Advertisement

Journal of Materials Science

, Volume 51, Issue 14, pp 6639–6661 | Cite as

Comparison of maximum likelihood approaches for analysis of composite stress rupture data

  • Amy Engelbrecht-Wiggans
  • Stuart Leigh Phoenix
Original Paper

Abstract

Stress rupture is a sudden, stochastic failure mode that occurs in continuous unidirectional fiber composites and in particular composite overwrapped pressure vessels subject to long-term, steady loads. A common approach for modeling stress rupture is the probabilistic classic power-law model for material breakdown within a Weibull framework (CPL-W). This model includes a number of parameters, which need to be estimated from real data. These parameters may be estimated in a variety of different ways. This paper investigates how best to estimate the parameters of the CPL-W model given a set of experimental data for both composite strength and composite lifetime obtained at multiple stress levels. Eight different maximum likelihood estimation approaches are investigated regarding their differing errors of estimation. The accuracy of each method is estimated by repeated Monte Carlo simulations of specific instances of the CPL-W model typical of various carbon/epoxy and aramid/epoxy fiber composite systems; no actual experimental data are analyzed. One particular approach stands out as having the least estimation error while a commonly used approach does very poorly.

Keywords

Failure Probability Load Level Failure Time Lifetime Data Stress Rupture 
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.

Notes

Acknowledgements

We would like to acknowledge Dr. Richard Engelbrecht-Wiggans for his guidance and advice. We would also like to thank Dr. Michael Kezirian for his helpful discussions regarding the context of this work in applications. Funding was provided under NIST Agreement ID 70NANB14H323.

Compliance with ethical standards

Conflict of Interest

The authors declare that they have no conflict of interest in presenting this work.

References

  1. 1.
    Blassiau S, Thionnet A, Bunsell A (2006) Micromechanisms of load transfer in a unidirectional carbon fibre–reinforced epoxy composite due to fibre failures. Part 1: Micromechanisms and 3D analysis of load transfer: the elastic case. Compos Struct 74:303–318CrossRefGoogle Scholar
  2. 2.
    Blassiau S, Thionnet A, Bunsell A (2006) Micromechanisms of load transfer in a unidirectional carbon fibre—reinforced epoxy composite due to fibre failures. Part 2: Influence of viscoelastic and plastic matrices on the mechanisms of load transfer. Compos Struct 74:319–331CrossRefGoogle Scholar
  3. 3.
    Blassiau S, Thionnet A, Bunsell A (2008) Micromechanisms of load transfer in a unidirectional carbon fibre–reinforced epoxy composite due to fibre failures. Part 3: Multiscale reconstruction of composite behaviour. Compos Struct 83:312–323CrossRefGoogle Scholar
  4. 4.
    Chou HY, Thionnet A, Mouritz A, Bunsell AR (2016) Stochastic factors controlling the failure of carbon/epoxy composites. J Mater Sci 51:311–333. doi: 10.1007/s10853-015-9390-5 CrossRefGoogle Scholar
  5. 5.
    Phoenix SL, Murthy PLN (2007) Pro’s and cons of proof testing carbon composite overwrapped pressure vessels: a comparison of two mathematical models, AIAA Paper No. 2007–2325, presented at 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, HonoluluGoogle Scholar
  6. 6.
    Tobolsky A, Eyring H (1943) Mechanical properties of polymeric materials. J Chem Phys 11:125–134CrossRefGoogle Scholar
  7. 7.
    Coleman BD (1956) Application of the theory of absolute reaction rates to the creep failure of polymeric filaments. J Polym Sci 20:447–455. doi: 10.1002/pol.1956.120209604 CrossRefGoogle Scholar
  8. 8.
    Coleman BD (1956) Time dependence of mechanical breakdown phenomena. J Appl Phys 27:862–866CrossRefGoogle Scholar
  9. 9.
    Coleman BD (1957) A stochastic process model for mechanical breakdown phenomena. Trans Soc Rheol 1:153–168CrossRefGoogle Scholar
  10. 10.
    Coleman BD, Knox AG (1957) The interpretation of creep failure in textile fibers as a rate process. Text Res J 27:393–399CrossRefGoogle Scholar
  11. 11.
    Coleman BD (1958) Time dependence of mechanical breakdown in bundles of fibers. III. The power law breakdown rule. Trans Soc Rheol 2:195–218CrossRefGoogle Scholar
  12. 12.
    Coleman BD (1958) Statistics and time dependence of mechanical breakdown in fibers. J Appl Phys 29:968–983CrossRefGoogle Scholar
  13. 13.
    Coleman BD, Knox AG, McDevit WF (1958) The effect of temperature on the rate of creep failure for 66 Nylon. Text Res J 28:393–399CrossRefGoogle Scholar
  14. 14.
    Phoenix SL, Tierney LJ (1983) A statistical model for the time dependent failure of unidirectional composite materials under local elastic load-sharing among fibers. Eng Fract Mech 18:193–215CrossRefGoogle Scholar
  15. 15.
    Phoenix SL (1978) Stochastic strength and fatigue of fiber bundles. Int J Fract 14:327–344. doi: 10.1007/BF00034692 Google Scholar
  16. 16.
    Miner MA (1945) Cumulative damage in fatigue. ASME J Appl Mech 12(3):159–164Google Scholar
  17. 17.
    Liang Y, Chen W (2015) A regularized Miner’s rule for fatigue reliability analysis with Mittag–Leffler statistics. Int J Damage Mech. doi: 10.1177/1056789515607610 Google Scholar
  18. 18.
    Phoenix SL (1979) The asymptotic distribution for the time to failure of a fiber bundle. Adv Appl Probab 11:153–187CrossRefGoogle Scholar
  19. 19.
    Reeder J (2012) Composite stress rupture: a new reliability model based on strength decay. Report NASA/TM-2012-217566, L-20122, NF1676L-14234Google Scholar
  20. 20.
    Kelly A, McCartney LN (1981) Failure by stress corrosion of bundles of fibres. Proc R Soc Lond A 374:1759CrossRefGoogle Scholar
  21. 21.
    Genschel U, Meeker WQ (2010) A comparison of maximum likelihood and median-rank regression for Weibull estimation. Qual Eng 22(4):236–255CrossRefGoogle Scholar
  22. 22.
    Olteanu D, Freeman L (2010) The evaluation of median-rank regression and maximum likelihood estimation techniques for a two-parameter Weibull Distribution. Qual Eng 22(4):256–272CrossRefGoogle Scholar
  23. 23.
    Knoester H, Hulshof, Meester (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
  24. 24.
    DeTeresa SJ and Groves SE (2001) Properties of fiber composites for advanced flywheel energy storage devices. In: SAMPE symposiumGoogle Scholar
  25. 25.
    Phoenix SL, Grimes-Ledesma L, Thesken JC, Murthy PLN (2006) Reliability modeling of the stress-rupture performance of kevlar 49/epoxy pressure vessels: revisiting a large body stress rupture data to develop new insights. In: Proceedings American Society for Composites, 21st annual technical conference, University of Michigan-Dearborn, DearbornGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Amy Engelbrecht-Wiggans
    • 1
  • Stuart Leigh Phoenix
    • 1
  1. 1.Sibley School of Mechanical and Aerospace EngineeringCornell UniversityIthacaUSA

Personalised recommendations