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

通过实验研究了循环电载荷作用下压电陶瓷材料性能的变化。利用阻抗分析仪测量了PZT的共振频率、反共振频率和电容，并估算了机电耦合系数、介电常数、弹性常数和压电常数。然后阐明了负电场的位移约束和频率引起的压应力与范围和平均电场的依赖关系，并对试件施加具有共振频率的电场，通过交流电流估计试件中心的内应力。结果表明，当内应力较大时，钛酸铅试件的机电耦合系数和压电常数显著降低。将压电本构方程和损伤演化方程应用于双悬臂梁模型，并采用基于连续损伤力学的局部断裂方法对裂纹扩展进行了简化分析。阐述了数值分析中的空间离散尺寸和机电载荷的位相差对裂纹扩展行为的影响。利用压电本构方程和损伤演化方程，采用有限差分方法对与多层压电致动器相关联的单胞进行了应力-电-损伤耦合分析。阐明了应力和电场分布与损伤发展的关系，裂纹萌生时间与外加电场的关系，以及电极附近的裂纹起始点。

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.