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Part of the book series: Solid Mechanics and its Applications ((SMIA,volume 60))

Abstract

Analysis of the inelastic behavior of fibrous composite laminates with detailed representation of the lamina microgeometry is described. Loading is limited to uniform in-plane stresses and out-of-plane normal stress, and to uniform changes in temperature. The objective is to predict the overall strains and the local fields in the constituents. This has been achieved by analysis of the laminates on two interacting structural scales, a microscopic scale which models the individual plies, and a macroscopic scale which provides the plies loading path. Macromechanical analysis of the laminate was conducted with the transformation field method, while micromechanical analysis of each ply was performed with the finite element method. Implementation of this methodology for laminates with a viscoplastic matrix is described.

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References

  • Aboudi, J. (1986) Elastoplasticity theory for composite materials, SolidMech. Archives 11, 141–183.

    MATH  Google Scholar 

  • Bahei-El-Din, Y.A. (1992) Uniform fields, yielding, and thermal hardening in fibrous composite laminates, Int. J. Plasticity 8, 867–892.

    Article  MATH  Google Scholar 

  • Bahei-El-Din, Y.A. (1994) V1SCOPAC Finite Element Program for Viscoplastic Analysis of Composites, User’s Manual, Structural Engineering Department, Cairo University, Giza, Egypt.

    Google Scholar 

  • Bahei-El-Din, Y.A. (1996) Finite element analysis of viscoplastic composite materials and structures, Mechanics of Composite Materials and Structures 3, 1–28.

    Article  Google Scholar 

  • Bahei-El-Din, Y.A. and Dvorak, O.J. (1989) A review of plasticity theory of fibrous composite materials, in W.S. Johnson (eds.), Metal Matrix Composites: Testing, Analysis, and Failure Modes, ASTM STP 1032, ASTM, Philadelphia, pp. 103–129.

    Chapter  Google Scholar 

  • Bahei-El-Din, Y.A. and Dvorak, G.J. (1997) Isothermal fatigue behavior of Sigma/Timetal 21S laminates, part ii: modeling and numerical analysis, Mechanics of Composite Materials and Structures 4, 131–158.

    Google Scholar 

  • Bahei-El-Din, Y.A., Shah, R.S., and Dvorak, G.J. (1991) Numerical analysis of the rate-dependent behavior of high temperature fibrous composites, in S.N. Singhal, W.F. Jones, T. Cruse, and C.T. Herakovich (eds.), Mechanics of Composites at Elevated and Cryogenic Temperatures, ASME, New York, AMD-vol. 118, pp. 67–78.

    Google Scholar 

  • Benveniste, Y. (1987) A new approach to the application of Mori-Tanaka’s theory in composite materials, Mech. of Mater. 6, 147–157.

    Article  Google Scholar 

  • Bigelow, C.A. (1992) The effect of uneven fiber spacing on thermal residual stresses in a unidirectional SCS-6/Ti-15-3 laminate, J. Composites Technology & Research 14, 211–220.

    Article  Google Scholar 

  • Brockenbrough, J.R., Suresh, S., and Wienecke, H.A. (1991) Deformation of metal-matrix composites with continuous fibers: geometrical effects of fiber distribution and shape, Acta Metall. Mater. 39, 735–752.

    Article  Google Scholar 

  • Chaboche, J.L. (1989) Constitutive equations for cyclic plasticity and cyclic viscoplasticity, Int. J. Plasticity 5, 247–302.

    Article  MATH  Google Scholar 

  • Chen, T., Dvorak, G.J. and Benveniste, Y. (1992) Mori-Tanaka estimates of the overall elastic moduli of certain composite materials, J. Appl. Mech. 59, 539–546.

    Article  MATH  Google Scholar 

  • Dvorak, G.J. (1991) Plasticity theories for fibrous composite materials, in R.K. Everett and R.J. Arsenault (eds.), Metal Matrix Composites, Mechanisms and Properties, vol. 2, Academic Press, Boston, pp. 1–77.

    Google Scholar 

  • Dvorak, G.J. (1992) Transformation field analysis of inelastic composite materials, Proc. R. Soc. Lond. A437, 311–327.

    ADS  MathSciNet  Google Scholar 

  • Dvorak, G.J. and Bahei-El-Din, Y.A. (1995) Transformation analysis of inelastic laminates, in R. Pyrz (ed.), IUTAM Symposium on Microstructure-Property Interactions in Composite Materials, Kluwer Academic Publishers, Netherlands, pp. 89–100.

    Google Scholar 

  • Dvorak, G.J., Bahei-El-Din, Y.A. and Wafa, A.M. (1994) Implementation of the transformation field analysis for inelastic composite materials, Computational Mechanics 14, 201–228.

    Article  MATH  ADS  Google Scholar 

  • Dvorak, G.J. and Teply, J.L. (1985) Periodic hexagonal array models for plasticity analysis of composite materials, in A. Sawczuk and V. Bianchi (eds.), Plasticity Today: Modelling, Methods and Applications, W. Olsazak Memorial Volume, Elsevier Scientific Publishing Co., Amsterdam, pp. 623–642.

    Google Scholar 

  • Eshelby, J.D. (1957) The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc. London A 241, 376–396.

    ADS  MATH  MathSciNet  Google Scholar 

  • Gear, C.W. (1971) Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1971.

    MATH  Google Scholar 

  • Hashin, Z. and Rosen, B. W. (1964) The elastic moduli of fiber-reinforced materials, J. Appl. Mech. 31, 223–232.

    Google Scholar 

  • Hill, R. (1963) Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids 11, 357–372.

    Article  ADS  MATH  Google Scholar 

  • Hill, R. (1964) Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour, J. Mech. Phys. Solids 12, 199–212.

    Article  MathSciNet  ADS  Google Scholar 

  • Hill, R. (1965a) Theory of mechanical properties of fibre-strengthened materials: III. Self-consistent model, J. Mech. Phys. Solids 13, 189–198.

    Article  ADS  Google Scholar 

  • Hill, R. (1965b) A self-consistent mechanics of composite materials, J. Mech. Phys. Solids 13, 213–222.

    Article  ADS  Google Scholar 

  • Hindmarsh, A.C. (1974) GEAR: Ordinary Differential Equations System Solver, Lawrence Livermore Laboratory, Report UCID-30001, Revision 3.

    Google Scholar 

  • Levin, V.M. (1967) Thermal expansion coefficients of heterogeneous materials. Mekhanika Tverdogo Tela. 2, 88–94, English Translation: Mech. of Solids 11, 58–61.

    Google Scholar 

  • Mori, T. and Tanaka, K. (1973) Average stress in matrix and average elastic energy of materials with misfitting inclusions, Ada. Metall. 21, 571–574.

    Article  Google Scholar 

  • Teply, J.L. and Dvorak, G.J. (1988) Bounds on overall instantaneous properties of elastic-plastic composites, J. Mech. Phys. Solids 36, 29–58.

    Article  MATH  ADS  Google Scholar 

  • Zienkiewicz, O.C. and Cormeau, I.C. (1974) Viscoplasticity-plasticity and creep in elastic solids-a unified numerical solution approach, Int. J. Numer. Methods Engng. 8, 821–845.

    Article  MATH  Google Scholar 

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© 1998 Kluwer Academic Publishers

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Bahei-El-Din, Y.A., Ibrahim, I.A., Botrous, A.G. (1998). Micromechanical Analysis of Inelastic Fibrous Laminates. In: Bahei-El-Din, Y.A., Dvorak, G.J. (eds) IUTAM Symposium on Transformation Problems in Composite and Active Materials. Solid Mechanics and its Applications, vol 60. Springer, Dordrecht. https://doi.org/10.1007/0-306-46935-9_4

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  • DOI: https://doi.org/10.1007/0-306-46935-9_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5122-1

  • Online ISBN: 978-0-306-46935-0

  • eBook Packages: Springer Book Archive

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