Effects of in-plane electric fields on the toughening behavior of ferroelectric ceramics

Abstract

Mode-I steady state crack growth in poled ferroelectric ceramics subjected to simultaneous electrical and mechanical loading is analyzed to investigate the effect of in-plane electric fields and polarization on the toughening behavior. A multiaxial, incremental constitutive law for domain switching is implemented within the finite element method to obtain the electromechanical crack tip fields. Simulation results are presented for the cases of initial remanent polarization states and applied electric fields perpendicular to the crack plane and parallel to the crack growth direction. Specific results from the calculations include the shapes and sizes of switching zones, and the toughening effects due to domain switching near the crack tip. Ferroelectric ceramics have been widely used in smart structure applications due to their large electromechanical coupling effects. Since ferroelectricdevices oftenoperate understrong mechanicaland electrical loading conditions, the brittle ferroelectric ceramic material is susceptible to fracture. Therefore, an understanding of ferroelectric fracture is a key issue for the efficient and reliable design of these devices. This paper is concerned with the study of the Mode-I fracture behavior of ferroelectric ceramics under combined in-plane electrical and mechanical loading. The scenario investigated here is illustrated in Figure 1. A ferroelectric material is initially poled by an electric field either perpendicular or parallel to the direction of crack growth. After the initial poling, an electric field is applied along (positive electric field) or opposite (negative electric field) to the initial poling direction. Finally, mechanical loading is applied and crack growth occurs. Experimental observations of the fracture properties of ferroelectrics under such conditions have been obtained on several materials from indentation tests and compact tension specimens. Using indentation tests on a PZT-8 material composition, Tobin and Pak [1993] showed that for cracks perpendicular to the poling direction, the apparent fracture toughness decreases with positive electric field and increases with a negative field. For cracks parallel to the poling direction, their results indicated that both positive and negative electric fields have little influence on the toughening. Tobin and Pak [1993] also observed that with no applied electric field the fracture toughness was greater for cracks parallel to the poling direction than for cracks perpendicular to the poling direction. Park and Sun [1995] investigated electric field effects on crack growth in a PZT-4 ceramic by using conventional compact tension fracture tests. Their results agree with those of Tobin and Pak [1993] for the case of electric field applied perpendicular to the cracksurface. However, theVickersindentationtestsofWangandSingh[1997]showedthatiftheapplied electricfields are perpendicular to the crack in a PZT EC-65 ceramic, then a positive electricfield impedes