Thermal conductivity of a material containing cracks of arbitrary shape

International Journal of Engineering Science

Volumn 44, Issue 8-9, 2006, Pages 513-528

  Sevostianov, Igor ^a  

^a New Mexico State University   (United States)

Author keywords

Conductivity; Crack; Effective properties; Heat flux

Indexed keywords

CRACKS; ELECTRIC CONDUCTIVITY; HEAT FLUX; TENSORS; THERMAL CONDUCTIVITY;

CRACK TIP; EFFECTIVE PROPERTIES; HEAT FLUX INTENSITY;

MATERIALS SCIENCE;

EID: 33746381958     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2006.04.001     Document Type: Article

References (40)

1. Markov K.Z. Elementary micromechanics of heterogeneous media. In: Markov K.Z., and Preziozi L. (Eds). Heterogeneous Media: Micromechanics Modeling Methods and Simulations (2000), Birkhauser, Boston 1-162
2. Miloh T., and Beneveniste Y. A generalized self-consistent method for the effective conductivity of composites with ellipsoidal inclusions and cracked bodies. J. Appl. Phys. 63 (1988) 789-796
3. Nan C.W., Birringer R., Clarke D.R., and Gleiter H. Effective thermal conductivity of particulate composites with interfacial thermal resistance. J. Appl. Phys. 81 (1997) 6692-6699
4. Weber L., Dorn J., and Mortensen A. On the electrical conductivity of metal matrix composites containing high volume fractions of non-conducting inclusions. Acta Mater. 51 (2003) 3199-3211
5. Shafiro B., and Kachanov M. Anisotropic effective conductivity of materials with non-randomly oriented inclusions of diverse ellipsoidal shapes. J. Appl. Phys. 87 (2000) 8561-8569
6. Bristow J.R. Microcracks, and the static and dynamic elastic constants of annealed heavily cold-worked metals. Br. J. Appl. Phys. 11 (1960) 81-85
7. A. Hoenig, Elastic and electric moduli of non-randomly cracked bodies, Ph.D. thesis. Harvard University, Cambridge MA, 1977.
8. Hoenig A. Electric conductivities of a cracked solid. Pure Appl. Geophys. 117 (1978) 690-710
9. Hoenig A. Thermal conductivities of a cracked solid. J. Compos. Mater. 17 (1983) 231-237
10. Benveniste Y., and Miloh T. An exact solution for the effective thermal conductivity of cracked bodies with oriented elliptical cracks. J. Appl. Phys. 66 (1989) 176-180
11. Kushch V.I., and Sangani A.S. Conductivity of a composite containing uniformly oriented penny-shaped cracks or perfectly conducting discs. Proc. Roy. Soc. Lond. A456 (2000) 683-699
12. Kushch V.I. Conductivity of a periodic particle composite with transversely isotropic phases. Proc. Roy. Soc. Lond. A453 (1997) 65-76
13. Rice J. Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms. In: Argon A. (Ed). Constitutive Equations in Plasticity (1975), MIT Press 23-75
14. Sevostianov I., and Kachanov M. Explicit cross-property correlations for anisotropic two-phase composite materials. J. Mech. Phys. Solids 50 (2002) 253-282
15. Sevostianov I., and Kachanov M. Connection between elastic and conductive properties of microstructures with Hertzian contacts. Proc. Roy. Soc. Lond. A 460 (2004) 1529-1534
16. Kachanov M., and Sevostianov I. On quantitative characterization of microstructures and effective properties. Int. J. Solids Struct. 42 (2005) 309-336
17. Benveniste Y., and Milton G.W. New exact results for the effective electric, elastic, piezoelectric and properties of composite ellipsoid assemblages. J. Mech. Phys. Solids 51 (2003) 1773-1813
18. Cherepanov G.P. Mechanics of Brittle Fracture (1979), McGraw-Hill
19. Sih G.C. Heat conduction in the infinite medium with lines of discontinuities. Trans. ASME J. Heat Transfer 87 (1965) 293-298
20. Chao C.K., and Chang R.C. Thermal interface crack problem in dissimilar anisotropic media. J. Appl. Phys. 72 (1992) 2598-2604
21. Budiansky B., and Rice J. Conservative laws and energy-release rate. J. Appl. Mech. 40 (1973) 201-203
22. Zimmerman R.W. Thermal conductivity of fluid saturated rocks. J. Petrol. Sci. Eng. 3 (1989) 219-227
23. Zimmerman R.W. Effective conductivity of a two-dimensional medium containing elliptical inhomogeneities. Proc. Roy. Soc. Lond. A453 (1996) 1713-1727
24. Sevostianov I., and Kachanov M. On the elastic compliances of irregularly shaped cracks. Int. J. Fracture 114 (2002) 245-257
25. Chao C.K., and Shen M.H. Thermal problem of curvilinear cracks in bonded dissimilar materials. J. Appl. Phys. 73 (1993) 7129-7137
26. D.P. Rooke, D.J. Cartwright, Compendium of Stress Intensity Factors, Her Majesty Stationery Office, London, 1976.
27. Budiansky B., and O'Connell R. Elastic moduli of a cracked solid. Int. J. Solids Struct. 12 (1976) 81-97
28. Lutz M.P., and Zimmerman R.W. Effect of inhomogeneous interphase zone on the elastic and thermal properties of a particulate composite. Int. J. Solids Struct. 42 (2005) 429-437
29. Kachanov M., Sevostianov I., and Shafiro B. Explicit cross-property correlations for porous materials with anisotropic microstructures. J. Mech. Phys. Solids 49 (2001) 1-25
30. Hashin Z. Analysis of composite materials. ASME J. Appl. Mech. 50 (1983) 481-505
31. Bruggeman D.A.G. Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielectrizitätkonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen. Ann. Phys. Leipzig 24 (1935) 636-679
32. McLaughlin R. A study of the differential scheme for composite materials. Int. J. Eng. Sci. 15 (1977) 237-244
33. Norris A.N. A differential scheme for the effective moduli of composites. Mech. Mater. 4 (1985) 1-16
34. Mossotti O.F. Discussione analitica sul'influenza che l'azione di un mezzo dielettrico ha sulla distribuzione dell'elettricità alla superficie di più corpi elettrici disseminati in eso. Mem. Mat. Fis. della Soc. Ital. di Sci. in Modena 24 (1850) 49-74
35. Mori T., and Tanaka K. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21 (1973) 571-574
36. Benveniste Y. A new approach to the application of the Mori-Tanaka's theory in composite materials. Mech. Mater. 6 (1987) 147-157
37. Benveniste Y., Dvorak G.J., and Chen T. On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media. J. Mech. Phys. Solids 39 (1991) 927-946
38. Kanaun S.K., and Levin V.M. Effective Field Method in the Mechanics of Composite Materials (1993), Petrozavodsk University (in Russian)
39. Irwin G.R. Crack-extension force for a part through crack in a plate. Trans. ASME J. Appl. Mech. 29 (1962) 651-654
40. Sevostianov I., Kachanov M., Ruud J., Lorraine P., and Dubois M. Quantitative characterization of microstructures of plasma-sprayed coatings and their conductive and elastic properties. Mater. Sci. Eng.-A 386 (2004) 164-174