waves polarized parallel to the stress. The electric voltage $u$ was detected by the ultrasonic pulser/receiver system and the electric voltage $u$ of specimen #A-1 at 20 MPa compressive stress state, as shown in Figure 6; the electric voltage $u$ of specimen #B-1 for 20 MPa tensile stress is shown in Figure 7. $T$ is the time interval between the first peak of the first back wall reflection and the first peak of the second back wall reflection, which is the ultrasonic propagation time in the sample.

4.2. Deformation in the Direction of Ultrasonic Propagation

In the range of 0–100 MPa compressive stress and 0–50 MPa tensile stress, the strains of the sample along the ultrasonic propagation direction, labeled as ${\epsilon }_1$_, and vertical to the stress direction, labeled as ${\epsilon }_2$, are demonstrated in Figure 8.

Within 0–100 MPa compressive stress, ${\epsilon }_1$ increases linearly with increasing stress, and within 0–50 MPa tensile stress, ${\epsilon }_2$ decreases linearly with increasing stress. The elongation along the ultrasonic propagation dh can be obtained by substituting ${\epsilon }_1$ or ${\epsilon }_2$ into Equation (6). For example, in the case of 50 MPa tensile stress, ${\epsilon }_2$ becomes −0.0013, shown in Figure 8, which indicates that the tensile deformation is −0.0013 out of the 10.005 mm original length, and thus, the calculated deformation dh is −0.013 mm.

4.3. Ultrasonic Propagation Time, Distance, and Wave Velocity

A pulse-echo method is applied to investigate the acoustoelastic effect in GIS epoxy specimens under uniaxial stress. Under applied compressive stress, the propagation time and strain in specimen A were measured. Under applied tensile stress, the ultrasonic propagation time and strain in specimen B were measured. Then, the ultrasonic wave velocities were derived.

The ultrasonic distance is measured using Equation (5), and the wave speed under loading stress is measured using Equation (4). Ultrasonic tests were performed on specimen A under 0–100 MPa compressive stress and specimen B under 0–50 MPa tensile stress, using 0.5 MHz transverse ultrasonic wave polarized vertically to the stress and 0.5 MHz transverse ultrasonic wave polarized parallel to the stress. The measured propagation time, distance, and wave speed of the #A-1 specimen and #B-1 specimen are demonstrated in Figure 9 and Figure 10, respectively.

In Figure 9, in the range of 0–100 MPa compressive stress, the propagation times $T_v$ and $T_p$ both decrease slightly with the stress increasing, and the decreased magnitude of $T_v$ (320 ns) is less than that of $T_p$ (480 ns). The propagation distance $L$ increases linearly with compressive stress increasing due to linear deformation under the stress loading. The wave velocities $V_v$ and $V_p$ increase, and the increment magnitude of $V_v$ (22 m/s) is less than that of $V_p$ (31 m/s).

In Figure 10, in the range of 0–50 MPa tensile stress, the propagation times $T_v$ and $T_p$ both increase slightly with the stress increasing, and the increased magnitude of $T_v$ (71 ns) is less than that of $T_p$ (121 ns). The propagation distance $L$ decreases linearly with tensile stress increasing due to linear deformation under the stress loading. The wave velocity $V_v$ and $V_p$ both decrease, and the reduction magnitude of $V_v$ (11 m/s) is less than that of $V_p$ (19 m/s).

Therefore, the variation in propagation time and velocity of transverse waves with polarization parallel to stress are more significant than those of transverse waves with polarization vertical to stress.

4.4. Relationship between Transverse Wave Velocity and Stress

To analyze the correlation between the transverse wave velocity and the loading stress, the average wave velocities of specimens #A-1, #A-2, and #A-3 were calculated, as well as the average wave velocities of specimens #B-1, #B-2, and #B-3. Then, the average values of the transverse wave velocity corresponding to the stress applied are demonstrated in Figure 11, in which the compressive stress is labeled with a negative sign, and tensile stress is labeled with a positive sign.

In Figure 11, it was found that the relationship between the transverse wave velocities $V_v$ or $V_p$ and the stress $\sigma$ follow linear variation, and two linear fitting lines $V_v$-$\sigma$ and $V_p$-$\sigma$ can be plotted. The correlation coefficients R² of the linear fitting line $V_v$-$\sigma$ and $V_p$-$\sigma$ are 0.94 and 0.96, indicating a significant linear correlation between the transverse wave velocity and the stress. Therefore, the acoustoelastic effect of transverse waves in GIS composites is verified. Moreover, it was found that the velocities of ultrasonic transverse waves increase linearly with the compressive stress and decrease linearly with the tensile stress.

In Figure 11, it can be found that the slopes ($k_v$ and $k_p$) of the linear fitting lines $V_v$-$\sigma$ and $V_p$-$\sigma$ are −0.20 m/s/MPa and −0.33 m/s/MPa, respectively, as shown in

Table 1. The linear fitting line slope and acoustoelastic coefficients of transverse waves with polarization vertical to stress and transverse waves with polarization parallel to stress and longitudinal waves.

Ultrasonic Waves to Measure Tangential Internal Stress	Linear Fitting Line Slope k (m/s/MPa)	Acoustoelastic Coefficient K (×10−4/MPa)
Transverse waves with polarization vertical to stress	−0.2	−1.18
Transverse waves with polarization parallel to stress	−0.3	−1.96
Longitudinal waves [2]	0.141	0.456

. Substituting the slopes above into Equation (5), the acoustoelastic coefficient of transverse waves with polarization vertical to stress $K_v$ is −1.18 × 10⁻⁴/MPa, and the acoustoelastic coefficient of transverse waves with polarization parallel to stress $K_p$ is −1.96 × 10⁻⁴/MPa, as shown in Table 1. For comparison, the line slope and acoustoelastic coefficients of longitudinal waves in the previous study are also demonstrated in Table 1 [2].

It can be found that ${ k}_p$ is larger than ${ k}_{v }$ and $K_p$ and is larger than $K_v$. This finding is consistent with the studies on acoustoelastic coefficients in metals [21]. Moreover, it can be found that the absolute slope and acoustoelastic coefficient of transverse waves with polarization parallel to stress is the largest. Considering that the slope of the linear fitting line is defined as the ratio of wave velocity change to stress change, and the acoustoelastic coefficient refers to the stress-velocity sensitivity, according to Equation (1), it can be concluded that the transverse wave with polarization parallel to stress shows the highest velocity-stress sensitivity.

4.5. Stress Measurement

Stress measurement tests were applied on the #A-4, #A-5, and #A-6 specimens and #B-4, #B-5, and #B-6 specimens. The calculated internal stress, using the transverse waves with polarization direction vertical to stress, was noted as ${\sigma }_{vc}$, while the calculated internal stress, using the transverse waves with polarization parallel to stress, was noted as ${\sigma }_{pc}$. The internal stresses ${\sigma }_{vc}$ and ${\sigma }_{pc}$ can be calculated based on Equation (3), in which the acoustoelastic coefficients had been calculated in Section 4.4 and the wave velocities of #A-4, #A-5, #A-6, #B-4, #B-5, and #B-6 specimens were measured using the same method as for #A-1, #A-2, #A-3, #B-1, #B-2, and #B-3 specimens. The average calculating results for ${\sigma }_{vc}$ and ${\sigma }_{pc}$ within −100 MPa to 50 Mpa mechanical stress are shown in Figure 12, where the mechanical compressive values were equivalent to the actual internal stress ${\sigma }_a$. The calculated stress ${\sigma }_{lc}$ of the longitudinal waves method investigated in a previous study is also compared in Figure 12 [2]. Then, the average relative error of calculated internal stress (the relative error for ${\sigma }_{vc}$ was noted as $E_{vr}$, and the relative error for ${\sigma }_{pc}$ was noted as $E_{pr}$) can be found by comparing between the calculated internal stress (${\sigma }_{vc}$ and ${\sigma }_{pc}$) and the actual internal stress ${\sigma }_a$, as demonstrated in Figure 12. The relative error $E_{lc}$ of longitudinal waves method investigated in a previous study is also compared in Figure 13 [2].

In Figure 13, it can be seen that the $E_{vr}$ varies in different stress states: the absolute values of $E_{vr}$ can reach almost 20–35% in the stress range of −40 MPa–30 MPa; the absolute values of $E_{vr}$ decrease to lower than 12% in the range of −100 MPa–50 MPa and 35 MPa–50 MPa. The maximum absolute value of $E_{vr}$ is 35.4% under the stress of 20 MPa. It can be seen that the $E_{pr}$ varies in different stress states as well: the absolute values of $E_{pr}$ can reach almost 10–26% in the stress range of −40 MPa–30 MPa; the absolute values of $E_{pr}$ also decrease to lower than 12% in the range of −100 MPa–−50 MPa and 35 MPa–50 MPa. The maximum absolute value of $E_{pr}$ is 26.3% under the stress of −10MPa. Comparing $E_{vr}$ and $E_{pr}$, it can be found that both of them are relatively large in the low-stress state and become smaller in the high-stress state. Moreover, $E_{pr}$ is smaller than $E_{vr}$ in the low-stress states, while no significant difference between them is observed in the high-stress states.

Comparing $E_{vr}$, $E_{pr}$, and $E_{lr}$ in the range of −70 MPa–0 MPa, it can be found that in low-stress states of −30 MPa–0 MPa, the absolute value of $E_{lr}$ is obviously largest (85–37%), followed by $E_{vr}$ (11–32%) and $E_{pr}$ (17–26%); in high-stress state, there is no significant difference among them. The reason for the large difference in results errors in the low-stress state maybe due to the deviation in acoustoelastic coefficients, which indicate the stress-velocity sensitivity. A larger acoustoelastic coefficient and higher wave stress-velocity sensitivity suggest larger variation in the wave velocity for the same stress variation. This may be beneficial for stress measurement in low-stress states, as it is easier to detect the velocity variation. In this research, the acoustoelastic coefficient of the transverse waves polarized parallel to stress is the largest, indicating the highest velocity-stress sensitivity, smallest stress measurement relative error, and highest accuracy in the low-stress states.

5. Conclusions

An ultrasonic testing system for measuring the internal stress in GIS epoxy composites with transverse waves was established. Conclusions can be summarized as follows:

• The acoustoelastic effect is verified using the transverse waves in GIS epoxy composites. The velocities of ultrasonic transverse waves increase linearly with the compressive stress and decrease linearly with the tensile stress. The acoustoelastic coefficients are −1.18 × 10⁻⁴ /MPa for transverse wave polarization vertical to stress and −1.96 × 10⁻⁴ /MPa for transverse waves parallel to stress.
• The maximum absolute values of relative errors are 35.4% and 26.3% for stress measurements with transverse wave polarization vertical and parallel to the stress direction, respectively.
• For the tangential internal stress measurements in GIS epoxy composites, in low-stress states, applying the transverse wave with polarization parallel to the stress obtains more accurate results compared to the transverse wave with polarization vertical to the stress and longitudinal waves. The maximum absolute value of relative error is 26.3% under 10 MPa compressive stress.

This research demonstrates that ultrasonic stress measurements for GIS composites with transverse waves are more accurate than measurements with longitudinal waves in the low-stress state. The method proposed in this article provides a basis for investigating the internal stress in GIS epoxy insulators. Studies employing Artificial Intelligence schemes to increase result accuracy and reduce measurement error caused by manual operation are carried out.