Summary
Constitutive equations are derived for nonisothermal loading of glassy polymers at finite strains. The model is based on the theory of temporary networks in a version of the concept of adaptive links. The specific mechanical energy of a temporary network is determined with account for the potential energies of deformation for individual links and the energy of interaction between them. Stress-strain relations and a differential equation for the evolution of temperature are obtained using the laws of thermodynamics. As examples, we study uniaxial extension of a bar and simple shear of a layer. Explicit formulas are derived for the temperature drops prior to necking of specimens. Good agreement is demonstrated between experimental data for polycarbonate at room temperature and predictions of the model.
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References
Liu, T.-M., Harrison, I. R.: Thermal effects in the necking of polymers. Polym. Eng. Sci.27, 1399–1402 (1987).
Zhou, Z., Chudnovsky, A., Bosnyak, C. P., Sehanobish, K.: Cold-drawing (necking) behavior of polycarbonate as a double glass transition. Polym. Eng. Sci.35, 304–309 (1995).
Matsuoka, S., Bair, H. E.: The temperature drop in glassy polymers during deformation. J. Appl. Phys.48, 4058–4062 (1977).
Struik, L. C. E.: Physical ageing in amorphous polymers and other materials. Amsterdam: Elsevier 1978.
Tant, M. R., Wilkes, G. L.: An overview of the nonequilibrium behavior of polymer glasses. Polym. Eng. Sci.21, 874–895 (1981).
Santore, M. M., Duran, R. S., McKenna, G. B.: Volume recovery in epoxy glasses subjected to torsional deformations: the question of rejuvenation. Polymer32, 2377–2381 (1991).
Struik, L. C. E.: On the rejuvenation of physically aged polymers by mechanical deformation. Polymer38, 4053–4057 (1997).
McKenna, G. B.: Dilatometric evidence for the apparent decoupling of glassy structure from the mechanical stress field. J. Non-Cryst. Solids172-174, 756–764 (1994).
McKenna, G. B., Leterrier, Y., Schultheisz, C. R.: The evolution of material properties during physical aging. Polym. Eng. Sci.35, 403–410 (1995).
Colucci, D. M., O'Connell, P. A., McKenna, G. B.: Stress relaxation experiments in polycarbonate: a comparison of volume changes for two commercial grades. Polym. Eng. Sci.37, 1469–1474 (1997).
Green, M. S., Tobolsky, A. V.: A new approach to the theory of relaxing polymeric media. J. Chem. Phys.14, 80–92 (1946).
Yamamoto, M.: The visco-elastic properties of network structure. 1. General formalism. J. Phys. Soc. Japan11, 413–421 (1956).
Lodge, A. S.: Constitutive equations from molecular network theories for polymer solutions. Rheol. Acta7, 379–392 (1968).
Tanaka, F., Edwards, S. F.: Viscoelastic properties of physically cross-linked networks. Transient network theory. Macromolecules25, 1516–1523 (1992).
Drozdov, A. D.: On constitutive laws for ageing viscoelastic materials at finite strains. Eur. J. Mech. A/Solids12, 305–324 (1993).
Drozdov, A. D.: A model of adaptive links for aging viscoelastic media. J. Rheol.,40, 741–759 (1996).
Drozdov, A. D.: A constitutive model for nonlinear viscoelastic media. Int. J. Solids Structures34, 2685–2707 (1997).
Drozdov, A. D.: A model of adaptive links in nonlinear viscoelasticity. J. Rheol.41, 1223–1245 (1997).
Drozdov, A. D.: A model for the nonlinear viscoelastic response in polymers at finite strains. Int. J. Solids Structures35, 2315–2347 (1998).
Drozdov, A. D.: Mechanics of viscoelastic solids. Chichester: Wiley 1998.
Treloar, L. R. G.: The physics of rubber elasticity. Oxford: Clarendon 1975.
Petruccione, F., Biller, P.: A numerical stochastic approach to network theories of polymeric fluids. J. Chem. Phys.89, 577–582 (1988).
Petruccione, F., Biller, P.: Rheological properties of network models with configuration-dependent creation and loss rates. Rheol. Acta27, 557–560 (1988).
Drozdov, A. D.: Finite elasticity and viscoelasticity. Singapore: World Scientific 1996.
Coleman, B. D., Gurtin, M. E.: Thermodynamics with internal state variables. J. Chem. Phys.47, 597–613 (1967).
Lu, H., Zhang, X., Knauss, W. G.: Uniaxial, shear, and Poisson relaxation and their conversion to bulk relaxation: studies on poly(methyl methacrylate). Polym. Eng. Sci.37, 1053–1064 (1997).
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Drozdov, A.D. The temperature drops in glassy polymers while strained. Acta Mechanica 139, 171–199 (2000). https://doi.org/10.1007/BF01170189
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DOI: https://doi.org/10.1007/BF01170189