Development of fracture analysis of piezoelectric ceramics based on the continuum damage mechanics

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Variation of material properties of piezoelectric ceramics under cyclic electric loading was evaluated experimentally. A resonance and an anti-resonance frequencies and a capacitance were measured by an impedance analyzer, then an electromechanical coupling coefficient, a permittivity, an elastic constant and a piezoelectric constant were estimated.An electric field with a frequency among 0.1 to 2 kHz was applied to a specimen of lead zirconate titanate (PZT) systematically. Then the dependence of the variation on the range and mean electric field, compressive stress due to the displacement constraint and frequency of negative AC electric field was clarified.An electric field with the resonance frequency was also applied to a specimen and an internal stress in the center of the specimen was estimated by the AC current. It was found that the electromechanical coupling coefficient and the piezoelectric constant of lead titanate specimen were decreased significantly when the internal stress was the largest.A piezoelectric constitutive equation and a damage evolution equation were applied to the double cantilever beam model, and a simplified analysis of crack growth was performed by a local approach of fracture based on the continuum damage mechanics. The effects of the space discretizing size in the numerical analysis and the phase difference between mechanical and electric loading on the crack growth behavior were elucidated.A coupled analysis of stress-electric-damage field for a unit cell associated with multilayer piezoelectric actuators was performed by a finite difference method using the piezoelectric constitutive equation and the damage evolution equation. Then distribution of stress and electric field depending on the damage development, relation between crack initiation time and applied electric field and crack initiation point near the electrode were clarified.