×

Micromechanics versus macromechanics: A combined approach for metal matrix composite constitutive modelling. (English) Zbl 0936.74007

The cyclic constitutive behaviour description of long fibre metal matrix composites needs to take into account viscoplasticity of the matrix, damage of the constituents and interfaces, manufacture residual stresses and damage deactivation effects. In order to incorporate in the model the main constituent characteristics and the composite parameters (volume fractions, fibre shape and arrangements), we propose here a combined approach, i.e. that of using a micromechanics-based analysis for the thermo-elastoviscoplasticity of the composite with damaging effects when the damage is active (i.e. when the microcracks are open). The developed model is based on transformation field analysis and on the effective stress-effective strain space within the continuum damage mechanics of the constituents.
The model is then applied to a SiC/Ti metal matrix composite with unidirectional long fibres.

MSC:

74A40 Random materials and composite materials
74E30 Composite and mixture properties
74M25 Micromechanics of solids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aboudi, J., Micromechanical prediction of initial and subsequent yield surfaces of metal matrix composites, Int. J. Plasticity, 6, 471-484 (1990)
[2] Aboudi, J.; Pindera, M.; Arnold, S., Elastic response of metal matrix composites with tailored microstructures to thermal gradients, Int. J. Solids Struct., 31, 10, 1393-1428 (1994) · Zbl 0945.74547
[3] Allen, D. H.; Groves, S. E.; Harris, C. E., A thermomechanical constitutive theory for elastic composites with distributed damage. Part I and II, Int. J. Solid Struct., 23, 1301-1338 (1987) · Zbl 0634.73108
[4] Allix, O.; Ladeveze, P.; Le Dantec, E.; Vittecoq, E., Damage mechanics for composite laminates under complex loading, (Yielding Damage and Failure of Anisotropic Solid (1990), EGF5, Mech. Eng. Publ: EGF5, Mech. Eng. Publ London), 551-569
[5] Baroumes, L.; Vinçon, I., Identification du comporteent thermoélasto-viscoplastique de l’alliage Ti-6242, (Int. Rep. (1995), LMT-Cachan: LMT-Cachan France)
[6] Buryachenko, V. A., The overall elastoplastic behavior of multiphase materials with isotropic components, Acta Mech., 119, 93-117 (1996) · Zbl 0877.73040
[7] Chaboche, J. L., Sur l’utilisation des variables d’état interne pour la description du comportement viscoplastique et de la rupture par endommagement, (Franco-Polish Symp. (1977), Rhéologie et Mécanique: Rhéologie et Mécanique Krakow, Poland)
[8] Chaboche, J. L., Le concept de contrainte effective, appliqué à l’élasticité et à la viscoplasticité en présence d’un endommagement anisotrope, (Coll. Euromech 115, 295 (1981), Éditions CNRS: Éditions CNRS Grenoble), 737-760 · Zbl 0516.73014
[9] Chaboche, J. L., Damage induced anisotropy: on the difficulties associated with the active/passive unilateral condition, Int. J. Damage Mech., 1, 2, 148-171 (1992)
[10] Chaboche, J. L., Development of CDM for elastic solids sustaining anisotropic and unilateral damage, Int. J. Damage Mech., 2, 311-329 (1993)
[11] Chaboche, J. L.; Kruchs, S.; El Mayas, N., Thermo-elastoviscoplastic constitutive equations for metal matrix composites, C.R. Acad. Sci. Paris, 319, 971-977 (1994), sér. II
[12] Chaboche, J. L.; Lesne, P. M.; Maire, J. F., A constitutive and damage model mixing scalar and tensorial damage variables, C.R. Acad. Sci. Paris, 322, 187-193 (1996), sér. IIB · Zbl 0919.73183
[13] Chaboche, J. L.; Lesne, O.; Pottier, T., Continuum damage mechanics of composites: towards a unified approach, (Voyiadjis, G. Z.; Ju, J. W.; Chaboche, J. L., McNu’97 Symp., Damage Mechanics in Engineering Materials (1997), Elsevier: Elsevier Amsterdam)
[14] Christensen, R.; Lo, K., Solution for effective shear properties in three phase sphere and cylinder models, J. Mech. Phys. Solids, 27, 315-330 (1979) · Zbl 0419.73007
[15] Cordebois, J. P.; Sidoroff, F., Anisotropie élastique induite par endommagement, (Coll. Euromech 115, Comportement mécanique des solides anisotropes, 295 (1981)), 761-774, Grenoble
[16] Duvaut, G., Analyse fonctionnelle et mécanique des milieux continus — application à l’étude des matériaux élastiques à structure périodique, (Koiter, W. T., Theoretical and Applied Mechanics (1976), North Holland Publ. Co: North Holland Publ. Co Amsterdam), 119-132 · Zbl 0373.73002
[17] Dvorak, G., On uniform fields in heterogeneous media, (Proc. R. Soc. Lond., A.431 (1990)), 89-110 · Zbl 0726.73002
[18] Dvorak, G., Transformation field analysis of inelastic composite materials, (Proc. R. Soc. Lond., A.437 (1992)), 311-327 · Zbl 0748.73007
[19] Dvorak, G., Micromechanics of inelastic composite materials: theory and experiment, ASME J. Eng. Mater. Tech., 115, 327-338 (1993)
[20] Dvorak, G.; Benveniste, Y., On transformation strains and uniform fields in multiphase elastic media, (Proc. R. Soc. Lond., A.437 (1992)), 291-310 · Zbl 0748.73003
[21] Dvorak, G.; Bahei-El-Din, Y.; Wafa, A., Implementation of the transformation field analysis for inelastic composite materials, Comput. Mech., 14, 201-228 (1994) · Zbl 0835.73038
[22] El Mayas, N., Modélisation microscopique et macroscopique du comportement d’un composite à matrice métallique, Thèse doctorat ENPC (1994)
[23] Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion and related problems, (Proc. R. Soc. Lond., A.241 (1957)), 376-396 · Zbl 0079.39606
[24] Hansen, N. R.; Schreyer, H. L., Thermodynamically consistent theories for elastoplasticity coupled with damage, (Damage Mechanics and Localization, AMD-Vol. 142/MD-Vol. 34 (1992), ASME), 53-67 · Zbl 0853.73006
[25] Hill, R., Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids, 13, 89-101 (1965) · Zbl 0127.15302
[26] Kachanov, M., Elastic solids with many cracks and related problems, (Hutchinson, J.; Wu, T., Adv. Appl. Mech., 30 (1993)), 259-445 · Zbl 0803.73057
[27] Kattan, P.; Voyiadjis, G. Z., Overall damage and elastoplastic deformation in fibrous metal matrix composites, Int. J. Plasticity, 931-949 (1993) · Zbl 0816.73040
[28] Kruch, S.; Chaboche, J. L.; Pottier, T., Two-scale viscoplastic and damage analysis of a metal matrix composite, (Voyiadjis, G. Z.; Allen, D. H., Damage and interfacial debonding in composites (1996), Elsevier: Elsevier Amsterdam), 45-55
[29] Ladevèze, P.; Gasser, A.; Allix, O., Damage mechanics modelling for ceramic composites, J. Eng. Mater. Tech., 116 (1994)
[30] Legrand, N.; Rémy, L., Comportement en fatigue d’un composite à matrice métallique à base de titane renforcée par des fibres sous chargement isotherme et anisotherme, (EUCLID program (1994))
[31] Legrand, N.; Rémy, L.; Dambrine, B.; Molliex, L., Étude micromécanique de la fatigue oligocyclique d’un composite à matrice métallique base titane renforcé par des fibres unidirectionnelles de SiC, (Baptiste, D.; Vautrin, A., Proc. JNC10 (1996), AMAC: AMAC Paris), 1349-1360
[32] Lemaitre, J.; Chaboche, J. L., (Mechanics of Solid Materials (1990)), Eng. ed.
[33] Léné, F., Contribution à l’étude des matériaux composites et de leur endommagement, (Thèse, doctorat d’État (1984), Univ. P. & M. Curie: Univ. P. & M. Curie Paris), 6
[34] Lesne, P. M.; Saanouni, K., Modelling of irreversible damage-induced strains in brittle elastic composites, Rech. Aérospatiale, 2, 23-37 (1993)
[35] Levin, V. M., Izv. An SSSR, Mekh. Tverdogo Tela, 2, 88-94 (1967)
[36] Levin, V. M., Izv. an SSSR, Mekh. Tverdogo Tela, 11, 137-145 (1976)
[37] Li, G.; Ponte Castañeda, P., The effect of particle shape and stiffness on the constitutive behaviour of metal matrix composites, Int. J. Solids Struct., 30, 23, 3189-3209 (1993) · Zbl 0817.73036
[38] Maire, J. F., Étude théorique et expérimentale du comportement de matériaux composites en contraintes planes, (Thèse, doctorat (1992), Univ. Besançon)
[39] Maire, J. F.; Chaboche, J. L., A new formulation of continuum damage mechanics for composite materials, Aerospace Sci. Tech., 2, 247-257 (1997) · Zbl 0928.74013
[40] Maire, J. F.; Lesne, P. M., A damage model for ceramic matrix composite, Aerospace Sci. Tech., 2, 259-266 (1997) · Zbl 0919.73179
[41] Mandel, J., Contribution théorique à l’étude de l’écrouissage et des lois de l’écoulement plastique, (Proc. \(11^{th}\) Cong. ICTAM. Proc. \(11^{th}\) Cong. ICTAM, Munich (1964))
[42] Michel, J. C.; Suquet, P., An analytical and numerical study of the overall behaviour of metal-matrix composites, Modell. Simul. Mater. Eng., 2, 637-658 (1994)
[43] Mori, T.; Takana, K., Average stress matrix and average elastic energy of materials with misfitting inclusions, Acta Metall., 21, 571-574 (1973)
[44] Perreux, D.; Oytana, C., Continuum damage mechanics for microcracks composite, Comp. Eng., 3, 122-155 (1993)
[45] Pottier, T.; Kruch, S.; Chaboche, J. L., Analyse de l’endommagement macroscopique d’un composite à matrice métallique, (Baptiste, D.; Vautrin, A., Proc. JNC10 (1996), AMAC: AMAC Paris), 1361-1371
[46] Sanchez-Palencia, Introduction aux méthodes asymptotiques et à l’homogénéisation (1992), Masson: Masson Paris
[47] Stolz, C., General relationships between micro- and macro-scales for the non linear behaviour of heterogeneous media, (Gittus, J.; Zarka, J., Modelling Small Deformations of Polycrystals (1985), Elsevier Appl. Sci. Publ: Elsevier Appl. Sci. Publ Amsterdam)
[48] Suquet, P., Plasticité et homogénéisation, (Thèse, doctorat d’État (1982), Univ. P. & M. Curie: Univ. P. & M. Curie Paris), 6
[49] Suquet, P., Overall properties of nonlinear composites: remarks on secant and incremental formulations, (Pineau, A.; Zaoui, A., Plasticity and Damage of Multiphase Materials (1996), Kluwer Acad. Publ: Kluwer Acad. Publ Dordrecht), 149-156
[50] Talreja, R., Transverse cracking and stiffness reduction in composite laminates, J. Comp. Mater., 19, 355-375 (1985)
[51] Talreja, R., Continuum modelling of damage in ceramic matrix composites, Mech. Mater., 12, 165-180 (1991)
[52] Voyiadjis, G.; Kattan, P., Damage of fiber-reinforced composite materials with micromechanical characterization, Int. J. Solids Struct., 30, 20, 2757-2778 (1993) · Zbl 0791.73061
[53] Voyiadjis, G.; Kattan, P., Équivalence of the overall and local approaches to damage in metal matrix composites, Int. J. Plasticity (1998), (in print) · Zbl 0911.73051
[54] Walker, K. P.; Jordan, E. H.; Freed, A. D., Equivalence of Green’s function and the Fourier series representation of composites with periodic microstructure, (Weng, G.; Taya, M.; Abe, H., Symp., Micromechanics and Inhomogeneity (1990), Springer Verlag: Springer Verlag San Francisco), 535-558
[55] Willis, J., Bounds and self-consistent estimates for the overall properties of anisotropic composites, J. Mech. Phys. Solids, 25, 185-202 (1977) · Zbl 0363.73014
[56] Willis, J. R., (Provan, J. W., Continuum models of discrete systems (1978), University Waterloo Press), 185-215
[57] Zaoui, A.; Raphanel, J. L., On the nature of the intergranular accomodation in the modelling of elastoviscoplastic behaviour of polycrystalline aggregates, (Teodosiu, C.; Raphanel, J.-L; Sidoroff, F., MECAMAT’91 (1993), Balkema: Balkema Rotterdam), 185-192
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.