Determination of the maximum mechanical stresses in the insulating material around a defect with a high dielectric permittivity in an electrostatic field

Abstract

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.