Formulation of damage development for piezoelectric ceramics under static compressive stress

In order to formulate a damage evolution equation, damage development of columnar specimens under static compressive stress was evaluated from variation of elastic coefficient based on the continuum damage mechanics. The elastic coefficient was evaluated from gradient of stress-strain relations of compression fracture tests. Then the damage evolution equation was formulated by an exponential function of strain with a threshold to start the damage development. Moreover, material functions of the damage variable were also formulated for the variation of material properties. By using the damage evolution equation and material functions, stress-strain relations were predicted properly taking into account the variation of elastic coefficient and accumulation of residual strain accompanied with damage development. Then the prediction was compared with experimental results, and the validity of the formulation was verified by the good agreement.