International Journal of Fracture

, Volume 144, Issue 3, pp 149–158 | Cite as

Modeling of fatigue damage evolution on the basis of the kinetic concept of strength

Orignal Paper


On the basis of the kinetic theory of strength, a new approach to the modeling of material degradation in cyclic loading has been suggested. Assuming that not stress changes, but acting stresses cause the damage growth in materials under fatigue conditions, we applied the kinetic theory of strength to model the material degradation. The damage growth per cycle, the effect of the loading frequency on the lifetime and on the stiffness reduction in composites were determined analytically. It has been shown that the number of cycles to failure increases almost linearly and the damage growth per cycle decreases with increasing the loading frequency.


Kinetic theory of strength Fatigue Damage Lifetime Frequency 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Case SW, Iyengar N, Reifsnider KL (1998) Life prediction tool for ceramic matrix composites at elevated temperatures. In: Bucinell RB (ed) Composite materials: fatigue and fracture, vol 7. ASTM STP 1330, pp. 165–178Google Scholar
  2. Cherepanov GP (1974) Mechanics of brittle fracture. Nauka, Moscow (in Russian)Google Scholar
  3. Fatemi A and Yang L (1998). Cumulative fatigue damage and life prediction theories: A survey of the stat of the art for homogeneous materials. Int J Fatigue 20(1): 9–34 CrossRefGoogle Scholar
  4. Hahn HT, Turkgenc O (2000) The effect of loading parameters on fatigue of composite laminates: part IV information systems, Contract report DOT/FAA/AR-00/48Google Scholar
  5. Hertzberg RW, Manson JA and Skibo M (1975). Frequency sensitivity of fatigue processes in polymeric solids. Poly Eng Sci 15(4): 252–260 CrossRefGoogle Scholar
  6. Holm S and Mare J (1988). A simple model for fatigue life. IEEE Trans Reliab 37: 314–322 MATHCrossRefGoogle Scholar
  7. Holm S, Josefsson L, de Mare J, Svensson T (1995) Prediction of fatigue life based on level crossings and a state variable Fatigue Fract Eng Mater Struct 18: 1089–1100Google Scholar
  8. Hsiao CC (1989) Kinetic strength of solids. In: Salama K et al (eds) Advanced research fracture: Proceedings of the 7th international conference on fracture. Pergamon, London, pp 2913–2918Google Scholar
  9. Kachanov M (1987). On modeling of anisotropic damage in elastic-brittle materials: a brief review. In: Wang, ASD and Haritos, GK (eds) Damage mechanics in composites, pp 99–105. ASCE, New York Google Scholar
  10. Lemaitre J (1992). A course on damage mechanics. Springer, Berlin MATHGoogle Scholar
  11. Lee S, Nguyen T and Chunang T (2003). Model of fatigue damage in strain-rate-sensitive composite materials. J Mater Res 18(1): 77–80 Google Scholar
  12. Mandell JF, Meier U (1983) Effects of stress ratio, frequency, and loading time on tensile fatigue of glass-reinforced epoxy. In: O’Brien TK (ed) Long-term behavior of composites. ASTM STP 813, American Society for Testing and Materials, Philadelphia, PA, pp 55–77Google Scholar
  13. Miner MA (1945). Cumulative damage in fatigue. J Appl Mech 67: A159–A164 Google Scholar
  14. Mishnaevsky L (1996). Determination for the time to fracture of solids. Int J Fract 79(4): 341–350 CrossRefGoogle Scholar
  15. Mishnaevsky L (1997). Methods of the theory of complex systems in modeling of fracture: a brief review. Eng Fract Mech 56(1): 47–56 CrossRefGoogle Scholar
  16. Mishnaevsky L Jr (1998) Damage and fracture of heterogeneous materials, Balkema, Rotterdam, 230 ppGoogle Scholar
  17. Mishnaevsky L Jr (2007) Computational mesomechanics of composites, Wiley and SonsGoogle Scholar
  18. Schmauder S and Mishnaevsky L (1997). Damage evolution and heterogeneity of materials: model based on Fuzzy set theory. Eng Fract Mech 57(6): 625–636 CrossRefGoogle Scholar
  19. Miyano Y, McMurray M, Enyama J and Nakada M (1994). Loading rate and temperature dependenc on flexural fatigue behavior of a satin-woven CFRP laminate. J Comp Mater 28(13): 538–550 Google Scholar
  20. Moskala E (1993). Effects of mean stress and frequency on fatigue crack propagation in rubber-toughened polycarbonate/copolyester blends. J Appl Poly Sci 49(1): 53–64 CrossRefGoogle Scholar
  21. Narisawa I, Ishikawa M and Ogawa H (1978). Delayed yielding of polycarbonate under constant load. J Poly Sci 16(8): 1459–1470 Google Scholar
  22. Oh HK and Yoon WG (1995). Derivation and application of a dynamic fatigue life equation. J Mater Process Technol 49(3–4): 279–285 CrossRefGoogle Scholar
  23. Oliveira FA (1998). Transition-state analysis for fracture nucleation in polymers: the Lennard-Jones chain. Phy Rev B 57: 10576–10582 CrossRefADSGoogle Scholar
  24. Palmgren A (1924) Lebensdauer von kugellagern. Verfahreenstechinik, Berlin, 68:339–341Google Scholar
  25. Paris PC, Gomez MP and Anderson WE (1961). A rational analytic theory of fatigue. Trend Eng Univ Washington 13(1): 9–14 Google Scholar
  26. Parsons M, Stepanov EV, Hiltner A and Baer E (2000). Effect of strain rate on stepwise fatigue and creep slow crack growth in high density polyethylene. J Mater Sci 35: 1857–1866 CrossRefGoogle Scholar
  27. Phoenix SL, Beyerlein IJ (2000) Statistical strength theory for fibrous composite materials. In: Kelly A, Zweben C, Chou TW (eds) Comprehensive composite materials, vol 1. Pergamon, pp 559–639Google Scholar
  28. Regel VR, Slutsker AI and Tomashevskiy IYe (1974). Kinetic nature of strength of solids. Nauka, Moscow Google Scholar
  29. Reifsnider KL (1990). Composite materials series: fatigue of composites, vol 4. Elsevier, New York Google Scholar
  30. Rotem A (1993). Load frequency effect on the fatigue strength of isotropic laminates. Compos Sci Technol 46: 129–138 CrossRefGoogle Scholar
  31. Saff CR (1983) Effect of load frequency and lay-up on fatigue life of composites. In: O’Brien TK (ed) Long-term behavior of composites. ASTM STP 813, American Society for Testing and Materials, Philadelphia, PA, pp 78–91Google Scholar
  32. Sun CT, Chan WS (1979) Frequency effect on the fatigue life of a laminated composite. Composite materials: testing and design (5th Conference), ASTM STP674, American Society for Testing and Materials, Philadelphia, PA, pp 418–430Google Scholar
  33. Suresh S (1998) Fatigue of materials. Cambridge University Press, Cambridge, 704 ppGoogle Scholar
  34. Svensson Th (1996) Fatigue life prediction in service a statistical approach, Dept of Mathematics, GøteborgGoogle Scholar
  35. Takemori MT (1992). Fatigue fracture of polycarbonate. Poly Eng Sci 22(15): 937–945 CrossRefGoogle Scholar
  36. Wnuk MP (1974). Quasi-static extension of a tensile crack contained in viscoelastic plastic solid. J Appl Mech 41: 234–248 MATHGoogle Scholar
  37. Yokobori T (1968). An interdisciplinary approach to fracture and strength of solids. Wolter-Noordhoff, Groningen MATHGoogle Scholar
  38. Yokobori T (1978). The scientific basis of strength and fracture of materials. Kiev, Naukova Dumka Google Scholar
  39. Zhurkov SN (1964). Kinetic concept of the strength of solids. Int J Fract Mech 1(4): 311–323 Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Materials Research Department, Risø National LaboratoryTechnical University of Denmark, AFM-228RoskildeDenmark

Personalised recommendations