Effect of electrical polarization saturation on stress intensity factors in a piezoelectric ceramic

The electric!_eld induced stress intensity factor in a piezoelectric medium of limited electrical polarization is evaluated based on a strip!saturation model of the Dugdale!type[ Particular emphasis is placed on the e}ect of the saturation condition on the near tip _eld and the stress intensity factor[ To this end\ the general solution is derived in terms of the "unspeci_ed# normal electrical displacement distribution along the saturated strip[ Since the saturated strip is representative of the unknown saturated zone\ the normal electrical displacement may su}er discontinuity across the saturated strip[ It is found that the crack!tip _eld and the stress intensity factors depend on the discontinuity of the normal electrical displacement across the saturated strip although this dependency disappears in some practically important cases[ A crack per! pendicular to the poling axis in a general poled ferroelectric is discussed in detail to illustrate the implications of the strip!saturation model for electric!_eld induced cracking[ The results show that some discrepancies between theory and experiments\ for which the classical linear piezoelectric model gives qualitatively incorrect results\ can be explained clearly in terms of the stress intensity factor given by the strip!saturation model[ In particular\ these results are independent of the form of the saturation condition imposed on the saturated strip