journal article·2017-08

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

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

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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.
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Research context

OpenAlex topics: Polymer crystallization and properties · Rheology and Fluid Dynamics Studies · Mechanical Behavior of Composites

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References (37)

Show source-provided references
1. 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.2004.07.02210.1016/j.matlet.2004.07.022 ↗
2. 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.2005.06.04010.1016/j.ijsolstr.2005.06.040 ↗
3. 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.2011.09.00710.1016/j.ijimpeng.2011.09.007 ↗
4. 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.2686910.1002/app.26869 ↗
5. 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.2013.02.00110.1016/j.jmatprotec.2013.02.001 ↗
6. 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.2014.01.00310.1016/j.mechrescom.2014.01.003 ↗
7. 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.2005.04.01610.1016/j.ijsolstr.2005.04.016 ↗
8. 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.2012.09.00310.1016/j.ijmecsci.2012.09.003 ↗
9. 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-y10.1007/s10999-013-9233-y ↗
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-y10.1007/s00707-010-0349-y ↗
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)90003-810.1016/0167-6636(88)90003-8 ↗
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)00651-010.1016/S0020-7683(02)00651-0 ↗
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.2008.11.00410.1016/j.ijplas.2008.11.004 ↗
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.2008.11.00510.1016/j.ijplas.2008.11.005 ↗
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.2008.08.02910.1016/j.ijsolstr.2008.08.029 ↗
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: 10.1080/15502287.2012.75695510.1080/15502287.2012.756955 ↗
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.2005.05.07910.1016/j.polymer.2005.05.079 ↗
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.2005.06.10310.1016/j.polymer.2005.06.103 ↗
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.2007.05.01810.1016/j.ijsolstr.2007.05.018 ↗
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/BF0054516210.1007/BF00545162 ↗
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)00614-510.1016/S0032-3861(00)00614-5 ↗
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:101438342744410.1023/A:1014383427444 ↗
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/ja01619a00810.1021/ja01619a008 ↗
25. Greaves GN, Greer AL, Lakes RS, Rouxel T (2011) Poisson’s ratio and modern materials. Nat Mater 10:823–837. doi: 10.1038/nmat313410.1038/nmat3134 ↗
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.2008.01.02610.1016/j.jsv.2008.01.026 ↗
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.2106010.1002/pen.21060 ↗
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.2011.6710.3144/expresspolymlett.2011.67 ↗
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-E10.1016/0167-6636(94)00034-E ↗
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)90013-610.1016/0022-5096(93)90013-6 ↗
31. Cohen A (1991) A Padé approximant to the inverse Langevin function. Rheol Acta 30:270–273. doi: 10.1007/BF0036664010.1007/BF00366640 ↗
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. Elsevier10.1016/B978-0-08-054819-7.00001-7 ↗
33. Bicerano J (2002) Prediction of polymer properties. CRC Press, USA10.1201/9780203910115 ↗
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.2010.01.00410.1016/j.ijplas.2010.01.004 ↗
36. Garg M, Mulliken AD, Boyce MC (2008) Temperature rise in polymeric materials during high rate deformation. J Appl Mech 75:1–810.1115/1.2745388 ↗
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.2012.11.01010.1016/j.polymer.2012.11.010 ↗