Skip to main content
SpringerLink
Log in

Modeling the Fatigue Behavior of Fiber-Reinforced Composite Materials Under Constant Amplitude Loading

  • Chapter
  • First Online:
Fatigue of Fiber-reinforced Composites

Part of the book series: Engineering Materials and Processes ((EMP))

Abstract

The fatigue behavior of fiber-reinforced composite materials under constant amplitude and variable amplitude loading depends on the type of material and a number of loading parameters. This chapter presents the concepts and theoretical formulations used in order to model the fatigue behavior of fiber-reinforced composite materials, independent of their nature. The commonly used S–N curve types are presented and their applicability to the examined material system dataset is evaluated. Curves estimated by novel computational methods are also presented and compared to traditional ones. The concept of the constant life diagrams (CLDs) used for the quantification of the effect of the mean cyclic stress on the fatigue life of the examined materials is also described. The commonly used CLDs and those most recently introduced are methodically presented. Their performance is evaluated based on their ability to predict S–N curves under “unseen” loading conditions, covering all possible R-ratios of tension-tension, tension-compression and compression-compression fatigue. An alternative approach for the modeling of the fatigue behavior of composite materials under constant amplitude loading is also introduced in this chapter. This approach, according to which stiffness is conceived as the damage metric, whose degradation dominates the fatigue behavior of the material, is based on stiffness degradation measurements during the fatigue life of the examined material. When a certain stiffness limit is reached, the material is considered as having failed. Use of stiffness degradation as a measure for the modeling of the constant amplitude fatigue life of the examined material leads to the derivation of S–N curves corresponding to a predefined level of stiffness degradation and not to ultimate material failure.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Z. Hashin, A. Rotem, A fatigue failure criterion for fiber–reinforced materials. J. Compos. Mater. 7(4), 448–464 (1973)

    Article  Google Scholar 

  2. H. El Kadi, F. Ellyin, Effect of stress ratio on the fatigue failure of fiberglass reinforced epoxy laminae. Composites 25(10), 917–924 (1994)

    Article  Google Scholar 

  3. H.A. Whitworth, A stiffness degradation model for composite laminates under fatigue loading. Compos. Struct. 40(2), 95–101 (1997)

    Article  Google Scholar 

  4. M. Kawai, S. Yajima, A. Hachinohe, Y. Takano, Off–axis fatigue behavior of unidirectional carbon fiber–reinforced composites at room and high temperatures. J. Compos. Mater. 35(7), 545–576 (2001)

    Article  Google Scholar 

  5. N.L. Post, Reliability based design methodology incorporating residual strength prediction of structural fiber reinforced polymer composites under stochastic variable amplitude fatigue loading, PhD Thesis, Virginia Polytechnic Institute and State University, March 18, Blacksburg, Virginia (2008)

    Google Scholar 

  6. A.P. Vassilopoulos, R. Bedi, Adaptive neuro-fuzzy inference system in modeling fatigue life of multidirectional composite laminates. Comp. Mater. Sci. 43(4), 1086–1093 (2008)

    Article  Google Scholar 

  7. A.P. Vassilopoulos, E.F. Georgopoulos, T. Keller, Genetic programming in modeling of fatigue life of composite materials. in 13th International Conference on Experimental Mechanics-ICEM13: Experimental Analysis of Nano and Engineering Materials and Structures, Alexandroupolis, Greece, July 1–6, 2007

    Google Scholar 

  8. A.P. Vassilopoulos, E.F. Georgopoulos, T. Keller, Comparison of genetic programming with conventional methods for fatigue life modeling of FRP composite materials. Int. J. Fatigue 30(9), 1634–1645 (2008)

    Article  CAS  Google Scholar 

  9. R.P.L. Nijssen, O Krause, T.P Philippidis, Benchmark of lifetime prediction methodologies, Optimat blades technical report, 2004, OB_TG1_R012 rev.001, http://www.wmc.eu/public_docs/10218_001.pdf

  10. T. Adam, G. Fernando, R.F. Dickson, H. Reiter, B. Harris, Fatigue life prediction for hybrid composites. Fatigue 11(4), 233–237 (1989)

    Article  CAS  Google Scholar 

  11. J.A. Epaarachchi, P.D. Clausen, An empirical model for fatigue behavior prediction of glass fiber reinforced plastic composites for various stress ratios and test frequencies. Compos. Part A-Appl. Sci. 34(4), 313–326 (2003)

    Article  Google Scholar 

  12. J.M. Whitney Fatigue characterization of composite materials. in Fatigue of Fibrous Composite Materials, ASTM STP 723, American Society for Testing and Materials, 1981, 133–151

    Google Scholar 

  13. G.P. Sendeckyj, Fitting models to composite materials, in Test methods and design allowables for fibrous composites, (ASTM STP 734, ed. by C.C. Chamis (American Society for Testing and Materials, West Conshohocken, PA, 1981), pp. 245–260

    Chapter  Google Scholar 

  14. J.A. Lee, D.P. Almond, B. Harris, The use of neural networks for the prediction of fatigue lives of composite materials. Compos. Part A-Appl. Sci. 30(10), 1159–1169 (1999)

    Article  Google Scholar 

  15. Y. Al-Assaf, H. El Kadi, Fatigue life prediction of unidirectional glass fiber/epoxy composite laminae using neural networks. Compos. Struct. 53(1), 65–71 (2001)

    Article  Google Scholar 

  16. J.A. Lee, D.P. Almond, A neural-network approach to fatigue-life prediction, in Fatigue in composites, ed. by B. Harris (Woodhead Publishing Ltd, Cambridge, UK, 2003), pp. 569–589

    Chapter  Google Scholar 

  17. A.P. Vassilopoulos, E.F. Georgopoulos, V. Dionysopoulos, Modeling fatigue life of multidirectional GFRP laminates under constant amplitude loading with artificial neural networks. Adv. Compos. Lett. 15(2), 43–51 (2006)

    Google Scholar 

  18. R.C.S.F. Junior, A.D.D. Neto, E.M.F. Aquino, Building of constant life diagrams of fatigue using artificial neural networks. Int. J. Fatigue 27(7), 746–751 (2005)

    Article  Google Scholar 

  19. A.P. Vassilopoulos, E.F. Georgopoulos, V. Dionysopoulos, Artificial neural networks in spectrum fatigue life prediction of composite materials. Int. J. Fatigue 29(1), 20–29 (2007)

    Article  CAS  Google Scholar 

  20. C.S. Lee, W. Hwang, H.C. Park, K.S. Han, Failure of carbon/epoxy composite tubes under combined axial and torsional loading 1. Experimental results and prediction of biaxial strength by the use of neural networks. Compos. Sci. Technol. 59(12), 1779–1788 (1999)

    Article  Google Scholar 

  21. J. Jia, J.G. Davalos, An artificial neural network for the fatigue study of bonded FRP-wood interfaces. Compos. Struct. 74(1), 106–114 (2006)

    Article  Google Scholar 

  22. M.A. Jarrah, Y. Al-Assaf, H. El Kadi, Neuro-Fuzzy modeling of fatigue life prediction of unidirectional glass fiber/epoxy composite laminates. J. Compos. Mater. 36(6), 685–699 (2002)

    Article  Google Scholar 

  23. AIM Learning Technology, http://www.aimlearning.com, last update 10.01.2007

  24. J.R. Koza, Genetic Programming on the Programming of Computers by Means of Natural Selection (MIT Press, Cambridge, MA, 1992)

    Google Scholar 

  25. J.R. Koza, Genetic Programming, in Encyclopaedia of Computer Science and Technology, ed. by J.G. Williams, A. Kent (Marcel-Dekker, NY, 1998), pp. 29–43. 39. Supplement 24

    Google Scholar 

  26. V. Babovic, M. Keijzer, Genetic programming as a model induction engine. J. Hydroinform 2(1), 35–60 (2000)

    Google Scholar 

  27. A.P. Vassilopoulos, B.D. Manshadi, T. Keller, Influence of the constant life diagram formulation on the fatigue life prediction of composite materials. Int. J. Fatigue 32(4), 659–669 (2009)

    Article  Google Scholar 

  28. N. Gathercole, H. Reiter, T. Adam, B. Harris, Life prediction for fatigue of T800/5245 carbon fiber composites: I. Constant amplitude loading. Int. J. Fatigue 16(8), 523–532 (1994)

    Article  CAS  Google Scholar 

  29. M.H. Beheshty, B. Harris, A constant life model of fatigue behavior for carbon fiber composites: the effect of impact damage. Compos. Sci. Technol. 58(1), 9–18 (1998)

    Article  CAS  Google Scholar 

  30. M. Kawai, M. Koizumi, Nonlinear constant fatigue life diagrams for carbon/epoxy laminates at room temperature. Compos.: Part A 38(11), 2342–2353 (2007)

    Article  Google Scholar 

  31. J.F. Mandell, D.D. Samborsky, L. Wang, N.K. Wahl, New fatigue data for wind turbine blade materials. J. Sol. Energy Eng. Trans. ASME 125(4), 506–514 (2003)

    Article  CAS  Google Scholar 

  32. H.J. Sutherland, J.F. Mandell, Optimized constant life diagram for the analysis of fiberglass composites used in wind turbine blades. J. Sol. Energy Eng. Trans. ASME 127(4), 563–569 (2005)

    Article  CAS  Google Scholar 

  33. T.P. Philippidis, A.P. Vassilopoulos, Complex stress state effect on fatigue life of GFRP laminates Part I, Experimental. Int. J. Fatigue 24(8), 813–823 (2002)

    Article  Google Scholar 

  34. B. Harris, A parametric constant-life model for prediction of the fatigue lives of fiber-reinforced plastics, in Fatigue in Composites, ed. by B. Harris (Woodhead Publishing Limited, Cambridge, UK, 2003), pp. 546–568

    Chapter  Google Scholar 

  35. M. Kawai, A method for identifying asymmetric dissimilar constant fatigue life diagrams for CFRP laminates. Key. Eng. mater. 334–335, 61–64 (2007)

    Article  Google Scholar 

  36. G.K. Boerstra, The multislope model: a new description for the fatigue strength of glass reinforced plastic. Int. J. Fatigue 29, 1571–1576 (2007)

    Article  CAS  Google Scholar 

  37. C. Kassapoglou, Fatigue life prediction of composite structures under constant amplitude loading. J. Compos. Mater. 41(22), 2737–2754 (2007)

    Article  Google Scholar 

  38. C. Kassapoglou, Fatigue of composite materials under spectrum loading. Compos. Part A-Appl. Sci. 41(5), 663–669 (2010)

    Article  Google Scholar 

  39. A.P. Vassilopoulos, B.D. Manshadi, T. Keller, Piecewise non-linear constant life diagram formulation for FRP composite materials. Int. J. Fatigue 32(10), 1731–1738 (2010)

    Article  CAS  Google Scholar 

  40. W.Z. Gerber, Bestimmung der zulässigen spannungen in eisen-constructionen (Calculation of the allowable stresses in iron structures). Z Bayer Archit. Ing-Ver 6(6), 101–110 (1874)

    Google Scholar 

  41. J. Goodman, Mechanics Applied to Engineering (Longman Green, Harlow, 1899)

    Google Scholar 

  42. V.A. Passipoularidis, T.P. Philippidis, A study of factors affecting life prediction of composites under spectrum loading. Int. J. Fatigue 31, 408–417 (2009)

    Article  CAS  Google Scholar 

  43. T.P. Philippidis, A.P. Vassilopoulos, Life prediction methodology for GFRP laminates under spectrum loading. Compos Part A–Appl S 35(6), 657–666 (2004)

    Article  Google Scholar 

  44. Awerbuch J, Hahn HT. Off-axis fatigue of graphite/epoxy composite. in Fatigue of Fibrous Composite Materials. ASTM STP 723, (American Society for Testing and Materials, 1981), pp. 243–273

    Google Scholar 

  45. M. Kawai, T. Murata, A three-segment anisomorphic constant life diagram for the fatigue of symmetric angle-ply carbon/epoxy laminates at room temperature. Compos Part A-Appl S 41(10), 1498–1510 (2010)

    Article  Google Scholar 

  46. Nijssen RPL. OptiDAT–fatigue of wind turbine materials database, 2006. <http://www.kc-wmc.nl/optimat_blades/index.htm>

  47. Mandell JF, Samborsky DD. DOE/MSU Composite Material Fatigue Database. Sandia National Laboratories, SAND97-3002 (online via www.sandia.gov/wind, v. 18, 21st March 2008 Updated)

  48. G.P. Sendeckyj. Fitting models to composite materials fatigue data. Test Methods and Design Allowables for Fibrous Composites. ASTM STP 734. C.C. CHAMIS, editor. American Society for Testing and Materials, 1981. p. 245–260

    Google Scholar 

  49. J. Degrieck, W.M. Paepegem, Fatigue damage modeling of fiber-reinforced composite materials: a review. Appl. Mech. Rev. 54(4), 279–300 (2001)

    Article  Google Scholar 

  50. G.P. Sendeckyj. Life prediction for resin-matrix composite materials. in Fatigue of Composite Materials, ed. by K.L. Reifsneider, Composite Materials Series 4 (Elsevier, Amsterdam, 1991)

    Google Scholar 

  51. A.L. Highsmith, K.L. Reifsneider, Stiffness Reduction Mechanisms, in Composite Laminates, Damage in Composite Materials, ASTM STP 775, ed. by K.L. Reifsneider (American Society for Testing and Materials, West Conshohocken, PA, 1982), pp. 103–117

    Google Scholar 

  52. R. Talreja, Fatigue of Composite Materials (Technomic, Lancaster Pennsylvania, 1987)

    Google Scholar 

  53. S.I. Andersen, P. Brondsted, H. Lilholt, Fatigue of polymeric composites for wingblades and the establishment of stiffness-controlled fatigue diagrams. in Proceedings of 1996 European Union Wind Energy Conference, Göteborg, Sweden, (20–24 May 1996) pp. 950–953

    Google Scholar 

  54. W. Van Paepegem, Fatigue damage modeling of composite materials with the phenomenological residual stiffness approach, in Fatigue Life Prediction of Composites and Composite Structures, ed. by A.P. Vassilopoulos (Woodhead Publishing Ltd., Cambridge, 2010)

    Google Scholar 

  55. W. Hwang, K.S. Han, Fatigue of composites-fatigue modulus concept and life prediction. J. Compos. Mater. 20(2), 154–165 (1986)

    Article  CAS  Google Scholar 

  56. H.T. Hahn, R.Y. Kim, Fatigue behavior of composite laminate. J. Compos. Mater. 10(2), 156–180 (1976)

    Article  Google Scholar 

  57. J.A.M. Ferreira, P.N. Reis, J.D.M. Costa, M.O.W. Richardson, Fatigue behavior of composite adhesive lap joints. Compos. Sci. Technol. 62(10–11), 1373–1379 (2002)

    Article  CAS  Google Scholar 

  58. T. Keller, A. Zhou, Fatigue behavior of adhesively bonded joints composed of pultruded GFRP adherends for civil infrastructure applications. Compos Part A-Appl S 37(8), 1119–1130 (2006)

    Article  Google Scholar 

  59. Y. Zhang, A.P. Vassilopoulos, T. Keller, Stiffness degradation and fatigue life prediction of adhesively-bonded joints for fiber-reinforced polymer composites. Int. J. Fatigue 30(10–11), 1813–1820 (2008)

    Article  CAS  Google Scholar 

  60. M.J. Salkind, Fatigue of composites, in Composite Materials, Testing And Design, ASTM STP 497, ed. by H.T. Corten (American Society for Testing and Materials, West Conshohocken, PA, 1972), pp. 143–169

    Google Scholar 

  61. T.P. Philippidis, A.P. Vassilopoulos, Fatigue design allowables for GFRP laminates based on stiffness degradation measurements. Compos. Sci. Technol. 60(15), 2819–2828 (2000)

    Article  CAS  Google Scholar 

  62. T.P. Philippidis, A.P. Vassilopoulos, Fatigue of composite laminates under off-axis loading. Int. J. Fat. 21, 253–262 (1999)

    Article  Google Scholar 

  63. Anon. IEC-TC88-WG8 test guideline: “Full-scale structural testing of rotor blades for WTGS’s”, IEC 61400–23 (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Composite Construction Laboratory (CCLab), École Polytechnique Fédérale De Lausanne (EPFL), School of Architecture, Civil and Environment (ENAC), Station 16, 1015, Lausanne, Switzerland

    Anastasios P. Vassilopoulos & Thomas Keller

Authors
  1. Anastasios P. Vassilopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Keller
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anastasios P. Vassilopoulos .

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag London Limited

About this chapter

Cite this chapter

Vassilopoulos, A.P., Keller, T. (2011). Modeling the Fatigue Behavior of Fiber-Reinforced Composite Materials Under Constant Amplitude Loading. In: Fatigue of Fiber-reinforced Composites. Engineering Materials and Processes. Springer, London. https://doi.org/10.1007/978-1-84996-181-3_4

Download citation

Publish with us

Policies and ethics

Search

Navigation