Limited permeable crack in an interlayer between piezoelectric materials with different zones of electrical saturation and mechanical yielding

International Journal of Solids and Structures

Volumn 47, Issue 14-15, 2010, Pages 1795-1806

  Loboda, V ^a   Lapusta, Y ^b   Sheveleva, A ^a  

^a OLES HONCHAR DNIPRO NATIONAL UNIVERSITY   (Ukraine)

^b UNIVERSITÉ CLERMONT AUVERGNE   (France)

Author keywords

Interlayer; Limited permeable crack; Piezoelectric material; Zones of mechanical yielding and electrical saturation

Indexed keywords

A-PLANE; ANALYTICAL EQUATIONS; ELECTRIC PERMEABILITY; ELECTRICAL POTENTIAL; ELECTRICAL SATURATION; ELECTROMECHANICAL LOADING; ENGINEERING APPLICATIONS; FRACTURE ZONE; INTERLAYER; INTERLAYER THICKNESS; LIMITED PERMEABLE CRACKS; LINEAR RELATIONSHIPS; MECHANICAL DISPLACEMENTS; NORMAL STRESS; SATURATED ZONE; SEMI INFINITE SPACE; TWO EQUATION;

FRACTURE MECHANICS; GRIFFITH CRACKS; MECHANICAL PERMEABILITY; MEMS; PIEZOELECTRIC DEVICES; PIEZOELECTRIC MATERIALS; PIEZOELECTRICITY; STRESSES;

FRACTURE;

EID: 77955231677     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2010.03.015     Document Type: Article

References (52)

1. G.I. Barenblatt The mathematical theory of equilibrium cracks in brittle fracture Adv. Appl. Mech. 7 1962 55 129
2. H.G. Beom, Y.H. Kim, C. Cho, and C.B. Kim A crack with an electric displacement saturation zone in an electrostrictive material Arch. Appl. Mech. 76 2006 19 31 (Pubitemid 44496618)
3. H.G. Beom, Y.H. Kim, C. Cho, and C.B. Kim Asymptotic analysis of an impermeable crack in an electrostrictive material subjected to electric loading Int. J. Solids Struct. 43 2006 6869 6886
4. Deeg, W.F., 1980. The analysis of dislocation, crack and inclusion problems in piezoelectric solids. Ph.D. Thesis, Stanford University.
5. D.S. Dugdale Yielding of steel sheets containing slits J. Mech. Phys. Solids 8 1960 100 108
6. M.L. Dunn The effect of crack faces boundary conditions on the fracture mechanics of piezoelectric solids Eng. Fract. Mech. 48 1994 25 39
7. C.-Y. Fan, M.-H. Zhao, and Y.-H. Zhou Numerical solution of polarization saturation/dielectric breakdown model in 2D finite piezoelectric media J. Mech. Phys. Solids 57 2009 1527 1544
8. H. Gao, and D.M. Barnett An invariance property of local energy release rate in a strip saturation model of piezoelectric fracture Int. J. Fract. 79 1996 R25 R29
9. H. Gao, T.Y. Zhang, and P. Tong Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic J. Mech. Phys. Solids 45 1997 491 510
10. V.B. Govorukha, V.V. Loboda, and M. Kamlah On the influence of the electric permeability on an interface crack in a piezoelectric bimaterial compound Int. J. Solids Struct. 43 2006 1979 1990
11. O. Gruebner, M. Kamlah, and D. Munz Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium Eng. Fract. Mech. 70 2003 1399 1413
12. T.H. Hao, and Z.Y. Shen A new electric boundary condition of electric fracture mechanics and its applications Eng. Fract. Mech. 47 1994 793 802
13. M.E. He, A.G. Evans, and J.W. Hutchinson Interface cracking phenomena in constrained metal layer Acta Mater. 44 1996 2963 2971
14. K.P. Herrmann, V.V. Loboda, and V.B. Govorukha On contact zone models for an electrically impermeable interface crack in a piezoelectric bimaterial Int. J. Fract. 111 2001 203 227
15. K.M. Jeong, I.O. Kim, and H.G. Beom Effect of electric displacement saturation on the stress intensity factor for a crack in a ferroelectric ceramic Mech. Res. Commun. 31 2004 371 382
16. N. Kakramkar, B. Bose, P. McLaughlin, and S. Santhanam The use of interlayer in modeling interface crack propagation Eng. Fract. Mech. 75 2008 5087 5100
17. A.A. Kaminsky, L.A. Kipnis, and L.A. Kolmakova Model of fracture process zone at the tip of a crack reaching the nonsmooth interface between elastic media Int. Appl. Mech. 44 10 2008 1084 1092
18. L.A. Kipnis, and.V. Polishchuk Analysis of the plastic zone at the corner point of interface Int. Appl. Mech. 45 2 2009 159 168
19. C.M. Landis Electrically consistent boundary conditions for electromechanical fracture Int. J. Solids Struct. 41 2004 6291 6315
20. Y. Lapusta, and V. Loboda Electro-mechanical yielding for a limited permeable crack in an interlayer between piezoelectric materials Mech. Res. Commun. 36 2009 183 192
21. M.Ya. Leonov, and V.V. Panasyuk Development of the smallest cracks in a rigid body Appl. Mech. 5 4 1959 391 401 (in Russian)
22. S. Li On saturation-strip model of a permeable crack in a piezoelectric ceramic Acta Mech. 165 2003 47 71
23. Q. Li, and Y.H. Chen Solution for a semi-permeable interface crack in elastic dielectric/piezoelectric bimaterials ASME J. Appl. Mech. 75 2008 011010-1 011010-13
24. W. Li, R.M. McMeeking, and C.M. Landis On the crack face boundary conditions in electromechanical fracture and an experimental protocol for determining energy release rates Eur. J. Mech. A/Solids 27 2008 285 301
25. V. Loboda, Y. Lapusta, and A. Sheveleva Electro-mechanical pre-fracture zones for an electrically permeable interface crack in a piezoelectric biomaterial Int. J. Solids Struct. 44 2007 5538 5553
26. V. Loboda, Y. Lapusta, and V. Govorukha Mechanical and electrical yielding for an electrically insulated crack in an interlayer between piezoelectric materials Int. J. Eng. Sci. 46 2008 260 272
27. R.M. McMeeking Crack tip energy release rate for a piezoelectric compact tension specimen Eng. Fract. Mech. 64 1999 217 244
28. N.I. Muskhelisvili Some Basic Problems in the Mathematical Theory of Elasticity 1963 Noordhoff Groningen
29. J.A. Nairn Analytical and numerical modeling of R curves for cracks with bridging zones Int. J. Fract. 155 2009 167 181
30. A. Needleman An analysis of tensile decohesion along an interface J. Mech. Phys. Solids 38 1990 289 324
31. Y.E. Pak Linear electro-elastic fracture mechanics of piezoelectric materials Int. J. Fract. 54 1992 79 100
32. Panasyuk, V.V., 1968. Limited equilibrium of brittle bodies with cracks. (Translation in English: Detroit. Michigan Inform. Serv. 1971.) Naukova Dumka Publishers, Kiev (in Russian).
33. V.Z. Parton Fracture mechanics of piezoelectric materials Acta Astronaut. 3 1976 671 683
34. V.Z. Parton, and B.A. Kudryavtsev Electromagnetoelasticity 1988 Gordon and Breach Science Publishers New York
35. C. Pickthall, C. Wang, and L.R.F. Rose Plasticity in constrained layer: model with point forces Eng. Fract. Mech. 69 2002 647 658
36. A. Ricoeur, and M. Kuna Electrostatic traction at dielectric interfaces and their implication for crack boundary conditions Mech. Res. Commun. 36 2009 330 335
37. C.Q. Ru Effect of electrical polarization saturation on stress intensity factors in a piezoelectric ceramics Int. J. Solids Struct. 36 1999 869 883
38. C.Q. Ru, and X. Mao Conducting crack in a piezoelectric ceramics of limited electrical polarization J. Mech. Phys. Solids 47 1999 2125 2146
39. S. Shen, T. Nishioka, Z.-B. Kuang, and Z. Liu Nonlinear electromechanical interfacial fracture for piezoelectric materials Mech. Mater. 32 2000 57 64
40. Z. Suo, C.M. Kuo, D.M. Barnett, and J.R. Willis Fracture mechanics for piezoelectric ceramics J. Mech. Phys. Solids 40 1992 739 765
41. M.R. Turner, and A.G. Evans An experimental study of the mechanisms of crack extension along an oxide/metal interface Acta Mater. 44 1996 863 871
42. V. Tvergard Resistance curves for mixed mode interface crack growth between different elastic-plastic solids J. Mech. Phys. Solids 49 2001 2689 2703
43. V. Tvergard, and J.W. Hutchinson The influence of plasticity on mixed mode interface toughness J. Mech. Phys. Solids 41 1993 1119 1135
44. V. Tvergard, and J.W. Hutchinson On the toughness of ductile adhesive joints J. Mech. Phys. Solids 44 1996 789 800
45. A.G. Varias, Z. Suo, and C.F. Shih Ductile failure of a constrained metal foil J. Mech. Phys. Solids 39 1991 963 986
46. C.H. Wang Analysis of cracks in constrained layers Int. J. Fract. 83 1997 1 17
47. T.C. Wang Analysis of strip electric saturation model of crack problem in piezoelectric materials Int. J. Solids Struct. 37 2000 6031 6049
48. B.-L. Wang, and Y.-W. Mai Applicability of the crack faces electromagnetic boundary conditions for fracture of magnetoelectroelastic materials Int. J. Solids Struct. 44 2007 387 398
49. B.L. Wang, and Y.W. May On the electrical boundary conditions on the crack surfaces in piezoelectric ceramics Int. J. Eng. Sci. 41 2003 633 652
50. B.L. Wang, and X.H. Zhang Fracture prediction for piezoelectric ceramics based on the electric field saturation concept Mech. Res. Commun. 32 2005 411 419
51. X. Xu, and R.K.N.D. Rajapakse On a plane crack in piezoelectric solids Int. J. Solids Struct. 38 2001 7643 7658
52. T.J. Zhang, and C.F. Gao Fracture behavior of piezoelectric materials Theor. Appl. Fract. Mech. 41 2004 339 379