Ferroelastic Characterization of Piezoelectrics

The elastic deformation behavior of an isotropic material is governed by Young’s modulus Y and Poisson’s ratio σ. Knowledge of the Young’s modulus, for instance, is necessary to split the total deformation S _i measured under load stress T _i into elastic S ^el _i and “plastic” S ^pl _i strain contributions

$$S_i = S_i^{\rm el} + S_i^{\rm pl} = {T_i \over Y} + S_i^{\rm pl}$$

((20.1))

, where Y is not necessarily a constant, but may depend on the amount of nonelastic strains, as will be shown later. The methods for the determination of the Young’s moduli, well-known from conventional ceramics and also applicable to unpoled piezoelectric materials, are much more complicated for nonisotropic materials due to the tensorial character of the modulus and the special electric boundary conditions [1]. The conditions of a constant electrical field, E _z ≡ E ₃ = const, or a constant dielectric displacement, D _z ≡ E ₃ = const, influence the elastic properties. This effect may be illustrated for a uniaxial stress state with T _x ≡ T ₁ ≠ 0 exclusively. In the case of a piezoelectric material, we are interested in the components

$$S_1 = s_{11}^{\rm E}T_1 + d_{31}E_3$$

,

$$D_3 = d_{31}T_1 + \varepsilon_{33}^T E_3$$

((20.2))

.