Journal of Mechanical Science and Technology

, Volume 33, Issue 1, pp 225–232 | Cite as

Craze density based fatigue-damage analysis in polyethylene methacrylate

  • Zongzhan GaoEmail author
  • Wei Liu
  • Qinghai Li
  • Shiling Liu
  • Zhufeng Yue
  • Baoxing Xu


The S-N curve, also known as the Wöhler curve, is well acknowledged and widely used in the prediction of fatigue life of engineering materials. In this study, we present a craze density model, as an alternative approach, to predict the fatigue life of polymer material-polyethylene methacrylate (PMMA). Our experiments show that craze grows rapidly with the increase of fatigue loadings after their initiation on the surface of PMMA till to the failure of specimens. Dynamic measurements indicate that the growth rate of craze density reaches a stable stage after a rapid accumulation at the beginning, and dominates the fatigue life of PMMA. Both initiation time of crazing and deformation energy of PMMA are probed through the recorded fatigue stress-strain curves and the optical microscope (OM) observations on crazing evolutions. The critical growth rate of the craze density is correlated with the yield stress and strain of PMMA at quasi-static loadings. On the basis of the craze density, an experimental model is established to predict the fatigue damage and life of PMMA. The predication shows good agreement with that from both experiments and traditional S-N curves in a broad range of fatigue loadings.


Fatigue life Craze density Deformation energy PMMA 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Y. Kim, K. Lee, H. C. Li, C. S. Seok, J. M. Koo, S. Y. Kwon and Y. H. Cho, Fatigue life prediction method for contact wire using maximum local stress, Journal of Mechanical Science and Technology, 29 (1) (2015) 67–70.CrossRefGoogle Scholar
  2. [2]
    Z. R. Wu, X. T. Hu, Z. X. Li, P. P. Xin and Y. D. Song, Probabilistic fatigue life prediction methodology for notched components based on simple smooth fatigue tests, Journal of Mechanical Science and Technology, 31 (1) (2017) 181–188.CrossRefGoogle Scholar
  3. [3]
    T. W. Bjerke and J. Lambros, Theoretical development and experimental validation of a thermally dissipative cohesive zone model for dynamic fracture of amorphous polymers, Journal of the Mechanics and Physics of Solids, 51 (2003) 1147–1170.CrossRefGoogle Scholar
  4. [4]
    A. S. Argon and J. G. Hannoosh, Initiation of crazes in polystyrene, Philosophical Magazine, 36 (1977) 1195–1216.CrossRefGoogle Scholar
  5. [5]
    A. S. Argon and M. Salama, Growth of crazes in glassy polymers, Philosophical Magazine, 36 (1977) 1217–1234.CrossRefGoogle Scholar
  6. [6]
    C. Bucknall, Quantitative approaches to particle cavitation, shear yielding, and crazing in rubber - toughened polymers, Journal of Polymer Science Part B: Polymer Physics, 45 (2007) 1399–1409.CrossRefGoogle Scholar
  7. [7]
    R. Kambour, A review of crazing and fracture in thermoplastics, Journal of Polymer Science: Macromolecular Reviews, 7 (1973) 1–154.Google Scholar
  8. [8]
    S. Sternstein and L. Ongchin, Yield criteria for plastic deformation of glassy high polymers in general stress fields, Polymer Preprints, 10 (1969) 1117–1124.Google Scholar
  9. [9]
    S. Sternstein and F. Myers, Yielding of glassy polymers in the second quadrant of principal stress space, Journal of Macromolecular Science, Part B: Physics, 8 (1973) 539–571.Google Scholar
  10. [10]
    A. Argon, Craze initiation in glassy polymers-revisited, Polymer, 52 (2011) 2319–2327.CrossRefGoogle Scholar
  11. [11]
    R. Oxborough and P. Bowden, Ageneral critical-strain criterion for crazing in amorphous glassy polymers, Philosophical Magazine, 28 (1973) 547–559.CrossRefGoogle Scholar
  12. [12]
    G. Marshall, L. Culver and J. Williams, Craze growth in polymethylmethacrylate: A fracture mechanics approach, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society (1970) 165–187.Google Scholar
  13. [13]
    M. James, C. Christopher, Y. Lu and E. Patterson, Fatigue crack growth and craze-induced crack tip shielding in polycarbonate, Polymer, 53 (2012) 1558–1570.CrossRefGoogle Scholar
  14. [14]
    M. James, Y. Lu, C. Christopher and E. Patterson, Crack path support for deformation mechanisms in fatigue of polycarbonate, Engineering Fracture Mechanics, 108 (2013) 89–97.CrossRefGoogle Scholar
  15. [15]
    H. Sami, B. Thierry, G. Cheng and K. Reijo, Continuum approach for modeling fatigue in amorphous glassy polymers. Applications to the investigation of damageratcheting interaction in polycarbonate, International Journal of Plasticity, 91 (2017) 109–133.CrossRefGoogle Scholar
  16. [16]
    R. Estevez, M. Tijssens and E. Van der Giessen, Modeling of the competition between shear yielding and crazing in glassy polymers, Journal of the Mechanics and Physics of Solids, 48 (2000) 2585–2617.CrossRefzbMATHGoogle Scholar
  17. [17]
    E. Van der Giessen, R. Estevez, K. Pijnenburg and M. Tijssens, Computational modeling of failure processes in polymers, European Conference on Computational Mechanics, München, Germany, Citeseer (1999).Google Scholar
  18. [18]
    S. Basu, D. K. Mahajan and E. Van der Giessen, Micromechanics of the growth of a craze fibril in glassy polymers, Polymer, 46 (2005) 7504–7518.CrossRefGoogle Scholar
  19. [19]
    R. Marissen, Craze growth mechanics, Polymer, 41 (2000) 1119–1129.CrossRefGoogle Scholar
  20. [20]
    E. J. Kramer and L. L. Berger, Fundamental processes of craze growth and fracture, Crazing in Polymers, Springer, 2 (1990) 1–68.Google Scholar
  21. [21]
    K. Amir and S. Pieter, Volgers. Fatigue damage assessment of unfilled polymers including self-heating effects, International Journal of Fatigue, 100 (2017) 367–376.CrossRefGoogle Scholar
  22. [22]
    W. Luo and W. Liu, Incubation time to crazing in stressed poly(methyl methacrylate), Polymer Testing, 26 (2007) 413–418.CrossRefGoogle Scholar
  23. [23]
    A. Huang, W. Yao and F. Chen, Analysis of fatigue life of PMMA at different frequencies based on a new damage mechanics model, Mathematical Problems in Engineering, 2014 (2014).CrossRefGoogle Scholar
  24. [24]
    F. Ellyin, Cyclic strain energy density as a criterion for multiaxial fatigue failure, ICBMFF2 (2013).Google Scholar
  25. [25]
    A. D. Drozdov and Q. Yuan, The viscoelastic and viscoplastic behavior of low-density polyethylene, International Journal of Solids and Structures, 40 (2003) 2321–2342.CrossRefGoogle Scholar
  26. [26]
    Z. P. Ding, Y. Zhang, S. C. Liu and D. Z. Nie, An energy-based fatigue life prediction of a mining truck welded frame, Journal of Mechanical Science and Technology, 30 (9) (2016) 3615–3624.Google Scholar
  27. [27]
    N. Saad-Gouider, R. Estevez, C. Olagnon and R. Seguela, Calibration of a viscoplastic cohesive zone for crazing in PMMA, Engineering Fracture Mechanics, 73 (2006) 2503–2522.CrossRefGoogle Scholar
  28. [28]
    A. S. Argon, Role of heterogeneities in the crazing of glassy polymers, Pure and Applied Chemistry, 43 (1975) 247–272.CrossRefGoogle Scholar
  29. [29]
    S. Chern and C. Hsiao, A generalized time-dependent theory on craze initiation in viscoelastic media, Journal of Applied Physics, 57 (1985) 1823–1834.CrossRefGoogle Scholar
  30. [30]
    W. Klemperer, Theodore von Karman anniversary volume, Appl. Mech. (1941) 328–329.Google Scholar
  31. [31]
    M. Shadman and H. Ziari, Laboratory evaluation of fatigue life characteristics of polymer modified porous asphalt: A dissipated energy approach, Construction and Building Materials, 138 (2017) 434–440.CrossRefGoogle Scholar
  32. [32]
    R. A. C. Deblieck, D. J. M. van Beek, K. Remerie and I. M. Ward, Failure mechanisms in polyolefines: The role of crazing, shear yielding and the entanglement network, Polymer, 52 (2011) 2979–2990.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Zongzhan Gao
    • 1
    Email author
  • Wei Liu
    • 1
  • Qinghai Li
    • 1
  • Shiling Liu
    • 1
  • Zhufeng Yue
    • 1
  • Baoxing Xu
    • 2
  1. 1.School of Mechanics, Civil Engineering and ArchitectureNorthwestern Polytechnical UniversityXianChina
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of VirginiaCharlottesvilleUSA

Personalised recommendations