测定静电场中高介电常数缺陷周围绝缘材料的最大机械应力

O. О. Palchykov
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引用次数: 0

摘要

引言所有绝缘的宏观均质固体材料在电场作用下都会改变形状。问题微小缺陷的存在会改变电场的分布,并在材料的特定部分造成机械应力的显著集中,在某些情况下会导致材料的部分或完全破坏。目标这项工作的目的是根据冯-米塞斯准则确定静电场中电离空气和水在缺陷周围绝缘材料中的最大机械应力。此外,还要分析以下参数对所示应力的影响:缺陷的位置、缺陷横截面半主轴的方向角、半主轴和半次要轴的比率、绝缘材料和缺陷的弹性和介电特性。研究方法研究基于各向同性片状均质介质的静电和结构力学相互关联的方程。这些方程的解是通过有限元法获得的。结果。获得了最大机械应力与缺陷椭圆截面半主轴和半次要轴比率的关系图。对于电离空气,表面裂缝和孔隙周围绝缘材料中最大应力的最小比率为 9.3 倍,而工作中考虑的缺陷横截面半主半次轴的最大比率为 10。对于水缺陷,类似比率为 2...5.6 倍,当绝缘材料的相对介电常数从 7 变为 2 时,比率会增加。当绝缘材料的杨氏模量从 1 MPa 增加到 100 GPa 时,电离空气(水)有界孔周围的最大机械应力线性化依赖关系与缺陷横截面主半轴和次半轴之比轴线的倾角在主半轴方向为 0° 和 45° 时分别增加了 35.9° (58.0°) 和 18.6° (20.1°)。独创性首次建立了由连续求解的静电方程和结构力学方程组成的二维数场数学模型,用于确定带有液态或气态缺陷的绝缘材料中的机械应力分布。该模型首次确定了绝缘材料和缺陷的弹性特性比决定了最大机械应力线性化依赖于缺陷横截面主半轴和次半轴之比轴线的倾斜角度。实用价值。在电场和应力场的共同作用下,导致绝缘材料老化程度最大的缺陷类型已经确定。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Determination of the maximum mechanical stresses in the insulating material around a defect with a high dielectric permittivity in an electrostatic field
Introduction. All insulating macrohomogeneous solid materials change shape under the influence of an electric field. Problem. The presence of minor defects changes the distribution of an electric field and causes a significant concentration of mechanical stresses in a given section of the material, which, under certain circumstances, can cause partial or complete destruction of this material. Goal. The purpose of the work is to determine maximum mechanical stresses according to the von Mises criterion in insulating materials around defects with ionized air and water in an electrostatic field. Also, to analyze the influence of the following parameters on the indicated stresses: the location of the defect, the orientation angle of the semi-major axis of the defect cross-section, the ratio of semi-major and semi-minor axes, elastic and dielectric properties of the insulating material and the defect. Methodology. The study is based on the interrelated equations of electrostatics and structural mechanics for an isotropic piecewise homogeneous medium. The solution of these equations is obtained by the finite element method. Results. Graphs of dependences of maximum mechanical stresses on the ratio of semi-major and semi-minor axes of the ellipsoidal cross-section of the defect have been obtained. The minimum ratio of the greatest stresses in the insulating materials around the surface cracks and pores for ionized air has been 9.3 times for the maximum ratio of major and minor semi-axes of the cross-section of the defect considered in the work, which is 10. For a water defect, the similar ratio has been 2...5.6 times, increasing when the relative dielectric permittivity of the insulating material changes from 7 to 2. When Young’s modulus of the insulating material increases from 1 MPa to 100 GPa, the angles of the inclination of the linearized dependences of maximum mechanical stresses around bounded pores with ionized air (water) to the axis of the ratio of major and minor semi-axes of the defect cross-section have been increased by 35.9° (58.0°) and 18.6° (20.1°) at orientations of major semi-axes at angles of 0° and 45°, respectively. Originality. The numerical-field mathematical two-dimensional model has been developed for the first time, which consists of sequentially solved equations of electrostatics and structural mechanics, for the determination of the distribution of mechanical stresses in an insulating material with a liquid or gaseous defect. It has been established for the first time that the ratio of the elastic properties of the insulating material and the defect determines the angle of the inclination of the linearized dependence of the maximum mechanical stress to the axis of the ratio of major and minor semi-axes of the defect cross-section. Practical value. The types of defects that contribute to the aging of insulation materials under the combined action of an electric field and a stress field to the greatest extent have been established.
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