experimental findings in [1-3]. There were no need to de-couple the electrical and mechanical effects nor was there the need to include nonlinear effects. 4. CONCLUSIONS When material microstructure plays a role in failure analyses, the possibility of multiscale cracking should be considered even though it was not needed for illustrating the influence of electric field reversal on crack growth. For a quantitative assessment of the failure stress, however, microcracking would need to be modeled since the compliance of the specimen would be altered. The initiation and growth of the macrocrack would also be affected accordingly. Such a situation has been discussed in [8] where the interaction of micro- and macro-cracking was accounted for by introducing an additional length parameter. Lacking at present is a knowledge of the initial states of the material microstructure, the behavior of which would depend sensitively on the stress/strain or energy density arising, say from the process of crystal nucleation and formation for metals. If the internal stresses trapped in the grains are of the same orders of magnitude as those induced by the applied loads, then the neglect of the influence of the initial states would leave any predictions in doubt. Such situations are no longer uncommon as the length scale of device components are being reduced to microns in size. Another seemingly innocent pitfall is the use of physical data extracted from test specimens that are orders of magnitude larger than the device under consideration. It appears that data correlation at the nano-, micro-, meso- and macro-scale requires extensive attention. Until the problem of scaling is better understood, the reliable use of ferroelectric ceramics in electronic devices leaves much to be desired. References [1] A. Tobin and Y. E. Pak, Effects of electric fields on fracture behavior of PZT ceramics, Smart Materials, ed. V. K. Varadan, 1916 (1993) 78-86. [2] Y. E. Pak and A. Tobin, On the electric field effects in fracture of piezoelectric materials, Mechanics of Electromagnetic Materials and Structures, AMD-161/MD-42, ASME (1993) [3] S. Park and C. T. Sun, Fracture criterion of piezoelectric ceramics, J. Am. Ceram. Soc., 78, (1995) 1475-1480. [4] W. Yang and Z. Suo, Cracking in ceramic actuators caused by electrostriction, J. Mech. Phys. Solids, 42 (1994) 649-663. [5] C. S. Lynch, W. Yang, L. Collier, Z. Suo and R. M. McMeeking, Electric field induced cracking in ferroelectric ceramics, Ferroelectrics, 166 (1995) 11-30. [6] H. Gao, T. Y. Zhang and P. Tong, Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic, J. Mech. Phys. Solids, 45 (1997) 491-510. [7] J. Z. Zuo and G. C. Sih, Energy density formulation and interpretation of cracking behavior for piezoelectric ceramics, J. of Theoretical and Applied Fracture Mechanics, 34(1) (2000) 17-33. [8] G. C. Sih and J. Z. Zuo, Multiscale behavior of crack initiation and growth in ferroelectric ceramics, J. of Theoretical and Applied Fracture Mechanics, 34(2) (2000) 123-141. [9] G. C. Sih, Mechanics of fracture initiation and propagation, Kluwer Academic Publishers, Boston, (1991).
RkJQdWJsaXNoZXIy MjM0NDE=