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Emergent failure patterns at sub-critical fields in polymeric dielectrics

Abstract

A generalized physical framework is presented for the simulation of electro-thermal ageing in large-size samples of polymeric dielectric by discretizing them into small-size elements using an orthogonal matrix. The individual elements are treated as thin-film samples with assigned generic morphological parameters, whose distribution in the matrix obeys their fitted thin-film distribution probabilities obtained from experiments. This allows the effect of spatial inhomogeneity in large-size samples to be included in the model. Quantitative simulations of the evolution of direct-current ageing up to eventual catastrophic failure are studied at sub-critical fields, and it is shown that the criterion for the onset of a deterministic runaway event is the enhancement of the local field, caused by self-organized degradation, to a temperature-dependent critical value. The lifetime is effectively the time taken to reach the critical value, and its statistics are fitted to the Weibull distribution. The failure patterns produced during ageing were found to be strongly dependent on the applied electric field, but not on temperature whose increases accelerated the ageing process instead. The global inhomogeneous properties of the dielectric were found to control the ageing process with stochastic percolation behaviour below the critical point at low applied fields. Increasing the applied field gradually strengthened the influence of local deterministic factors.

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References

  1. 1

    Dissado LA, Fothergill JC (1992) Electrical degradation and breakdown in polymers. The Institution of Engineering and Technology, London

  2. 2

    Xu B, Yang H, Dai K et al (2018) Thermo-compression-aligned functional graphene showing anisotropic response to in-plane stretching and out-of-plane bending. J Mater Sci 53:6574–6585. https://doi.org/10.1007/s10853-018-2021-1

  3. 3

    Pelrine R, Kornbluh R, Pei Q, Joseph J (2000) High-speed electrically actuated elastomers with strain greater than 100%. Science 287:836–839

  4. 4

    Chen F, Liu K, Wang Y, Zou J, Gu G, Zhu X (2019) Automatic design of soft dielectric elastomer actuators with optimal spatial electric fields. IEEE Trans Robot 35:1150–1165

  5. 5

    Fothergill JC (2007) Ageing, space charge and nanodielectrics: ten things we don’t know about dielectrics. In: 2007 IEEE international conference on solid dielectrics, ICSD, pp 1–10

  6. 6

    Shen ZH, Wang JJ, Jiang JY, Huang SX, Lin YH, Nan CW, Chen LQ, Shen Y (2019) Phase-field modeling and machine learning of electric-thermal-mechanical breakdown of polymer-based dielectrics. Nat Commun 10:1843

  7. 7

    Duxbury PM, Beale PD, Leath PL (1986) Size effects of electrical breakdown in quenched random media. Phys Rev Lett 57:1052–1055

  8. 8

    Beale PD, Duxbury PM (1988) Theory of dielectric breakdown in metal-loaded dielectrics. Phys Rev B 37:2785–2791

  9. 9

    Coppard RW, Dissado LA, Rowland SM (1989) Dielectric breakdown in metal-loaded polyethylene. J Phys: Condens Matter 1:3041–3045

  10. 10

    Dissado LA, Fothergill JC, Wise N, Willby A, Cooper J (2000) A deterministic model for branched structures in the electrical breakdown of solid polymeric dielectrics. J Phys D Appl Phys 33:L109–L112

  11. 11

    Dissado LA (2002) Understanding electrical trees in solids: from experiment to theory. IEEE Trans Dielectr Electr Insul 9:483–497

  12. 12

    Champion JV, Dodd SJ (2001) Simulation of partial discharges in conducting and non-conducting electrical tree structures. J Phys D Appl Phys 34:1235–1242

  13. 13

    Dodd SJ (2003) A deterministic model for the growth of non-conducting electrical tree structures. J Phys D Appl Phys 36:129–141

  14. 14

    Dammig Quiña PL, Irurzun IM, Salvatierra LM, Mola EE (2010) Field fluctuations and fractality in electrical breakdown trees. Phys Rev E 82:041106

  15. 15

    Yang Y, He J, Li Q et al (2019) Self-healing of electrical damage in polymers using superparamagnetic nanoparticles. Nat Nanotechnol 14:151–155

  16. 16

    Werelius P, Tharning P, Eriksson R, Holmgren B, Gafvert U (2001) Dielectric spectroscopy for diagnosis of water tree deterioration in XLPE cables. IEEE Trans Dielectr Electr Insul 8:27–42

  17. 17

    Flandin L, Vouyovitch L, Beroual A, Bessede JL, Alberola ND (2005) Influences of degree of curing and presence of inorganic fillers on the ultimate electrical properties of epoxy-based composites: experiment and simulation. J Phys D Appl Phys 38:144–155

  18. 18

    Dissado LA, Thabet A (2008) Simulation of electrical ageing in insulating polymers using a quantitative physical model. J Phys D Appl Phys 41:085412

  19. 19

    Dissado LA, Mazzanti G, Montanari GC (1997) The role of trapped space charges in the electrical aging of insulating materials. IEEE Trans Dielectr Electr Insul 4:496–506

  20. 20

    Mazzanti G, Montanari GC, Dissado LA (1999) A space-charge life model for ac electrical aging of polymers. IEEE Trans Dielectr Electr Insul 6:864–875

  21. 21

    Mazzanti G, Montanari GC, Dissado LA (2005) Electrical aging and life models: the role of space charge. IEEE Trans Dielectr Electr Insul 12:876–890

  22. 22

    Jones JP, Llewellyn JP, Lewis TJ (2005) The contribution of field-induced morphological change to the electrical aging and breakdown of polyethylene. IEEE Trans Dielectr Electr Insul 12:951–966

  23. 23

    Crine JP (2005) On the interpretation of some electrical aging and relaxation phenomena in solid dielectrics. IEEE Trans Dielectr Electr Insul 12:1089–1107

  24. 24

    Montanari GC, Seri P, Dissado LA (2019) Aging mechanisms of polymeric materials under dc electrical stress: a new approach and similarities to mechanical aging. IEEE Trans Dielectr Electr Insul 26:634–641

  25. 25

    Zuo Z, Dissado LA, Chalashkanov NM, Dodd SJ, Yao C (2018) Dielectric breakdown at sub-critical fields. Appl Phys Lett 113:112901

  26. 26

    Dissado LA (2018) The theory of everything in the electrical breakdown of polymeric dielectrics: maybe. In: 2018 IEEE 2nd international conference on dielectrics, ICD, pp 1–5

  27. 27

    Witten TA, Sander LM (1981) Diffusion-limited aggregation, a kinetic critical phenomenon. Phys Rev Lett 47:1400–1403

  28. 28

    Niemeyer L, Pietronero L, Wiesmann HJ (1984) Fractal dimension of dielectric breakdown. Phys Rev Lett 52:1033–1036

  29. 29

    Peruani F, Solovey G, Irurzun IM, Mola EE, Marzocca A, Vicente JL (2003) Dielectric breakdown model for composite materials. Phys Rev E 67:066121

  30. 30

    Wu K, Dissado LA, Okamoto T (2004) Percolation model for electrical breakdown in insulating polymers. Appl Phys Lett 85:4454–4456

  31. 31

    Zuo Z, Yao C, Dissado LA, Chalashkanov NM, Dodd SJ (2017) Simulation of electro-thermal ageing and breakdown in polymeric insulation under high frequency trapezoidal wave pulses. IEEE Trans Dielectr Electr Insul 24:3766–3775

  32. 32

    Boksiner J, Leath PL (2003) Dynamics of dielectric breakdown paths. Phys Rev E 67:066610

  33. 33

    Dakin TW (1948) Electrical insulation deterioration treated as a chemical rate phenomenon. AIEE Trans 67:113–322

  34. 34

    Dissado LA (2002) Predicting electrical breakdown in polymeric insulators from deterministic mechanisms to failure statistics. IEEE Trans Dielectr Electr Insul 9:860–875

  35. 35

    Vaughan AS, Hosier IL, Dodd SJ, Sutton SJ (2006) On the structure and chemistry of electrical trees in polyethylene. J Phys D Appl Phys 39:962–978

  36. 36

    Wu D, Chen J, Liu C (2007) Numerical evaluation of effective dielectric properties of three-dimensional composite materials with arbitrary inclusions using a finite-difference time-domain method. J Appl Phys 102:024107

  37. 37

    Herrmann HJ, Stanley HE (1984) Building blocks of percolation clusters: volatile fractals. Phys Rev Lett 53:1121–1124

  38. 38

    Zuo Z, Dissado LA, Yao C, Chalashkanov NM, Dodd SJ, Gao Y (2020) Modeling for life estimation of HVDC cable insulation based on small-size specimens. IEEE Electr Insul Mag 36:20–31

  39. 39

    Mazzanti G (2017) Life and reliability models for high voltage DC extruded cables. IEEE Elect Insul Mag 33:42–52

  40. 40

    Lei W, Wu K, Wang Y et al (2017) Are nano-composites really better DC insulators? A study using silica nanoparticles in XLPE. IEEE Trans Dielectr Electr Insul 24:2268–2270

  41. 41

    Lei W, Dissado LA, Dodd SJ, Chalashkanov NM, Fothergill JC, Cheng Y, Zheng X (2007) DC breakdown voltage tests may not be a good indicator of long-term ageing behaviour. In: IEEE international symposium on electrical insulating materials, ISEIM, pp 425–428

  42. 42

    Diaham S, Belijar G, Locatelli ML, Lebey T (2017) Filamentary electrical conduction in polyimide films detected by infrared thermography before thermal breakdown. Appl Phys Lett 110:162902

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Acknowledgements

Z. Zuo and C. Yao acknowledge the support of the National Natural Science Foundation of China Grant No. 51321063 for this work.

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Correspondence to L. A. Dissado or C. Yao.

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Zuo, Z., Dissado, L.A., Yao, C. et al. Emergent failure patterns at sub-critical fields in polymeric dielectrics. J Mater Sci 55, 4748–4761 (2020). https://doi.org/10.1007/s10853-019-04320-y

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