Examination of Longitudinal AC Breakdown Strength of Dielectric Surfaces as a function of Elastic Modulus

This paper examines the influence of the elastic modulus of the polymer insulation on the tangential AC breakdown strength (BDS) of polymer interfaces theoretically and experimentally. In the experiments, four different materials with different elastic moduli, namely crosslinked polyethylene (XLPE), cured end product of epoxy resin (EPOXY), polyether ether ketone (PEEK) and silicone rubber (SiR) were employed under various contact pressures. The BDS of each interface increased as the contact pressure was augmented. As the contact pressure became threefold, the interfacial BDS rose by a factor of 2.4, 1.7, 1.8, and 1.4 in the case of the PEEK, EPOXY, XLPE and SiR interface, in a sequence following the decrease of the elastic modulus. Under the same contact pressure, it was observed that the lower the elastic modulus, the higher the BDS. The employed contact theory also suggested a decreasing BDS as the modulus was augmented; however, the experimental results tended to deviate widely from the estimated results as the pressure was significantly increased.


Introduction
Subsea cable connectors are vital components of oil and gas installations, future offshore wind and wave energy systems.Although materials and production technologies for subsea applications have gained a fair amount of experience over the years, cable connectors and joints where solid-solid interfaces emerge are still considered the weaker parts of complete cable systems [1][2][3].
One of the main reasons of a solid-solid interface being weaker than its intrinsic material is that an interface contains microscopic imperfections such as cavities (see Fig. 1), protrusions, and contaminants.Such defects reduce the tangential AC electric breakdown strength (BDS) of the interface notably [1,2].Even in cases when the magnitude of the longitudinal electric field is much lower than the dielectric strength of the intrinsic insulation, the imperfections at the interface cause local electric field enhancements.They are, thus, likely to initiate partial discharges (PD), electrical treeing, and a complete flashover might eventually follow [1][2][3].
Study of insulating materials and BDS of applications for cables and accessories have been covered to a large extent in the literature.Greenwood et al. and Bhusnan reported that total area of contact at an interfacial surface substantially increases in the cases when the elastic modulus is decreased, the contact pressure is augmented, or both [4,5].The interfacial breakdown between two dielectric surfaces was reported to represent one of the principal causes of failure for power cable joints and connectors, in which elastic modulus of the dielectric material plays a key role [3][4][5].There is; however, still a lack of knowledge on the correlation between the elastic modulus and the BDS of the interfacial surfaces.Therefore, the primary objective of this paper is to theoretically and experimentally examine the influence of the elastic modulus on the longitudinal AC breakdown strength of dry-assembled solid-solid interfaces under various contact pressures.

E y x
Fig. 1: An illustration of the air-filled cavities at the interface in twodimensional profile.Reference [2] revealed that the voids at the interface are much larger in the tangential direction.They are, thus, referred to as channels [2].

Theory
In this work, the contact theory [1,3] is employed to model a dry contact between dielectric surfaces.The contact theory suggests that two potential mechanisms are dominating the interfacial breakdown phenomenon [1].The first hypothesis suggests that the BDS of the contact spots, i.e. the total real area of contact, governs the BDS of the entire interface.Equation (1) yields the ratio between the total real area of contact A re (microscopic) and the nominal contact area A a (macroscopic) as a function of the applied contact pressure p a , the effective elastic modulus E ′ of two materials in contact, the standard deviation of the asperities' heights σ and the mean radius of the asperities' summit β m [5].Thus, the hypothesis renders studying A re in connection with the interfacial BDS possible under various E ′ and p a .
On the other hand, the second hypothesis assumes that the PD in the air-filled microscopic channels, as delineated in Fig. 1, governs the interfacial BDS.Because a flashover across a single channel is analogous to the onset of the PD activity at the interface [2] that might eventually evolve to the interfacial breakdown.Following the approach in [1,3], we can estimate the PD inception field strength (PDIE) of a channel using the left-hand side Paschen's curve provided that the average channel size be estimated.The average size of the channels is determined by the following assumptions with regards to the contact theory: • The summits of the asperities are assumed spherical with a mean radius β m .• The asperities have a Gaussian distribution in height about a mean plane in a two-dimensional plane.• The number of air-filled channels is assumed equal to the number of contact spots at the interface, resulting in one contact spot between two consecutive cavities.
After manipulating the set of formulas provided in [1,3], the correlation between the elastic modulus and the average channel size d reduces to where n is the expected number of the contact spots [1].
Given the fact that d is the average estimated channel size, the PD activity presumably commences at the largest channel(s); however, whether a single or a few large channels can achieve a complete flashover along the interface was not studied.Nor was the duration until the PD activity evolves to a complete flashover examined.With this limited information, we roughly assume that PDIE is linearly proportional to the BDS with the relation of where α is a numerical coefficient.Both hypotheses will be evaluated in comparison with the measured BDS values in the discussion section.

Mechanical Test Setup
A simple illustration of the test arrangement with the dimensions of the core components is depicted in Fig. 2. There, two rectangular prism-shaped samples (55 mm x 4 mm x 25 mm) were placed on top of each other under dry ambient conditions between two Rogowski-type electrodes, forming a 4 mm-wide interface traversed by the tangentially applied field.For the details of the mechanical setup, readers are advised to refer to [2].
All the breakdown tests were performed with the setup immersed in transformer oil to prevent any external flashover.To avoid ingress of oil at the interface, we applied the contact pressure prior to filling the test chamber with the oil.

Setup for AC Breakdown Tests
Fig. 3 shows the whole electrical test setup.A 50 Hz variac (0 − 230 V) was used to energize the primary side of a 100 kV transformer, generating AC ramp voltage on the secondary winding at the rate of 1 kV/s.A water resistor was employed to limit the breakdown current.Also, a voltage divider was connected in parallel to the test object to transmit secondary voltage information to a PC via a data acquisition unit.

Preparation of the Samples
The XLPE and PEEK samples were cut in the aforementioned size from a commercial, XLPE-insulated 145 kV power cable and VESTAKEEP 4000R smooth rod [6], respectively.Whereas, we cast the EPOXY (Casting Resin XB 5950, and Hardener XB 5951 APG without any fillers [7]) and SiR (Elastosil LR 3003 − 60 A & B [8]) samples in the laboratory.
The contact surfaces of the samples were polished using STRUERS Abramin table-top, rotating, grinding machine.As shown in [1,2], the specimens were fixed on a steel rotating disk, and a round-SiC sandpaper of the desired grit was placed on the rotating plane.The speed of the rotating plane was set to 150 rpm, and the force that presses the steel disk towards sandpaper was fixed to 30 bar during polishing of all the samples, ensuring that surfaces underwent the same procedure.Only grit #500 type sandpaper was used when polishing the sample surfaces since the influence of various surface roughness on BDS was not studied in this work.
The samples were sanded for 2−3 minutes with a continuous flow of water to remove any by-products and polymer remnants, and to avoid heating caused by friction.
Subsequently, the samples were rinsed in tap water and were left to dry in air.Then, the dry samples were cleaned using filtered compressed air before they were washed briefly in isopropanol.Finally, the samples were left to dry again at the room temperature.

Elastic Modulus Measurement
The elastic modulus (Young's modulus) of each material was measured using Lloyd LR5K gauge under tensile testing.The values were determined by the initial slope of the obtained stress-strain curves following the ASTM D 790 standard.Subsequently, the effective elastic modulus E ′ of assembled surfaces were calculated using the following relation where E 1 , v 1 and E 2 , v 2 are the elastic modulus and Poisson's ratio of each surface, respectively [9].The obtained results are displayed in Table 1.

Surface Characterization
A 3D optical profilometer (Bruker Contour GT-K 3D Optical Microscope) was used to obtain the surface topography of the polished sample surfaces.The assessment area of the profile was 1.26 mm x 0.95 mm, which was about 5.5% of the nominal contact area A a (4 mm x 55 mm).
Several scans were performed at different sections to ensure consistency.Surface characterization parameters of σ, β m , and n were then obtained following the procedure in [1] and are the summarized in Table 2.

Test Procedure and Data Processing
Initial breakdown tests were performed to identify minimum and maximum forces that the constructed setup permits without oil ingress and deformation of the samples, respectively.The minimum and maximum pressure values together with the intermediate steps determined for each interface are shown in Table 3.The desired force was exerted using weights ranging between 3 − 75 kg to press the samples against one another vertically.In each case, the contact pressure was then calculated using p a = F/A a , where F is the exerted force in N.For each set of experiments, 8 measurements were taken using a virgin pair of samples.The obtained results were statistically evaluated using the two-parameter Weibull distribution.For further evaluation, the 63.2 percentile value with its 90% confidence interval was used.

Results
The experimental data presented in Fig. 4 demonstrate that an increased elastic modulus (i.e. a harder material) results in a reduced BDS.From the minimum contact pressure (p a,min = p a1 ) to the maximum (p a,max = p a4 ), the interfacial BDS rose by a factor of 1.4 − 2.4 following the decrease of the elastic modulus among the chosen materials.The 63.2 percentile and mean BDS   values for each interface are displayed in Table 4.The dashed lines represent the fitted straight lines to the data points and are extrapolated in the entire pressure range in Fig. 4. The extrapolated SiR data points beyond 5 bar are much higher than the tested dielectric strength of the intrinsic SiR (∼ 22 kV/mm [8]), the line is, thus, truncated at 22 kV/mm.Besides, a closer look at the overlapped sections of the bars in Fig. 4 is provided in Fig. 5 in the form of Weibull plots where all the data points are visible.
In addition to the experimentally acquired values, the estimated PDIE values were plotted with the dashed lines in Fig. 6 using the obtained average channel sizes by (2) along with the tabulated data in Table 2. Thus, the variation of α in (3) can be computed by comparing the estimated and experimental data.

Discussion
The results presented in Fig. 4 and Table 4 indicated that the rate of change in the BDS from p a,min to p a,max culminates when E ′ = 8808 MPa (PEEK-PEEK); whereas, the lowest gradient is encountered in the case of E ′ = 109 MPa (SiR-SiR).However, the ratio of p a,max /p a,min in the case of SiR-SiR is not as high as those in the other cases.Because the SiR is a challenging soft material to work with, making it difficult to reduce p a,min further to prevent oil ingress while p a,max could not have been increased due to substantial deformation of the samples.Nevertheless, it can still be inferred that the elastic modulus of the material plays a crucial role in the interfacial BDS as follows.In Fig. 4, the 63.2 percentile BDS of the EPOXY and PEEK interfaces can compare with that of the SiR interface only at contact pressures at least ten times as high.It is interesting to observe that materials with low modulus such as the SiR can achieve such high BDS values even at low contact pressures.
As (1)−(2) reveals, the elastic modulus affects both the size of channels and the total area of contact at the interface.In the case of a material with low elastic modulus, increasing the contact pressure will apparently increase the total real area of contact A re further than it does in the event of a material with high elastic modulus.That, in turn, yields shorter channels as (2) suggests, resulting in a higher PDIE and hence a higher BDS in accordance with (3).With the increase in pressure, overlapped parts of the bars in Fig. 4 at the same pressure becomes larger particularly in the case of the EPOXY and PEEK interfaces, indicating that increase in modulus renders the average channel sizes comparable.
The experimentally obtained BDS values start to deviate considerably from the estimated PDIE values in Fig. 6 as the pressure is increased.Thus, much higher α coefficients arise as the pressure is raised.For instance, the α varies from 1.1 to 1.6 at 11.6 bar; whereas, the range at 33.4 bar becomes 1.7 − 2.5 as the modulus is augmented.It can, then, be argued that the interfacial breakdown phenomenon is not directly governed by the air-filled channels at high pressures; in other words, the second hypothesis starts not to hold true as the pressure is increased.There are two plausible explanations as follows: First, the increased contact pressure probably renders the channels much shorter in practice than the model predicts.Therefore, the model estimating the channel sizes should be improved.Secondly, as the first hypothesis suggests, the interfacial BDS might be dominated by the breakdown of the total area of contact at high pressures.The intrinsic insulation is reported to have a nominal BDS range of 22 − 42, 20 − 24 and 16 − 21 kV/mm for XLPE, EPOXY to PEEK, respectively by the manufacturer data sheets [3,6,7].On that account, the experimental BDS data in Fig. 6 at 33.4 bar are closer to those of the intrinsic materials, favoring the first hypothesis over the second.
Despite the probable coexistence of minuscule channels-whose BDS values are rather high-and contact spots, the intrinsic BDS values are almost reached especially in the cases of EPOXY and PEEK at 33.4 bar.Nevertheless, both the mechanisms are likely to take place simultaneously in real-life.Depending on the contact pressure and the elastic modulus, either of mechanisms prevails over the other.

Conclusion
• The experiments show that the BDS increases with the increased contact pressure in all cases irrespective of the elastic modulus of the insulation.
• The experimental results indicate that the lower the elastic modulus, the higher the BDS, where a much higher BDS is achieved using softer materials with low elastic modulus.
• The theoretical model suggests that the channel size and hence the PDIE decreases as the elastic modulus is reduced.
• When considering the breakdown of the interfaces, both the breakdown of air-filled channels and real area of contact are essential, since either of them dominates the interfacial BDS, depending strongly on the contact pressure and the modulus.
• To improve the theoretical model and to correlate the interfacial BDS with the elastic modulus in a clearer way, further experiments on the PDIE is essential.

Fig. 2 :
Fig. 2: The simplified sketch of the mechanical test setup.

Fig. 3 :
Fig. 3: The sketch of the overall electrical test setup.

Fig. 4 :
Fig.4: The 63.2 percentile BDS with the 90% confidence intervals vs. the contact pressure.The vertical bars feature the 90% confidence interval of the 63.2 percentile for each case; whereas, the markers point the 63.2 percentile.The dashed lines represent the fitted straight lines to the data points.

Fig. 6 :
Fig. 6: The estimated PDIE (dashed line) vs. the experimentally obtained 63.2 percentile BDS (marker) with the 90% confidence interval thereof (bar) as a function of the modulus.For the sake of clarity, only the data at common pressures are covered.[exp: experimental data, extr: extrapolated data, est: estimated data.]

Table 1 :
Measured Young's modulus of each sample

Table 2 :
Surface characterization parameters

Table 3 :
Overview of the applied contact pressure values

Table 4 :
Overview of the experimental results 63% Mean p a [bar] 63% Mean p a [bar] 63% Mean p a [bar] 63% Mean p a1