Modeling of material properties of piezoelectric ceramics taking into account damage development under static compression

We have carried out static compression tests in the poling direction for PZT ceramics and evaluated the material properties by measuring the resonance and anti-resonance frequencies and electrostatic capacity at regular intervals. Then the variation in the material properties up to fracture was clarified. Also, the development of internal damage was also clarified quantitatively by evaluating a damage variable on the basis of the continuum damage mechanics. The damage variable was calculated from the ratio of the elastic coefficient to its initial value. In the present paper, the development of internal damage was formulated as an evolution equation of the damage variable. In the formulation, a threshold stress leading to the onset of damage was considered. Moreover, the variation in material properties was related to the damage variable and formulated as material functions of the damage variable. The development of internal damage and the variation in material properties were simulated by the equations proposed in the present paper and the validity of the equations was verified by comparing the predictions with experimental results.