13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- j j j j j j j j j j j j j j j j b e q C a e b C m e a e b g C a e b C f C a γ λ γ γ γ ) ( ) , ( ) ( , 1) ( 33 33 31 13 31 11 33 33 13 15 2 44 − − = + − = + − = + − = (A.3) ( , ) ( , ), lim , lim , lim , lim lim 0 0 0 0 0 p Y p f Y f q g q g j j ij ij j j j j j j ξ γ γ ξ ξ ξ ξ ξ ξ →∞ →∞ →∞ →∞ →∞ = = = = = (A.4) References [1] S.F. Li, P.A. Mataga, Dynamic crack propagation in piezoelectric materials-Part I: Electrode solution. J Mech Phys Solids, 44 (1996) 1799-1830. [2] S.F. Li, P.A. Mataga, Dynamic crack propagation in piezoelectric materials-Part II: Vacuum solution. J Mech Phys Solids, 44 (1996) 1731-1866. [3] Y. Shindo, H. Katsura, W. Yan, Dynamic stress intensity factor of a cracked dielectric medium in a uniform electric field. Acta Mech, 117 (1996) 1-10. [4] Z.T. Chen, B.L. Karihaloo, S.W. Yu, A Griffith crack moving along the interface of two dissimilar piezoelectric materials, Int J Fract, 91(1998) 197-203. [5] Z.T. Chen, S.W. Yu, Semi-infinite crack under anti-plane mechanical impact in piezoelectric materials. Int J Fract, 88 (1998) L53-56. [6] X.Y. Wang, S.W. Yu, Transient response of a crack in piezoelectric strip subjected to the mechanical and electrical impacts: mode-I problem. Mech Mater, 33 (2001) 11-20. [7] T. Zhu, W. Yang, Crack kinking in a piezoelectric solid. Int J Solids Struct, 36 (1999) 5013-5027. [8] B.L. Wang, N. Noda, Mixed mode crack initiation in piezoelectric ceramic strip. Theor Appl Fract Mech, 34 (2000) 35-47. [9] K.Q. Hu, Z. Zhong, A moving mode-III crack in a functionally graded piezoelectric strip. Int J Mech Mater Design, 2 (2005) 61-79. [10] Z. Suo, C.-M. Kuo, D.M. Barnett, J.R. Willis, Fracture mechanics for piezoelectric ceramics. J Mech Phys Solids, 40 (1992) 739-765. [11] P.S. Theocaris, N.I. Ioakimidis, Numerical integration methods for the solution of singular integral equations. Q Appl Math, 35 (1977) 173-183. [12] X.F. Li, K.Y. Lee, Three-dimensional electroelastic analysis of a piezoelectric material with a penny-shaped dielectric crack. J Appl Mech, 71 (2004) 866-878. [13]A. Azhdari, S. Nemat-Nasser, Hoop stress intensity factor and crack-kinking in anisotropic brittle solids. Int J Solids Struct, 33 (1996) 2023-2037. [14]W. Yang, Mechatronic Reliability: Electric Failures, Mechanical-Electrical Coupling, Domain Switching, Mass-Flow Instabilities. Springer Verlag, New York, 2002. [15] Y. Shindo, F. Narita, H. Mitsuru, Dynamic fatigue of cracked piezoelectric ceramics under electromechanical loading: Three-point bending test and finite element analysis. J Mech Mater Struct, 4 (2009) 719-729. [16]J.W. Hutchinson, Z. Suo, Mixed mode cracking in layered materials. Adv Appl Mech, 29 (1992) 63-191.
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