Energy density theory formulation and interpretation of cracking behavior for piezoelectric ceramics

Any attempt made to separate energy into electrical and mechanical parts may lead to inconsistencies as they do not necessarily decouple. This is illustrated by application of the energy density function in the linear theory of piezoelasticity. By assuming that a critical energy density function prevails at the onset of crack initiation, it is possible to establish the relative size of an inner and outer damage zone around the crack tip; they correspond to the ligaments at failure caused by pure electric ®eld and pure mechanical load. On physical grounds, the relative size of these zones must depend on the relative magnitude of the mechanical and electrical load. Hence, they can vary in size depending on the electromechanical material and damage resistance properties. Numerical results are obtained for the PZT-4, PZT-5H, and P-7 piezoelectric ceramics. These two ligaments for the two damage zones may coincide for appropriate values of the applied electrical ®eld and mechanical load. Explicit expression of the energy density factor S is derived showing the mixed mode electromechanical coupling e€ects. The factor S can increase or decrease depending on the direction of the applied electric ®eld with reference to the poling direction. This is in contrast to the result obtained from the energy release rate quantity, which remains unchanged for electric ®eld in the direction of poling or against it. Ó 2000 Elsevier Science Ltd. All rights reserved.