Multiscale behavior of crack initiation and growth in piezoelectric ceramics

The multiscale nature of cracking in ferroelectric ceramics is explored in relation to the crack growth enhancement and retardation behavior when the direction of applied electric ®eld is reversed with reference to that of poling. An a priori knowledge of the prevailing fracture behavior is invoked for the energy dissipated in exchange of the macroand micro-crack surface. To avoid the formalism of developing a two-scale level model, a single dominant crack is considered where the e€ect of microcracking could be re ̄ected by stable crack growth prior to macro-crack instability. This is accounted for via a length ratio parameter k. Microand macro-crack damage region would necessarily overlap in the simpli®ed approach of applying equilibrium mechanics solutions to di€erent scale ranges that are connected only on the average over space and time. The strain energy density theory is applied to determine the crack growth segments for conditions of positive, negative and zero electric ®eld. The largest and smallest crack segments were found to correspond, respectively, to the positive and negative ®eld. All of the three piezoceramics PZT-4, PZT5H and P-7 followed such a trend. This removes the present-day controversy arising from the use of the energy release rate concept that yields results independent of the sign of the electric ®eld. Interaction of non-similar crack growth with the direction of electric ®eld is also discussed in relation to Mode II cracking. The crack initiation angle plays a dominant role when the growth segment is suciently small. Otherwise, a more complex situation prevails where consideration should also be given to the growth segment length. Failure stresses of Modes I and II cracking are also obtained and they are found to depend not only on the electric ®eld density but also on crack length and the extent of slow crack growth damage. These ®ndings suggest a series of new experiments. Ó 2000 Elsevier Science Ltd. All rights reserved.