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TECHNICAL PAPERS

Scission and Healing in a Spinning Elastomeric Cylinder at Elevated Temperature

[+] Author and Article Information
A. S. Wineman

Mechanical Engineering, The University of Michigan, G042 Auto Lab, Ann Arbor, MI 48109e-mail: lardan@engin.umich.edu

J. A. Shaw

Aerospace Engineering, The University of Michigan, 1320 Beal Avenue, Ann Arbor, MI 48109-2140 e-mail: jashaw@engin.umich.edu

J. Appl. Mech 69(5), 602-609 (Aug 16, 2002) (8 pages) doi:10.1115/1.1485757 History: Received April 05, 2001; Revised February 05, 2002; Online August 16, 2002
Copyright © 2002 by ASME
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References

Tobolsky, A. V., 1960, Properties and Structures of Polymers, John Wiley and Sons, New York, Chap. 5, pp. 223–265.
Wineman,  A. S., and Rajagopal,  K. R., 1990, “On a Constitutive Theory for Materials Undergoing Microstructural Changes,” Arch. Mech., 42, pp. 53–74.
Rajagopal,  K. R., and Wineman,  A. S., 1992, “A Constitutive Equation for Non-linear Solids Which Undergo Deformation Induced Microstructural Changes,” Int. J. Plast., 8, pp. 385–395.
Horgan, C. O., and Saccomandi, G., 2001, “Large Deformations of a Rotating Solid Cylinder for Non-Gaussian Isotropic, Incompressible Hyperlastic Materials,” ASME J. Appl. Mech., to appear.
Chadwick,  P., Creasy,  C. F. M., and Hart,  V. G., 1977, “The Deformation of Rubber Cylinders and Tubes by Rotation,” J. Austral. Math. Soc., 20 (Series 13), pp. 62–96.
Tobolsky,  A. V., Prettyman,  I. B., and Dillon,  J. H., 1944, “Stress Relaxation of Natural and Synthetic Rubber Stocks,” J. Appl. Phys., 15, pp. 380–395.
Neubert,  D., and Saunders,  D. W., 1944, “Some Observations of the Permanent Set of Cross-Linked Natural Rubber Samples After Heating in a State of Pure Shear,” Rheol. Acta, 1, pp. 151–157.
Fong,  J. T., and Zapas,  L. J., 1976, “Chemorheology and the Mechanical Behavior of Vulcanized Rubber,” Trans. Soc. Rheol., 20, pp. 319–338.
Rivlin,  R. S., and Saunders,  D. W., 1951, “Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber,” Philos. Trans. R. Soc. London, Ser. A, A243, pp. 251–288.
Gent,  A. N., 1996, “A New Constitutive Relation for rubber,” Rubber Chem. Technol., 69, pp. 59–61.
Knowles,  J. K., 1977, “The Finite Anti-plane Shear Field Near the Tip of a Crack for a Class of Incompressible Elastic Solids,” Int. J. Fract., 13, pp. 611–639.
Arruda,  E. M., and Boyce,  M. C., 1993, “A Three Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials,” J. Mech. Phys. Solids, 41, pp. 389–412.

Figures

Grahic Jump Location
Reference and current configuration for spinning cylinder
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Characteristic time for scission and healing for Eact=127.24 kJ/mol
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Evolution of axial stretch for Neo-Hookean material: (a) no healing (η=0), (b) partial healing (η=0.5), (c) complete healing (η=1)
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Dependence of initial axial stretch for Mooney-Rivlin material with nondimensional angular velocity, Ω, for different ratios of MR constants, β=W20/W10
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Evolution of axial stretch for Mooney-Rivlin material with β=0.2: (a) no healing (η=0), (b) partial healing (η=0.5), (c) complete healing (η=1)
Grahic Jump Location
Dependence of initial axial stretch for Arruda-Boyce material with nondimensional angular velocity, Ω, for different locking stretch ratios, λm
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Evolution of axial stretch for Arruda-Boyce material with λm=3: (a) no healing (η=0), (b) partial healing (η=0.5), (c) complete healing (η=1)

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