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Abstrakty
The constitutive law of a two-phase isotropic polymer blending described by fractional derivative models is obtained through a classical self-consistent scheme. A parametric analysis is driven to describe the influence of the four parameters associated with the constitutive law description and to comprise the conditions of application of the model. An identification of the set of parameters is performed by mechanical spectroscopy for two amorphous polymers: the polymethyl methacrylate (PMMA) and the styrene acrylonytrile copolymer (SAN) and their mixture, to evaluate the ability of the model to reproduce the experimental results obtained from the Dynamic Mechanical Thermal Analysis.
Czasopismo
Rocznik
Tom
Strony
135--156
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
autor
- Laboratoire de Mecanique, Biomecanique, Polymeres et Structures, Ecole Nationale d'Ingenieurs de Metz, Ile du Saulcy, 57045 Metz Cedex 01, France, lipinski@enim.fr
Bibliografia
- 1. R.C- KOELLER, Applications of fractional calculus to the theory of visco-elasticity, J. Appl. Mech., 51, 299-307, 1984.
- 2. K.B. OLDHAM, J. SPANIBR, The fractional calculer, Academic Press, San Diego, L.A., 1974.
- 3. P. SUQUET, Elements of homogenisation for inelastic solid mechanics, homogenisation Techniques for composite media, E. SANCHEZ-PALENCIA, A. ZAOUI [Eds.], Berlin Springer Verlag, 193-278, 1985.
- 4. A. MOLINARI, G. CANOVA, S. AHZI, A self-consistent approach of the large, deformation polycrystals, Acta Metall., 25, 2983-2994, 1987.
- 5. N. LAHELLEC, P. SUQUET, Effective behavior of linear viscoelastic composites: A time-integration approach, Int. J. of Solids and Struct.. 44, 507-529, 2007.
- 6. A. PAQUIN, H. SABAR, M. BERVEILLER, Integral formulation and self-consistent modeling of elastic-plastic constitutive law of polycrystals, Arch. Appl. Mech., 69, 14-35, 1999.
- 7. M. COULIBAY, Modelisation micromecanique et caracterisation experimental^ du comportement des materiaux heterogcnes elastovicoplastiques. Application a la valorisation des polymcres recycles, PhD Thesis, Universite Paul Verlaine de Metz, Juillet 2008.
- 8. J. MANDEL, Mecanique des milieux continus, Gauthier-Villars, Paris, 1966.
- 9. N. LAWS, R. MCLAUGHLIN, Self-consistent estimates for the visco-elastic creep compliances of composite materials, Proc. R. Soc. Lond., 359, 251-273, 1978.
- 10. Y. ROUGIER, C. STOLZ, A. ZAOUI, Representation spectrale en viscoelasticite lineaire des materiaux heterogfnes, C.R. Acad. Sci. Paris II, 316, 1517-1522, 1994.
- 11. S. BEURTHEY, A. ZAOUI, Structural morphology and relaxation spectra of visco-elastic heterogeneous materials, Eur. J. Mech. A/Solids, 19, 1-16, 2001.
- 12. A.V. HERSHEY, The elasticity of an isotropic aggregate of anisotropic cubic crystals, J. Appl. Mech., 21, 236-240, 1954.
- 13. R. BRENNER, R. MASSON, O. CASTELNAU, A. ZAOUI, A 'quasi-elastic' affine formulation for the homogenised behaviour of nonlinear visco-elasiic polycrystals and composites, Eur, J. Mech. A/Solids, 21, 943-960, 2002.
- 14. R.A. SCHAPERY, Approximate methods of transform inversion for visco-elastic stress analysis, Proc. U.S. Nat. Congr. Appl. Mech. ASME 4th, 1, 1075-1085, 1962.
- 15. J.D. FERRY, Visco-elastic properties of polymers, John Wiley, 1980.
- 16. L. BOLTZMANN, Zur Theorie des elastischen Nachwirkung, Annalen der Physik und Chemie, 27, 624-654, 1876.
- 17. M. ENELUND, P. OLSSON, Damping described by fading memory analysis and application to fractional derivative models, Int. J. of Solids and Struct., 36, 939-970, 1999.
- 18. M. ENELUND, G. LESIEUTRE, Time domain modeling of damping using anelastic displacement fields and fractional calculus, Int. J. of Solids and Struct., 36, 4447-4472, 1999.
- 19. B. HARTMANN, G.F. LEE, J.D. LEE, Loss factor height and width limits for polymer relaxations, J. Acoust. Soc. Am. 95, 1, 226-233, 1994.
- 20. R.O. DAVIES, J. LAMB, Ultrasonic analysis of molecular relaxation process in liquids, Q. Rev., 11, 134-161, 1957.
- 21. S. HAVRILIAK. S. NEGAMI, A complex plane analysis of a-dispersions in some poly mer systems, [in:] Transitions and Relaxations in Polymers, J. Polym. Sci. Part C, 14, R. F. BOYER [Ed.], Interscience, New-York, 99-117, 1966.
- 22. F. DINZART, P. LIPINSKI, Improved five-parameter fractional derivative model for elastomers, Archives of Mechanics, 61, 459-474, 2009.
- 23. R. HILL, A self-consistent mechanics of composite materials, J. Mech. Phys. Solids, 13, 213-222, 1965.
- 24. W.P. Fox, Generalized nonlinear regression, maple procedure, www.mapleapps.com.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT1-0037-0018