The interaction of two parallel Mode-I limited-permeable cracks in a functionally graded piezoelectric material

European Journal of Mechanics, A/Solids

Volumn 27, Issue 5, 2008, Pages 824-846

  Zhou, Zhen Gong ^a   Chen, Zeng Tao ^b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF NEW BRUNSWICK   (Canada)

Author keywords

Crack; Functionally graded piezoelectric materials; Mechanics of solids

Indexed keywords

CRACK DETECTION; CRACK TIPS; CRACKS; ELECTRIC FIELDS; ELECTROACUPUNCTURE; FLOW INTERACTIONS; FOURIER TRANSFORMS; INTEGRAL EQUATIONS; MATERIALS PROPERTIES; MATHEMATICAL MORPHOLOGY; MEMS; NUMERICAL METHODS; PAPER; PERMITTIVITY; PIEZOELECTRIC DEVICES; PIEZOELECTRIC MATERIALS; PIEZOELECTRICITY; PIGMENTS; SPECTROSCOPIC ANALYSIS; SURFACES;

ALMANSI'S THEOREM; CRACK SURFACES; DUAL INTEGRAL EQUATIONS; ELECTRIC DISPLACEMENTS; ELECTRIC PERMITTIVITIES; ELSEVIER (CO); FOURIER; FUNCTIONALLY GRADED PIEZOELECTRIC MATERIAL (FGPM); FUNCTIONALLY GRADED PIEZOELECTRIC MATERIALS (FGPM); GRADIENT PARAMETERS; INTENSITY FACTORS; JACOBI POLYNOMIALS; PARALLEL MODES; PERMEABLE CRACKS; SHIELDING EFFECTS;

FUNCTIONALLY GRADED MATERIALS;

EID: 46749084773     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2007.11.007     Document Type: Article

References (42)

1. Chen J., Liu Z.X., and Zou Z.Z. Electromechanical impact of a crack in a functionally graded piezoelectric medium. Theoretical and Applied Fracture Mechanics 39 (2003) 47-60
2. Dascalu D., and Homentcovschi D. An intermediate crack model for flaws in piezoelectric solids. Acta Mechanica 154 1-4 (2002) 85-100
3. Ding H.J., Chen B., and Liang J. General solutions for coupled equations for piezoelectric media. International Journal of Solids and Structures 33 16 (1996) 2283-2296
4. In: Erdelyi A. (Ed). Tables of Integral Transforms, vol. 1 (1954), McGraw-Hill, New York
5. Gao C.F., Kessler H., and Balke H. Crack problems in magnetoelectroelastic solids. Part I: exact solution of a crack. International Journal of Engineering Science 41 9 (2003) 969-981
6. Gao H.J., Zhang T.Y., and Tong P. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramics. Journal of Mechanics and Physics of Solids 45 4 (1997) 491-510
7. Gradshteyn I.S., and Ryzhik I.M. Table of Integrals, Series and Products (1980), Academic Press, New York
8. Han J.J., and Chen Y.H. Multiple parallel cracks interaction problem in piezoelectric ceramics. International Journal of Solids and Structures 36 (1999) 3375-3390
9. Hao T.H. Multiple collinear cracks in a piezoelectric material. International Journal of Solids and Structures 38 50-51 (2001) 9201-9208
10. Hao T.H., and Shen Z.Y. A new electric boundary condition of electric fracture mechanics and its applications. Engineering Fracture Mechanics 47 6 (1994) 793-802
11. Itou S. Three dimensional waves propagation in a cracked elastic solid. Journal of Applied Mechanics 45 6 (1978) 807-811
12. Jin D.R. Functionally graded PZT/ZnO piezoelectric composites. Journal of Materials Science Letters 22 (2003) 971-974
13. Jin B., and Zhong Z. A moving Mode-III crack in functionally graded piezoelectric material: permeable problem. Mechanics Research Communications 29 (2002) 217-224
14. Li C.Y., and Weng G.J. Antiplane crack problem in functionally graded piezoelectric materials. Journal of Applied Mechanic 69 4 (2002) 481-488
15. Liu J.X., Liu X.L., and Zhao Y.B. Green's functions for anisotropic magnetoelectroelastic solids with an elliptical cavity or a crack. International Journal of Engineering Science 39 12 (2001) 1405-1418
16. McMeeking R.M. On mechanical stress at cracks in dielectrics with application to dielectric breakdown. Journal of Applied Physics 62 (1989) 3116-3122
17. Mikhailov G.K., and Parton V.S. Electromagnetoelasticity (1990), Hemisphere, New York
18. Morse P.M., and Feshbach H. Methods of Theoretical Physics, vol. 1 (1958), McGraw-Hill, New York
19. Ou Z.C., and Wu Y. On the crack-tip stress singularity of interfacial cracks in transversely isotropic piezoelectric bimaterials. International Journal of Solids and Structures 40 (2003) 7499-7511
20. Pak Y.E. Crack extension force in a piezoelectric material. Journal of Applied Mechanics 57 (1990) 647-653
21. Parton V.S. Fracture mechanics of piezoelectric materials. Acta Astronautica 3 (1976) 671-683
22. Ratwani M., and Gupta G.D. Interaction between parallel cracks in layered composites. International Journal of Solids and Structure 10 7 (1974) 701-708
23. Soh A.K., Fang D.N., and Lee K.L. 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/Solids 19 (2000) 961-977
24. Soon M.K. Electrical nonlinear anti-plane shear crack in a functionally graded piezoelectric strip. International Journal of Solids and Structures 40 (2003) 5649-5667
25. Sosa H. On the fracture mechanics of piezoelectric solids. International Journal of Solids and Structures 29 (1992) 2613-2622
26. Suo Z., Kuo C.M., Barnett D.M., and Willis J.R. Fracture mechanics for piezoelectric ceramics. Journal of the Mechanics and Physics of Solids 40 4 (1992) 739-765
27. Takagi K., Li J.F., Yokoyama S., and Watanabe R. Fabrication and evaluation of PZT/Pt piezoelectric composites and functionally graded actuators. Journal of the European Ceramic Society 10 (2003) 1577-1583
28. Tian W.Y., and Gabbert U. Multiple crack interaction problem in magnetoelectroelastic solids. European Journal of Mechanics A/Solids 23 (2004) 599-614
29. Ueda S. Transient response of a center crack in a functionally graded piezoelectric strip under electromechanical impact. Engineering Fracture Mechanics 73 (2006) 1455-1471
30. Wang B.L. A Mode-III crack in functionally graded piezoelectric materials. Mechanics Research Communications 30 (2003) 151-159
31. Yang F.Q. Fracture mechanics for a Mode I crack in piezoelectric materials. International Journal of Solids and Structures 38 (2001) 3813-3830
32. Zhang T.Y., Qian C.F., and Tong P. Linear electro-elastic analysis of a cavity or a crack in a piezoelectric material. International Journal of Solids and Structures 35 (1998) 2121-2149
33. Zhang T.Y., and Tong P. Fracture mechanics for a mode III crack in a piezoelectric material. International Journal of Solids and Structures 33 (1996) 343-359
34. Zhong Z., and Meguid S.A. Analysis of a circular arc-crack in piezoelectric materials. International Journal of Fracture 84 (1997) 143-158
35. Zhou Z.G., Bai Y.Y., and Zhang X.W. Two collinear Griffith cracks subjected to uniform tension in infinitely long strip. International Journal of Solids and Structures 36 (1999) 5597-5609
36. Zhou Z.G., and Wang B. 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 Structures 39 (2003) 1731-1742
37. Zhou Z.G., and Wang B. Two parallel symmetry permeable cracks in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading. International Journal of Solids and Structure 41 (2004) 4407-4422
38. Zhou Z.G., and Wang B. Non-local theory solution of two collinear cracks in the functionally graded materials. International Journal of Solids and Structures 43 5 (2006) 887-898
39. Zhou Z.G., Wu L.Z., and Wang B. The behavior of a crack in functionally graded piezoelectric/piezomagnetic materials under anti-plane shear loading. Archive of Applied Mechanics 74 8 (2005) 526-535
40. Zhou Z.G., Zhang P.W., and Wu L.Z. Two parallel limited-permeable Mode-I cracks or four parallel limited-permeable Mode-I cracks in the piezoelectric materials. International Journal of Solids and Structures 44 11-12 (2007) 4184-4205
41. Zhu X., Wang Q., and Meng Z. A functionally gradient piezoelectric actuator prepared by metallurgical process in PMN-PZ-PT system. Journal of Material Science Letters 14 (1995) 516-518
42. Zhu X., Zhu J., Zhou S., Li Q., and Liu Z. Microstructures of the monomorph piezoelectric ceramic actuators with functionally gradient. Sensor Actuators A 74 (1999) 198-202