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The Effects of Thermal, Plastic and Elastic Stress Concentrations on the Overall Behavior of Metal Matrix Composites

  • F. Corvasce
  • P. Lipinski
  • M. Berveiller
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

This study deals with the modelling of the inelastic thermomechanical behavior of Metal Matrix Composites considered as microinhomogeneous and macrohomogeneous materials. The theory is developed within the framework of the classical thermoelastoplasticity without damage. At first, the local constitutive equation is recalled. Introducing stress and (or) strain concentration tensors for mechanical and thermal fields, the behavior of the equivalent homogeneous medium is deduced in a compact form. In order to determine these concentration tensors, both for the reinforcements and the grains of the polycrystalline matrix, a general integral equation is proposed. Some various approximation methods for solving such an equation are listed.

The self-consistent approach is developed for a granular medium in order to determine the thermoelastic (linear) as well as the thermoelastoplastic behavior.

Results concerning monotonic loading are presented. A special attention is given to residual stresses. For complex loading pathes (biaxial loading), initial and subsequent yield surfaces are shown.

Keywords

Metal Matrix Composite Equivalent Inclusion Concentration Tensor Localisation Tensor Shear Stress Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Reference

  1. Benveniste, Y., Dvorak, G.J., 1990, “On a correspondance between Mechanical and Thermal effects in Two Phase Composites”, Micromechanics and Inhomogeneity, G.J. Weng and al. eds, Springer Verlag, New York.Google Scholar
  2. Berveiller, M. and Zaoui, A., 1979, “An Extension of the self consistent scheme to plastically flowing polycrystals”, J. Mech. Phys. Sol., Vol 26, pp 325–339.CrossRefGoogle Scholar
  3. Berveiller, M. and Zaoui, A., 1984, “Modelling of the plastic behavior of inhomogeneous media”, J. of Engng. Mat. and Tech., Vol 106, pp 295–298.CrossRefGoogle Scholar
  4. Berveiller, M., Fassi-Fehri, O., Hihi, A., 1987, “The problem of two plastic and heterogeneous inclusions in an anisotropic medium”, Int. J. Engineering Sciences, Vol 25, n° 6, pp 691–709.CrossRefGoogle Scholar
  5. Budiansky, B., 1965, “On the elastic moduli of some heterogeneous materials”, J. Mech. Phys. Solids, Vol 13, pp 201–203.CrossRefGoogle Scholar
  6. Dederichs, P.H. and Zeller, R., 1973, “Variational treatment of the elastic constants of disordered materials”, Z. Phys., Vol 259, pp 103–116.CrossRefGoogle Scholar
  7. De Silva, A.R.T. and Chadwick, G.A., 1969, “Thermal Stresses in Fiber reinforced composites”, J. of Mech. Phys. of Sol., Vol 17, pp 387–403.CrossRefGoogle Scholar
  8. Dvorak, G.J. and Rao, M.S.M., 1976, “Thermal stresses in heat-treated fibrous composites”, ASME J. of Applied Mechanics, Vol 98, pp 619–624.CrossRefGoogle Scholar
  9. Dvorak, G.J., 1986, “Thermal expansion of elastic-plastic composite materials”, ASME J. of Applied Mechanics, Vol 53, pp 737–743.CrossRefGoogle Scholar
  10. Fassi-Fehri, O., Hihi, A., Berveiller, M., 1989, “Multiple site self consistent scheme”, Int. J. Engng Sci., Vol 27, n° 5, pp 495–502.CrossRefGoogle Scholar
  11. Hill, R., 1967, “The essential structure of constitutive laws for metal composites and polycrystals”, J. Mech. Phys. of Solids, Vol 15, pp 79–89.CrossRefGoogle Scholar
  12. Hutchinson, J.W., 1970, “Elastic-plastic behavior of polycrystalline metals and composites”, Proc. Roy. Soc, Vol A319, pp 247–272.Google Scholar
  13. Korringa, J., 1973, “Theory of elastic constants of heterogeneous media”, J. Math. Phys., Vol 14, pp 9–17.CrossRefGoogle Scholar
  14. Kröner, E., 1958, “Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls”, Z. Phys., Vol 151, pp 504–518.CrossRefGoogle Scholar
  15. Kröner, E., 1961, “Zur plastischen Verformung des Vielkristalls”, Act. Metall., Vol 9, pp 155–161.CrossRefGoogle Scholar
  16. Kröner, E., 1977, “Bounds for effective elastic moduli of disordered materials”, J. Mech. Phys. Solids, Vol 21, pp 9–17.Google Scholar
  17. Laws, N., 1973, “On the thermostatics of composite materials”, J. Mech. Phys. Solids, Vol 21, pp 9–17.CrossRefGoogle Scholar
  18. Levin, V.M., 1967, “Thermal expansion coefficients of heterogeneous materials”, Mekhanika Tverdogo Tela, n° 2, pp 88–94.Google Scholar
  19. Lipinski, P. and Berveiller, M., 1989, “Elastoplasticity of micro-inhomogeneous metals at large strains”, Int. J. Plasticity, Vol 5, pp 149–172.CrossRefGoogle Scholar
  20. Patoor, E., Eberhardt, A., Berveiller, M., 1989, “Thermomechanical behavior of shape memory alloys”, Arch. of Mechanics, Vol 40 (In press).Google Scholar
  21. Walpole, L.J., 1981, “Elastic Behavior of Composite Materials: Theoretical fondations”, Adv. in Appl. Mechanics, Vol 21, pp 169–242.CrossRefGoogle Scholar
  22. Willis, J.R., 1977, “Bounds and self consistent estimates for the overall properties of anisotropic composites”, J. Rech. Phys. Solids, Vol 25, pp 185–202.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1991

Authors and Affiliations

  • F. Corvasce
    • 1
  • P. Lipinski
    • 1
  • M. Berveiller
    • 1
  1. 1.Laboratoire de Physique et Mécanique des Matériaux, CNRS, ISGMPUniversity of MetzFrance

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