Phase-Field Analysis of the Suppression of Electrical Tree Propagation at a Two-Layer Dielectric Interface

Electromechanical breakdown is a phenomenon in which electric fields and mechanical stress simultaneously act on a material, leading to insulation failure. This mechanism is particularly important in soft materials with low elastic moduli. In this study, the propagation of electrical trees in a two-layer structure with different elastic moduli is analyzed using a phase-field method. In the proposed model, electrostatic and strain energy, which are generated by electric fields and mechanical stress, influence the progression of electrical trees, while the progression itself also alters the distribution of these energies. This bidirectional relationship is represented by incorporating both spatial and temporal dependencies. Simulation results successfully reproduced a “barrier effect,” in which tree propagation is temporarily halted or delayed at the interface between the soft and stiff layers. This effect arises from a sharp reduction in strain energy at the interface, relaxation of the electric field, and spatial dispersion of energy. The barrier effect becomes more prominent as the contrast in elastic modulus increases; however, it disappears when the modulus of the stiff layer is reduced or when the soft layer becomes excessively compliant.