Nitrile로 개질된 에폭시 수지계에서 트링 열화현상의

프랙탈 차원에 미치는 온도의 영향

조영신, 심미자*, 김상욱

서울시립대학교 화학공학과, *생명과학과

Effects of Temperature on Fractal Dimension of Treeing Deterioration Phenomena in Epoxy Resin System Modified with Nitrile

Young Shin Cho, Mi Ja Shim*, Sang Wook Kim

Dept. of Chem. Eng., The Univ. of Seoul, Seoul 130-743, Korea

*Dept. of Life Sci., The Univ. of Seoul, Seoul 130-743, Korea

1. Introduction

The long term deterioration and dielectric breakdown by electrical treeing phenomena in the polymeric insulator is one of the main cause of electrical failure. The tree initiation and propagation mechanism has been studied by many researchers to design a good insulator under various combined stresses. The treeing pattern is too complex and difficult to classify.

Electrical tree starting from the electrically conducting inclusions, rough electrode surfaces, voids, cracks, etc. propagates toward outer electrode, step by step with time. To describe the characteristics of electrical trees grown in the polymer insulator, the fractal concept of self-similarity has been adopted[1,2].

In this study the effects of temperature on the complex pattern and fractal dimension of electrical tree in a polymeric insulator DGEBA/MDA system modified with GN were investigated. The needle-plane needle electrode geometry was used to accelerate the electrical tree propagation.

2. Experiment

2-1. Materials and specimen preparation

DGEBA(EPON 828 grade) and MDA were used as the base material for this study. A reactive additive GN(10 phr) was added to modify the conventional epoxy resin system DGEBA/MDA which was too brittle because of its high cross linking density[3]. The mixture was degassed and cast into the mold at 80℃. The ultrasonically washed needle electrodes(tip curvature radius of 3 □, tip angle of 30o) were placed at the mold. The overall curing condition of epoxy resin composite system was 1st curing at 80℃ for 1.5 hr and 2nd curing at 150℃ for 1.0 hr. The thermally cured specimen was cooled down to the room temperature inside oven slowly to prevent the formation of voids and cracks. The specimens were sliced to the standard size and checked by microscope. The specimens without defects such as voids and cracks at the tip of needle electrode were selected and stressed.

2.2. Treeing deterioration test

Silver paint was applied on the bottom of the specimen to reduce the electrical resistance between counter-plane electrode and specimen. The specimen was immersed into the insulating oil for the suppression of the surface discharge under high electric field. The needle electrode was connected to the high voltage generator until dielectric breakdown to determine the tree propagation with an optical microscope and camera. The fractal dimension was measured by using scale covering method described in the references.

3. Results and Discussion

Fig. 1 Temperature dependence of dielectric breakdown strength.

Fig. 1 shows the effects of temperature on dielectric breakdown strength of DGEBA/MDA/GN(10 phr) system with electrode separation of 1 mm between needle electrode and plane bottom electrode. As the temperature increased the dielectric breakdown strength decreased from the lower temperature than heat distortion temperature(HDT, 103℃) and abrupt decrease was observed at the HDT and Tg of 115℃. At high temperature, the polymer chains move freely and electrons emitted

(a)

(b)

Fig. 2 Electrical tree from the tip of needle electrode at different temperature.

from the surface of electrode fly into the material, easily. So the time to dielectric breakdown decreases and the dielectric breakdown strength measured at the voltage rising rate of 500 V/sec decreases, especially, at DTG and Tg.

Fig. 2. shows the electrical treeing phenomena in DGEBA/MDA/GN system at different temperature. The real electrical tree was observed from the needle electrode by using optical microscope. The dielectric breakdown process by treeing deterioration phenomena growing under inhomogeneous high electric field consists of 3 steps of tree initiation, tree propagation, and breakdown. As high electric field is applied, continuously, the reinforced electric stress at the tip of needle electrode exceeds the limit of mechanical strength to resist the stress and goes following the distortion of the material by Maxwell compressive stress and tree initiates. The branch density of electrical tree depends on the applied voltage, frequency, temperature, etc.

Fig. 3 Fractal dimension of electrical tree by scale covering method.

The fractal dimension of complex phenomena can be determined by covering the object with boxes of different sizes, and accounting the number of boxes. The number of boxes varies as N(s)∝s-Df and the exponent Df is the fractal dimension which indicates the complexity of an object, quantitatively[4]. The value of Df can be determined directly by plotting log N(s) against log s on the log-log paper, and the slope is -Df. This method is known as scale covering method. Fig. 3 indicates that the electrical tree is fractal from the linear relation between scale and the things to be interest to observe. The fractal theory is useful for quantifying a complex pattern with only fractal dimension(Df). Electrical treeing pattern and fractal dimension depend on the temperature, frequency, electric field, etc.

Fig. 4 shows the fractal dimension dependences on tree propagation behaviour in DGEBA/MDA/GN system at different temperature. The fractal dimension (Df) increased from 1.0 with increasing tree length and saturated to 1.5 at room temperature of 25℃. At high temperature of 100℃ the initial fractal dimension was 1.5 and increased a little and saturated to 1.6. It is clear that the electrical tree was more complex at high temperature because the tree grow easily and three spatially. Tree length dependence changes on the fractal dimension of the trees are used to explain the complexity of the pattern. The initial tree generally has low fractal

Fig. 4 Temperature dependence of fractal dimension in DGEBA/MDA/GN system.

dimension and increases with increasing tree length to some extent. This is because the density of branch is low[5]. And the propagating tree has almost constant fractal dimension with same tree density. All the 2-D projected tree in DGEBA/MDA/GN system at various temperature had Df richer than 1.0 and lower than 2.0.

4. Conclusions

From the test results of the temperature dependence on fractal dimension of electrical treeing deterioration phenomena in polymer insulator DGEBA/MDA/GN system at different temperature, the following conclusions were obtained. The electrical trees observed at the system were dendrite type and fractals from the linear relationship between observation scale and object to be interest on double logarithmic axes. The fractal dimension at high temperature was higher than that of low temperature. Both of the fractal dimension at low and high temperature increased and saturated as the voltage applying time increased. The fractal dimension showed the complexity, quantitatively, well.

Acknowledgement

The authors wish to acknowledge the financial support of the Korea Research Foundation made in the Program Year 1996.

References

1. M. Ruike, S. Fujita and F. Noto, T. IEE Japan, 115-A, 744 (1995).

2. S. Maruyama, S. Kobayashi and K. Kudo, T. IEE Japan, 114-A, 47(1994).

3. Y.S. Cho, H.K. Lee, M.J. Shim and S.W. Kim, J. Korean Ind. & Eng. Chemistry, 3, 171(1997).

4. L. Satish and W.S. Zaengl, IEEE Trans. Dielectrics EI, 2, 352(1995).

5. Y.S. Cho, M.J. Shim, and S.W. Kim, J. Korean Ind. & Eng. Chemistry, 6, 707(1995).