Micromechanics as a Basis for Damage Mechanics

  • D. H. Allen
  • J. G. Boyd
Conference paper
Part of the IUTAM Symposia book series (IUTAM)


A review of the micromechanics of composites is given herein. This includes the concepts of geometric scales, the representative volume element, and volume averaging of state variables in the representative volume element. These concepts are first reviewed for composites composed of linear elastic constituents and then extended to include the case of composites with time dependent microcracks. A brief review is then given of recent micromechanics solutions which include the effects of damage. Results are discussed for both laminated composites and composites with one or more inelastic phases.

The development of locally averaged damage dependent constitutive equations is discussed, and evolution laws for damage accumulation are reviewed. Finally, a brief overview of the role of micromechanics in life prediction is presented.


Energy Release Rate Representative Volume Element Laminate Composite Life Prediction Matrix Crack 
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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  1. 1.
    Jones, R.M.: Mechanics of Composite Materials. McGraw-Hill 1975.Google Scholar
  2. 2.
    Hill, R.: Elastic Properties of Reinforced Solids: Some Theoretical Principles. J. Mech. Phys. Solids 11 (1963) 357–372.CrossRefMATHGoogle Scholar
  3. 3.
    Hashin, Z.: Analysis of Composite Materials. J. Appl. Mech. 50 (1983) 481–505.CrossRefMATHGoogle Scholar
  4. 4.
    Eringen, A.C.: Continuum Mechanics at Atomic Scale. Crystal Lattice Defects 7 (1977) 109.Google Scholar
  5. 5.
    Eringen, A.C.: Theory of Nonlocal Elasticity and Some Applications. Res. Mechanica, 21 (1987) 213.Google Scholar
  6. 6.
    Taya, M.; Arsenault, R.J.: Metal Matrix Composites. New York: Pergamon 1989.Google Scholar
  7. 7.
    Eldridge, J.L.; Honecy, F.S.: Interface Characterization. HITEMP Review 1989, NASA Conference Publication 10039 (1989) 4–1–4–10.Google Scholar
  8. 8.
    Hashin, Z.; Rosen, B.W.: The Elastic Moduli of Fiber-Reinforced Materials. J. Appl. Mech. 31 (1964) 223.CrossRefGoogle Scholar
  9. 9.
    Hill, R.: A Self-Consistent Mechanics of Composite Materials. J. Mech. Phys. Solids 13 (1965) 213–222.CrossRefGoogle Scholar
  10. 10.
    Budiansky, B.: On the Elastic Moduli of Some Heterogeneous Materials. J. Mech. Phys. Solids 13 (1965) 223.CrossRefGoogle Scholar
  11. 11.
    Eshelby, J.D,: The Continuum Theory of Lattice Defects. Progress in Solid State Physics, F. Seitz and D. Turnbull, Eds. New York: Academic Press 3 (1956) 79.Google Scholar
  12. 12.
    Mori, T.; Tanaka, K.: Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions. Acta Metallurgica 21 (1973) 571–574.CrossRefGoogle Scholar
  13. 13.
    Benveniste, Y.: A New Approach to the Application of Mori-Tanaka’s Theory in Composite Materials. Mechanics of Materials 6 (1987) 147–157.CrossRefGoogle Scholar
  14. 14.
    Teply, J.L.: Periodic Hexagonal Array Model for Plasticity Analysis of Composite Materials. Ph.D. Dissertation, The University of Utah 1984.Google Scholar
  15. 15.
    Hashin, Z.: Analysis of Orthogonally Cracked Laminates under Tension. J. Appl. Mech. (1987).Google Scholar
  16. 16.
    Han, Y.M.; Hahn, H.T.; Croman, R.B.: A Simplified Analysis of Transverse Ply Cracking in Cross-Ply Laminates. Composites Science and Technology 31 (1988) 165–177.CrossRefGoogle Scholar
  17. 17.
    Tsai, C.-L.; Daniel, I.M.; Lee, J.-W.: Progressive Matrix Cracking of Crossply Composite Laminates Under Biaxial Loading. Microcracking-Induced Damage in Composites, G.J. Dvorak and D.C. Lagoudas, Eds., American Society of Mechanical Engineers, AMD 111 (1990) 9–18.Google Scholar
  18. 18.
    Highsmith, A.L.; Stinchcomb, W.W.; Reifsnider, K.L.: Stiffness Reduction Resulting from Transverse Cracking in Fiber-Reinforced Composite Laminates. Virginia Polytechnic Institute and State University, VPI-E-81.33 (1981).Google Scholar
  19. 19.
    Lee, J.W.; Allen, D.H.; Harris, C.E.: Internal State Variable Approach for Predicting Stiffness Reductions in Fibrous Laminated Composites with Matrix Cracks. Journal of Composite Materials 23 No. 12 (1989) 1273–1291.CrossRefGoogle Scholar
  20. 20.
    Allen, D.H.; Lee, J.W.: Matrix Cracking in Laminated Composites Under Monotonic and Cyclic Loadings. Microcracking-Induced Damage in Composites, G.J. Dvorak and D.C. Lagoudas, Eds., American Society of Mechanical Engineers, AMD Vol. 111 (1990)65–76.Google Scholar
  21. 21.
    Lee, J.W.; Allen, D.H.: Harris, C.E.: The Upper Bounds of Reduced Axial and Shear Moduli in Cross-Ply Laminates with Matrix Cracks. Composite Materials: Fatigue and Fracture (Third Volume), ASTM STP 1110, T.K. O’Brien, Ed., American Society for Testing and Materials, Philadelphia (1991) 56–69.Google Scholar
  22. 22.
    Nairn, J.A.: The Strain Energy Release Rate of Composite Microcracking: A Variational Approach. J. Composite Materials 23 (1989) 1106–1127.CrossRefGoogle Scholar
  23. 23.
    Lee, S.W.; Aboudi, J.: Analysis of Composite Laminates with Matrix Cracks. Report No. CCMS-88-03, Virginia Tech Center for Composite Materials and Structures (1988).Google Scholar
  24. 24.
    Laws, N.; Dvorak, GJ.; Hejazi, M.: Stiffness Changes in Unidirectional Composites Caused by Crack Systems. Mechanics of Materials 2, North Holland (1983) 123–137.Google Scholar
  25. 25.
    Whitcomb, J.D.: Analysis of Delamination Growth Near Intersecting Ply Cracks. Center for Mechanics of Composites Report No. 91-1, Texas A&M University, 1991.Google Scholar
  26. 26.
    Aboudi, J.: Constitutive Relations for Cracked Metal Matrix Composites. Mechanics of Materials 6 (1987) 303–315.CrossRefGoogle Scholar
  27. 27.
    Aboudi, J.: Constitutive Equations for Elastoplastic Composites with Imperfect Bonding. International Journal of Plasticity 4 (1988) 103–125.CrossRefMATHGoogle Scholar
  28. 28.
    Tvergaard, V.: Micromechanical Modelling of Fibre Debonding in a Metal Reinforced by Short Fibres. Proc. IUTAM Symposium on Inelastic Deformation of Composite Materials, Troy, N.Y., G.J. Dvorak, Ed., Springer-Verlag (1990) 99–114.Google Scholar
  29. 29.
    Boyd, J.G.; Jones, R.H.; Allen, D.H.: The Effect of Laminate Thickness on Fiber/Matrix Debonding in Metal Matrix Composites. Anisotropy and Localization of Plastic Deformation, Proc. of Plasticity’ 91: The Third International Symposium on Plasticity and its Current Applications, J-P. Boehler and A.S. Kahn, eds., Elsevier (1991) 11–14.Google Scholar
  30. 30.
    Boyd, J.G.; Allen, D.H.; Highsmith, A.L.: A Self-Consistent Thermoviscoplastic Constitutive Model for Short-Fiber Composites. Microcracking-Induced Damage in Composites, G.J. Dvorak and D.C. Lagoudas, Eds., American Society of Mechanical Engineers, AMD Vol. 111 (1990) 141–150.Google Scholar
  31. 31.
    Boyd, J.G.; Allen, D.H.: A Thermo-Viscoplastic Micromechanics Model for Short Fiber Composites. Proc. ASME Winter Annual Meeting 1991 (to appear).Google Scholar
  32. 32.
    Allen, D.H.; Boyd, J.G.; Jones, R.H.: Analysis of Effects of Matrix Viscoplasticity on Damage Evolution in Metal Matrix Composites. Proc. Sixth Technical Conference, American Society for Composites, Albany, New York (1991) to appear.Google Scholar
  33. 33.
    Lerch, B.A.; Hull, D.R.; Leonhardt, T.A.: Microstructure of a SiC/Ti-15-3 Composite. Composites 21 No. 3 (1990) 216–224.CrossRefGoogle Scholar
  34. 34.
    Cosserat, E.; Cosserat, F.: Theorie des Corps Deformable. Paris: Hermann (1909).Google Scholar
  35. 35.
    Erickson, J.L.; Truesdell, C: Exact Theory of Stresses and Strains in Rods and Shells, Arch. Rational Mech. Anal. 1 (1958) 295–323.CrossRefGoogle Scholar
  36. 36.
    Green, A.E. Rivlin, R.S.: Multipolar Continuum Mechanics. Arch. Rational Mech. Anal. 17(1964) 113–147.MATHMathSciNetGoogle Scholar
  37. 37.
    Green, A.E.; Rivlin, R.S.: Simple Force and Stress Multipole. Arch. Rational Mech. Anal. 17 (1964) 325–353.Google Scholar
  38. 38.
    Suquet, P.M.: Local and Global Aspects in the Mathematical Theory of Plasticity. Plasticity Today: Modelling, Methods and Applications, A. Sawczuk and G. Biahchi, Eds., Elsevier (1985) 279–310.Google Scholar
  39. 39.
    Stolz, C.: General Relationships between Micro and Macro Scales for the Non-Linear Behaviour of Heterogeneous Media. Modelling Small Deformations of Polycrystals, J. Gittus and J. Zarka, Eds., Elsevier (1986) 89–115.Google Scholar
  40. 40.
    Lo, D.C.; Allen, D.H.; Buie, K.D.: Damage Prediction in Laminated Composites with Continuum Damage Mechanics. Proc. ASCE Materials Engineering Conference, Denver (1990).Google Scholar
  41. 41.
    Allen, D.H.; Lo, D.C.: A Model for the Progressive Failure of Laminated Composite Structural Components. Proc. ASME Winter Annual Meeting, American Society of Mechanical Engineers (1991) to appear.Google Scholar
  42. 42.
    Rice, J.R.; Rudnicki, J.W.: A Note on Some Features of the Theory of Localization of Deformation. Int. J. Solids Structures 16 (1980) 597–605.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag, Berlin Heidelberg 1992

Authors and Affiliations

  • D. H. Allen
    • 1
  • J. G. Boyd
    • 1
  1. 1.Center for Mechanics of CompositesTexas A&M UniversityCollege StationUSA

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