Analysis of an interface crack between two dissimilar piezoelectric solids

Engineering Fracture Mechanics

Volumn 89, Issue , 2012, Pages 114-127

  Sladek, J ^a   Sladek, V ^a   Wunsche M ^b   Zhang, Ch ^b  

^a INSTITUTE OF CONSTRUCTION AND ARCHITECTURE   (Slovakia)

^b UNIVERSITY OF SIEGEN   (Germany)

Author keywords

Houbolt method; Intensity factors; Interface crack; Meshless local Petrov Galerkin method (MLPG); Moving least squares approximation; Permeable and impermeable conditions

Indexed keywords

HOUBOLT METHOD; IMPERMEABLE CONDITIONS; INTENSITY FACTORS; INTERFACE CRACK; MESHLESS LOCAL PETROV-GALERKIN METHODS; MOVING LEAST SQUARES APPROXIMATION;

ELECTRIC POTENTIAL; EQUATIONS OF MOTION; FUNCTIONALLY GRADED MATERIALS; GALERKIN METHODS; ORDINARY DIFFERENTIAL EQUATIONS; PIEZOELECTRIC DEVICES; PIEZOELECTRIC MATERIALS;

CRACKS;

EID: 84862120428     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.engfracmech.2012.04.032     Document Type: Article

References (64)

1. Williams M.L. The stresses around a fault or crack in dissimilar media. Bull Seism Soc Am 1959, 49:199-204.
2. England A.H. A crack between dissimilar media. ASME J Appl Mech 1965, 32:400-402.
3. Sih G.C., Rice J.R. The bending of plates of dissimilar materials with cracks. ASME J Appl Mech 1964, 31:477-482.
4. Comninou M. The interfacial crack. ASME J Appl Mech 1977, 44:631-636.
5. Comninou M., Schmeser D. The interfacial crack in a combined tension-compression and shear field. ASME J Appl Mech 1979, 46:345-348.
6. Atkinson C. On stress singularities and interfaces in linear elastic fracture mechanics. Int J Fract 1977, 13:807-820.
7. Sinclair G.B. On the stress singularity at an interface crack. Int J Fract 1980, 16:111-119.
8. Mak A.F., Keer L.M., Chen S.H., Lewis J.L. A no-slip interface crack. ASME J Appl Mech 1980, 47:347-350.
9. Yuuki R., Cho S.B. Efficient boundary element analysis of stress intensity factors for interface cracks in dissimilar materials. Engng Fract Mech 1989, 34:179-188.
10. Parton V.Z. Fracture mechanics of piezoelectric materials. Acta Astronaut 1976, 3:671-683.
11. Dokmeci M.C. Recent advances: vibrations of piezoelectric crystals. Int J Engng Sci 1980, 18:431-448.
12. Dokmeci M.C. Recent progress in the dynamic applications of piezoelectric crystals. Shock Vib Digest 1988, 20:3-20.
13. Loboda V., Lapusta Y., Sheveleva A. Analysis of pre-fracture zone for an electrically permeable crack in an interlayer between piezoelectric materials. Int J Fract 2006, 142:307-313.
14. Winzer S.R., Shankar N., Ritter A. Designing cofired multilayer electrostrictive actuators for reliability. J Am Ceram Soc 1989, 72:2246-2257.
15. Hao T.H., Gong X., Suo Z. Fracture mechanics for the design of ceramic multilayer actuators. J Mech Phys Solids 1996, 44:23-48.
16. Ru C.Q., Mao X., Epstein M. Electric-field induced interfacial cracking in multilayer electrostrictive actuators. J Mech Phys Solids 1998, 46:1301-1318.
17. Uchino K. Materials issues in design and performance of piezoelectric actuators: an overview. Acta Mater 1998, 46:3745-3753.
18. Suo Z., Kuo C.M., Barnett D.M., Willis J.R. Fracture mechanics for piezoelectric ceramics. J Mech Phys Solids 1992, 40:739-765.
19. Ru C.Q. Effect of electrode-ceramic interfacial cracks in piezoelectric multilayer materials. J Appl Mech 2000, 67:255-261.
20. Ru C.Q. Exact solution for finite electrode layers embedded at the interface of two piezoelectric half-planes. J Mech Phys Solids 2000, 48:693-708.
21. Ou Z.C., Chen Y.H. Near-tip stress fields and intensity factors for an interface crack in metal/piezoelectric bimaterials. Int J Engng Sci 2004, 42:1407-1438.
22. Ou Z.C., Chen Y.H. Interface crack-tip generalized stress field and stress intensity factors in transversally isotropic piezoelectric bimaterials. Mech Res Commun 2004, 31:421-428.
23. Wang B.L., Mai Y.W. Modeling surface electrodes on a piezoelectric layer. J Appl Mech 2008, 75:021007.
24. Janas V.F., Safari A. Overview of fine-scale piezoelectric ceramic/polymer composite processing. J Am Ceram Soc 1995, 78:2945-2955.
25. Choi J.S., Ashida F., Noda N. Control of thermally induced elastic displacement of an isotropic structural plate associated bonded to a piezoelectric ceramic plate. Acta Mech 1997, 122:49-63.
26. Beom H.G., Atluri S.N. Conducting cracks in dissimilar piezoelectric media. Int J Fract 2002, 118:285-301.
27. Beom H.G. Permeable cracks between two dissimilar piezoelectric materials. Int J Solids Struct 2003, 40:6669-6679.
28. Liu M., Hsia K.J. Interfacial cracks between piezoelectric and elastic materials under in-plane electric loading. J Mech Phys Solids 2003, 51:921-944.
29. Li Q., Chen Y.H. Solution for a semi-permeable interface crack in elastic dielectric/piezoelectric bimaterials. J Appl Mech 2008, 75:011010.
30. Ru C.Q. A hybrid complex-variable solution for piezoelectric/isotropic elastic interfacial cracks. Int J Fract 2008, 152:169-178.
31. Gruebner O., Kamlah M., Munz D. Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium. Engng Fract Mech 2003, 70:1399-1413.
32. Govorukha V., Kamlah M. Asymptotic fields in the finite element analysis of electrically permeable interfacial cracks in piezoelectric bimaterials. Arch Appl Mech 2004, 74:92-101.
33. Enderlein M., Ricoeur A., Kuna M. Finite element techniques for dynamic crack analysis in piezoelectrics. Int J Fract 2005, 134:191-208.
34. Kuna M. Finite element analyses of crack problems in piezoelectric structures. Comput Mater Sci 1998, 13:67-80.
35. Kuna M. Finite element analyses of cracks in piezoelectric structures - a survey. Arch Appl Mech 2006, 76:725-745.
36. Pan E. A BEM analysis of fracture mechanics in 2D anisotropic piezoelectric solids. Engn Anal Bound Elem 1999, 23:67-76.
37. Davi G., Milazzo A. Multidomain boundary integral formulation for piezoelectric materials fracture mechanics. Int J Solids Struct 2001, 38:2557-2574.
38. Gross D., Rangelov T., Dineva P. 2D wave scattering by a crack in a piezoelectric plane using traction BIEM. SID-Struct Integ Durab 2005, 1:35-47.
39. Garcia-Sanchez F., Saez A., Dominguez J. Anisotropic and piezoelectric materials fracture analysis by BEM. Comput Struct 2005, 83:804-820.
40. Garcia-Sanchez F., Zhang Ch., Sladek J., Sladek V. 2-D transient dynamic crack analysis in piezoelectric solids by BEM. Comput Mater Sci 2007, 39:179-186.
41. Sheng N., Sze K.Y. Multi-region Trefftz boundary element method for fracture analysis in plane piezoelectricity. Comput Mech 2006, 37:381-393.
42. Denda M. BEM analysis of semipermeable piezoelectric cracks. Key Engng Mater 2008, 383:67-84.
43. Wünsche M., Garcia-Sanchez F., Saez A., Zhang Ch. A 2D time domain collocation-Galerkin BEM for dynamic crack analysis in piezoelectric solids. Engn Anal Bound Elem 2010, 34:377-387.
44. Ohs R.R., Aluru N.R. Meshless analysis of piezoelectric devices. Comput Mech 2001, 27:23-36.
45. Liu G.R., Dai K.Y., Lim K.M., Gu Y.T. A point interpolation mesh free method for static and frequency analysis of two-dimensional piezoelectric structures. Comput Mech 2002, 29:510-519.
46. Sladek J., Sladek V., Zhang Ch., Garcia-Sanchez F., Wünsche M. Meshless local Petrov-Galerkin method for plane piezoelectricity. CMC-Comput Mater Continua 2006, 4:109-118.
47. Sladek J., Sladek V., Zhang Ch., Solek P., Starek L. Fracture analyses in continuously nonhomogeneous piezoelectric solids by the MLPG. CMES - Comput Model Engng Sci 2007, 19:247-262.
48. Sladek J., Sladek V., Zhang Ch., Solek P., Pan E. Evaluation of fracture parameters in continuously nonhomogeneous piezoelectric solids. Int J Fract 2007, 145:313-326.
49. Atluri S.N., Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput Mech 1998, 22:117-127.
50. Atluri S.N., Sladek J., Sladek V., Zhu T. The local boundary integral equation (LBIE) and its meshless implementation for linear elasticity. Comput Mech 2000, 25:180-198.
51. Atluri S.N., Han Z.D., Shen S. Meshless local Petrov-Galerkin (MLPG) approaches for solving the weakly-singular traction & displacement boundary integral equations. CMES - Comput Model Engng Sci 2003, 4:507-516.
52. Atluri S.N. The meshless method, (MLPG) for domain & BIE discretizations 2004, Tech Science Press, Forsyth.
53. Sladek J., Sladek V., Atluri S.N. Meshless local Petrov-Galerkin method in anisotropic elasticity. CMES - Comput Model Engng Sci 2004, 6:477-489.
54. Li Q., Shen S., Han Z.D., Atluri S.N. Application of meshless local Petrov-Galerkin (MLPG) to problems with singularities, and material discontinuities, in 3-D elasticity. CMES - Comput Model Engng Sci 2003, 4:571-585.
55. Wang D., Sun Y., Li L. A discontinuous Galerkin meshfree modeling of material interface. CMES - Comput Model Engng Sci 2009, 45:57-82.
56. Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P. Meshless methods; an overview and recent developments. Comput Meth Appl Mech Engng 1996, 139:3-47.
57. Houbolt J.C. A recurrence matrix solution for the dynamic response of elastic aircraft. J Aeronaut Sci 1950, 17:371-376.
58. Parton V.Z., Kudryavtsev B.A. Electromagnetoelasticity, piezoelectrics and electrically conductive solids 1988, Gordon and Breach Science Publishers, New York.
59. Hao TH, Shen ZY. A new electric boundary condition of electric fracture mechanics and its applications. Engng Fract Mech 1994;47:793-802.
60. Fleming M., Chu Y.A., Moran B., Belytschko T. Enriched element-free Galerkin methods for crack tip fields. Int J Num Meth Engng 1997, 40:1483-1504.
61. Krongauz Y., Belytschko T. EFG approximation with discontinuous derivatives. Int J Num Meth Engng 1998, 41:1215-1233.
62. Cordes L.W., Moran B. Treatment of material discontinuity in the element free Galerkin method. Comput Meth Appl Mech Engng 1996, 139:75-89.
63. Wünsche M., Zhang Ch., Sladek J., Sladek V., Hirose S., Kuna M. Transient dynamic analysis of interface cracks in layered anisotropic solids under impact loading. Int J Fract 2009, 157:131-147.
64. Sladek J., Sladek V., Zhang Ch., Wünsche M. Crack analysis in piezoelectric solids with energetically consistent boundary conditions by the MLPG. CMES - Comput Model Engng Sci 2010, 68:185-220.