Abstract
Free surface moulding processes such as thermoforming and blow moulding involve thermal and spatial varying rate dependent biaxial deformation of polymer. These processes are so rapid that the entire forming took place in a matter of seconds. As a result of the elevated rate of deformation, assumption that the deforming polymers experience no time dependent viscous dissipation or perfectly elastic up to large strain has became a common practice in numerical simulation. Following the above assumption, Cauchy’s elastic and hyperelastic theories, originally developed for vulcanised natural rubber has been widely used to represent deforming polymeric materials in free surface moulding processes. To date, various methodologies were applied in the development of these theories, the most significant are those develop purely based on mathematical interpolation (mathematical models) and a more scientific network theories that involves the interpretation of macro-molecular structure within the polymer. In this chapter, the most frequently quoted Cauchy’s elastic and hyperelastic theories, including Ogden, Mooney–Rivlin, neo-Hookean, 3-chain, 8-chain, Van der Waals full network, Ball’s tube model, Edwards–Vilgis crosslinks-sliplinks model and the elastic model of Sweeney–Ward are reviewed. These models were analysed and fitted to a series of experimental high strain rate, high temperature, biaxial deformations data of polypropylene (PP) and high impact polystyrene (HIPS). The performance and suitability of the various models in capturing the polymer’s complex deformation behaviour during free surface moulding processes is presented.
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References
Hooke, R., De Potentia Restitutiva or of Spring Explaining the Power of Springing Bodies, p. 23. London (1678)
Markovitz, H.: The emergency of rheology. Physics Today (American Institute of Physics) 21(4), 23–33 (1968)
Truesdell, C.A., Cauchy’s First Attempt at Molecular Theory of Elasticity, Bollettino di Storia delle Scienze Matematiche. Il Giardino di Archimede 1(2), 133–143 (1981)
Bogolyubov, A.N., Augustin Cauchy and His Contribution to Mechanics and Physics (Russian), Studies in the History of Physics and Mechanics, pp. 179–201. Nauka, Moscow (1988)
Dahan-Dalmédico, A., La Propagation Des Ondes En Eau Profonde Et Ses Développements Mathématiques (Poisson, Cauchy, 1815–1825), in The History of Modern Mathematics II, pp. 129–168. Boston, MA (1989)
Truesdell, C.A.: Cauchy and the modern mechanics of continua. Rev. Hist. Sci. 45(1), 5–24 (1992)
Mooney, M.: A theory of large elastic deformation. J. Appl. Phys. 11(9), 582–592 (1940)
Rivlin, R.S.: Large elastic deformations of isotropic materials, I, II, III, fundamental concepts. Philos. Trans. R. Soc. Lond. Ser. A 240, 459–525 (1948)
Rivlin, R.S.: Large elastic deformations of isotropic materials, IV, further developments of the general theory. Philos. Trans. R. Soc. Lond. Ser. A 241(835), 375–397 (1948)
Ogden, R.W., Large deformation isotropic elasticity: on the correlation of theory and experiment for incompressible rubberlike solids. In: Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, vol. 365, pp. 565–584 (1972)
Treloar, L.R.G.: Stress-strain data for vulcanized rubber under various types of deformation. Trans. Faraday Soc. 40, 59–70 (1944)
Ward, I.M., Mechanical Properties of Solid Polymers, 2nd edn. Wiley, Hoboken (1983)
Treloar, L.R.G.: The elasticity of a network of long chain molecules I. Trans. Faraday Soc. 39, 36–64 (1943)
Treloar, L.R.G.: The elasticity of a network of long chain molecules II. Trans. Faraday Soc. 39, 241–246 (1943)
Kuhn, W., Grun, F.: Beziehungen zwichen elastischen Konstanten und Dehnungsdoppelbrechung hochelastischer stoffe. Kolloideitschrift 101, 248–271 (1942)
James, H.M., Guth, E.: Theory of elastic properties of rubber. J. Chem. Phys. 11(10), 455–481 (1943)
Wang, M.C., Guth, E.: Statistical theory of networks of non-gaussian flexible chains. J. Chem. Phys. 20, 1144–1157 (1952)
Arruda, E.M., Boyce, M.C.: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41(2), 389–412 (1993)
Treloar, L.R.G., Riding, G., A non-gaussian theory for rubber in biaxial strain I, mechanical properties. In: Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, vol. 369, pp. 261–280 (1979)
Wu, P.D., Van der Giessen, E.: On improved 3-D non-Gaussian network models for rubber elasticity. Mech. Res. Commun. 19(5), 427–433 (1992)
Wu, P.D., Van der Giessen, E.: On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers. J. Mech. Phys. Solids 41(3), 427–456 (1993)
Flory, P.J., Erman, B.: Theory of elasticity of polymer networks. Macromolecules 15(3), 800–806 (1982)
Ball, R.C., Doi, M., Edwards, S.F., Warner, M.: Elasticity of entangled networks. Polymer 22(8), 1010–1018 (1981)
Doi, M., Edwards, S.F.: The theory of polymer dynamics. Oxford University Press, Oxford (1986)
Kilian, H.G.: Equation of state of real networks. Polymer 22, 209–217 (1981)
Kilian, H.G.: Energy balance in networks simply elongated at constant temperature. Colloid Polym. Sci. 259, 1084–1091 (1981)
Vilgis, T.H., Kilian, H.G.: The van der waals-network—a phenomenological approach to dense networks. Polymer 25, 71–74 (1984)
Kilian, H.G., Vilgis, T.H.: Fundamental aspects of rubber-elasticity in real networks. Colloid Polym. Sci. 262, 15–21 (1984)
Kilian, H.G.: An interpretation of the strain-invariants in largely strained networks. Colloid Polym. Sci. 263, 30–34 (1985)
Edwards, S.F., Vilgis, T.H.: The effect of entanglements in rubber elasticity. Polymer 27(4), 483–492 (1986)
Edwards, S.F., Vilgis, T.H.: The stress-strain relationship in polymer glasses. Polymer 28(3), 375–378 (1987)
Rouse, P.E.: A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 21, 1272–1280 (1953)
Flory, P.J.: Principles of Polymer Chemistry. Cornell University Press, New York (1966)
Flory, P.J.: Theory of Polymer Networks. The Effect of Local Constraints on Junctions. J. Chem. Phys. 66(12), 5720 (1977)
Sweeney, J., Ward, I.M.: The modeling of multiaxial necking in polypropylene using a sliplink-crosslink theory. J. Rheol. 39(5), 861–872 (1995)
Sweeney, J., Kakadjian, S., Craggs, G., Ward, I.M., The multiaxial stretching of polypropylene at high temperatures. In: ASME Mechanics of Plastics and Plastic Composites, MD vol. 68 / AMD vol. 215 pp. 357–364 (1995)
Sweeney, J., Ward, I.M.: A constitutive law for large deformations of polymers at high temperatures. J. Mech. Phys. Solids 44(7), 1033–1049 (1996)
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Tshai, K.Y., Harkin-Jones, E.M.A., Martin, P.J. (2014). Performance of Hyperelastic Material Laws in Simulating Biaxial Deformation Response of Polypropylene and High Impact Polystyrene. In: Bonora, N., Brown, E. (eds) Numerical Modeling of Materials Under Extreme Conditions. Advanced Structured Materials, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54258-9_9
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