Crack bifurcation predicted for dynamic anti-plane collinear cracks in piezoelectric materials using a non-local theory

Theoretical and Applied Fracture Mechanics

Volumn 39, Issue 2, 2003, Pages 171-182

  Zhou, Z G ^a   Sun, Y G ^a   Wang, B ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Crack; Elastic waves; Fourier integral transform; Non local theory; Piezoelectric materials; Schmidt method

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; CRACKS; ELASTICITY; FOURIER TRANSFORMS; INTEGRAL EQUATIONS; SHEAR WAVES;

COLLINEAR CRACKS;

PIEZOELECTRIC DEVICES;

CRACK;

EID: 0037343753     PISSN: 01678442     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8442(02)00157-X     Document Type: Article

References (29)

1. W.E.F. Deeg, The analysis of dislocation, crack and inclusion problems in piezoelectric solids, Ph.D. Thesis, Stanford University, 1980.
2. Z. Suo, C.M. Kuo, D.M. Barnett, J.R. Willis, Fracture mechanics for piezoelectric ceramics, J. Mech. Phys. Solids. 40 (1992) 739-765.
3. T.Y. Zhang, P. Tong, Fracture mechanics for a mode III crack in a piezoelectric material, Int. J. Solids Struct. 33 (1996) 343-359.
4. H.A. Sosa, Y.E. Pak, Three-dimensional eigenfunction analysis of a crack in a piezoelectric ceramics, Int. J. Solids Struct. 26 (1990) 1-15.
5. Z.G. Zhou, B. Wang, M.S. Cao, Analysis of two collinear cracks in a piezoelectric layer bonded to dissimilar half-spaces subjected to anti-plane shear, Eur. J. Mech. A/Solids 20 (2001) 213-226.
6. A.K. Soh, D.N. Fang, K.L. Lee, Analysis of a bi-piezoelectric ceramic layer with an interfacial crack subjected to anti-plane shear and in-plane electric loading, Eur. J. Mech. A/Solid 19 (2000) 961-977.
7. P.M. McMeeking, On mechanical stress at cracks in dielectrics with application to dielectric breakdown, J. Appl. Phys., 62 (1989) 3122-3316.
8. A.C. Eringen, C.G. Speziale, B.S. Kim, Crack tip problem in non-local elasticity, J. Mech. Phys. Solids, 25 (1977) 339-355.
9. A.C. Eringen, Linear crack subject to shear, Int. J. Fract., 14 (1978) 367-379.
10. A.C. Eringen, Linear crack subject to antiplane shear, Engng. Fract. Mech. 12 (1979) 211-219.
11. Z.G. Zhou, J.C. Han, S.Y. Du, Investigation of a Griffith crack subject to anti-plane shear by using the non-local theory, Int. J. Solids Struct. 36 (1999) 3891-3901.
12. Z.G. Zhou, S.Y. Du, J.C. Han, Non-local theory solution for in-plane shear of through crack, Theoret. Appl. Fract. Mech. 30 (1998) 185-194.
13. Z.G. Zhou, X.W. Zhang, Y.Y. Bai, Investigation of two Griffith cracks subject to uniform tension by using the non-local theory, Int. J. Engng. Sci. 37 (1999) 1709-1722.
14. Z.G. Zhou, B. Wang, S.Y. Du, Scattering of harmonic anti-plane shear waves by a finite crack by using the non-local theory, Int. J. Fract. 91 (1998) 13-22.
15. Z.G. Zhou, Y.P. Shen, Investigation of the scattering of harmonic shear waves by two collinear cracks using the non-local theory, ACTA Mech. 135 (1999) 169-179.
16. J.L. Nowinski, On non-local aspects of the propagation of love waves, Int. J. Engng. Sci. 22 (1984) 383-392.
17. J.L. Nowinski, On non-local theory of wave propagation in elastic plates, ASME J. Appl. Mech. 51 (1984) 608-613.
18. A.C. Eringen, Non-local elasticity and waves, In P. Thoft-Christensen (Ed.), Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics, Holland, Dordrecht, 1974, pp. 81-105.
19. A.C. Eringen, Continuum mechanics at the atomic scale, Crystal Lattice Def. 7 (1977) 109-130.
20. P.M. Morse, H. Feshbach, Methods of Theoretical Physics, vol. 1 McGraw-Hill, New York, 1958.
21. G.C. Sih, Mechanics of Fracture, vol. 4 Noordhoff (New Kluwer Academic), Holland, 1973
22. I.S. Gradshteyn, I.M. Ryzhik, Table of Integral, Series and Products, Academic Press, New York, 1980.
23. A. Erdelyi (Ed.), Tables of Integral Transforms, vol. 1, McGraw-Hill, New York, 1954.
24. S. Itou, Three dimensional waves propagation in a cracked elastic solid, ASME J. Appl. Mech. 45 (1978) 807-811.
25. G.C. Sih, Mechanics of Fracture Initiation and Propagation, Kluwer Academic Publishers.Dordrecht, 1991.
26. J.Z. Zuo, G.C. Sih, Energy density formulation and interpretation of cracking behavior for piezoelectric ceramics, Theoret. Appl. Fract. Mech. 34 (1) (2000) 17-33.
27. G.C. Sih, J.Z. Zuo, Energy density formulation and interpretation of cracking behavior for piezoelectric ceramics, Theoret. Appl. Fract. Mech. 34 (2) (2000) 123-141.
28. A.C. Eringen, Interaction of a dislocation with a crack, J. Appl. Phys. 54 (1983) 6811.
29. Z.G. Zhou, S.Y. Du, B. Wang, Investigation of anti-plane shear behavior of a Griffith crack in a piezoelectric materials by using the non-local theory, Int. J. Fract. 111 (2001) 105-117.