Abstract
Adequacy of a material model that is based on isothermal properties becomes questionable for non-isothermal cases such as polymer processing which includes continuous change in temperature and rate. For true prediction of thermomechanical response of amorphous polymers under non-isothermal conditions, it is necessary to formulate temperature-dependent material properties and flow rules to provide a smooth transition around glass transition temperature.
An improved version of dual-mechanism viscoplastic constitutive model is presented that is used to describe thermomechanical response of amorphous polymers below and above glass transition temperature. Material property definitions, evolution of internal state variables, and plastic flow rules were revisited to provide a smooth and continuous transition in material response around glass transition temperature, θ g . The elastic-viscoplastic constitutive model is developed based on a thermodynamics framework. For damage evolution in complex thermomechanical problems such as polymer processing, irreversible entropy production rate is used as a damage metric [a.k.a Basaran Damage Evolution Model].
References
N.M. Ames et al., A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part II: applications. Int. J. Plast. 25(8), 1495–1539 (2009)
L. Anand, Moderate deformations in extension-torsion of incompressible isotropic elastic materials. J. Mech. Phys. Solids 34, 293–304 (1986)
L. Anand, H. On, Hencky’s approximate strain-energy function for moderate deformations. J. Appl. Mech. 46, 78–82 (1979)
L. Anand et al., A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part I: formulation. Int. J. Plast. 25(8), 1474–1494 (2009)
N. Aravas, Finite-strain anisotropic plasticity and the plastic spin. Model. Simul. Mater. Sci. Eng. 2(3A), 483–504 (1994)
E.M. Arruda, M.C. Boyce, Evolution of plastic anisotropy in amorphous polymers during finite straining. Int. J. Plast. 9(6), 697–720 (1993)
E.M. Arruda, M.C. Boyce, R. Jayachandran, Effects of strain rate, temperature and thermomechanical coupling on the finite strain deformation of glassy polymers. Mech. Mater. 19(2–3), 193–212 (1995)
C. Basaran, M. Lin, Damage mechanics of electromigration induced failure. Mech. Mater. 40(1–2), 66–79 (2007)
C. Basaran, S. Nie, A thermodynamics based damage mechanics model for particulate composites. Int. J. Solids Struct. 44(3–4), 1099–1114 (2007)
C. Basaran, C.Y. Yan, A thermodynamic framework for damage mechanics of solder joints. J. Electron. Packag. 120(4), 379–384 (1998)
C. Bauwens-Crowet, J.C. Bauwens, G. Homès, Tensile yield-stress behavior of glassy polymers. J. Polym. Sci. Part A-2 Polym. Phys. 7(4), 735–742 (1969)
J.S. Bergström, M.C. Boyce, Constitutive modeling of the large strain time-dependent behavior of elastomers. J. Mech. Phys. Solids 46(5), 931–954 (1998)
L. Boltzmann, Lectures on Gas Theory (Dover, New York, 1995)
M.C. Boyce, S. Socrate, P.G. Llana, Constitutive model for the finite deformation stress–strain behavior of poly(ethylene terephthalate) above the glass transition. Polymer 41(6), 2183–2201 (2000)
A. Chudnovsky et al., in On Fracture of Solids in Studies on Elasticity and Plasticity, ed. by L. Kachanov (Leningrad University Press, Leningrad, 1973), pp. 3–41
A.C. Eringen, Mechanics of Continua (Wiley, New York, 1967)
D.G. Fotheringham, B.W. Cherry, The role of recovery forces in the deformation of linear polyethylene. J. Mater. Sci. 13(5), 951–964 (1978)
D. Fotheringham, B.W. Cherry, C. Bauwens-Crowet, Comment on “the compression yield behaviour of polymethyl methacrylate over a wide range of temperatures and strain-rates”. J. Mater. Sci. 11(7), 1368–1371 (1976)
P. Francisco, S. Gustavo, B.H. Élida, Temperature and strain rate dependence of the tensile yield stress of PVC. J. Appl. Polym. Sci. 61(1), 109–117 (1996)
A.N. Gent, A new constitutive relation for rubber. Rubber Chem. Technol. 69(1), 59–61 (1996)
J. Gomez, C. Basaran, Damage mechanics constitutive model for Pb/Sn solder joints incorporating nonlinear kinematic hardening and rate dependent effects using a return mapping integration algorithm. Mech. Mater. 38(7), 585–598 (2006)
L.M. Kachanov, Introduction to continuum damage mechanics (M. Nijhoff, Dordrecht/Boston, 1986)
E. Kontou, G. Spathis, Application of finite strain viscoplasticity to polymeric fiber composites. Int. J. Plast. 22(7), 1287–1303 (2006)
E. Kröner, Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Arch. Ration. Mech. Anal. 4(1), 273–334 (1959)
E.H. Lee, Elastic–plastic deformation at finite strains. J. Appl. Mech. 36, 1–6 (1969)
J. Mandel, Plasticite Classique et Viscoplasticite (Lecture Notes) (International Center for Mechanical Sciences, Udine, 1972)
G. Palm, R.B. Dupaix, J. Castro, Large strain mechanical behavior of poly(methyl methacrylate) (PMMA) near the glass transition temperature. J. Eng. Mater. Technol. 128(4), 559–563 (2006)
F. Povolo, B.H. Élida, Phenomenological description of strain rate and temperature-dependent yield stress of PMMA. J. Appl. Polym. Sci. 58(1), 55–68 (1995)
J. Richeton et al., A formulation of the cooperative model for the yield stress of amorphous polymers for a wide range of strain rates and temperatures. Polymer 46(16), 6035–6043 (2005a)
J. Richeton et al., A unified model for stiffness modulus of amorphous polymers across transition temperatures and strain rates. Polymer 46(19), 8194–8201 (2005b)
J. Richeton et al., 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(7–8), 2318–2335 (2006)
J. Richeton et al., 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(24), 7938–7954 (2007)
V. Srivastava et al., A thermo-mechanically-coupled large-deformation theory for amorphous polymers in a temperature range which spans their glass transition. Int. J. Plast. 26(8), 1138–1182 (2010)
J. Sweeney et al., Application of an elastic model to the large deformation, high temperature stretching of polypropylene. Polymer 38(24), 5991–5999 (1997)
C. Truesdell, The Non-linear Field Theories of Mechanics, 3rd edn. (Springer, New York, 2004)
M. Wallin, M. Ristinmaa, Deformation gradient based kinematic hardening model. Int. J. Plast. 21(10), 2025–2050 (2005)
M.L. Williams, R.F. Landel, J.D. Ferry, The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc. 77(14), 3701–3707 (1955)
H. Ye, C. Basaran, D.C. Hopkins, Damage mechanics of microelectronics solder joints under high current densities. Int. J. Solids Struct. 40(15), 4021–4032 (2003)
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Basaran, C., Gunel, E. (2014). Damage Mechanics Unified Constitutive Modeling for Polymers. In: Voyiadjis, G. (eds) Handbook of Damage Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8968-9_28-1
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DOI: https://doi.org/10.1007/978-1-4614-8968-9_28-1
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