On oscillatory necking in polymers
Authors:
B. J. Matkowsky and G. I. Sivashinsky
Journal:
Quart. Appl. Math. 37 (1979), 23-34
DOI:
https://doi.org/10.1090/qam/99637
MathSciNet review:
QAM99637
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Abstract: The phenomenon of oscillatory necking in the stretching of polyethylene films is described. We propose an extension of a model of Barenblatt for isothermic necking in polymers, and we show that oscillatory necking may arise, for example, in polymers for which the effect of diffusion of stresses exceeds that of diffusion of oriented material. In such polymers, at sufficiently low temperatures, uniform necking is no longer stable and self-oscillations are observed.
W. H. Carothers and J. W. Hill, Studies of polymerization and ring formation. XV. Artificial fiber from synthetic linear condensation superpolymers, J. Amer. Chem. Soc. 54, N4 (1932)
A. Nadai, Theory of flow and fractures of solids, McGraw-Hill N. Y., Toronto, London (1952)
- G. I. Barenblatt, On some general concepts of the mathematical theory of brittle fracture, J. Appl. Math. Mech. 28 (1964), 778–792. MR 0184492, DOI https://doi.org/10.1016/0021-8928%2864%2990063-2
G. I. Barenblatt, Isothermal propagation of a neck in polymers, Mechanics of Solids (MMT) N6, 89–96 (1972)
Y. B. Zeldovich, Theory of flame propagation, Zh. Fiz. Khim. 22, no. 1 (1948) (in Russian)
Yu. S. Lazurkin, Cold-drawing of glass-like and crystalline polymers, J. Polymer Sci. 30, no. 121 (1958)
P. J. Vincent, The necking and cold drawing of rigid plastics, Polymer 1, no. 1 (1960)
G. P. Andrianova, V. A. Kargin and A. S. Kechekyan, Periodic oscillations in extension of polyethylene terephtalate, J. Macromolecular Compounds (Vysokomolekulyarnye Soedineniya) 12, no. 8, 1970 (in Russian)
Ya. B. Zel’dovich and G. I. Barenblatt, Theory of flame propagation, Combustion and Flame 3, 61–74 (1959)
G. I. Barenblatt, Self-oscillatory propagation of a neck in polymers, Mechanics of Solids (MMT) N5, 110–118 (1970)
G. I. Sivashinsky, The structure of Bunsen flames, J. Chem. Physics, 62, 638–643 (1975)
G. I. Sivashinsky, The diffusion stratification effect in Bunsen flames, J. Heat Transfer, ASME Transactions N1l, 530–535 (1974)
- B. J. Matkowsky and G. I. Sivashinsky, Propagation of a pulsating reaction front in solid fuel combustion, SIAM J. Appl. Math. 35 (1978), no. 3, 465–478. MR 507948, DOI https://doi.org/10.1137/0135038
B. J. Matkowsky and G. I. Sivashinsky, A nonlinear theory of cellular flames, to appear
W. H. Carothers and J. W. Hill, Studies of polymerization and ring formation. XV. Artificial fiber from synthetic linear condensation superpolymers, J. Amer. Chem. Soc. 54, N4 (1932)
A. Nadai, Theory of flow and fractures of solids, McGraw-Hill N. Y., Toronto, London (1952)
G. I. Barenblatt, On the extension of neck of polymer specimens under tension, Appl. Math, and Mech. (PMM) 28, 1264–1276 (1964)
G. I. Barenblatt, Isothermal propagation of a neck in polymers, Mechanics of Solids (MMT) N6, 89–96 (1972)
Y. B. Zeldovich, Theory of flame propagation, Zh. Fiz. Khim. 22, no. 1 (1948) (in Russian)
Yu. S. Lazurkin, Cold-drawing of glass-like and crystalline polymers, J. Polymer Sci. 30, no. 121 (1958)
P. J. Vincent, The necking and cold drawing of rigid plastics, Polymer 1, no. 1 (1960)
G. P. Andrianova, V. A. Kargin and A. S. Kechekyan, Periodic oscillations in extension of polyethylene terephtalate, J. Macromolecular Compounds (Vysokomolekulyarnye Soedineniya) 12, no. 8, 1970 (in Russian)
Ya. B. Zel’dovich and G. I. Barenblatt, Theory of flame propagation, Combustion and Flame 3, 61–74 (1959)
G. I. Barenblatt, Self-oscillatory propagation of a neck in polymers, Mechanics of Solids (MMT) N5, 110–118 (1970)
G. I. Sivashinsky, The structure of Bunsen flames, J. Chem. Physics, 62, 638–643 (1975)
G. I. Sivashinsky, The diffusion stratification effect in Bunsen flames, J. Heat Transfer, ASME Transactions N1l, 530–535 (1974)
B. J. Matkowsky and G. I. Sivashinsky, Propagation of a pulsating reaction front in solid fuel combustion, SIAM J. Applied Math. 35, 465–478 (1978)
B. J. Matkowsky and G. I. Sivashinsky, A nonlinear theory of cellular flames, to appear
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Article copyright:
© Copyright 1979
American Mathematical Society
