Abstract
A nonlinear chain breakage-and-reformation network theory is presented using a temporarily crosslinked network model. The main assumptions are as follows: (1) The number of segments in a polymer chain is constant; (2) a renewed segment is reformed in the stress free state; (3) the length of a segment is constant and (4) segments are Gaussian chains. Third assumption gives rise to the nonlinear theory. The constitutive equation is obtained as a natural extension of linear equation. The following predictions are obtained. The relaxation modulus is the product of the time dependent and strain dependent terms for both shear and elongation. At the onset of flow, the shear stress growth shows overshoot at high shear rate, but not the normal stress growth, the elongational stress grows monotonously and the elongational viscosity is nearly proportional to the inverse of the elongation rate.
Similar content being viewed by others
Article PDF
References
A. S. Lodge, Rheol. Acta, 7, 379 (1968).
A. S. Lodge, “Elastic Liquids,” Academic Press, New York, 1964.
J. L. White and A. B. Metzner, J. Polym. Sci., 7, 1867 (1963).
R. B. Bird, Chem. Eng. Prog. Symp. Sec., 58, 61 (1965).
T. W. Spriggs, Chem. Eng. Sci., 20, 931 (1965).
R. B. Bird and P. J. Carreau, Chem. Eng. Sci., 23, 437 (1968).
L. J. Zapas and J. C. Philps, J. Res. Nat. Bur. Stand., 75A, 93 (1971).
M. Yamamoto, J. Phys. Soc. Jpn., 25, 239 (1968).
M. Yamamoto, Appl. Polym. Symp., 23, 3 (1973).
M. Yamamoto, J. Soc. Mater. Sci. Jpn., 21, 355 (1972).
M. Yamamoto, Trans. Soc. Rheol., 15, 331 (1971).
M. Takahashi and S. Onogi, J. Soc. Rheol. Jpn., 2, 95 (1974).
M. Takahashi and S. Onogi, J. Soc. Rheol. Jpn., 3, 1 (1975).
T. W. Spriggs, J. D. Huppler, and R. B. Bird, Trans. Soc. Rheol., 10, 191 (1965).
M. Takahashi, T. Masuda, and S. Onogi, J. Soc. Rheol. Jpn., 1, 16 (1973).
K. Osaki, M. Fukuda, S. Ota, and M. Kurata, J. Soc. Rheol. Jpn., 2, 106 (1974).
M. Fukuda, K. Osaki, and M. Kurata, J. Soc. Rheol. Jpn., 2, 110 (1974).
Y. Einaga, K. Osaki, M. Kurata, S. Kimura, and M. Tamura, Polym. J., 2, 550 (1971).
Y. Einaga, K. Osaki, M. Kurata, S. Kimura, N. Yamada, and M. Tamura, Polym. J., 5, 91 (1973).
K. Osaki, Y. Einaga, M. Kurata, N. Yamada, and M. Tamura, Polym. J., 5, 283 (1973).
M. Yamamoto, “Mechanics of Body Deformation” (in Japanese), Seibundo Shinkosha Publishing Co., Tokyo, 1972.
R. B. Bird, R. C. Armstrong, and O. Hassager, “Dynamics of Polymer Liquids,” Vol. I, II, Wiley, New York, 1976.
G. Astarita and G. Marricci, “Principle of Non-Newtonian Fluid Mechanics,” McGraw-Hill, London, 1972.
A. S. Lodge, “Body Tensor Fields in Continum Mechanics,” Academic Press, New York, 1974.
W. W. Grassley, Adv. Polym. Sci., 16, 1 (1974).
M. Doi, Kobunshi, 27, 649 (1978).
M. Doi, Physique, 36, 607 (1975).
M. Doi and S. F. Edwards, J. Chem. Soc., Faraday Trans. 2, 74, 560, (1978).
M. Doi and S. F. Edwards, J. Chem. Soc., Faraday Trans. 2, 74, 918, (1978).
M. Doi and S. F. Edwards, J. Chem. Soc., Faraday Trans. 2, 74, 1802 (1978).
M. Doi and S. F. Edwards, J. Chem. Soc., Faraday Trans. 2, 75, 38, (1979).
M. Yamamoto, J. Phys. Soc. Jpn., 11, 413 (1956).
M. Yamamoto, J. Phys. Soc. Jpn., 12, 1148 (1957).
M. Yamamoto, J. Phys. Soc. Jpn., 13, 1200 (1958).
A. S. Lodge, Trans. Faraday Soc., 52, 120 (1959).
K. W. Scott and R. S. Stein, J. Chem. Phys., 21, 1281 (1959).
S. Hayashi, Prog. Theor. Phys., Suppl., 10, 82 (1959).
S. Hayashi, J. Phys. Soc. Jpn., 18, 131 (1963).
S. Hayashi, J. Phys. Soc. Jpn., 19, 101 (1964).
S. Hayashi and Y. Takano, J. Phys. Soc. Jpn., 23, 1063 (1967).
Y. Takano, Polym. J., 6, 61 (1974).
Y. Takano, J. Soc. Rheol. Jpn., 2, 87 (1974).
S. Hayashi, J. Soc. Rheol. Jpn., 3, 159 (1975).
S. Hayashi, Polym. J., 10, 59 (1978).
S. Hayashi, Polym. J., 13, 693 (1981).
S. Hayashi, J. Macromol. Sci., Phys., B19, 632 (1981).
N. E. Hudson and J. Ferguson, Trans. Soc. Rheol., 20, 265 (1976).
H. Munstedt, Trans. Soc. Rheol., 23, 421 (1979).
R. N. Shroff, L. V. Vacio, and M. Shida, Trans. Soc. Rheol., 21, 429 (1977).
R. S. Stratton, J. Colloid Sci., 22, 517 (1966).
J. Meissner, Rheol. Acta, 10, 230 (1971).
S. Hayashi, Rep. Prog. Polym. Phys. Jpn., 21, 97 (1978).
S. Hayashi, Rep. Prog. Polym. Phys. Jpn., 23, 113 (1980).
S. Hayashi, Rep. Prog. Polym. Phys. Jpn., 26, 95, (1983).
S. Hayashi, Rep. Prog. Polym. Phys. Jpn., 26, 99 (1983).
J. D. Huppler, I. F. Macdonald, E. Ashare, T. W. Spriggs, R. B. Bird, and L. A. Holmes, Trans. Soc. Rheol., 11, 181 (1967).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hayashi, S. Theory of Nonlinear Viscoelasticity in Temporarily Crosslinked Polymer Systems. Polym J 17, 597–606 (1985). https://doi.org/10.1295/polymj.17.597
Issue Date:
DOI: https://doi.org/10.1295/polymj.17.597