Loss in Coupling Due to Crack in Piezoelectric Wafer Based Sensors and Actuators

Abstract

oand 90 o domain switching, and the other addressing the energy required to overcome the cracks in piezoelectric materials. By modeling piezoelectric materials as tetragonal crystallites with dipole moments, evolution of polarization due to applied electric filed is derived. Furthermore, dielectric, mechanical, and electromechanical losses due to the inclusions of cracks in piezoelectric solids are investigated. The influence of the existence of a crack is described through the characterization of the perturbation to stress and strain distribution. The strain energy release rates are used to determine the energy dissipation due to the crack. Correspondence principle is then applied to determine loss factors such that the constitutive laws governing the energy loss in dielectric, mechanical, and piezoelectric domains can be quantified. Therefore, the complex electromechanical coupling relations can be expressed by using a phase lag, which indicates the property degradation of piezoelectric materials. Nomenclature a = crack half-length ij B = dielectric constants D = electric displacement E = electric field c E = coercive electric field ) (P E = function represents hysteresis relation between polarization and electric field ERR = energy release rate ijk G = linear piezoelectric constants i p e = direction of the i-th dipole P = total polarization d P = polarization required to align dipoles in P = polarization required to overcome inclusions r P = remnant polarization s P = saturation polarization i p = moment vector of the i-th dipole ijkl S = elastic compliance m e U U , = pure dielectric and elastic energies stored, respectively em U = electric energy stored and induced by applied electric field me U = mechanical energy stored and induced by applied mechanical load