Skip to main content
Log in

Mullins’ effect in semicrystalline polymers: experiments and modeling

  • Original Article
  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

Experimental data are reported on isotactic polypropylene in uniaxial cyclic tensile tests with various maximum strains at room temperature. It is demonstrated that polypropylene reveals all characteristic features (hysteresis of energy, damage accumulation, and strain-hardening) of the Mullins effect. Constitutive equations are derived for the viscoplastic behavior of semicrystalline polymers at three-dimensional deformations with small strains. Adjustable parameters in the stress–strain relations are found by fitting the observations. Numerical simulation shows that the model adequately predicts the viscoplastic response of polypropylene in uniaxial and biaxial cyclic tests.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Mullins L (1947) Effect of stretching on the properties of rubber. J Rubber Res 16:275–289

    Google Scholar 

  2. Mullins L (1969) Softening of rubber by deformation. Rubber Chem Technol 42:339–362

    Article  Google Scholar 

  3. Diani J, Fayolle B, Gilormini P (2009) A review on the Mullins effect. Eur Polym J 45:601–612

    Article  Google Scholar 

  4. Bueche F (1961) Mullins effect and rubber–filler interaction. J Appl Polym Sci 5:271–281

    Article  Google Scholar 

  5. Hanson DE, Hawley M, Houlton R, Chitanvis K, Rae P, Orler EB, Wrobleski DA (2005) Stress softening experiments in silica-filled polydimethylsiloxane provide insight into a mechanism for the Mullins effect. Polymer 46:10989–10995

    Article  Google Scholar 

  6. Coquelle E, Bossis G (2006) Mullins effect in elastomers filled with particles aligned by a magnetic field. Int J Solids Struct 43:7659–7672

    Article  MATH  Google Scholar 

  7. Cheng M, Chen W (2003) Experimental investigation of the stress-stretch behavior of EPDM rubber with loading rate effects. Int J Solids Struct 40:4749–4768

    Article  Google Scholar 

  8. Merabia S, Sotta P, Long DR (2008) A microscopic model for the reinforcement and the nonlinear behavior of filled elastomers and thermoplastic elastomers (Payne and Mullins effects). Macromolecules 41:8252–8266

    Article  ADS  Google Scholar 

  9. Drozdov AD (2009) Mullins’ effect in thermoplastic elastomers: experiments and modeling. Mech Res Commun 36:437–443

    Article  Google Scholar 

  10. Franceschini G, Bigoni D, Regitnig P, Holzapfel GA (2006) Brain tissue deforms similarly to filled elastomers and follows consolidation theory. J Mech Phys Solids 54:2592–2620

    Article  ADS  MATH  Google Scholar 

  11. Ciarletta P, Dario P, Micera S (2008) Pseudo-hyperelastic model of tendon hysteresis from adaptive recruitment of collagen type I fibrils. Biomaterials 29:764–770

    Article  Google Scholar 

  12. Webber RE, Creton C, Brown HR, Gong JP (2007) Large strain hysteresis and Mullins effect of tough double-network hydrogels. Macromolecules 40:2919–2927

    Article  ADS  Google Scholar 

  13. Wilde TP, McDowell DL, Jacob KI, Aneja AP (2006) A modified Mullins model for compressive behavior of goose down fiber assemblies. Mech Adv Mater Struct 13:83–93

    Article  Google Scholar 

  14. Meunier L, Chagnon G, Favier D, Orgeas L, Vacher P (2008) Mechanical experimental characterisation and numerical modelling of an unfilled silicone rubber. Polym Test 27:765–777

    Article  Google Scholar 

  15. Ogden RW, Roxburgh DG (1999) A pseudo-elastic model for the Mullins effect in filled rubber. Proc R Soc A 455:2861–2877

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Drozdov AD, Dorfmann A (2001) Stress-strain relations in finite viscoelastoplasticity of rigid-rod networks: applications to the Mullins effect. Continuum Mech Thermodyn 13:183–205

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Elias-Zuniga A, Beatty MF (2003) Stress-softening effects in the transverse vibration of a non-Gaussian rubber string. Meccanica 38:419–433

    Article  MathSciNet  MATH  Google Scholar 

  18. Chagnon G, Verron E, Gornet L, Marckmann G, Charrier P (2004) On the relevance of continuum damage mechanics as applied to the Mullins effect in elastomers. J Mech Phys Solids 52:1627–1650

    Article  ADS  MATH  Google Scholar 

  19. Horgan CO, Ogden RW, Saccomandi G (2004) A theory of stress softening of elastomers based on finite chain extensibility. Proc R Soc A 460:1737–1754

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. Göktepe S, Miehe C (2005) A micro-macro approach to rubber-like materials. Part III: the micro-sphere model of anisotropic Mullins-type damage. J Mech Phys Solids 53:2259–2283

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Chagnon G, Verron E, Marckmann G, Gornet L (2006) Development of new constitutive equations for the Mullins effect in rubber using the network alteration theory. Int J Solids Struct 43:6817–6831

    Article  MATH  Google Scholar 

  22. De Tommasi D, Puglisi G, Saccomandi G (2006) A micromechanics–based model for the Mullins effect. J Rheol 50:495–512

    Google Scholar 

  23. Meissner B, Matejka L (2006) A structure-based constitutive equation for filler-reinforced rubber-like networks and for the description of the Mullins effect. Polymer 47:7997–8012

    Article  Google Scholar 

  24. D’Ambrosio P, De Tommasi D, Ferri D, Puglisi G (2008) A phenomenological model for healing and hysteresis in rubber-like materials. Int J Eng Sci 46:293–305

    Article  MATH  Google Scholar 

  25. Li J, Mayau D, Lagarrigue V (2008) A constitutive model dealing with damage due to cavity growth and the Mullins effect in rubber-like materials under triaxial loading. J Mech Phys Solids 56:953–973

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. Aboudi J (2009) Finite strain micromechanical analysis of rubber-like matrix composites incorporating the Mullins damage effect. Int J Damage Mech 18:5–29

    Article  Google Scholar 

  27. Cantournet S, Desmorat R, Besson J (2009) Mullins effect and cyclic stress softening of filled elastomers by internal sliding and friction thermodynamics model. Int J Solids Struct 46:2255–2264

    Article  MATH  Google Scholar 

  28. Drozdov AD (1999) Viscoelastoplasticity of rubbery polymers at finite strains. Meccanica 34:85–102

    Article  MathSciNet  MATH  Google Scholar 

  29. Xia Z, Shen X, Ellyin F (2005) An assessment of nonlinearly viscoelastic constitutive models for cyclic loading: the effect of a general loading/unloading rule. Mech Time-Depend Mater 9:281–300

    Article  Google Scholar 

  30. Yakimets I, Lai D, Guigon M (2007) Model to predict the viscoelastic response of a semi-crystalline polymer under complex cyclic mechanical loading and unloading conditions. Mech Time-Depend Mater 11:47–60

    Article  ADS  Google Scholar 

  31. Johnson MA, Beatty MF (1993) A constitutive equation for the Mullins effect in stress controlled uniaxial extension experiments. Continuum Mech Thermodyn 5:301–318

    Article  MathSciNet  ADS  Google Scholar 

  32. Govindjee S, Simo JC (1992) Mullins effect and the strain amplitude dependence of the storage modulus. Int J Solids Struct 29:1737–1751

    Article  MATH  Google Scholar 

  33. Itskov M, Haberstroh E, Ehret AE, Vöhringer MC (2006) Experimental observation of the deformation induced anisotropy of the Mullins effect in rubber. KGK Kautschuk Gummi Kunststoffe 59:93–96

    Google Scholar 

  34. Drozdov AD, de Christiansen JC (2003) The effect of annealing on the elastoplastic response of isotactic polypropylene. Eur Polym J 39:21–31

    Article  Google Scholar 

  35. Samios D, Tokumoto S, Denardin ELG (2005) Large plastic deformation of isotactic poly(propylene) (iPP) evaluated by WAXD techniques. Macromol Symp 229:179–187

    Article  Google Scholar 

  36. Machado G, Kinast EJ, Scholten JD, Thompson A, Vargas TD, Teixeira SR, Samios D (2009) Morphological and crystalline studies of isotactic polypropylene plastically deformed and evaluated by small-angle X-ray scattering, scanning electron microscopy and X-ray diffraction. Eur Polym J 45:700–713

    Article  Google Scholar 

  37. Hiss R, Hobeika S, Lynn C, Strobl G (1999) Network stretching, slip processes, and fragmentation of crystallites during uniaxial drawing of polyethylene and related copolymers. A comparative study. Macromolecules 32:4390–4403

    Article  ADS  Google Scholar 

  38. Nitta K-H, Takayanagi M (1999) Role of tie molecules in the yielding deformation of isotactic polyprolylene. J Polym Sci B: Polym Phys 37:357–368

    Article  ADS  Google Scholar 

  39. Kolarik J, Pegoretti A (2006) Non-linear tensile creep of polypropylene: time-strain superposition and creep prediction. Polymer 47:346–356

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. D. Drozdov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Drozdov, A.D., Christiansen, J.d. Mullins’ effect in semicrystalline polymers: experiments and modeling. Meccanica 46, 359–370 (2011). https://doi.org/10.1007/s11012-010-9314-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-010-9314-z

Keywords

Navigation