Electrical treeing is a main cause of long term degradation of polymeric insulation and inorganic nanofillers have been added to improve the treeing resistance of polymers. In this work, a phase field model for the propagation of electrical tree in nanocomposites is presented, in which the damage status of insulation is described with a spatially and time dependent continuous variable. The evolution of damage phase is described with a modified Allen-Cahn equation, which is driven by the free energies originated from the phase separation, interface and electric field. The electric field distribution during growth of electrical tree is obtained by solving the iterative form of Poisson's equation with the spectral iterative perturbation method. Then the phase field model is applied to investigate the influence of nanofillers shape and distribution on propagation process of electrical tree. The results indicate that the phase field model can reproduce the dendritic shape of electrical tree, and the parallel nanosheet presents superior performance in hindering electrical tree than nanoparticle and random nanosheet.

中文翻译：

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纳米复合材料中电树传播的相场模型


电树化是聚合物绝缘材料长期降解的主要原因，添加无机纳米填料以提高聚合物的耐树化性。在这项工作中，提出了纳米复合材料中电树传播的相场模型，其中绝缘体的损坏状态用空间和时间相关的连续变量来描述。损伤相的演变用修正的 Allen-Cahn 方程描述，该方程由相分离、界面和电场产生的自由能驱动。通过谱迭代摄动法求解泊松方程的迭代形式，得到了电树生长过程中的电场分布。然后应用相场模型研究纳米填料的形状和分布对电树传播过程的影响。结果表明，相场模型可以再现电树的树枝状形状，并且平行纳米片在阻碍电树方面表现出比纳米颗粒和随机纳米片更优越的性能。