Journal of Materials Science

, Volume 52, Issue 4, pp 1898–1910 | Cite as

A probabilistic approach on residual strength and damage buildup of high-performance fibers

  • Henk Knoester
  • Joost Hulshof
  • Ronald Meester
Original Paper


An elementary, probabilistic model for fiber failure, developed by Coleman in the fifties of the last century, predicts a Weibull distributed time-to-failure for fibers subject to a constant load. This has been experimentally confirmed, not only for fibers but for load-bearing products in general. In this paper, we analyze residual strength, i.e., the strength after having survived a given load program. We demonstrate that the Weibull modulus, describing variability of time-to-failure, affects residual strength. It determines (a) how fast residual strength of fibers decays during their service life, (b) the residual strength variability, and (c) the fraction of surviving fibers during service life. Experiments show that residual strength of Twaron fiber (p-aramid fiber), exceeding predictions of Coleman’s model, remains unrelentingly high (close to virgin strength) during service life.


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Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Coleman BD (1958) Statistics and time dependence of mechanical breakdown in fibers. J Appl Phys 29(6):968–983CrossRefGoogle Scholar
  2. 2.
    Coleman BD (1957) Time dependence of mechanical breakdown in bundles and fibers. I. Constant total load. J Appl Phys 28(9):1058–1067CrossRefGoogle Scholar
  3. 3.
    Coleman BD (1958) On the strength of classical fibre and fibre bundles. J Mech Phys Solids 7:60–70CrossRefGoogle Scholar
  4. 4.
    Phoenix SL (1978) The asymptotic time to failure of a mechanical system of parallel members. Siam J Appl Math 34(2):227–246CrossRefGoogle Scholar
  5. 5.
    Phoenix SL (1978) Stochastic strength of fatigue of fiber bundles. Int J Fracture 14(3):327–344Google Scholar
  6. 6.
    Knoester H, Hulshof J, Meester RWJ (2015) Modeling failure of high performance fibers: on the prediction of long-term time-to-failure. J Mater Sci 50(19):6277–6290. doi: 10.1007/s10853-015-9161-3 CrossRefGoogle Scholar
  7. 7.
    Chou PC, Croman R (1978) Residual strength in fatigue based on the strength-life equal rank assumption. J Compos Mater 12:177–194CrossRefGoogle Scholar
  8. 8.
    Barnard PM, Butler RJ, Curtis PT (1988) The strength-life equal rank assumption and its application to the fatigue life prediction of composite materials. Int J Fatigue 10(3):171–177CrossRefGoogle Scholar
  9. 9.
    Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech Trans ASME 18(3):293–297Google Scholar
  10. 10.
    Peirce FT (1926) Tensile tests for cotton yarns v. The Weakest Link theorems on the strength of long and of composite specimens. J Text I 17:T355Google Scholar
  11. 11.
    Paramonov Yu, Andersons J (2007) A family of weakest link models for fiber strength distribution. Compos Part A Appl Sci Manuf 38:1227–1233CrossRefGoogle Scholar
  12. 12.
    Van der Zwaag S (1989) The concept of filament strength and the Weibull modulus. J Test Eval 17(5):292–298CrossRefGoogle Scholar
  13. 13.
    Knoff WF (1993) Combined weakest link and random defect model for describing strength variability in fibres. J Mater Sci 28:921–931. doi: 10.1007/BF00400876 CrossRefGoogle Scholar
  14. 14.
    Sutherland LS, Shenoi RA, Lewis SM (1999) Size and scale effects in composites: I. Literature review. Compos Sci Technol 59(2):209–220CrossRefGoogle Scholar
  15. 15.
    Wagner HD, Phoenix SL, Schwartz P (1984) A study of statistical variability in the strength of single aramid filaments. J Compos Mater 28:312–327CrossRefGoogle Scholar
  16. 16.
    Shih TT (1980) An evaluation of the probabilistic approach to brittle design. Eng Fract Mech 13(2):257–271CrossRefGoogle Scholar
  17. 17.
    Yang JN (1977) Residual strength degradation model and theory of periodic proof tests for graphite/epoxy laminates. J Compos Mater 11:176–203CrossRefGoogle Scholar
  18. 18.
    Kenney MC, Mandell JF, McGarry FJ (1985) Fatigue behaviour of synthetic fibres, yarns and ropes. J Mater Sci 20:2045–2059. doi: 10.1007/BF01112288 CrossRefGoogle Scholar
  19. 19.
    Philippidis TP, Passipoularidis VA (2007) Residual strength after fatigue in composites: Theory vs. experiment. Int J Fatigue 29:2104–2116CrossRefGoogle Scholar
  20. 20.
    Knoester H, Den Decker P, Van den Heuvel CJM, Tops NAN, Elkink F (2012) Creep and failure time of aramid yarns subjected to constant loads. Macromol Mater Eng 297(6):559–575CrossRefGoogle Scholar
  21. 21.
    Christensen RM (1981) Residual strength determination in polymeric materials. J Rheol 25(5):529–536CrossRefGoogle Scholar
  22. 22.
    Ibnabdeljalil M, Phoenix SL (1995) Creep-rupture of brittle matrix composites reinforced with time dependent fibers: scalings and Monte Carlo simulations. J Mech Phys Solids 43(6):897–931CrossRefGoogle Scholar
  23. 23.
    Wingo RD (1989) The left-truncated Weibull distribution: theory and computation. Stat Pap 30:39–48CrossRefGoogle Scholar
  24. 24.
    McEwen RP, Parresol BR (1991) Moment expressions and summary statistics for the complete and truncated Weibull distribution. Commun Stat Theory Methods 20(4):1361–1372CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Teijin AramidArnhemThe Netherlands
  2. 2.VU UniversityAmsterdamThe Netherlands

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