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Modelling effective properties of composite materials using the inclusion concept. General considerations

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Języki publikacji
EN
Abstrakty
EN
This paper is devoted to some general theoretical considerations concerning the modelling of the effective properties of composite materials based on the inclusion concept. Starting from the kinematical integral equation for inhomogeneous materials, all principal homogenisation methods are reviewed and analysed. Special attention is focused on three approaches, namely the self-consistent scheme, the Mori-Tanaka method and incremental procedure derived from the differential scheme. Mono-site and multi-site versions of these approximate solutions are considered. Limitations of the traditional self-consistent scheme are recognized. Improvements are proposed such as composite or coated inclusions and the incremental method mentioned above. Direct and iterative procedures allowing the determination of strain concentration tensors derived from the integral equation are established. The numerical implementation of all the schemes presented in this article will be considered in the next paper. Extreme configurations will be analysed such as composites with voids or very stiff inclusions with respect to matrix properties.
Rocznik
Strony
207--239
Opis fizyczny
Bibliogr. 65 poz.
Twórcy
autor
autor
autor
  • Laboratoire de Physique et Mecanique des Materiaux, URA 1215 CNRS, Centre de Caracterisation des Materiaux et Structures, ENIM, Metz, France
Bibliografia
  • 1. J.D. ESHELBY, The determination of the elastic field of an ellipsoidal inclusion and related problem, Proc. R. Soc. Lond., Series A141, 3, 76-396, 1957.
  • 2. R. HILL, A self-consistent mechanics of composite materials, J. Mech. Phys. Solids, 13, I 213-222, 1965.
  • 3. E. KRONER, Berechnung der elastischen Konstanten des Viel Kristalls aus den Konstan-ten der Einkristalls, Z. Physik, 151, 504-518, 1958.
  • 4. P. LIPINSKI, Modelisation du comportement des meubtaux, en transformations elasto-plastiques finies, a partir des methodes de transition d'echelles, Habilitation, Universite de Metz, 1993.
  • 5. F. CORVASCE, P. LIPINSKI, M. BERVEILLER, The effects of thermal plastic and elastic stress concentrations on the overall behavior of metal matrix composites, IUTAM Symposium on Inelastic deformation of composite materials, 389-408, Troy, USA 1990.
  • 6. A.V. HERSHEY, The elasticity of an isotropic aggregate of anisotropic cubic crystals, J. Appl. Mech., 21, 236-241,1954.
  • 7. B. BUDIANSKI, T.T. Wu, Theorical prediction of plastic strains of polycrystals, Proc. 4th U. S. Nat. Congr. Appl. Mech., 1175-1185, 1962.
  • 8. P. ZATTARIN, P. LIPINSKI, P. VIEVILLE, , Modelisation a sites multiples du comportement anisotrope des composites ordonnes, 3®"^ Congres Marocain de Mecanique, 839-844,1997.
  • 9. P. VIEVILLE, P. LIPINSKI, Application du schema autocoherent par etapes a la modelisa-tion des proprietes viscoelastiques des composites, Qournees Nationales des Composites, Paris, France, 392-397, 1995.
  • 10. T. MORI, K, TANAKA, Average stress in matrix and average energy of materials with misfitting inclusions, Acta. Metall., 21, 571-574, 1973.
  • 11. Y. TAKO, T.W. CHU, M. TAYA, Effective longitudinal Young's modulus of mis oriented short fibre composites, J. Appl. Mech., 49, 536-540, 1982.
  • 12. P. BREBAN, D. BAPTISTE, Modele de Tanaka et Mori, Applications aux composites a fibres discontinues, 36""' Colloque Annuel MECAMAT, Evian, France, 1990.
  • 13. M. EL MOUDEN, Une nouvelle methode d'homogeneisation des materiaux composites elas-tiques, These, Universite de Metz, 1995.
  • 14. H. MA, G. Hu, Z. HUANG, A micromechanical method for particulate composites with finite particle concentration, Mechanics of Materials, 36, 359-368, 2004.
  • 15. F. XUN, G. Hu, Z. HUANG, Effective in-plane moduli of composites with a micropolar matrix and coated fibers, Int. J. Solids Struct., 41, 247-265, 2004.
  • 16. H. FROHLICH, R. SACK, Theory of the Theological properties of dispersions, Proc. Roy. Soc. London, 18, 5, 415-430, 1946.
  • 17. R M. CHRISTENSEN, K.H. Lo, Solutions for effective shear properties in three phase sphere and cylinder models, J. Mech, Phys. Solids, 27, 315-330, 1979.
  • 18. E. HERVE, A. ZAOUI, Modeling the effective behaviour of nonlinear matrix-inclusion composites, Eur. J. Mech., A/Solids, 9, 505-515, 1990.
  • 19. M. CHERKAOUI, H. SABAR, M. BERVEILLER, Micromechanical approach of the coated inclusion problem and applications to composite materials, J. Eng. Mater. Technol., 116, 274-278, 1994.
  • 20. D.A.G. BRUGGEMAN, Berechnung verschiedener physikalischer Konstante van hetero-gene Substanzen, Ann. Physik, 24, 636, 1935.
  • 21. R. ROSCOE, The viscosity of suspensions of rigid spheres, Brit. J. Appl. Phys., 3, 267-269, 1952.
  • 22. S. BOUCHER, Modules effectifs de materiaux composites quasi homogenes et quasi isotropp.R constitue.s d'une matrice elastique et d 'inclusions elastiques. I Cas des concentrations infiniLesimales en inclusions, Revue M, 21, 3, 1-7, 1975; II Cas des concentrations finies en inclusions, Revue M, 22, 1, 1-6, 1976.
  • 23. R. MCLAUGHLIN, A study of the differential scheme for composite material, Int. J. Engng. ScL, 15, 237-244, 1977.
  • 24. R.L. SALGANIK, Mechanics of bodies with many cracks, Mekhanika tverdogo tela (Mech. Mats), 8, 135, 1973.
  • 25. N. LAWS, G.J. DVORAK, The effect of fiber breaks and aligned penny-shaped cracks on the stiffness and energy release rates in unidirectional composites. Int. J. Solids Struct., 23, 9, 1269-1283, 1987.
  • 26. 2. HASHIN, The differential scheme and its applications to cracked materials, J. Mech. Phys. Solids, 36, 6, 719-734, 1988.
  • 27. A. BENSOUSSAN, J.L. LIONS, G. PAPANICOLAOU, Asymptotic analysis for periodic structures, North-Holland Publishing Company, 1978.
  • 28. G. DUVAUT, Materiaux elastiques composites a structure periodiques. Homogeneisation. Theorical and applied mechanics, W.T. KOITER [Ed.] North-Holland Publishing Company, 1978.
  • 29. E. SANCHEZ-PALENCIA) Non-homogeneous media and vibration theory, Lecture Notes in Physics, 127, 1980.
  • 30. D. BEGIS, G. DUVAUT, A. HASSIM, Homogeneisation par elements finis des modules de comportements elastiques de materiaux composites, RR No 101 INRIA, 1981.
  • 31. E. BATEL, Determination des proprietes elastiques et du retrait d'un ceme annuel de chene dans Ie plan transverse : description de la morphologic, mesure des proprietes micro scopoiques et calculs d'homogeneisation, These ENGREF, 1999.
  • 32. N. TAKANO, M. ZAKO, F. KUBO, K. KIMURA, Microstructure-based stress analysis and evaluation for porous ceramics by homogenization method with digital image-based modeling, Int. J. Solids Struct., 40, 1225-1242, 2003.
  • 33. H. MOULINEC, P. SUQUET, A fast numerical method for computing the linear and nonlinear properties of composites, C.R. Acad. Sc. Paris, Serie II, 318, 1417-1423, 1994.
  • 34. H. MOULINEC, P. SUQUET, A FFT-based numerical method for computing the mechanical properties of composites from images of their microstructure, [in:] R. PYRZ, [Ed.] Microstructure-Property Interactions in Composit Materials Kluwer Academic Publ., Dordrecht, 235-246, 1995.
  • 35. H. MOULINEC, P. SUQUET, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Compt. Methods App. Mech. Engrg. 157,69-94, 1998.
  • 36. E. KRONER, H. KOCH, Effective properties of disordered materials, SM Arch., 1, 183-238, 1976.
  • 37. E. KRONER, Bounds for effective elastic moduli of disordered materials, J. Mech. Phys. Solids, 25, 137-155, 1977.
  • 38. P. PONTE CASTANEDA, J.R. WILLIS, The effect of spatial distribution on the effective behavior of composite materials and cracked media, J. Mech. Phys. Solids, 43, 1919-1951, 1995.
  • 39. C. STOLZ, A. ZAOUI, Analyse morphologique et approche variationnelles du comportement d'un milieu elastique heterogene, C.R. Acad. Sci. Paris, Serie II, 312, 143-150, 1991.
  • 40. M. BORNERT, C. STOLZ, A. ZAOUI, Morphologically representative pattern-based bounding in elasticity, J. Mech. Phys. Solids, 44, 307-331, 1996.
  • 41. 0. FASSI-FEHRI, Le probleme de la paire d'inclusions plastiques et heterogenes dans une matrice anisotrope - Application a V etude du comportement des materiaux composites et de la plasticite, These d'etat, Universite de Metz, 1985.
  • 42. 0. FASSI-FEHRI, A. HIHI, M. BERVEILLER, Multiple site self consistent scheme, Int. J. Engng. Sci., 495-502, 1989.
  • 43. P. ZATTARIN, P. LIPINSKI, Modelisation du comportement anisotrope des composites par le schema auto-coherent multisite, 1361"6 Congres Francais de Mecanique, 357-360, 1997.
  • 44. M. CHERKAOUI, Comportement thermomecanique global des composites a renforts enrobes. Modelisation micromecanique et application, These, University of Metz, 1995.
  • 45. P. VIEVILLE, Influence des para/metres architecturaux sur les caracteristiques viscoelas-tiques du bois a ses differentes echelles d'heterogeneite, These, Institut National Polytech-nique de Lorraine, 1992.
  • 46. P. VIEVILLE, D. GUITARD, Analyse de la liaison microstructure-anisotropie du materiau bois a ses differentes echelles d'heterogeneite par Ie schema auto-coherent par etapes, Ann. Sci. For. S3, 1137-1151, 1996.
  • 47. P. VIEVILLE, P. LIPINSKI, Application du schema autocoherent par etapes a la modelisa-tion des proprietes viscoelastiques des composites, J.N.C. 9, 545-554, 1994.
  • 48. A. BROOHM, P. VIEVILLE, A.-S. BONNET, P. LIPINSKI, Micromechanical description of damage in composite materials, International Journal of Mechanical Production Systems Engineering, Special Issue : New Trends in Fatigue and Fracture, 8, 65-71, 2004.
  • 49. J.R. WILLIS, Variational and related methods for the overall properties of composites, Advances in Appl. Mech., 21, 1-78, 1981.
  • 50. P.H. DEDERICHS, R. ZELLER, Variational treatment of the elastic constants of disordered materials, Z. Phys. Stat., 259, 103-113, 1973.
  • 51. L.J. VOIGT, Uber die Berechung zwischen den beiden Elastizitatskonstanten isotroper Kdrper, Wied. Ann. 33, 573-587, 1889.
  • 52. A. REUSS, Berechnung der Fliessgrenze von Mischkristalen auf Grund der Plastizitdtsbe-dingung fur Einkristalle, Z. Angew. Math. Mech., 9, 49-58, 1929.
  • 53. P. ZATTARIN, A. CARMASOL, P. LIPINSKI, Une nouvelle approche numerique pour cal-culer les interactions entre deux inclusions dans un milieu anisotrope, 2eme Congres Maro-cain de Mecanique, 845-850, 1995.
  • 54. S.K. GARG, Analysis of structural composite material, M. Dekker, New-York 1973.
  • 55. A. BROOHM, P. ZATTARIN, P. LIPINSKI, Prediction of mechanical behaviour of inhomo-geneous and anisotropic materials using an incremental scheme, Arch. Mech., 6, 949-967, 2000.
  • 56. 0. ISHAI, O.J. COHEN, Elastic properties of filled and porous epoxy composites, Int. J. Mech. Sci., 9, 539-546, 1967.
  • 57. Y. HUANG, K.X. Hu, X. WEI, A. CHANDRA, A generalized self-consistent mechanics method for composite materials with multiphase inclusions, J. Mech.; Phys. Solids, 42, 491-504, 1994.
  • 58. A.N. NORRIS, A differential scheme for effective moduli of composites, Mechanics of materials, 4, 1-16, 1985.
  • 59. R. ROSCOE, Isotropic composites with elastic or viscoelastic phases: General bounds for the moduli and solutions for special geometries. Rheol. Acta, 12, 404-411, 1973.
  • 60. E. HERVE, A. ZAOUI, N-layered inclusion-based micromechanical modelling. Int. J. Eng. Sci., 31, 1-10, 1993.
  • 61. R, HILL, An invariant treatment of interfacial discontinuities in elastic composites. In "Continuum mechanics and related problems of analysis, Muskhelishvili 80-th anniversary volume" 597-604, Moscow 1972.
  • 62. L.J. WALPOLE, Elastic behaviour of composite materials: theoretical foundations. Advances in Appl. Mech., 169-242, 1981.
  • 63. P. LIPINSKI, EL H. BARDHADI, M. CHERKAOUI, Micromechanical modeling of an arbitrary ellipsoidal multi-coated inclusion, Phil. Mag., in press.
  • 64. EL H. BARDHADI, Modelisation micromecanique des materiaux composites a renforts ellipsozdaux multienrobes et applications, PLD thesis, Metz University, 2005.
  • 65. M. EL MOUDEN, M. CHERKAOUI, A. MOLINARI, M. BERVEILLER, The overall elastic response of materials containing coated inclusions in periodic array. Int. J. Eng. Sci., 36, 813-829, 1998.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT7-0004-0010
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