Journal of Materials Science

, Volume 43, Issue 22, pp 7192–7202 | Cite as

A theory for yield phenomenon of glassy polymers based on the strain non-uniformity under loading conditions

  • G. SpathisEmail author


In this work, the yield phenomenon and its related features have been investigated under the concept of strain inhomogeneity, emerged inside the material during deformation processes. This strain non-uniformity in glassy polymers is either a direct consequence of the local microstructural density fluctuations existing in such materials or is the result of the manner by which the free volume is frozen in the glassy state. Assuming a simple strain density distribution function, the rate of plastic deformation can be extracted without any further assumption on a molecular conformational base or any other thermal activated process. The two model parameters required have a physical base related with the magnitude of the free volume and its fluctuation in glassy polymers. Appling this theory on the experimental results for three representative amorphous glassy polymers (PMMA, PS, and PC), all features of yield process, including strain softening effect, are easily described.


PMMA Free Volume Amorphous Polymer Strain Softening Stretch Ratio 


  1. 1.
    Bowden PB, Raha S (1974) Philos Mag 29:146. doi: CrossRefGoogle Scholar
  2. 2.
    Robertson RE (1966) J Chem Phys 44:3950. doi: CrossRefGoogle Scholar
  3. 3.
    Argon AS (1973) Philos Mag 28:839. doi: CrossRefGoogle Scholar
  4. 4.
    G’Sell C, Jonas JJ (1981) J Mater Sci 14:583CrossRefGoogle Scholar
  5. 5.
    Boyce MC, Parks DM, Argon AS (1988) Mech Mater 7:15. doi: CrossRefGoogle Scholar
  6. 6.
    Hasan OA, Boyce MC (1993) Polymer (Guildf) 34:5085. doi: CrossRefGoogle Scholar
  7. 7.
    Hasan OA, Boyce MC (1995) Polym Eng Sci 35:331. doi: CrossRefGoogle Scholar
  8. 8.
    Hasan OA, Boyce MC, Li XS, Berko S (1993) J Polym Sci Phys 31:185. doi: CrossRefGoogle Scholar
  9. 9.
    Eyring HJ (1936) J Chem Phys 4:283. doi: CrossRefGoogle Scholar
  10. 10.
    Dlubek G, Bondarenko V, Pionteck J, Supej M, Wutzler A, Krause-Rehberg R (2003) Polymer (Guildf) 44:1921. doi: CrossRefGoogle Scholar
  11. 11.
    Schmidt M, Maurer FHJ (2000) Polymer (Guildf) 41:8419. doi: CrossRefGoogle Scholar
  12. 12.
    Kanaya T, Tsukushi T, Kaji K, Bartos J, Kristiak J (1999) Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 60(2):1906. doi: CrossRefGoogle Scholar
  13. 13.
    Higuchi H, Yu Z, Jamieson AM, Simha R, McGervey JD (1995) J Pol Sci B: Polym Phys 33:2295. doi: CrossRefGoogle Scholar
  14. 14.
    Xiao-Yan Wang KM, Lee Y, Stone MT, Sanchez IC, Freeman BD (2004) Polymer (Guildf) 45:3907. doi: CrossRefGoogle Scholar
  15. 15.
    Rubin MB (1994) Int J Solids Struct 31(19):2615. doi: CrossRefGoogle Scholar
  16. 16.
    Rubin MB (1994) Int J Solids Struct 31(19):2635. doi: CrossRefGoogle Scholar
  17. 17.
    Spathis G, Kontou E (1998) Polymer (Guildf) 24:189Google Scholar
  18. 18.
    Spathis G, Kontou E (1999) J Appl Polym Sci 71:2007. doi:10.1002/(SICI)1097-4628(19990321)71:12<2007::AID-APP10>3.0.CO;2-WCrossRefGoogle Scholar
  19. 19.
    Wendorff JH, Fisher EW (1973) Kolloid Z Z Polym 251:876. doi: CrossRefGoogle Scholar
  20. 20.
    Curro JJ, Roe RJ (1984) Polymer (Guildf) 25:1424. doi: CrossRefGoogle Scholar
  21. 21.
    Roe RJ, Curro JJ (1983) Macromolecules 16:428. doi: CrossRefGoogle Scholar
  22. 22.
    Williams ML, Landel RF, Ferry JD (1955) J Am Chem Soc 77:3701. doi: CrossRefGoogle Scholar
  23. 23.
    Malhotra BD, Pethrick RA (1983) Eur Polym J 19:45. doi: CrossRefGoogle Scholar
  24. 24.
    Malhotra BD, Pethrick RA (1983) Polymer (Guildf) 24:165Google Scholar
  25. 25.
    Goyanes S, Rubiolo G, Salgueiro W, Somoza A (2005) Polymer (Guildf) 46:9081. doi: CrossRefGoogle Scholar
  26. 26.
    Lee EH (1966) Elastic–plastic deformation at finite strain. J Appl Mech 36:1CrossRefGoogle Scholar
  27. 27.
    Eckard C (1984) Phys Rev 73:373. doi: CrossRefGoogle Scholar
  28. 28.
    Besseling JF (1968) In: Proceedings of IUTAM symposium on irreversible aspects of continuum mechanics, Vienna, Springer, pp 16–53Google Scholar
  29. 29.
    Chau CC, Blackson J (1995) Polymer (Guildf) 36:2511. doi: CrossRefGoogle Scholar
  30. 30.
    Anglan H, El-Hadik GY, Faughnan P, Bryan C (1999) J Mater Sci 34:83. doi: CrossRefGoogle Scholar
  31. 31.
    Matsuoka S (1992) Relaxation phenomena in polymers, 2nd edn. Hanser, Ch. 3Google Scholar
  32. 32.
    Spitzing WA, Richmon O (1979) Polym Eng Sci 19:1129. doi: CrossRefGoogle Scholar
  33. 33.
    Wolfram SS (1993) Mathematica, a system for doing mathematics by computer, 2nd edn. Wolfram Research, New YorkGoogle Scholar
  34. 34.
    Boyce MC, Arruda EM (1990) Polym Eng Sci 30(20):1288. doi: CrossRefGoogle Scholar
  35. 35.
    Hoy RS, Robbins MO (2008) Phys Rev E Stat Nonlin Soft Matter Phys 77:031801. doi: CrossRefGoogle Scholar
  36. 36.
    Hoy RS, Robbins MO (2007) Phys Rev Lett 99:117801. doi: CrossRefGoogle Scholar
  37. 37.
    Hoy RS, Robbins MO (2006) J Pol Sci B: Polym Phys 44:3487. doi: CrossRefGoogle Scholar
  38. 38.
    James HM, Guth E (1943) J Chem Phys 11:455. doi: CrossRefGoogle Scholar
  39. 39.
    Oleynik EF (1990) In: Baer E, Moet S (eds) High performance polymer. Munchen, Ch., 4, p 80Google Scholar

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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.School of Applied Mathematical and Physical Sciences, Section of MechanicsNational Technical University of AthensAthensGreece

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