Advertisement

Mechanics of Composite Materials

, Volume 44, Issue 4, pp 389–396 | Cite as

Markov model for analyzing the residual static strength of a fiber-reinforced composite

  • Yu. Paramonov
  • J. Andersons
  • M. Kleinhofs
  • A. Paramonova
Article

Abstract

The possibility of using a unified mathematical model, based on the theory of Markov chains, to describe the distribution of the conditional fatigue limit at a fixed number of loading cycles and the residual strength of a specimen after cyclic loading is demonstrated. Numerical examples are presented.

Keywords

composite fiber fatigue life strength program loading 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yu. Paramonov, M. Kleinhof, and A. Paramonova, “Markov model of connection between the distribution of static strength and fatigue life of a fibrous composite,” Mech. Compos. Mater., 42, No. 5, 431–442 (2006).CrossRefGoogle Scholar
  2. 2.
    J. Andersons, I. Grušeckis, and J. Korsgaard, “The effect of overloads on the residual strength and life of laminated GRP,” Mech. Compos. Mater., 35, No. 6, 461–464 (1999).CrossRefGoogle Scholar
  3. 3.
    M. S. Found and M. Quaresimin, “Two-stage fatigue loading of woven carbon fibre reinforced laminates,” Fatigue Fract. Eng. Mater. Struct., 26, 17–26 (2003).CrossRefGoogle Scholar
  4. 4.
    A. M. Freudenthal and E. J. Gumbel, “Physical and statistical aspects of fatigue,” Adv. Appl. Mech. Vol. IV, Academic Press, New York (1956).Google Scholar
  5. 5.
    V. V. Bolotin, Statistical Methods in Structural Mechanics [in Russian], GSM, Moscow (1961).Google Scholar
  6. 6.
    J. Kemeny and J. Snell, Finite Markov Chains [Russian translation], Nauka, Moscow (1970).Google Scholar
  7. 7.
    A. Yu. Paramonova, M. A. Kleinhof, and Yu. M. Paramonov, “Binomial version of Markov model of fatigue life of composite with two reasons for failure,” Aviation, 8, No. 2, 15–20 (2004).Google Scholar
  8. 8.
    Yu. M. Paramonov, M. A. Kleinhof, and A. Yu. Paramonova, “A probabilistic model of the fatigue life of composite materials for fatigue-curve approximations,” Mech. Compos. Mater., 38, No. 6, 485–492 (2002).CrossRefGoogle Scholar
  9. 9.
    M. Kleinhof, Yu. Paramonov, and A. Paramonova, “Regression model based on Markov chain theory for composite fatigue curve approximation,” Acta Commentat. Univ. Tartuensis Math., 8, 143–153 (2004).Google Scholar
  10. 10.
    Yu. M. Paramonov, M. A. Kleinhof, and A. Yu. Paramonova, “Estimating the parameters of fatigue curve of a composite material,” Mech. Compos. Mater., 41, No. 1, 77–86 (2005).CrossRefGoogle Scholar
  11. 11.
    V. Tamuzs, J. Andersons, K. Aniskevich, J. Jansons, and J. Korsgaard, “Creep and damage accumulation in orthotropic composites under cyclic loading,” Mech. Compos. Mater., 34, No. 4, 321–330 (1998).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • Yu. Paramonov
    • 1
  • J. Andersons
    • 2
  • M. Kleinhofs
    • 1
  • A. Paramonova
    • 1
  1. 1.Aviation InstituteRiga Technical UniversityRigaLatvia
  2. 2.Institute of Polymer MechanicsUniversity of LatviaRigaLatvia

Personalised recommendations