1 Introduction

The electrical breakdown performance is one of the most important parameters to design insulation systems. Typically, this parameter is determined by applying the standard IEC 60243. For plastics, a plate–plate electrode arrangement is recommended. Between the electrodes, a plate of the test material is placed and the whole arrangement (Fig. 1) is filled with an insulating fluid to eliminate surface discharges [1]

To compare different materials under different environmental conditions, IEC 60243 is not applicable, because the different permittivities and specific conductivity of the test material and surrounding material lead to different electrical field distributions. Especially the triple point, shown in the zoomed view in Fig. 1 between electrode, plastic and surrounding medium causes inhomogeneous electrical fields which distort the results of the dielectric breakdown measurement. Furthermore, a numerical field calculation of this point is not very accurate, because of the unknown micro geometry in the triple point. In the following chapters, the problem is highlighted using the IEC 60243-1 (Tests at power frequencies). Afterward, a new specimen design was developed, which eliminates the above-mentioned downsides of the IEC standard arrangement [1].

2 Methods, specimens and materials

The following chapter gives an overview of the used methods, specimens and materials. PBT (polybutylene terephthalate) (Table 1) serves as an example for this paper, but the method is generally applicable for mold materials (see Sect. 2.5).

2.1 Dielectric breakdown performance (AC)

Figure 2 shows the AC-test setup, which was used to determine the dielectric breakdown performance. An adjustable high-voltage transformer was used to stress the specimens with a voltage ramp of \(2~\mathrm {kV/s}\). The voltage measurement was taken with a capacitive divider. The series resistor \(R_v\) limits the current in case of a breakdown [1].

Fig. 1
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Specimen according to IEC 60243-1 [1] (left) and a detailed view of the triple point (right)

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Table 1 Electrical properties of the used materials [1]
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2.2 Statistical evaluation

The results of the dielectric breakdown performance of PBT plates were evaluated with the Weibull distribution. The parameters were determined with the maximum likelihood method. In all following diagrams, a confidence interval of \(90 \%\) is used.

2.3 Numerical field calculation

The numerical calculations of the electrical field were performed with COMSOL Multiphysics®. The model is a rotationally symmetric, two-dimensional geometry that uses the electric currents interface of the COMSOL-AC/DC module. The program uses the finite element method (FEM) to calculate the relevant field variables depending on the used modules and interfaces. In this model, COMSOL solves the fundamental equations of Ohm’s law, the continuity equation for electric charge, and Gauss’s law [1].

2.4 Microstructural analysis of the plastics

To obtain a high surface quality and clean polished surfaces of the interface between the softer polymer matrix and the harder glass-fibers, the test specimens were prepared in cross section using a cross-section polisher for microstructural analysis. Following the preparation, high-resolution microstructural analysis was performed by light microscopy and scanning electron microscopy (SEM). For further analysis, different x-ray pictures were taken [1].

2.5 Specimen and materials

To investigate the triple point problem, the specimen according to IEC 60243-1, shown in Fig. 1, was used. For this study, two thermoplastic materials have been used. These were polybutylene terephthalate (PBT) materials with a glass-fiber content of \(25 \%\). The two materials were provided by two different suppliers (sample code: PBT-SA and PBT-SB). The test specimens were fabricated by injection molding and had dimensions of \(60\,\textrm{mm} \times 60\,\textrm{mm} \times 1\,\textrm{mm}\). As surrounding materials transformer oil, castor oil and 3 M™ Novec™ 7200 were used. Table 1 shows the electric material properties [1].

3 Dielectric breakdown performance (AC) according to IEC 60243-1

This chapter shows the above-mentioned problem of the IEC arrangement in respect of the triple point and gives a possible solution with a new design of the specimens used for the dielectric breakdown tests.

Fig. 2
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AC-test system to determine the dielectric strength of the plastics [1]

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Fig. 3
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Mesh generated by COMSOL to solve the model (a). Numerical field calculation of triple point with PBT-SA transformer oil under normal conditions (\(23{\,}^\circ \textrm{C} \pm 2{\,}^\circ \textrm{C},\ 50\% \pm 5\% \mathrm {r.h.}\)) (b) [1]

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Figure 3a shows the FEM-mesh of the model, used by COMSOL, according to the IEC 60243-1 specimen. The resulting electrical field strength of the simulation can be seen in Fig. 3b. It is clearly visible that the highest field strength occurs in the triple point. Figure 4 illustrates this in more detail. Here, the field strength along the interface of the PBT plate (Fig. 4b) is plotted. The field strength peak in the diagram is caused by the triple point and depends strongly on the chosen discretization [1].

Fig. 4
figure 4

Numerical field calculation of triple point with PBT-SA transformer oil under normal conditions (\(23\,^\circ \textrm{C} \pm 2\,^\circ \textrm{C},\ 50{\% \pm 5\,\% \mathrm {r.h.}}\)); field strength curve (b) along the PBT plate (a) [1]. Arc length refers to the relative position in the blue highlighted line in (a), which is the cross-sectional edge of the PBT plate

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To illustrate the influence of the triple point, the breakdown voltage of PBT-SA under normal conditions (\(23 \mathrm {^\circ C} \pm 2 \mathrm {^\circ C},\ 50{\% \pm 5{\% \ \text {r.h.}}}\)) was investigated with the three different surrounding fluids. The results are shown in Table 2.

The influence of the surrounding medium is clearly visible. The higher the permittivity of the ambient medium, the more field strength is shifted into the PBT material and out of the triple point, leading to a higher breakdown voltage. Furthermore, all plates, which are surrounded by transformer oil (permittivity less than the PBT plate permittivity), have a breakdown in the triple point region of the electrode. This indicates that high field strengths in the triple point trigger the breakdown. Using castor oil, the breakdown voltage increases which can be explained by a displacement of the maximum field strength into the PBT plate. This is caused by the higher permittivity of the castor oil compared to PBT. Changing the surrounding medium to 3 M™ Novec™ 7200 causes a further increase of the breakdown voltage. One reason for this could be a cooling effect of this surrounding medium due to its low boiling temperature. Once again this demonstrates the strong influence of the surrounding medium on the breakdown voltage. The same problem occurs if the PBT plate is conditioned at different ambient conditions (Table 1) and then tested while using the identical surrounding medium for the different plates.

In summary, it can be concluded that the best way to determine the “real” breakdown field strength is to use the same material or a very similar in means of electrical properties as the surrounding material [1].

Table 2 63%—quantile of the breakdown field strength of PBT-SA depending on the surrounding medium [1]
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4 New specimen design

Based on the results obtained in the previous chapter, in this chapter, a solution for the triple point problem is developed. At first, the following sections concentrate on the requirements, the design as well as the testing of a new specimen for the dielectric breakdown tests as a solution for the above mentioned problems in the IEC 60243-1 arrangement. With this new specimen the breakdown performance of PBT-SA and PBT-SB were evaluated at normal conditions to prove that the new specimen design is working [1, 2].

4.1 Requirements

The main requirement for the new specimen design is the ability to investigate the influence of different environmental conditions on the electric breakdown and aging behavior. In past investigations, the influence of humidity and surrounding medium on the electric breakdown often was not taken into consideration. As a result of the above-mentioned problems, the following design parameters and requirements for the new specimen design arise [3]:

  • The focus of the specimen is on thermoplastics thus the production should be done via injection molding.

  • Electrodes must have very good adhesion to the investigated plastic to prevent a local increase of electrical field strength.

  • The distance of the electrodes must be chosen so, that the average case thickness is considered. As suggested in IEC 60243, an electrode distance of \(1\,\textrm{mm}\) is defined.

  • The electric field in the investigated insulation material must be as homogeneous as possible.

  • To achieve economic times for conditioning and therefore a fast permeation of water molecules in the thermoplastic material, the investigated area of the specimen must be designed accordingly.

  • Due to the contradiction of economic conditioning times and the highest possible testing voltage, the specimen is designed for a maximum testing voltage of \(40\,\mathrm {kV_{peak}}\).

  • The high field strengths necessitate long creepage distance.

4.2 Specimen design

The breakdown performance of the investigated polymers strongly depends on the homogeneity of the electric field. For the here described manufacturing technique, the simplest and most suitable electrode configuration is rod electrodes with half-round heads as shown in Fig. 5.

Fig. 5
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Rod electrode configuration with the dimensions in mm[4]

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Via COMSOL, this electrode configuration was modeled and surrounded by the thermoplastic. The resulting specimen design is shown in Fig. 6 as a 3D model of the simulation software.

The double rips at both ends of the specimen act as an extension of the creepage distance and the highly stressed area between the electrodes is sufficiently dimensioned to allow a fast permeation of water molecules under defined relative humidity if conditioning is required.

The next step was a pre-investigation with an electrical field simulation of the new specimen model with a voltage of \(40\,\mathrm {kV_{peak}}\). In Fig. 7, the relative electrical field strength inside the polymer is shown, whereas in Fig. 8 the relative electrical field strength outside the polymer in the surrounding air is shown [5, 6].

Fig. 6
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3D model of the new specimen design with copper rod electrodes and the surrounding thermoplastic material[3]

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To evaluate the homogeneity of the electrode configuration, the Schwaiger utilization factor can be used. This factor describes the relation between maximum field strength in the electrode system in question and the homogeneous field strength of a plate capacitor with the same plate distance as in Eq. 1 is shown [5, 6].

Fig. 7
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Electrical field strength inside the polymer [5]

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Fig. 8
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Electrical field strength in the surrounding air [5]

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Fig. 9
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Characteristic of the field strength across the junction between polymer and air. Arc length refers to the relative position on the blue highlighted line along the cross-sectional edge of the specimen [5]

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$$\begin{aligned} \eta = \frac{E_0}{E_\textrm{max}} \end{aligned}$$
(1)

The resulting, calculated maximum field strength is located between the rod electrodes, as seen in Fig. 7, and the calculated value is \(44.9 \mathrm {kV_{peak}}\). Using equation 1 leads to a degree of homogeneity of 89.09%. Additionally, the junction between polymer and air must be considered as shown in Fig. 8, the area directly above the stressed volume between the electrodes can be seen as the critical zone of this junction. Figure 9 shows the detailed characteristic of the field strength across the junction between polymer and air, represented by the blue line in Fig. 9. The critical zone is marked by the red circle [5, 6].

5 Validating of the new specimen design

In this chapter, the new specimen design is tested in terms of material quality and the dielectric breakdown performance under normal conditions as well as the influence of humidity and temperature.

Fig. 10
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SEM of a polish of cross section of the testing volume [4, 6]

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5.1 Quality of the material

Figure 10 shows a SEM of a polish of cross section of the testing volume near the copper electrode. As an example, a micro-fissure on the abrasive surface of the electrode is shown in Fig. 10a. It is to assume that these fissures occur during the cooling process of the injection molding. Due to the different thermal expansion coefficients (CTE) of copper and polymer, increased thermal stresses arise inside the thermoplastic. Structural weak points, such as the high abrasive surface of the electrode, lead to a reduced adhesion between copper and plastic which facilitate the development of fissures. Also, the composition of the thermoplastic material influences the behavior during the injection molding and cooling process. Figure 10b shows a SEM picture of the final specimen. Here, the parameters for surface roughness as well as injection molding were optimized. With these optimized parameters, there is a homogeneous junction between electrode and polymer matrix. To assure the quality of thermoplastic material and the distance between the electrodes, the specimen was analyzed using an X-ray unit. A result is shown in Fig. 11, [4, 6].

Fig. 11
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X-ray picture of the specimen[4, 6]

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As shown, the polymer matrix is homogenous and displays no indication of defects like voids or fissures between the electrodes. This implies a high quality of the injection molded specimen [4, 6].

5.2 Dielectric breakdown test under normal conditions

After the designing and manufacturing of the specimens, a dielectric breakdown test under normal conditions was performed. The results of the dielectric breakdown measurement are shown in Fig. 12. PBT-SA has a 63%-quantile of \(43.3 \pm 3.2\,\mathrm {kV/mm}\) and with that a slightly higher breakdown voltage than PBT-SB with a \(36 \pm 3.2\,\mathrm {kV/mm}\) 63%-quantile. In comparison with chapter 3 where PBT-SA was used with the IEC 60243-1 arrangement, the breakdown field strength was highly dependent on the surrounding medium in a range between \(36.21 \pm 0.69\,\mathrm {kV/mm}\) and \(57.54 \pm 3.00\,\mathrm {kV/mm}\).

Fig. 12
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Weibull diagram of the breakdown voltage under normal conditions for PBT-SA and PBT-SB [4, 6]

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To gain knowledge about the breakdown channel in the new specimen design an X-ray analysis was made after the breakdown test. This is shown in Fig. 13 [5, 6]. In Fig. 13a, the breakdown channel is located in the middle between the electrodes and the breakdown voltage, in this case, was \(10\,\textrm{kV}\). In contrast, Fig. 13b shows a decentral breakdown which is on the periphery of the electrode. The breakdown voltage of this specimen was \(27\,\textrm{kV}\). A very well-formed insulation area between the electrodes probably leads to a higher breakdown voltage so that the electric field strength on the periphery gets so high that the breakdown occurs in that area.

Fig. 13
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X-ray pictures of the breakdown channel in the specimen [4, 6]

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The executed investigations and X-ray analysis clearly show that the new specimen design allows a realistic investigation of the material properties of thermoplastics [4, 6].

6 Discussion and conclusion

The experimental studies and simulations show that test specimens, according to IEC 60243, are limited for electrical breakdown investigations on plastics. Only if the electric properties of the surrounding medium and test plate are coordinated with each other, reasonable results are possible. These limitations are shown by simulation and measurement. In the next step, a new specimen was designed which took into account of different requirements. The measurements and investigations with these new specimens for the two different PBT materials are showing that the breakdown performance is similar to the specimens tested according to the IEC standard but without the variance of measurement results for different surrounding materials. Thus, there is no need to coordinate the surrounding medium with the actual testing plate when using the new specimen design.

In additional investigations [7] it was shown that the breakdown and lifetime performance is highly correlated to the microstructure of the polymer and therefore a direct derivation of the material quality. These investigations show that the new design allows investigations under different ambient conditions to evaluate the influence of temperature and humidity on the breakdown and lifetime performance.