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International Journal of Material Forming

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23-07-2016 | Original Research

Numerical implementation of an elastic-viscoplastic constitutive model to simulate the mechanical behaviour of amorphous polymers

Authors: C. A. Bernard, J. P. M. Correia, Said Ahzi, N. Bahlouli

Published in: International Journal of Material Forming | Issue 4/2017

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Abstract

Due to their high deformation capabilities, polymeric materials are widely used in several industries. However, polymers exhibit a complex behaviour with strain rate, temperature and pressure dependencies. Numerous constitutive models were developed in order to take into account their specific behaviour. Among these models, the ones proposed by Richeton et al Polymer 46:6035–6043 (2005a), Polymer 46:8194–8201 (2005b) seem to be particularly suitable. They proposed expressions for the Young modulus and the yield stress with strain rate and temperature dependence. Moreover, these models were also implemented in a finite elastic-viscoplastic deformation approach using a flow rule based on thermally activated process. The increase of computational capabilities allowed simulating polymer forming processes using finite element (FE) codes. The aim of the study is to implement the proposed constitutive model in a commercial FE code via a user material subroutine. The implementation of the model was verified using compressive tests over a wide range of strain rates. Next, FE simulations of an impact test and of a plane strain forging process were carried out. The FE predictions are in good agreement with the experimental results taken from the literature.

previous article Experimental prediction of sheet metal formability of AW-5754 for non-linear strain paths by using a cruciform specimen and a blank holder with adjustable draw beads on a sheet metal testing machine

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Wu H, Ma G, Xia Y (2004) Experimental study of tensile properties of PMMA at intermediate strain rate. Mater Lett 58:3681–3685. doi:10.1016/j.matlet.2004.07.022 CrossRef

Richeton J, Ahzi S, Vecchio KS, et al. (2006) Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: characterization and modeling of the compressive yield stress. Int J Solids Struct 43:2318–2335. doi:10.1016/j.ijsolstr.2005.06.040 CrossRef

Forquin P, Nasraoui M, Rusinek A, Siad L (2012) Experimental study of the confined behaviour of PMMA under quasi-static and dynamic loadings. Int. J. Impact Eng. 40–41:46–57. doi:10.1016/j.ijimpeng.2011.09.007 CrossRef

Makradi A, Belouettar S, Ahzi S, Puissant S (2007) Thermoforming process of amorphous polymeric sheets: modeling and finite element simulations. J Appl Polym Sci 106:1718–1724. doi:10.1002/app.26869 CrossRef

O’Connor CPJ, Martin PJ, Sweeney J, et al. (2013) Simulation of the plug-assisted thermoforming of polypropylene using a large strain thermally coupled constitutive model. J Mater Process Technol 213:1588–1600. doi:10.1016/j.jmatprotec.2013.02.001 CrossRef

Jeridi M, Chouchene H, Keryvin V, Saï K (2014) Multi-mechanism modeling of amorphous polymers. Mech Res Commun 56:136–142. doi:10.1016/j.mechrescom.2014.01.003 CrossRef

Mulliken AD, Boyce MC (2006) Mechanics of the rate-dependent elastic–plastic deformation of glassy polymers from low to high strain rates. Int J Solids Struct 43:1331–1356. doi:10.1016/j.ijsolstr.2005.04.016 CrossRefMATH

Fleischhauer R, Dal H, Kaliske M, Schneider K (2012) A constitutive model for finite deformation of amorphous polymers. Int J Mech Sci 65:48–63. doi:10.1016/j.ijmecsci.2012.09.003 CrossRef

Dar U, Zhang W, Xu Y (2014) Numerical implementation of strain rate dependent thermo viscoelastic constitutive relation to simulate the mechanical behavior of PMMA. Int J Mech Mater Des 10:93–107. doi:10.1007/s10999-013-9233-y CrossRef

10.

Bouvard JL, Ward DK, Hossain D, et al. (2010) A general inelastic internal state variable model for amorphous glassy polymers. Acta Mech 213:71–96. doi:10.1007/s00707-010-0349-y CrossRefMATH

11.

Boyce MC, Parks DM, Argon AS (1988) Large inelastic deformation of glassy polymers. Part I: rate dependent constitutive model. Mech Mater 7:15–33. doi:10.1016/0167-6636(88)90003-8 CrossRef

12.

Anand L, Gurtin ME (2003) A theory of amorphous solids undergoing large deformations, with application to polymeric glasses. Int J Solids Struct 40:1465–1487. doi:10.1016/S0020-7683(02)00651-0 CrossRefMATH

13.

Anand L, Ames NM, Srivastava V, Chester SA (2009) A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part I: Formulation Int J Plasticity 25:1474–1494. doi:10.1016/j.ijplas.2008.11.004 MATH

14.

Ames NM, Srivastava V, Chester SA, Anand L (2009) A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part II: Applications Int J Plasticity 25:1495–1539. doi:10.1016/j.ijplas.2008.11.005 MATH

15.

Miehe C, Göktepe S, Méndez Diez J (2009) Finite viscoplasticity of amorphous glassy polymers in the logarithmic strain space. Int J Solids Struct 46:181–202. doi:10.1016/j.ijsolstr.2008.08.029 CrossRefMATH

16.

Danielsson M (2013) A stress update algorithm for constitutive models of glassy polymers. Int. J. Comput. Methods Eng. Sci. Mech. 14:336–342. doi:10.1080/15502287.2012.756955 MathSciNetCrossRef

17.

Richeton J, Ahzi S, Daridon L, Rémond Y (2005) A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures. Polymer 46:6035–6043. doi:10.1016/j.polymer.2005.05.079 CrossRef

18.

Richeton J, Schlatter G, Vecchio KS, et al. (2005) A unified model for stiffness modulus of amorphous polymers across transition temperatures and strain rates. Polymer 46:8194–8201. doi:10.1016/j.polymer.2005.06.103 CrossRef

19.

Richeton J, Ahzi S, Vecchio KS, et al. (2007) Modeling and validation of the large deformation inelastic response of amorphous polymers over a wide range of temperatures and strain rates. Int J Solids Struct 44:7938–7954. doi:10.1016/j.ijsolstr.2007.05.018 CrossRefMATH

20.

Fotheringham D, Cherry BW (1976) Comment on “the compression yield behaviour of polymethyl methacrylate over a wide range of temperatures and strain-rates. J Mater Sci 11:1368–1371. doi:10.1007/BF00545162 CrossRef

21.

Simulia (2007) ABAQUS/explicit users manual. Providence, RI, USA

22.

Mahieux C, Reifsnider K (2001) Property modeling across transition temperatures in polymers: a robust stiffness–temperature model. Polymer 42:3281–3291. doi:10.1016/S0032-3861(00)00614-5 CrossRef

23.

Mahieux CA, Reifsnider KL (2002) Property modeling across transition temperatures in polymers: application to thermoplastic systems. J Mater Sci 37:911–920. doi:10.1023/A:1014383427444 CrossRef

24.

Williams ML, Landel RF, Ferry JD (1955) The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J Am Chem Soc 77:3701–3707. doi:10.1021/ja01619a008 CrossRef

25.

Greaves GN, Greer AL, Lakes RS, Rouxel T (2011) Poisson’s ratio and modern materials. Nat Mater 10:823–837. doi:10.1038/nmat3134 CrossRef

26.

Mott PH, Dorgan JR, Roland CM (2008) The bulk modulus and Poisson’s ratio of “incompressible” materials. J Sound Vib 312:572–575. doi:10.1016/j.jsv.2008.01.026 CrossRef

27.

Pandini S, Pegoretti A (2008) Time, temperature, and strain effects on viscoelastic Poisson’s ratio of epoxy resins. Polym Eng Sci 48:1434–1441. doi:10.1002/pen.21060 CrossRef

28.

Pandini S, Pegoretti A (2011) Time and temperature effects on Poisson’s ratio of poly(butylene terephthalate). Express Polym Lett 5:685–697. doi:10.3144/expresspolymlett.2011.67 CrossRef

29.

Arruda EM, Boyce MC, Jayachandran R (1995) Effects of strain rate, temperature and thermomechanical coupling on the finite strain deformation of glassy polymers. Mech Mater 19:193–212. doi:10.1016/0167-6636(94)00034-E CrossRef

30.

Arruda EM, Boyce MC (1993) A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41:389–412. doi:10.1016/0022-5096(93)90013-6 CrossRefMATH

31.

Cohen A (1991) A Padé approximant to the inverse Langevin function. Rheol Acta 30:270–273. doi:10.1007/BF00366640 CrossRef

32.

Van Krevelen DW, Te Nijenhuis K (2009) Properties of polymers: their correlation with chemical structure; their numerical estimation and prediction from additive group contributions. Elsevier

33.

Bicerano J (2002) Prediction of polymer properties. CRC Press, USACrossRef

34.

Boyce MC (1986) Large inelastic deformation of glassy polymers. Massachusetts Institute of Technology, Cambridge

35.

Srivastava V, Chester SA, Ames NM, Anand L (2010) A thermo-mechanically-coupled large-deformation theory for amorphous polymers in a temperature range which spans their glass transition. Int J Plast 26:1138–1182. doi:10.1016/j.ijplas.2010.01.004 CrossRefMATH

36.

Garg M, Mulliken AD, Boyce MC (2008) Temperature rise in polymeric materials during high rate deformation. J Appl Mech 75:1–8CrossRef

37.

Furmanski J, Cady CM, Brown EN (2013) Time–temperature equivalence and adiabatic heating at large strains in high density polyethylene and ultrahigh molecular weight polyethylene. Polymer 54:381–390. doi:10.1016/j.polymer.2012.11.010 CrossRef

Title: Numerical implementation of an elastic-viscoplastic constitutive model to simulate the mechanical behaviour of amorphous polymers
Authors: C. A. Bernard
J. P. M. Correia
Said Ahzi
N. Bahlouli
Publication date: 23-07-2016
Publisher: Springer Paris
Published in: International Journal of Material Forming / Issue 4/2017
Print ISSN: 1960-6206
Electronic ISSN: 1960-6214
DOI: https://doi.org/10.1007/s12289-016-1305-8

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