The M-integral for calculating intensity factors of an impermeable crack in a piezoelectric material

Engineering Fracture Mechanics

Volumn 75, Issue 5, 2008, Pages 901-925

  Banks Sills, Leslie ^a   Motola, Yael ^a   Shemesh, Lucy ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Finite element method; Interaction energy integral; M integral; Piezoelectric material; Stress and electric flux density intensity factors

Indexed keywords

ASYMPTOTIC ANALYSIS; DENSITY (SPECIFIC GRAVITY); EXTRAPOLATION; INTEGRAL EQUATIONS; STRESS INTENSITY FACTORS;

ELECTRIC FLUX DENSITY INTENSITY FACTORS; FINITE LENGTH CRACK; INTERACTION ENERGY INTEGRAL; M-INTEGRAL;

PIEZOELECTRIC MATERIALS;

ASYMPTOTIC ANALYSIS; DENSITY (SPECIFIC GRAVITY); EXTRAPOLATION; INTEGRAL EQUATIONS; PIEZOELECTRIC MATERIALS; STRESS INTENSITY FACTORS;

EID: 36749036608     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.engfracmech.2007.05.009     Document Type: Article

References (57)

1. Curie J., and Curie P. Développement par pression de l'électricité polaire dans les cristaux hémièdres à faces inclines. Comp Rend, Paris 91 (1880) 294-296
2. Curie J., and Curie P. Déformations électriques du quartz. Comp Rend, Paris 95 (1882) 914-916
3. Lippmann G. Sur le principe de la conversation de l'électricité ou second principe de la theorie des phenomenes electriques. Ann Chim Phys 24 (1881) 145-177
4. Langevin P. French Patent no. 505,703, 1920.
5. Parton V.Z. Fracture mechanics of piezoelectric materials. Acta Astro 3 (1976) 671-683
6. Deeg WFJ. The analysis of dislocation, crack, and inclusion problems in piezoelectric solids. Ph.D. thesis, Stanford University, 1980.
7. Stroh A.N. Dislocations and cracks in anisotropic elasticity. Philos Mag 3 (1958) 625-646
8. Sosa H.A., and Pak Y.E. Three-dimensional eigenfunction analysis of a crack in a piezoelectric material. Int J Solids Struct 26 (1990) 1-15
9. Shindo Y., Ozawa E., and Nowacki J.P. Singular stress and electric fields of a cracked piezoelectric strip. Appl Elect Mater 1 (1990) 77-87
10. Sosa H.A. Plane problems in piezoelectric media with defects. Int J Solids Struct 28 (1991) 491-505
11. Suo Z. Mechanics concepts for failure in ferroelectric ceramics. Smart structures and materials. AMD 123 (1991), American Society of Mechanical Engineering 1-6
12. Sosa H.A. On the fracture mechanics of piezoelectric solids. Int J Solids Struct 29 (1992) 2613-2622
13. Pak Y.E. Linear electro-elastic fracture mechanics of piezoelectric materials. Int J Fract 54 (1992) 79-100
14. Suo Z. Models for breakdown-resistant dielectric and ferroelectric ceramics. J Mech Phys Solids 41 (1993) 1155-1176
15. Hao T.-H., and Shen Z.-Y. A new electric boundary condition of electric fracture mechanics and its applications. Engng Fract Mech 47 (1994) 793-802
16. He M.-Y., Suo Z., McMeeking R.M., Evans A.G., and Lynch C.S. The mechanics of some degradation mechanisms in ferroelectric ceramic actuators. SPIE 2189 (1994) 344-356
17. Dunn M.L. The effects of crack face boundary conditions on the fracture mechanics of piezoelectric solids. Engng Fract Mech 48 (1994) 25-39
18. Dunn M.L., and Taya M. Electroelastic field concentrations in and around inhomogeneities in piezoelectric solids. J Appl Mech 61 (1994) 474-475
19. Park S.B., and Sun C.T. Effect of electric field on piezoelectric ceramics. Int J Fract 70 (1995) 203-216
20. Sosa H., and Khutoryansky N. New developments concerning piezoelectric materials with defects. Int J Solids Struct 33 (1996) 3399-3414
21. Hao T.H., Gong X., and Suo Z. Fracture mechanics for the design of ceramic multilayer actuators. J Mech Phys Solids 44 (1996) 23-48
22. Kumar S., and Singh R.N. Energy release rate and crack propagation in piezoelectric materials. Part I: mechanical/electrical load. Acta Mater 45 (1997) 849-857
23. Kumar S., and Singh R.N. Energy release rate and crack propagation in piezoelectric materials. Part II: Combined mechanical and electrical loads. Acta Mater 45 (1997) 859-868
24. Kumar S., and Singh R.N. Influence of applied electric field and mechanical boundary condition on the stress distribution at the crack tip in piezoelectric materials. Mater Sci Engng A 231 (1997) 1-9
25. Kumar S., and Singh R.N. Effect of the mechanical boundary condition at the crack surfaces on the stress distribution at the crack tip in piezoelectric material. Mater Sci Engng A 252 (1998) 64-77
26. Zhang T.-Y., Zhao M., and Tong P. Fracture of piezoelectric ceramics. Adv Appl Mech 38 (2001) 147-280
27. Cherepanov G.P. Mechanics of brittle fracture. [Peabody AL, De Wit R, Cooley WC, Trans.] (1979), McGraw-Hill, New York p. 317-36
28. Pak Y.E., and Herrmann G. Conservation laws and the material momentum tensor for the elastic dielectric. Int J Engng Sci 24 (1986) 1365-1374
29. Pak Y.E., and Herrmann G. Crack extension force in a dielectric medium. Int J Engng Sci 24 (1986) 1375-1388
30. McMeeking R.M. A J-integral for the analysis of electrically induced mechanical stress at cracks in elastic dielectrics. Int J Engng Sci 28 (1990) 605-613
31. Pak Y.E. Crack extension force in a piezoelectric material. J Appl Mech 57 (1990) 647-653
32. Suo Z., Kuo C.-M., Barnett D.M., and Willis J.R. Fracture mechanics for piezoelectric ceramics. J Mech Phys Solids 40 (1992) 739-765
33. McMeeking R.M. The energy release rate for a Griffith crack in a piezoelectric material. Engng Fract Mech 71 (2004) 1149-1163
34. Landis C.M. Energetically consistent boundary conditions for electromechanical fracture. Int J Solids Struct 41 (2004) 6291-6315
35. Haojiangh D., Guoqing W., and Weiqui C. A boundary integral formulation and 2D fundamental solutions for piezoelectric media. Comput Meth Appl Mech Engng 158 (1998) 65-80
36. Heyer V., Schneider G.A., Balke H., Drescher J., and Bahr H.-A. A fracture criterion for conducting cracks in homogeneously poled piezoelectric PZT-PIC 151 ceramics. Acta Mater 46 (1998) 6615-6622
37. Kuna M. Finite element analyses of crack problems in piezoelectric structures. Comput Mater Sci 13 (1998) 67-80
38. Abendroth M., Groh U., Kuna M., and Ricoeur A. Finite element-computation of the electromechanical J-integral for 2-D and 3-D crack analysis. Int J Fract 114 (2002) 359-378
39. Ricoeur A., and Kuna M. Influence of electric fields on the fracture of ferroelectric ceramics. J Eur Ceram Soc 23 (2003) 1313-1328
40. Shang F., Kuna M., and Scherzer M. Analytical solutions for two penny-shaped crack problems in thermo-piezoelectric materials and their finite element comparisons. Int J Fract 117 (2002) 113-128
41. Shang F., Kuna M., and Abendroth M. Finite element analyses of three-dimensional crack problems in piezoelectric structures. Engng Fract Mech 70 (2003) 143-160
42. Wippler K., Ricoeur A., and Kuna M. Towards the computation of electrically permeable cracks in piezoelectrics. Engng Fract Mech 71 (2004) 2567-2587
43. Enderlein M., Ricoeur A., and Kuna M. Finite element techniques for dynamic crack analysis in piezoelectrics. Int J Fract 134 (2005) 191-208
44. Lekhnitskii SG. Theory of elasticity of an anisotropic body [Fern P, Trans.]. San Francisco: Holden-Day; 1950, in Russian; 1963, in English.
45. Ikeda T. Fundamentals of piezoelectricity (1990), Oxford University Press, Oxford
46. Banks-Sills L. Application of the finite element method to linear elastic fracture mechanics. Appl Mech Rev 44 (1991) 447-461
47. Denda M., and Mansukh M. Upper and lower bounds analysis of electric induction intensity factors for multiple piezolectric cracks by the BEM. Engng Anal Bound Elem 29 (2005) 533-550
48. Yau J.F., Wang S.S., and Corten H.T. A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J Appl Mech 47 (1980) 335-341
49. Wang S.S., Yau J.F., and Corten H.T. A mixed-mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity. Int J Fract 16 (1980) 247-259
50. Banks-Sills L., Wawrzynek P.A., Carter B., Ingraffea A.R., and Hershkovitz I. Methods for calculating stress intensity factors in anisotropic materials: Part II - arbitrary geometry. Engng Fract Mech 74 (2007) 1293-1307
51. Banks-Sills L., and Sherman D. On the computation of stress intensity factors for three-dimensional geometries by means of the stiffness derivative and J-integral methods. Int J Fract 53 (1992) 1-20
52. ANSYS, Release 8.1, Ansys, Inc. Canonsburg, Pennsylvania, 2004.
53. Berlincourt D, Krueger HA. Properties of Morgan Electro Ceramic Ceramics. Technical Publication TP-226. Morgan Electro Ceramics. 1959.
54. Jelitto H., Kessler H., Schneider G.A., and Balke H. Fracture behavior of poled piezoelectric PZT under mechanical and electrical loads. J Eur Ceram Soc 25 (2004) 749-757
55. ESIS Procedures and Documentations. Procedure for determining the fracture toughness of ceramics using the single-edge-V-notched beam (SEVNB) method, ESIS P5-00/VAMAS. European Structural Integrity Society; 2000.
56. Ting T.C.T. Anisotropic elasticity-theory and applications (1996), Oxford University Press, New York
57. Qin Q.H. Fracture mechanics of piezoelectric materials (2001), WIT Press, England