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Some specific features and consequences of the thermal response of rubber under cyclic mechanical loading

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Abstract

The present paper deals with the specificities of the thermal response of rubber under cyclic mechanical loading at constant ambient temperature. This question is important, since the stabilized thermal response is used in fatigue life criteria, especially for the fast evaluation of fatigue life. For this purpose, entropic coupling in a thermo-hyperelastic framework is first used to predict the variation in the heat source produced or absorbed by the material during cyclic loading. The heat diffusion equation is then used to deduce temperature variations under adiabatic and non-adiabatic conditions. The influence of several parameters on the stabilized thermal response is studied: signal shape, frequency, minimum and maximum stretch levels, multiaxiality of the mechanical state. The results show that, in the steady-state regime, the mean value between the maximum and minimum temperature variations over a mechanical cycle is different from zero. This is due to the specific variation in the heat source, which depends on both the stretch rate and the stretch level. This result has numerous consequences, in particular for fatigue. Indeed, the stabilized mean value between the maximum and minimum temperature variations during fatigue tests does not reflect only fatigue damage, since the entropic coupling also leads to a value different from zero. This is a major difference with respect to materials exhibiting only isentropic coupling, such as metallic materials.

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References

  1. Mullins L.: Effect of stretching on the properties of rubber. Rubber Chem. Technol. 21, 281–300 (1948)

    Article  Google Scholar 

  2. Marckmann G., Verron E., Gornet L., Chagnon G., Charrier P., Fort P.: A theory of network alteration for the Mullins effect. J. Mech. Phys. Solids 50, 2011–2028 (2002)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  4. Fletcher W.P., Gent A.N.: Non-linearity in the dynamic properties of vulcanised rubber compounds. Trans. Inst. Rubber Ind. 29, 266–280 (1953)

    Google Scholar 

  5. Payne A.R.: The dynamic properties of carbon black-loaded natural rubber vulcanizates. Part I. J. Appl. Phys. 6(19), 57–63 (1962)

    Google Scholar 

  6. Rendek M., Lion A.: Strain-induced transient effects of filler-reinforced elastomers with respect to the Payne-effect: experiments and constitutive modelling. Z Angew Math. Mech. 90, 436–458 (2010)

    Article  MATH  Google Scholar 

  7. Barick A.K., Tripathy D.K.: Thermal and dynamic mechanical characterization of thermoplastic polyurethane/organoclay nanocomposites prepared by melt compounding. Mater. Sci. Eng. A 527, 812–823 (2010)

    Article  Google Scholar 

  8. Barmouz M., Seyfi J., KazemBesharati Givi M., Hejazi I., Davachi S.M.: A novel approach for producing polymer nanocomposites by in-situ dispersion of clay particles via friction stir processing. Mater. Sci. Eng. A 528, 3003–3006 (2011)

    Article  Google Scholar 

  9. Stringfellow R., Abeyaratne R.: Cavitation in an elastomer: comparison of theory with experiment. Mater. Sci. Eng. A 112, 127–131 (1989)

    Article  Google Scholar 

  10. Le Cam J.-B, Toussaint E.: Volume variation in stretched natural rubber: competition between cavitation and stress-induced crystallization. Macromolecules 41, 7579–7583 (2008)

    Article  Google Scholar 

  11. Le Cam J.-B., Toussaint E.: Cyclic volume changes in rubbers. Mech. Mater. 41, 898–901 (2009)

    Article  Google Scholar 

  12. Toki S., Fujimaki T., Okuyama M.: Strain-induced crystallization of natural rubber as detected real-time by wide-angle x-ray diffraction technique. Polymer 41, 5423–5429 (2000)

    Article  Google Scholar 

  13. Toki, S., Sics, I., Ran, S., Liu, L., Hsiao, B.S., Murakami, S., Senoo, K., Kohjiya, S.: New insights into structural development in natural rubber during uniaxial deformation by in situ synchrotron X-ray diffraction. Macromolecules 35, 6578–6584 (2002)

    Google Scholar 

  14. Trabelsi S., Albouy P.-A., Rault J.: Stress-induced crystallization around a crack tip in natural rubber. Macromolecules 35, 10054–10061 (2002)

    Article  Google Scholar 

  15. Trabelsi S., Albouy P.-A., Rault J.: Effective local deformation in stretched filled rubber. Macromolecules 36, 9093–9099 (2003)

    Article  Google Scholar 

  16. Huneau B.: Strain-induced crystallization of natural rubber: a review of x-ray diffraction investigations. Rubber Chem. Technol. 84, 425–452 (2011)

    Article  Google Scholar 

  17. Lion A., Peters J.: Coupling effects in dynamic calorimetry: frequency-dependent relations for specific heat and thermomechanical responses: a one-dimensional approach based on thermodynamics with internal state variables. Thermochim. Acta 500, 76–87 (2010)

    Article  Google Scholar 

  18. Gough, J.: Proc Lit and Phil Soc Manchester, 2nd, ser. 1, p. 288 (1805)

  19. Joule J.P.: On some thermodynamic properties of solids. Phil. Mag. 4(h, 14), 227 (1857)

  20. Mars W.V., Fatemi A.: A literature survey on fatigue analysis approaches for rubber. Int. J. Fatigue 24, 949–961 (2002)

    Article  MATH  Google Scholar 

  21. Mars W.V.: Cracking energy density as a predictor of fatigue life under multiaxial conditions. Rubber Chem. Technol. 75, 1–17 (2002)

    Article  Google Scholar 

  22. Le Cam, J.-B.: Endommagement en fatigue des elastomères. PhD thesis, Université de Nantes, École Centrale de Nantes (2005)

  23. Saintier N., Cailletaud G., Piques R.: Multiaxial fatigue life prediction for a natural rubber. Int. J. Fatigue 28, 530–539 (2006)

    Article  MATH  Google Scholar 

  24. Chadwick P., Creasy C.M.F.: Modified entropic elasticity of rubberlike materials. J. Mech. Phys. Solids 32, 337–357 (1984)

    Article  MATH  Google Scholar 

  25. Pottier T., Moutrille M.-P., Le Cam J.-B., Balandraud X., Grédiac M.: Study on the use of motion compensation technique to determine heat sources. application to large deformations on cracked rubber specimens. Exp. Mech. 49, 561–574 (2009)

    Article  Google Scholar 

  26. Promma N., Raka B., Grédiac M., Toussaint E., Le Cam J.-B., Balandraud X., Hild F.: Application of the virtual fields method to mechanical characterization of elastomeric materials. Int. J. Solids Struct. 46, 698–715 (2009)

    Article  MATH  Google Scholar 

  27. Le Cam J.-B., Toussaint E., Dubois O.: Effect of thermal cycles on the deformation state at the crack tip of crystallizable natural rubber. Strain 48, 153–156 (2011)

    Article  Google Scholar 

  28. Le Cam J.-B.: A review of the challenges and limitations of full-field measurements applied to large heterogeneous deformation of rubbers. Strain 48, 174–188 (2012)

    Article  Google Scholar 

  29. Toussaint E., Balandraud X., Le Cam J.-B., Grédiac M.: Combining displacement, strain, temperature and heat source fields to investigate the thermomechanical response of an elastomeric specimen subjected to large deformations. Polym. Test. 31, 916–925 (2012)

    Article  Google Scholar 

  30. Verron, E., Le Cam, J.-B., Gornet, L.: A multiaxial criterion for crack nucleation in rubber. Mech. Res. Commun. 33:493–498 (2006)

  31. Samaca Martinez J.R., Le Cam J.-B., Balandraud X., Toussaint E., Caillard J.: Mechanisms of deformation in crystallizable natural rubber. Part 2: quantitative calorimetric analysis. Polymer 54, 2727–2736 (2013)

    Article  Google Scholar 

  32. Samaca Martinez J.R., Le Cam J.-B., Balandraud X., Toussaint E., Caillard J.: Filler effects on the thermomechanical response of stretched rubbers. Polym. Test. 32, 835–841 (2013)

    Article  Google Scholar 

  33. Lemaitre J., Chaboche J.L.: Mechanics of Solids Materials. Cambridge University Press, Cambridge (1990)

    Book  Google Scholar 

  34. Maugin, G.A.: The Thermodynamics of Nonlinear Irreversible Behaviors: An Introduction, volume 27 of Series A. World scientific series on Nonlinear Science (1999)

  35. Holzapfel, G.A.: Non linear solid mechanics: a continuum approach for engineering. Wiley (2000)

  36. Chrysochoos, A.: Analyse du comportement des matériaux par thermographie infrarouge. Photomécanique 95, Y. Berthaud (ed.), Eyrolles, pp. 203–211, Cachan, France, 14–16 March (1995)

  37. Chrysochoos A., Pham H., Maisonneuve O.: Energy balance of thermoelastic martensite transformation under stress. Nucl. Eng. Des. 162, 1–12 (1996)

    Article  Google Scholar 

  38. Balandraud X., Ernst E., Soos E.: Rheological phenomena in shape memory alloys. C.R. Acad. Sci. Ser. IIb Mec 327, 33–39 (1999)

    MATH  Google Scholar 

  39. Boulanger T., Chrysochoos A., Mabru C., Galtier A.: Calorimetric analysis of dissipative and thermoelastic effects associated with the fatigue behavior of steels. Int. J. Fatigue 26, 221–229 (2004)

    Article  Google Scholar 

  40. Berthel B., Chrysochoos A., Wattrisse B., Galtier A.: Infrared image processing for the calorimetric analysis of fatigue phenomena. Exp. Mech. 48, 79–90 (2008)

    Article  Google Scholar 

  41. Giancane S., Chrysochoos A., Dattoma V., Wattrisse B.: Deformation and dissipated energies for high cycle fatigue of 2024-T3 aluminium alloy. Theor. Appl. Fract. Mech. 52, 117–121 (2009)

    Article  Google Scholar 

  42. Chrysochoos A., Louche H.: An infrared image processing to analyse the calorific effects accompanying strain localisation. Int. J. Eng. Sci. 38, 1759–1788 (2000)

    Article  Google Scholar 

  43. Chrysochoos A., Louche H.: Thermal and dissipative effects accompanying luders band propagation. Mater. Sci. Eng. A struct. 307, 15–22 (2001)

    Article  Google Scholar 

  44. Balandraud X., Chrysochoos A., Leclercq S., Peyroux R.: Influence of the thermomechanical coupling on the propagation of a phase change front. C.R. Acad. Sci. Ser. IIB Mech. 329, 621–626 (2001)

    Google Scholar 

  45. Chrysochoos A., Wattrisse B., Muracciole J.-M., El Kaim Y.: Fields of stored energy associated with localized necking of steel. J. Mech. Mater. Struct. 4, 245–262 (2009)

    Article  Google Scholar 

  46. Maquin F., Pierron F.: Heat dissipation measurements in low stress cyclic loading of metallic materials: From internal friction to micro-plasticity. Mech. Mater. 41, 928–942 (2009)

    Article  Google Scholar 

  47. Dumoulin S., Louche H., Hopperstad O.S., Borvik T.: Heat sources, energy storage and dissipation in high-strength steels: experiments and modelling. Eur. J. Mech. A Solids 29, 461–474 (2010)

    Article  Google Scholar 

  48. Verron E., Andriyana A.: Definition of a new predictor for multiaxial fatigue crack nucleation in rubber. J. Mech. Phys. Solids 56, 417–443 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  49. Baaser H., Hopmann C., Schobel A.: Reformulation of strain invariants at incompressibility. Arch. Appl. Mech. 83, 273–280 (2013)

    Article  Google Scholar 

  50. Meunier L., Chagnon G., Favier D., Orgéas L., Vacher P.: Experimental and numerical study of the mechanical behaviour of an unfilled silicone rubber. Polym. Test. 27, 765–777 (2008)

    Article  Google Scholar 

  51. Treloar, L.R.G.: The elasticity of a network of long chain molecules (I and II). Transactions of the Faraday Society 39:36–64, 241–246 (1943)

    Google Scholar 

  52. Dulieu-Barton J.M., Stanley P.: Development and application of thermoelastic stress analysis. J. Strain Anal. Eng. Des. 33, 93–104 (1998)

    Article  Google Scholar 

  53. Joule, J.P.: India-rubber, 33. In: The Scientific Papers of James Prescott Joule, vol. 1. The Physical Society of London, Taylor and Francis, red lion court, fleet street (1884)

  54. Anthony R.L., Caston R.H., Guth E.: Equations of state for naturals and synthetic rubber like materials: unaccelerated natural soft rubber. J. Phys. Chem. 46, 826 (1942)

    Article  Google Scholar 

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Authors and Affiliations

  1. CLERMONT UNIVERSITÉ, Institut Français de Mécanique Avancée, Institut Pascal, BP 10448, 63000, Clermont-Ferrand, France

    X. Balandraud

  2. CNRS, UMR 6602, Université Blaise Pascal, Institut Pascal, 63171, Aubière, France

    X. Balandraud

  3. UNIVERSITÉ DE RENNES 1, Institut de Physique de Rennes, UMR 6251, CNRS/Université de Rennes 1, Campus de Beaulieu, 35042, Rennes, France

    J. -B. Le Cam

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Balandraud, X., Le Cam, J.B. Some specific features and consequences of the thermal response of rubber under cyclic mechanical loading. Arch Appl Mech 84, 773–788 (2014). https://doi.org/10.1007/s00419-014-0832-3

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