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Mechanics of Composite Materials

, Volume 52, Issue 4, pp 497–506 | Cite as

Modeling the Residual Strength of a Fibrous Composite Using the Residual Daniels Function

  • Yu. Paramonov
  • V. Cimanis
  • S. Varickis
  • M. Kleinhofs
Article

The concept of a residual Daniels function (RDF) is introduced. Together with the concept of Daniels sequence, the RDF is used for estimating the residual (after some preliminary fatigue loading) static strength of a unidirectional fibrous composite (UFC) and its S–N curve on the bases of test data. Usually, the residual strength is analyzed on the basis of a known S–N curve. In our work, an inverse approach is used: the S–N curve is derived from an analysis of the residual strength. This approach gives a good qualitive description of the process of decreasing residual strength and explanes the existence of the fatigue limit. The estimates of parameters of the corresponding regression model can be interpreted as estimates of parameters of the local strength of components of the UFC. In order to approach the quantitative experimental estimates of the fatigue life, some ideas based on the mathematics of the semiMarkovian process are employed. Satisfactory results in processing experimental data on the fatigue life and residual strength of glass/epoxy laminates are obtained.

Keywords

Daniels sequence strength fatigue life 

References

  1. 1.
    V. Cimanis and Yu. Paramonov, “Fatigue curve approximation using Daniels’ sequence and Markov chains,” Material digest of the XXIV Sci. and Practical Conf. Theory and Practice in Physical, Mathematical and Technical Sciences, London: IASHE, 31-33 (2012).Google Scholar
  2. 2.
    Yu. Paramonov, V. Cimanis, and S. Varickii, “Aproximation of fatigue curve and fatigue limit of fibre composite using random Daniels’ sequence and Markov chains,” Aviation. 17, No. 3, 91-97 (2013).CrossRefGoogle Scholar
  3. 3.
    Yu. Paramonov., V. Cimanis, S. Varickii, and M. Kleinhofs, “Investigation of the reliability and longevity of parallel systems with defects using Daniels’ sequences,” Automatic Control and Computer Sci., 47, No. 2, 87-93 (2013).Google Scholar
  4. 4.
    Yu. Paramonov., V. Cimanis, S. Varickii, and M. Kleinhofs, “Modeling the strength and fatigue life of a unidirectional fibrous composite using Daniels sequences and Markov chains,” Mech. of Compos. Mater., 49, No. 5, 821-838 (2013).Google Scholar
  5. 5.
    Yu. Paramonov., R. Chatys, J. Andersons, V. Cimanis, and M. Kleinhofs, “Markov models for tensile and fatigue reliability analysis of unidirectional fiber composite,” PT & A, 7, No. 3(26), 53-65 (2012).Google Scholar
  6. 6.
    Yu. Paramonov and M. Kleinhofs. Models of Reliability Analysis of Composite. - Lambert Saarbrucken, Germany, 2014.Google Scholar
  7. 7.
    Yu. Paramonov, A. Kuznetsov, and M. Kleinhofs,. “Reliabilty of fatigue-prone airframes and composite materials,” Riga: RTU, 2011. (<http://gnedenko-forum.org/library/Paramonov/Reliability_Paramonov.pdf>)
  8. 8.
    H. E. Daniels, “The statistical theory of the strength of bundles of threads,” Proc. Royal Soc. London, Ser. A., No. 183, 405-435 (1945).Google Scholar
  9. 9.
    H. E. Daniels, “The maximum of a Gaussian process whose mean path has a maximum, with an application to the strength of bundles of fibers,” Advances in Appl. Probability, 21, No. 2, 315-333 (1989).CrossRefGoogle Scholar
  10. 10.
    T. P. Philippidis and V. A. Passipoularidis, “Residual strength after fatigue in composites: Theory vs.exsperiment,” Int. J. of Fatigue, 29, 2104-2116 (2007).CrossRefGoogle Scholar
  11. 11.
    L. J. Broutman and S. Sahu “A new theory to predict cumulative fatigue damage in fibergfass reinforced plastics,” Composite Materials: Testing and Design. ASTM STP, 497, 170-188 (1972).Google Scholar
  12. 12.
    H. T. Hahn and R. Y. Kim, “Proof testing of composite materials,” J. Compos. Mater., 9, 297-311 (1975).CrossRefGoogle Scholar
  13. 13.
    J. N. Yang and M. D. Liu, “Residual strength degradation model and theory of periodic proof test for grasphite/epoxy laminates,” J. Compos. Mater., 11, 176-203 (1977).CrossRefGoogle Scholar
  14. 14.
    J. N. Yang and S. Du, “An exploratory study into the fatigue of composites under spectrum loading,” J. Compos. Mater., 17, 511-526 (1983).CrossRefGoogle Scholar
  15. 15.
    T. Adam, R. F. Dickson, C. J. Jones, H. Reiter, and B. Harris, “A power law fatigue damage model for fiber-reinforced plastic laminates,” Proc. Inst. Mech. Engrs., No. 200 (C3), 155-166 (1986).Google Scholar
  16. 16.
    G. P. Sendeckyj, “Life prediction for resin-matrix composite materials,” Composite Material, Ser. 4., Elsevier, 1991, 431-483.Google Scholar
  17. 17.
    G. P. Sendeckyj, “Fitting models to composite materials fatigue data. Test methods and design allowables for fibrous composites,” ASTM. STP, 734., 245-260 (1981).Google Scholar
  18. 18.
    Yu. Paramonov., R. Chatys, J. Andersons, and M. Kleinhofs, “Markov model of fatigue of a composite material in the Poisson process of defect initiation,” Mech. Compos. Mater., 48, No. 2, 315-330 (2012).Google Scholar
  19. 19.
    Yu. Paramonov., R. Chatys, J. Andersons, V. Cimanis, and M. Kleinhofs, “Markov models for tensile and fatigue reliability analysis of unidirectional fiber composite,” PT & A, 7, No. 3(26), 53-65 (2012).Google Scholar
  20. 20.
    T. P. Philippidis, T. T. Assimakopoulou, V. A. Passipoularidis, and A. E. Antoniou, “Static and Fatigue Tests on ISO Standard ±45°, Coupons, Main Test Phase I, OB_TG2_R020_rev.00, August 2004. Available from: http://www.kcwmc.nl/optimatblades/Publications.
  21. 21.
    T. P. Philippidis, T. T. Assimakopoulou, A. E. Antoniou, and V. A. Passipoularidis, Residual Strength Tests on ISO Standard ±45°. Coupons, Main Test Phase I, OB_TG5_R008 _rev.000, July 2005. Available from: http://www.kc-wmc.nl/optimatblades/Publications.
  22. 22.
    T. P. Philippidis, T. T. Assimakopoulou, A. E. Antoniou, and V. A. Passipoularidis, Residual Strength Tests on ISO Standard ± 45 ° Coupons, Main Test Phase II, OB_TG2_R037.rev.000, June 2006. Available from: http:// www.kcwmc.nl/optimatblades/Publications <http://www.kc-wmc.nl/optimatblades/Publications>.

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Yu. Paramonov
    • 1
  • V. Cimanis
    • 1
  • S. Varickis
    • 1
  • M. Kleinhofs
    • 1
  1. 1.Institute of AeronauticsRiga Technical UniversityRigaLatvia

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