Investigation of anti-plane shear behavior of a Griffith permeable crack in functionally graded piezoelectric materials by use of the non-local theory

Composite Structures

Volumn 78, Issue 4, 2007, Pages 575-583

  Zhou, Zhen Gong ^a   Du, Shan Yi ^a   Wu, Lin Zhi ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Crack; Functionally graded piezoelectric materials; Non local theory

Indexed keywords

CRACKS; ELASTICITY; FOURIER TRANSFORMS; INTEGRAL EQUATIONS; PIEZOELECTRIC MATERIALS; SHEAR DEFORMATION;

ANTI-PLANE SHEAR BEHAVIOR; GRIFFITH CRACK; NON-LOCAL THEORY; SCHMIDT METHOD;

FUNCTIONALLY GRADED MATERIALS;

ELASTICITY; FOURIER TRANSFORM ANALYSIS; MATHEMATICAL ANALYSIS; SHEAR PROPERTY;

EID: 33751520064     PISSN: 02638223     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruct.2005.11.020     Document Type: Article

References (46)

1. Beom H.G., and Atluri S.N. Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media. Int J Fract 75 2 (1996) 163-183
2. Gao H., Zhang T.Y., and Tong P. Local and global energy rates for an elastically yielded crack in piezoelectric ceramics. J Mech Phys Solids 45 2 (1997) 491-510
3. Han X.L., and Wang T. Interacting multiple cracks in piezoelectric materials. Int J Solids Struct 36 27 (1999) 4183-4202
4. Narita K., Shindo Y., and Watanabe K. Anti-plane shear crack in a piezoelectric layered to dissimilar half spaces. JSME Int J Ser A 42 1 (1999) 66-72
5. Yu S.W., and Chen Z.T. Transient response of a cracked infinite piezoelectric strip under anti-plane impact. Fatigue Eng Mater Struct 21 (1998) 1381-1388
6. Zhank T.Y., and Hack J.E. Mode-III cracks in piezoelectric materials. J Appl Phys 71 (1992) 5865-5870
7. Takagi K., Li J.F., Yokoyama S., and Watanabe R. Fabrication and evaluation of PZT/Pt piezoelectric composites and functionally graded actuators. J Eur Ceram Soc 23 10 (2003) 1577-1583
8. Chue C.-H., and Qu Y.-L. Mode III crack problems for two bonded functionally graded piezoelectric materials. Int J Solids Struct 42 (2005) 3321-3337
9. Chen J., Liu Z.X., and Zou Z.Z. Electromechanical impact of a crack in a functionally graded piezoelectric medium. Theor Appl Fract Mech 39 1 (2003) 47-60
10. Jin B., and Zhong Z. A moving mode-III crack in functionally graded piezoelectric material: permeable problem. Mech Res Commun 29 4 (2002) 217-224
11. Wang B.L. A mode-III crack in functionally graded piezoelectric materials. Mech Res Commun 30 2 (2003) 151-159
12. Kwon S.M. Electrical nonlinear anti-plane shear crack in a functionally graded piezoelectric strip. Int J Solids Struct 40 21 (2003) 5649-5667
13. Li C.Y., and Weng G.J. Antiplane crack problem in functionally graded piezoelectric materials. J Appl Mech 69 4 (2002) 481-488
14. Rice J.R. A path independent integral and the approximate analysis of strain concentrations by notches and cracks. ASME J Appl Mech 35 (1968) 379-386
15. Xia Z.C., and Hutchinson J.W. Crack tip fields in strain gradient plasticity. J Mech Phys Solids 44 (1996) 1621-1648
16. Eringen A.C., Speziale C.G., and Kim B.S. Crack tip problem in nonlocal elasticity. J Mech Phys Solids 25 (1977) 339-346
17. Eringen A.C. Linear crack subject to shear. Int J Fract 14 (1978) 367-379
18. Eringen A.C. Linear crack subject to anti-plane shear. Eng Fract Mech 12 (1979) 211-219
19. Edelen D.G.B. Nonlocal field theory. In: Eringen A.C. (Ed). Continuum physics vol. 4 (1976), Academic Press, New York 75-204
20. Eringen A.C. Nonlocal polar field theory. In: Eringen A.C. (Ed). Continuum physics vol. 4 (1976), Academic Press, New York 205-267
21. Green A.E., and Rivilin R.S. Multipolar continuum mechanics: functional theory. I. Proc Roy Soc London A 284 (1965) 303-315
22. Pan K.L., and Takeda N. Nonlocal stress field of interface dislocations. Arch Appl Mech 68 (1998) 179-184
23. Pan K.L., and Xing J. On presentation of the boundary condition in nonlocal elasticity. Mech Res Commun 24 (1997) 325-330
24. Pan KL, Takeda N. Stress distribution on bi-material interface in nonlocal elasticity. In: Proceeding of the 39th JSASS/JSME structure conference, Osaka, Japan, 1997. p. 181-4.
25. Pan K.L. The image force on a dislocation near an elliptic hole in nonlocal elasticity. Arch Appl Mech 62 (1992) 557-564
26. Pan K.L. The image force theorem for a screw dislocation near a crack in nonlocal elasticity. J Appl Phys 27 (1994) 344-346
27. Pan K.L. Interaction of a dislocation with a surface crack in nonlocal elasticity. Int J Fract 69 (1995) 307-318
28. Pan K.L., and Fang J. Nonlocal interaction of dislocation with a crack. Arch Appl Mech 64 (1993) 44-51
29. Eringen A.C., and Kim B.S. On the problem of crack in nonlocal elasticity. In: Thoft-Christensen P. (Ed). Continuum mechanics aspects of geodynamics and rock fracture mechanics (1974), Reidel, Dordrecht, Holland 81-113
30. Eringen A.C., and Kim B.S. Relation between nonlocal elasticity and lattice dynamics. Cryst Lattice Defects 7 (1977) 51-57
31. Forest B. Modelling slip, kind and shear banding in classical and generalized single crystal plasticity. Acta Mater 46 (1998) 3265-3281
32. Zhou Z.G., Han J.C., and Du S.Y. Investigation of a Griffith crack subject to anti-plane shear by using the non-local theory. Int J Solids Struct 36 (1999) 3891-3901
33. Zhou Z.G., Wang B., and Du S.Y. Investigation of the scattering of harmonic elastic anti-plane shear waves by a finite crack using the non-local theory. Int J Fract 91 (1998) 13-22
34. Zhou Z.G., Du S.Y., and Wang B. On anti-plane shear behavior of a Griffith permeable crack in piezoelectric materials by use of the non-local theory. Acta Mech Sinica 19 2 (2003) 181-188
35. Zhou Z.G., and Wang B. Investigation of anti-plane shear behavior of two collinear impermeable cracks in the piezoelectric materials by using the nonlocal theory. Int J Solids Struct 39 (2003) 1731-1742
36. Zhou Z.G., and Wang B. Investigation of the interaction of two collinear cracks in anisotropic elasticity materials by means of the nonlocal theory. Int J Eng Sci 43 (2005) 1107-1120
37. Zhou ZG, Wang B. Non-local theory solution of two collinear cracks in the functionally graded materials. Int J Solids Struct, in press.
38. Zhou Z.G., Sun J.L., and Wang B. Investigation of the behavior of a crack in a piezoelectric material subjected to a uniform tension loading by use of the non-local theory. Int J Eng Sci 42 19-20 (2004) 2041-2063
39. Morse P.M., and Feshbach H. Methods of theoretical physics vol. 1 (1958), McGraw-Hill, New York
40. Eringen A.C. Non-local elasticity and waves. In: Thoft-Christensen P. (Ed). Continuum mechanics aspects of geodynamics and rock fracture mechanics (1974), Kluwer Academic Publishers Group, Dordrecht, Holland 81-105
41. Eringen A.C. Continuum mechanics at the atomic scale. Cryst Lattice Defects 7 (1977) 109-130
42. 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. Eur J Mech A/Solid 19 (2000) 961-977
43. Gradshteyn I.S., and Ryzhik I.M. Table of integral, series and products (1980), Academic Press, New York
44. In: Erdelyi A. (Ed). Tables of integral transforms vol. 1 (1954), McGraw-Hill, New York
45. Eringen A.C. Interaction of a dislocation with a crack. J Appl Phys 54 (1983) 6811-6818
46. Shbeeb N.I., and Binienda W.K. Analysis of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness. Eng Fract Mech 64 (1999) 693-720