Finite Element Analysis of Plastic Yielding at a Circular Hole in a Laminated Composite Plate Based on Refined Plate Theory

  • Tasneem Pervez

Abstract

An elastic-plastic analysis of anisotropic laminated composite plate with a hole is carried out using a two dimensional finite element model based on higher order shear deformation theory (HSDT) of anisotropic laminated composite plates. The variation in material properties through thickness is made possible by discrete layer approach. The generalized Huber-Mises yield criterion, developed by Hill, for anisotropic material, is used to determine the onset of plastic flow. The inclusion of anisotropic parameters of plasticity generalizes the plastic yield function. These anisotropic parameters of plasticity are updated during the work hardening history of anisotropic laminated composite plate. The plastic potential, which is an anisotropic yield function, is used to determine an associated flow rule. Finally, an elastic-plastic incremental constitutive relation is obtained using finite element method. By means of an incremental and iterative procedure, the numerical solution of deformation problems in nonlinear anisotropic laminated plates is achieved based on first order shear deformation theory and higher order shear deformation theory. The transverse shear effects on the load deformation characteristics and on the spread of plastic zones around the circular hole are discussed. This method yields accurate values for transverse shear stresses as compared to other shear deformation theories and hence the growth of plastic zones.

Keywords

Plastic Zone Transverse Shear Circular Hole Laminate Plate Shear Deformation Theory 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I.L. Dillamore, A.J. Hazel and T.W. Watson, An experimental study of the mechanical anisotropy of some common metals, Interna. J. Mech. Sci. 13 (1971) 1049–1061.CrossRefGoogle Scholar
  2. 2.
    V. Mises, Mechanik der plastischen formanderungen von kristallen, ZAMM, (1928).Google Scholar
  3. 3.
    W. Prager, A new method for analyzing stress-strain relations in work hardening plastic solids, J. Appl. Mech. 23 (1956) 493–501.Google Scholar
  4. 4.
    H. Ziegler, A modification of Prager’s hardening rule, Quart. Appl. Math. 17(1) (1959) 55–66.Google Scholar
  5. 5.
    Z. Morz, An attempt to describe the behavior of metals under cyclic loads using a more general work hardening model, Acta Mechanica 7 (1969) 191–212.Google Scholar
  6. 6.
    R.D. Krieg, A practical two surface plasticity theory, J. Appl. Mech. 42, 641–646.Google Scholar
  7. 7.
    R. Hill, The mathematical theory of plasticity, Clarendon press, Oxford (1950).Google Scholar
  8. 8.
    R. Hill, A theory of yielding and plastic flow of anisotropic metals, Proc. Roy. Soc. of London, Ser. A. 193 (1948) 281–298.CrossRefGoogle Scholar
  9. 9.
    J.C. Fisher, Anisotropic plastic flow, ASME Trans. 71(4) (1949) 349–356.Google Scholar
  10. 10.
    F. Edelman and D.C. Drucker, Some extensions of elementary plasticity theory, J. Franklin Institute 251 (1951) 581–605.CrossRefGoogle Scholar
  11. 11.
    L.W. Hu and J. Martin, Anisotopic lading function for combined stresses in the plastic range, J. Appl. Mech. (1955) 77–85.Google Scholar
  12. 12.
    Y. Hoshimura, Hypothetical theory of anisotropy and the Bauschinger effect due to plastic strain history, Aeronautical Research Institute, University of Tokyo, Report NO. 349 (1959) 221–247.Google Scholar
  13. 13.
    D.C. Bouge, The yield stress and plastic strain theory for anisotropic materials, Oak Ridge National Laboratory, Oak Ridge, Tennesse (1967) Rep. No. ORNL-TM-1869.CrossRefGoogle Scholar
  14. 14.
    S.N. Shabashi and A. Shelton, The anisotropic yield flow and creep behavior of pre-strained En-24 steel, J. Mechanical Engrg. Sci. 17(2) (1975) 93–104.CrossRefGoogle Scholar
  15. 15.
    A.J.M. Spencer, Deformations of fiber reinforced material, Clanderon press, (1972).Google Scholar
  16. 16.
    T.H. Lin, D. Salinas and Y.M. Ito, Elastic -plastic analysis of unidirectional composites, J. Composite Materials 6 (1972) 55–68.CrossRefGoogle Scholar
  17. 17.
    B. Whang, Elasto-plastic orthotropic plates and shells, Proc. Symp. on Application of F.E.M. in Civil Engineering, Vanderbilt University, Tennessee, (1973) 481–515.Google Scholar
  18. 18.
    D.R.J. Owen and J.A. Figueras, Elastio-plastic analysis of anisotropic plates and shells by the Semiloof element, Internat. J. Numer. Meths. Engrg. 19 (1983) 521–539.CrossRefGoogle Scholar
  19. 19.
    D.R.J. Owen and J.A. Figueras, Anisotropic elastic-plastic finite element analysis of thick and thin plates and shells, Internat. J. Numer. Meths. Engrg. 19 (1983) 541–556.CrossRefGoogle Scholar
  20. 20.
    T. Pervez, “Transient Dynamic, Damping and Elasto-plastic Analysis of Higher Order Laminated Anisotropic Composite Plates Using Finite Element Method”, Doctoral Thesis, University of Minnesota, USA, September 1991.Google Scholar
  21. 21.
    T. Pervez and N. Zabaras, Transient dynamic and damping analysis of laminated anisotropic plates using a refined theory, Internat. J. Numer. Meths. Engrg., Vol. 72, 1992.Google Scholar
  22. 23.
    T. Pervez, “A Higher Order Shear Deformation Theory of Anisotropic Laminated Composite Plates and Its Application in Defense Industry”, Seminar on ‘Research and Development in Support of Technologies with military Applications’ at PNS Naval Engineering College, May 1992.Google Scholar
  23. 24.
    N. Zabaras and T. Pervez, A viscous damping approximation of laminated anisotropic composite plates using the finite element method, Comput. Meths. Appl. Mech. Engrg. 81(3) (1990) 291–316.CrossRefGoogle Scholar
  24. 25.
    T. Pervez, “Finite Element Structural Analysis Via A New Integrated Force Method”, Proceedings of 2nd International Naval Engineering Conference, Karachi, (1993).Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Tasneem Pervez
    • 1
  1. 1.Faculty of EngineeringInternational Islamic University MalaysiaMalaysia

Personalised recommendations