13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- IV Kˆ and θ. Theoretically, larger values of II Kˆ imply larger values of θ. Recall that the fracture criteria were developed for self-similar crack propagation. For these small propagation angles, the results appear to be acceptable. But if one has a substantial value for θ, the criteria presented here may not be used. Acknowledgements I would like to acknowledge the contributions of Dr. Yael Motola, Ms. Liat Heller, Dr. Victor Fourman and Mr. Rami Eliasi in carrying out tests and analyses described here. References [1] A.G. Tobin, Y.E. Pak, Effect of electric fields on fracture behavior of PZT ceramics. SPIE, 1916 (1993) 78–86. [2] S. Park, C.T. Sun, Fracture criteria for piezoelectric ceramics. J Am Cer Soc, 78 (1995) 1475–1480. [3] H. Wang, R.N. Singh, Crack propagation in piezoelectric ceramics: effects of applied electric field. J Appl Phys, 81 (1997) 7471–7479. [4] C.S. Lynch, Fracture of ferroelectric and relaxor electro-ceramics: influence of electric field. Acta Mater, 46 (1998) 599–608. [5] R. Fu, T-Y. Zhang, Effects of an electric field on the fracture toughness of poled lead zirconate titanate ceramics. J Am Cer Soc, 83 (2000) 1215–1218. [6] Y. Shindo, M. Oka, K. Horiguchi, Analysis and testing of indentation fracture behavior of piezoelectric ceramics under an electric field. J Engng Mater Techno, 123 (2001) 293–300. [7] Y. Shindo, F. Narita, M. Mikami, Double torsion testing and finite element analysis for determining the electric fracture properties of piezoelectric ceramics. J Appl Phys, 97 (2005) 114109-1–114109-7. [8] G.A. Schneider, F. Felten, R.M. McMeeking, The electrical potential difference across cracks in PZT measured by Kelvin Probe Microscopy and the implications for fracture. Acta Mater, 51 (2003) 2235–2241. [9] X.P. Zhang, S. Galea, L. Ye, Y.W. Mai, Characterization of the effects of applied electric fields on fracture toughness and cyclic electric field induced fatigue crack growth for piezoceramic PIC 151. Smart Mater Struc, 13 (2004) 9–16. [10] H. Jelitto, H. Kessler, G.A. Schneider, H. Balke, Fracture behavior of poled piezoelectric PZT under mechanical and electrical loads. J Euro Cer Soc, 25 (2005) 749–757. [11] Y. Motola, L. Banks-Sills, V. Fourman, On fracture testing of piezoelectric ceramics. Int J Fract, 159 (2009) 167–190. [12] L. Banks-Sills, L. Heller, V. Fourman, A supplementary study on fracture tests of piezoelectric material: cracks parallel to the poling direction. Int J Fract, 175 (2012) 109–125. [13] Z. Suo, Mechanics concepts for failure in ferroelectric ceramics, in: A.V. Srinivasan (Ed.), Smart Structures and Materials, AMD 123, American Society of Mechanical Engineers, New York, 1991, pp. 1–6. [14] H. Gao, T-Y. Zhang, 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. [15] C.C. Fulton, H. Gao, Effect of local polarization switching on piezoelectric fracture. J Mech Phys Solids, 49 (2001) 927–952. [16] H. Jellito, F. Felten, C. Hausler, H. Kessler, H. Balke, G.A. Schneider, Measurment of energy release rates for cracks in PZT under electromechanical loads. J Euro Cer Soc, 25 (2005) 2817–2820. [17] S. Park, C.T. Sun, Effect of electric field on fracture of piezoelectric ceramics. Int J Fract, 70 (1995) 203–216.
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