The nonlocal theory solution of a Mode-I crack in functionally graded materials

Science in China, Series E: Technological Sciences

Volumn 52, Issue 4, 2009, Pages 1101-1111

  Liang, Jun ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Crack; Functionally graded materials; Mechanics of solids; The non local theory

Indexed keywords

CRACK INITIATION; CRACK TIPS; FOURIER TRANSFORMS; INTEGRAL EQUATIONS; LATTICE CONSTANTS; MECHANICS; PLATES (STRUCTURAL COMPONENTS); YIELD STRESS;

CRACK LENGTHS; CRACK SURFACES; DUAL INTEGRAL EQUATIONS; ELASTIC SOLUTIONS; ELASTICITY SOLUTIONS; FINITE CRACKS; FRACTURE CRITERION; JACOBI POLYNOMIALS; LATTICE PARAMETERS; MATERIALS CONSTANTS; MAXIMUM STRESS; MECHANICS OF SOLIDS; MODE-I CRACKS; NON LOCALS; NUMERICAL EXAMPLES; SHEAR MODULUS; STRESS FIELDS; STRESS SINGULARITIES; THE NON-LOCAL THEORY;

FUNCTIONALLY GRADED MATERIALS;

EID: 63349103731     PISSN: 10069321     EISSN: 1862281X     Source Type: Journal    
DOI: 10.1007/s11431-008-0152-3     Document Type: Article

References (38)

1. Koizumi M. The concept of FGM. In: Holt J B, Koizumi M, Hirai T, et al, eds. Ceramic Transactions. Vol. 34, Functionally Graded Materials. Westerville, Ohio: American Ceramic Society, 1993. 3-10
2. Y. D. Lee F. Erdogan 1994 Residual/thermal stress in FGM and laminated thermal barrier coating Int J Fract 69 145 165
3. F. Delale F. Erdogan 1988 On the mechanical modeling of the interfacial region in bonded half-planes J Appl Mech 55 317 324
4. Chen Y F. Interface crack in nonhomogeneous bonded materials of finite thickness. Ph.D. Thesis. Bethlehem, PA: Lehigh University, 1990
5. M. Ozturk F. Erdogan 1996 Axisymmetric crack problem in bonded materials with a graded interfacial region Int J Solids Struct 33 193 219
6. F. Erdogan H. B. Wu 1996 Crack problems in FGM layer under thermal stress J Therm Stress 19 237 265
7. Y. F. Chen F. Erdogan 1996 The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate J Mech Phys Solids 44 5 771 787
8. J. R. Rice 1968 A path independent integral and the approximate analysis of strain concentrations by notches and cracks J Appl Mech 35 379 386
9. Z. C. Xia J. W. Hutchinson 1996 Crack tip fields in strain gradient plasticity J Mech Phys Solids 44 1621 1648
10. A. C. Eringen C. G. Speziale B. S. Kim 1977 Crack tip problem in nonlocal elasticity J Mech Phys Solids 25 339 346
11. A. C. Eringen 1978 Linear crack subject to shear Int J Fract 14 367 379
12. A. C. Eringen 1979 Linear crack subject to anti-plane shear Eng Fract Mech 12 211 219
13. Edelen D G B. Nonlocal field theory. In: Eringen A C, ed. Continuum Physics. New York: Academic Press, 1976. 75-204
14. A. E. Green R. S. Rivilin 1965 Multipolar continuum mechanics: Functional theory. I Proc Royal Soc London A 284 303 315
15. Eringen A C. Nonlocal polar field theory. In: Eringen A C, ed. Continuum Physics. New York: Academic Press, 1976. 205-267
16. K. L. Pan N. Takeda 1998 Nonlocal stress field of interface dislocations Arch Appl Mech 68 179 184
17. K. L. Pan 1994 The image force theorem for a screw dislocation near a crack in nonlocal elasticity J Appl Phys 27 344 346
18. K. L. Pan 1995 Interaction of a dislocation with a surface crack in nonlocal elasticity Int J Fract 69 307 318
19. A. C. Eringen B. S. Kim 1977 Relation between nonlocal elasticity and lattice dynamics Cryst Latt Defects 7 51 57
20. A. C. Eringen 1977 Continuum mechanics at the atomic scale Cryst Latt Defects 7 109 130
21. A. C. Eringen 1972 Linear theory of nonlocal elasticity and dispersion of plane waves Int J Eng Sci 10 425 435
22. J. L. Nowinski 1984 On nonlocal aspects of the propagation of Love waves Int J Eng Sci 22 383 392
23. B. Forest 1998 Modelling slip, kind and shear banding in classical and generalized single crystal plasticity Acta Mater 46 3265 3281
24. Z. G. Zhou Y. Y. Bai X. W. Zhang 1999 Two collinear Griffith cracks sub jected to uniform tension in infinitely long strip Int J Solids Struct 36 5597 5609
25. Z. G. Zhou J. C. Han S. Y. Du 1999 Investigation of a Griffith crack subject to anti-plane shear by using the nonlocal theory Int J Solids Struct 36 3891 3901
26. Z. G. Zhou Y. P. Shen 1999 Investigation of the scattering of harmonic shear waves by two collinear cracks using the nonlocal theory Acta Mech 135 169 179
27. Z. G. Zhou B. Wang 2003 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 1731 1742
28. Z. G. Zhou B. Wang S. Y. Du 2003 Investigation of anti-plane shear behavior of two collinear permeable cracks in a piezoelectric material by using the nonlocal theory J Appl Mech 69 388 390
29. Z. G. Zhou B. Wang 2006 Non-local theory solution of two collinear cracks in the functionally graded materials Int J Solids Struct 43 5 887 898
30. Z. G. Zhou B. Wang 2006 The nonlocal theory solution for two collinear cracks in functionally graded materials subjected to the harmonic elastic anti-plane shear waves Struct Eng Mech 23 1 63 74
31. Morse P M, Feshbach H. Methods of Theoretical Physics. New York: McGraw-Hill, 1958. 926
32. W. F. Yan 1967 Axisymmetric slipless indentation of an infinite elastic cylinder SIAM J Appl Math 15 219 227
33. Gradshteyn I S, Ryzhik I M. Table of Integrals, Series and Products. New York: Academic Press, 1980. 480
34. Erdelyi A. Tables of Integral Transforms. New York: McGraw-Hill, 1954
35. S. Itou 1978 Three dimensional waves propagation in a cracked elastic solid J Appl Mech 45 807 811
36. P. W. Zhang Z. G. Zhou L. Z. Wu 2007 Basic solutions of two parallel Mode-I permeable cracks or four parallel Mode-I permeable cracks in magnetoelectroelastic composite materials Phil Magazine 87 22 1 34
37. P. W. Zhang Z. G. Zhou L. Z. Wu 2008 Basic solution of two parallel Mode-I permeable cracks in functionally graded piezoelectric materials Arch Appl Mech 78 6 411 430
38. A. C. Eringen 1983 Interaction of a dislocation with a crack J Appl Phys 54 6811 6817