Mechanics of Composite Materials

, Volume 44, Issue 4, pp 349–360 | Cite as

A comparative study of fiber-matrix interactions by using micromechanical models

  • E. Günay
  • Z. Ece
  • M. A. Esi


The purpose of this study is to describe the interfacial interactions in terms of stress distributions on short fibers in fiber-matrix unit-cell models. The fiber and matrix are subjected to tensile loading. The study consists of three main parts. First, fiber-matrix cell segments are modeled using a 3D finite-element analysis (FEA) with ANSYS. Three different finite-element geometrical unit-cell models are generated in order to simulate the Cox analytical model: a fiber-matrix combination, a single fiber, and a single matrix element. The second part contains the results of 3D FE analyses, which are applied to the Cox formulations by using a computer program developed. In the last part, the analytical solutions for distributions of normal and shear stresses are investigated. Cox 2D linear elasticity solutions, together with finite-element ones, are presented in detail in graphs. The interfacial interactions between the fibers and matrix are also discussed considering the relative changes in the distributions of normal and shear stresses.


fiber-matrix interaction short fibers micromechanics finite-element analysis tensile loading 


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  1. 1.
    H. L. Cox, “The elasticity and strength of paper and fibrous materials,” Brit. J. Appl. Phys., 3, 72–79 (1952).CrossRefGoogle Scholar
  2. 2.
    F. J. Mc Garry and M. Fujiwara, “Resin-fiber load transfer in reinforced plastics,” Modern Plastics — Technical Section, 143–167 (1968).Google Scholar
  3. 3.
    M. R. Piggott, “Interface properties and their influence on fiber-reinforced polymers,” in: Composite Applications the Rule of Matrix Fiber and Interface, New York (1992).Google Scholar
  4. 4.
    B. A. Bednardcyk and S. M. Arnold, “Micromechanics-based deformation and failure prediction for longitudinally reinforced titanium composites,” Compos. Sci. Technol., 61, 705–729 (2001).CrossRefGoogle Scholar
  5. 5.
    J. K. Wells, Ph.D Thesis, Cambridge University (1982).Google Scholar
  6. 6.
    A. Takaku and R. G. C. Arridge, “The effect of interfacial radial and shear stress on fiber pull-out in composite materials,” J. Phys. D: Appl. Phys., 6, 2038–2047 (1973).CrossRefGoogle Scholar
  7. 7.
    P. Lawrence, “Some theoretical considerations of fiber pull-out from an elastic matrix,” J. Mater. Sci., 7, 1–6 (1972).CrossRefGoogle Scholar
  8. 8.
    S. J. Hwang and R. F. Gibson, “Micromechanical modeling of damping in discontinuous fiber composites using a strain energy/finite element approach,” J. Eng. Mater. Technol., 109, 47–52 (1987).Google Scholar
  9. 9.
    M. Paley and J. Aboudi, “Micromechanical analysis of composites by the generalized cell model,” Mech. Mater., 14, 127–139 (1992).CrossRefGoogle Scholar
  10. 10.
    S. Ghosh, K. Lee, and S. Moorthy, “Two scale analysis of heterogeneous elastic-plastic materials with asymptotic homogenization and Voronoi cell finite element model,” Comput. Meth. Appl. Mech. Eng., 132, 63–116 (1996).CrossRefGoogle Scholar
  11. 11.
    R. Yosomiya, K. Morimoto, A. Nakajima, Y. Ikada, and T. Suzuki, “Interface analyses of composite materials,” in: Adhesion and Bonding in Composites. Marcel Dekker Inc., New York (1990).Google Scholar
  12. 12.
    B. L. Lessard and F. K. Chang, “Effect of load distribution on the fiber buckling strength of unidirectional composites,” J. Compos. Mater., 25, 65–87 (1991).Google Scholar
  13. 13.
    M. Narkis and E. J. H. Chen, “Review of methods for characterization of interfacial fiber-matrix interactions,” Polym. Compos., 9, No. 4, 245–251 (1988).CrossRefGoogle Scholar
  14. 14.
    N. G. McCrum, C. P. Buckley, and C. B. Bucknall, “Reinforced polymers,” in: Principles of Polymer Engineering. Oxford University, New York Press (1997).Google Scholar
  15. 15.
    A. Kelly and W. R. Tyson, “Tensile properties of fiber reinforced metals: copper/tungsten and copper/molybdenum,” J. Mech. Phys. Solids, 13, 329–350 (1965).CrossRefGoogle Scholar
  16. 16.
    R. F. Gibson, S. K. Chaturvedi, and C. T. Sun, “Complex moduli of aligned discontinuous fiber reinforced polymer composites,” J. Mater. Sci., 17, 3499–3509 (1982).CrossRefGoogle Scholar
  17. 17.
    B. W. Rosen, “Mechanics of composite strengthening” in: Fiber Composite Materials, American Society for Metals, Metals Park O.H. (1965), pp. 37–75.Google Scholar
  18. 18.
    S. Suarez, R. F. Gibson, C. T. Sun, and S. K. Chaturvedi, “The influence of fiber length and fiber orientation on damping and stiffness of polymer composite materials,” Experim. Mech., 26, No. 2, 175–184 (1986).CrossRefGoogle Scholar
  19. 19.
    S. J. Hwang, Finite Element Modeling of Damping in Discontinuous Fiber Composites, M.Sc. Thesis, University of Idaho, Moscow ID (1985).Google Scholar
  20. 20.
    S. J. Hwang and R. F. Gibson, “Micromechanical modeling of damping in discontinuous fiber composites using a strain energy/finite element approach,” J. Eng. Mater. Technol., 109, 47–52 (1987).CrossRefGoogle Scholar
  21. 21.
    C. T. Sun and J. K. Wu, “Stress distributions of aligned short fiber composites under axial load,” J. Reinf. Plast. Compos., 3, 130–144 (1984).CrossRefGoogle Scholar
  22. 22.
    R. F. Gibson, “Analysis of a discontinuous fiber-reinforced lamina,” in: Principles of Composite Material Mechanics, McGraw-Hill Inc., Singapore (1994).Google Scholar
  23. 23.
    D. H. Pahr and S. M. Arnold, “The applicability of the generalized method of cells for analyzing discontinuously reinforced composites,” Composites, Pt. B, 33, 153–170 (2002).CrossRefGoogle Scholar
  24. 24.
    Z. Ece, Analytical Solution and Finite Element Analysis of the Fiber Matrix Interactions in Fiber Composite Materials, M.Sc. Thesis, The Institute of Science and Technology of Gazi University, Ankara, Turkey (2003).Google Scholar
  25. 25.
    ANSYS, User Manual, ANSYS Release 8.1 (2002).Google Scholar
  26. 26.
    S. P. Timoshenko and J. N. Goodier, “Axisymmetric stress and deformation in a solid of revolution,” in: Theory of Elasticity, McGraw-Hill International Editions, Singapore (1970).Google Scholar
  27. 27.
    F. B. Hildebrand, “Series solutions of differential equations,” in: Advanced Calculus for Applications, Prentice Hall Inc., New Jersey (1976).Google Scholar
  28. 28.
    M. V. Barton and N. Y. Ithaca, “The circular cylinder with a band of uniform pressure on a finite length,” J. Appl. Mech., A97–A104 (1941).Google Scholar
  29. 29.
    M. L. James, G. M. Smith, and J. C. Wolford, “Numerical integration and differentiation,” in: Applied Numerical Methods for Digital Computation with FOR TRAN and CSMP, Harper&Row Publishers, New York (1977).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • E. Günay
    • 1
  • Z. Ece
    • 2
  • M. A. Esi
    • 3
  1. 1.Departement of Mechanical EngineeringUniversity of GaziMaltepe, AnkaraTurkey
  2. 2.General Directorate of State Hydraulic Works Equipment and Supply DivisionAnkaraTurkey
  3. 3.Scientific and Technical Research Council of TurkeyAnkaraTurkey

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