تحلیل عددی رفتار مکانیکی پلیمرهای نیمه‌بلوری از دیدگاه مکانیک آسیب محیط پیوسته

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک، دانشگاه تهران

2 دانشگاه تهران، دانشکده مهندسی مکانیک

چکیده

در پژوهش حاضر، برای تحلیل رفتار پلیمرهای نیمه‌بلوری، با استفاده از دیدگاه مکانیک آسیب محیط پیوسته، یک مدل مکانیکی ارائه شده است. در این مدل، یک نقطه مادی از پلیمر نیمه‌بلوری به صورت مجموعی از توده‌ها، شامل دو فاز بلوری و بی‌شکل و صفحه مرزی فازها درنظر گرفته شده و معادلات اساسی هر یک از فازها تشریح شده است. سپس الگوریتمی عددی برای حل معادلات اساسی هر فاز به صورت مرحله به مرحله ارائه شده است. همچنین با استفاده از میانگین گیری حجمی، رفتار کلی ماده برحسب رفتار هرکدام از فازها مشخص گردیده است. به دلیل در دسترس بودن پارامترهای مادی برای پلی‌اتیلن، رفتار این ماده مورد تحلیل قرار گرفته است. نتایج عددی بدست آمده با نتایج مدل‌ها و آزمایشات قبلی مقایسه شده است، پس از تأیید اعتبار مدل ارائه شده، تأثیر پارامترهای نرخ آسیب فاز بلوری، پارامتر رهایی، نرخ آسیب فاز بی‌شکل، آسیب اشباع، مدول برشی لاستیکی و مقاومت فاز بی‌شکل بر رفتار پلی‌اتیلن مورد بررسی قرار گرفته است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Numerical Analysis of Mechanical Behavior of Semi-Crystalline Polymers Based on Continuum Damage Mechanics

نویسندگان [English]

  • Hadi Mehdipour 1
  • Mahdi Ganjiani 2
1 M.Sc student, University of Tehran
2 Faculty of Mechanical Engineering, University of Tehran
چکیده [English]

In the current study, semi-crystalline polymers and their properties are introduced, and then a mechanical model is precisely presented in order to predict the behavior of these materials. In this model, a material point of the semi-crystalline polymer is considered as an aggregate of inclusions of two phases, namely, the crystalline and the amorphous phase, with the interface plane of these two phases. Constitutive equations of each phase are demonstrated. A numerical algorithm is presented for solving the constitutive equations of each phase, in stages. Moreover, the general behavior of the material is determined in terms of each phase behavior using volume averaging. Because of the availability of the material parameters for polyethylene, this material has been taken into account. Obtained numerical results are reported and compared to that of previous models. After supporting the validity of the presented model, the effect of some material parameters including crystalline phase damage rate, release parameter, amorphous phase damage rate, saturation damage, rubber shear modulus, and amorphous phase strength on polyethylene behavior has been discussed in details.

کلیدواژه‌ها [English]

  • Continuum damage mechanics
  • Semi-crystalline polymers
  • Numerical algorithm
  • Polyethylene
[1]  Ö.F. Erkendirci, Investigation of the quasi static penetration resistance behavior of carbon fiber reinforced laminate HDPE composites, Composites Part B: Engineering, 93 (2016) 344-351.
[2]     W.W. Müller, F. Saathoff, Geosynthetics in geoenvironmental engineering, Science and technology of advanced materials, 16(3) (2015) 034605.
[3]  J. He, J. Liu, J. Li, Y. Lai, X. Wu, Enhanced ionic conductivity and electrochemical capacity of lithium  ion battery based on PVDF-HFP/HDPE membrane, Materials Letters, 170 (2016) 126-129.
[4]  M. Boyce, E. Arruda, An experimental and anaiytical investigation of the large strain compressive and tensile response of glassy polymers, Polymer Engineering & Science, 30(20) (1990) 1288-1298.
[5]  C. G’sell, V. Favier, J. Hiver, A. Dahoun, M. Philippe, G. Canova, Microstructure transformation and stress‐strain behavior of isotactic polypropylene under large plastic deformation, Polymer Engineering & Science, 37(10) (1997) 1702-1711.
[6]  T. Amornsakchai, R. Olley, D. Bassett, M. Al-Hussein, A. Unwin, I. Ward, On the influence of initial morphology on the internal structure of highly drawn polyethylene, Polymer, 41(23) (2000) 8291-8298.
[7]  C. G’sell, J. Jonas, Determination of the plastic behaviour of solid polymers at constant true strain rate, Journal of materials science, 14(3) (1979) 583-591.
[8]  C. G’sell, A. Dahoun, Evolution of microstructure in semi- crystalline polymers under large plastic deformation, Materials Science and Engineering: A, 175(1-2) (1994) 183-199.
[9]   M. Uchida, N. Tada, Sequential evaluation of continuous deformation field of semi-crystalline polymers during tensile deformation accompanied by neck propagation, International Journal of Plasticity, 27(12) (2011) 2085-2102.
[10]                    F.  ZaÃŊri,  M.  NaÃŊt-Abdelaziz,  K. Woznica, J.-M. Gloaguen, Elasto-viscoplastic  constitutive  equations for the description of glassy polymers behavior at constant strain rate, Journal of Engineering Materials and Technology, 129(1) (2007) 29-35.
[11]  S. Ahzi, A. Makradi, R. Gregory, D. Edie, Modeling of deformation behavior and strain-induced crystallization in poly (ethylene terephthalate) above the glass transition temperature, Mechanics of materials, 35(12) (2003) 1139-1148.
[12]  G. Ayoub, F. Zaïri, C. Fréderix, J.-M. Gloaguen, M. Naït- Abdelaziz, R. Seguela, J.-M. Lefebvre, Effects of crystal content on the mechanical behaviour of polyethylene under finite strains: experiments and constitutive modelling, International Journal of Plasticity, 27(4) (2011) 492-511.
[13]  G. Ayoub, F. Zaïri, M. Naït-Abdelaziz, J. Gloaguen, Modelling large deformation behaviour under loading– unloading of semicrystalline  polymers:  application  to a high density polyethylene, International Journal of Plasticity, 26(3) (2010) 329-347.
[14]  J. Richeton, S. Ahzi, K. Vecchio, F. Jiang, A. Makradi, Modeling and validation of the large deformation inelastic response of amorphous polymers over a wide range of temperatures and strain rates, International journal of solids and structures, 44(24) (2007) 7938-7954.
[15]  S. Nikolov, R. Lebensohn, D. Raabe, Self-consistent modeling of large plastic deformation, texture and morphology evolution in semi-crystalline polymers, Journal of the Mechanics and Physics of Solids, 54(7) (2006) 1350-1375.
[16]  M. Boyce, S. Socrate, P. Llana, Constitutive model for the finite deformation stress–strain behavior of poly (ethylene terephthalate) above the glass transition, Polymer, 41(6) (2000) 2183-2201.
[17]  B. Lee, A. Argon, D. Parks, S. Ahzi, Z. Bartczak, Simulation of large strain plastic deformation and texture evolution in high density polyethylene, Polymer, 34(17) (1993) 3555-3575.
[18]  B. Lee, D. Parks, S. Ahzi, Micromechanical modeling of large plastic deformation and texture evolution in semi-crystalline polymers, Journal of the Mechanics and Physics of Solids, 41(10) (1993) 1651-1687.
[19]    J.A. Alvarado-Contreras, M.A. Polak, A. Penlidis, Constitutive modeling of damage evolution in semicrystalline polyethylene, Journal of Engineering Materials and Technology, 132(4) (2010) 041009.
[20]   J. Lemaitre, How to use damage mechanics, Nuclear engineering and design, 80(2) (1984) 233-245.
[21]   C. Bunn, Molecular Structure and the Crystallinity of Long‐Chain Polymers, Journal of Applied Physics, 25(7) (1954) 820-825.
[22]    P. Bowden, R. Young, Deformation mechanisms in
crystalline polymers, Journal of Materials Science, 9(12) (1974) 2034-2051.
[23]     R. Seguela, Dislocation approach to the plastic deformation of semicrystalline polymers: kinetic aspects for polyethylene and polypropylene, Journal of Polymer Science Part B: Polymer Physics, 40(6) (2002) 593-601.
[24]   J. Hutchinson, Bounds and self-consistent estimates for creep of polycrystalline materials, in: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society, 1976, pp. 101-127.
[25]  S. Schoenfeld, S. Ahzi, R. Asaro, Elastic-plastic crystal mechanics for low symmetry crystals, Journal of the Mechanics and Physics of Solids, 43(3) (1995) 415-446.
[26] D.M. Parks, S. Ahzi, Polycrystalline plastic deformation and texture evolution for crystals lacking five independent slip systems, Journal of the Mechanics and Physics of Solids, 38(5) (1990) 701-724.
[27]     J.   Alvarado‐Contreras,   M.A.   Polak,   A.   Penlidis, Micromechanical approach to modeling damage in crystalline polyethylene, Polymer Engineering & Science, 47(4) (2007) 410-420.
[28]  J. Lemaitre, A course on damage mechanics, Springer Science & Business Media, 2012.
[29]  M.C. Boyce, E.M. Arruda, Constitutive models of rubber
elasticity: a review, Rubber chemistry and technology, 73(3) (2000) 504-523.
[30]  A. Cohen, A Padé approximant to the inverse Langevin function, Rheologica acta, 30(3) (1991) 270-273.
[31]  P. Fotiu, H. Irschik, F. Ziegler, Dynamic plasticity: structural drift and modal projections, Nonlinear
dynamics in engineering systems (Schiehlen, W., ed.), (1990) 75-82.
[32]  L.R.G. Treloar, The physics of rubber elasticity, Oxford University Press, USA, 1975.
[33] P.  Lequeu,  P.  Gilormini,  F.  Montheillet,  B. Bacroix, J.  Jonas,  Yield  surfaces  for  textured  polycrystals— I. Crystallographic approach, Acta Metallurgica, 35(2) (1987) 439-451.
[34]  J.J.  Craig,  Introduction  to  robotics:  mechanics  and control, Pearson Prentice Hall Upper Saddle River, 2005.
[35]  A. MORAWIEC, Orientations and Rotations. Computations in Crystallographic Textures. x+ 200 pp, in, Berlin, Heidelberg, New York: Springer-Verlag. Price Euros, 2004.
[36]  J. Alvarado-Contreras, M. Polak, A. Penlidis, Numerical implementation of a damage-coupled material law for semicrystalline polyethylene, Engineering Computations, 29(3) (2012) 295-320.
[37]  J. Simo, T.J. Hughes, Computational inelasticity, volume 7 of interdisciplinary applied mathematics, in, Springer-Verlag, Berlin, 1998.
[38]  J. Angeles, Rational kinematics, Springer Science & Business Media, 2013.
[39]  C. G’sell, J. Jonas, Yield and transient effects during the plastic deformation of solid polymers, Journal of Materials Science, 16(7) (1981) 1956-1974.