Investigation of the behavior of a crack in a piezoelectric material subjected to a uniform tension loading by use of the non-local theory

International Journal of Engineering Science

Volumn 42, Issue 19-20, 2004, Pages 2041-2063

  Zhou, Zhen Gong ^a   Sun, Jian Liang ^a   Wang, Biao ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Crack; Fourier integral transform; Lattice parameter; Piezoelectric materials; Schmidt method; The non local theory

Indexed keywords

CRACK PROPAGATION; ELASTICITY; ELECTRIC FIELDS; FOURIER TRANSFORMS; FRACTURE; INTEGRAL EQUATIONS; LATTICE CONSTANTS; LOADING; POLYNOMIALS; SHEAR STRESS; STRESS ANALYSIS; VACUUM;

CRACK; FOURIER INTEGRAL TRANSFORMS; SCHMIDT METHOD; THE NON-LOCAL THEORY;

PIEZOELECTRIC MATERIALS;

EID: 9244227955     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2004.08.004     Document Type: Article

References (26)

1. W.E.F. Deeg, The analysis of dislocation, crack and inclusion problems in piezoelectric solids, Ph.D. thesis, Stanford University, 1980.
2. H. Gao, T.Y. Zhang, P. Tong, Local and global energy rates for an elastically yielded crack in piezoelectric ceramics, Journal of Mechanics and Physics of Solids 45 (4) (1997) 491-510.
3. Z.Q. Wang, Analysis of strip electric saturation model of crack problem in piezoelectric materials. Acta Mechunica Sinica 31 (3) (1999) 311-319 (in Chinese).
4. T.Y. Zhang, J.E. Hack, Mode-III cracks in piezoelectric materials. Journal of Applied Physics 71(12) (1992) 5865-5870.
5. M.L. Dunn, The effects of crack face boundary conditions on the fracture mechanics of piezoelectric solids. Engineering Fracture Mechanics 48 (1) (1994) 25-39.
6. H. Sosa, N. Khutoryansky, Transient dynamic response of piezoelectric bodies subjected to internal electric impulses. International Journal of Solids and Structures 36 (35) (1999) 5467-5484.
7. 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, European Journal of Mechanics A: Solid 19 (6) (2000) 961-977.
8. A.C. Eringen, C.G. Speziale, B.S. Kim, Crack tip problem in non-local elasticity, Journal of Mechanics and Physics of Solids 25 (5) (1977) 339-355.
9. A.C. Eringen, Linear crack subject to shear, International Journal of Fracture 14 (4) (1978) 367-379.
10. A.C. Eringen, Linear crack subject to anti-plane Shear, Engineering Fracture Mechanics 12 (2) (1979) 211-219.
11. Z.G. Zhou, J.C. Han, S.Y. Du, Non-local theory solution for in-plane shear of through crack, Theoretical and Applied Fracture Mechanics 30 (3) (1998) 185-194.
12. 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, International Journal of Solids and Structures 36 (26) (1999) 3891-3901.
13. Z.G. Zhou, B. Wang, S.Y. Du, Investigation of the scattering of harmonic elastic anti-plane shear waves by a finite crack using the non-local theory, International Journal of Fracture 91 (1) (1998) 13-22.
14. Z.G. Zhou, Y.P. Shen, Investigation of the scattering of harmonic shear waves by two collinear cracks using the non-local theory, Acta Mechanica 135 (3-4) (1999) 169-179.
15. Z.G. Zhou, B. Wang, S.Y. Du, Investigation of anti-plane shear behavior of two collinear permeable cracks in a piezoelectric material by using the non-local theory, ASME Journal of Applied Mechanics 69 (3) (2002) 388-390.
16. Z.G. Zhou, B. Wang, Investigation of anti-plane shear behavior of two collinear impermeable cracks in the piezoelectric materials by using the non-local theory, International Journal of Solids and Structure 39 (7) (2002) 1731-1742.
17. P.M. Morse, H. Feshbach, Methods of Theoretical Physics vol. 1, McGraw-Hill, New York, 1958, pp. 828-930.
18. A.C. Eringen, Non-local elasticity and waves, in: P. Thoft-Christensen (Ed.), Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics, North-Holland, Dordrecht, 1974, pp. 81-105.
19. A.C. Eringen, Continuum mechanics at the atomic scale, Crystal Lattice Defects 7 (2) (1977) 109-130.
20. F.Q. Yang, Fracture mechanics for a Mode I crack in piezoelectric materials, International Journal of Solids and Structures 38 (2001) 3813-3830.
21. H.J. Ding, B. Chen, J. Liang, General solutions for coupled equations for piezoelectric media, International Journal of Solids and Structures 33 (16) (1996) 2283-2296.
22. I.S. Gradshteyn, I.M. Ryzhik, Table of Integral, Series and Products, Academic Press, New York, 1980, pp. 1159-1161.
23. A. Erdelyi (Ed.), Tables of Integral Transforms, vol. 1, McGraw-Hill, New York, 1954, p. 449.
24. S. Itou, Three dimensional waves propagation in a cracked elastic solid, Journal of Applied Mechanics 45 (6) (1978) 807-811.
25. A. Amemiya, T. Taguchi, Numerical Analysis and Fortran, Maruzen, Tokyo, 1969, pp. 425-430.
26. A.C. Eringen, Interaction of a dislocation with a crack, Journal of Applied Physics 54 (14) (1983) 6811.