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TECHNICAL PAPERS

Observations of the Constitutive Response and Characterization of Filled Natural Rubber Under Monotonic and Cyclic Multiaxial Stress States

[+] Author and Article Information
W. V. Mars

Cooper Tire and Rubber Company, 701 Lima Ave., Findlay, Ohio 45840

A. Fatemi

The University of Toledo, 2801 W. Bancroft Street, Toledo, Ohio 43606

J. Eng. Mater. Technol 126(1), 19-28 (Jan 22, 2004) (10 pages) doi:10.1115/1.1631432 History: Received December 09, 2002; Revised August 01, 2003; Online January 22, 2004
Copyright © 2004 by ASME
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References

Mars,  W. V., and Fatemi,  A., 2002, “A Literature Survey on Fatigue Analysis Approaches for Rubber,” Int. J. Fatigue, 24(9), pp. 949–961.
Mars,  W. V., and Fatemi,  A., 2004, “Factors that Affect the Fatigue Life of Rubber: A Literature Survey,” Rubber Chem. Technol., 76 (3).
Ogden,  R. W., and Roxburgh,  D. G., 1999, “A pseudo-elastic model for the Mullins effect in filled rubber,” Proc. R. Soc. London, Ser. A, 455, pp. 2861–2877.
ABAQUS Theory Manual, 2000, HKS, Pawtuckett, RI.
Ogden, R. W., 1997, Non-Linear Elastic Deformations, Dover Publications, Mineola, New York.
Peng, S. H., 1995, “A Compressible Approach in Finite Element Analysis of Rubber-Elastic Materials: Formulation, Programming, and Application,” Ph.D. dissertation, University of Southern California.
Rivlin,  R. S., 1948, “Large elastic deformations of isotropic materials. I. Fundamental concepts. II. Some uniqueness theorems for pure, homogeneous deformation,” Proc. R. Soc. London, Ser. A, 240, pp. 459–508.
Mooney,  M., 1940, “A theory of large elastic deformation,” J. Appl. Phys., 11, pp. 582–592.
Ogden,  R. W., 1972, “Large deformation isotropic elasticity I: on the correlation of theory and experiment for incompressible rubber-like solids,” Proc. R. Soc. London, Ser. A, 326, pp. 565–584.
Gent,  A. N., 1996, “A new constitutive relation for rubber,” Rubber Chem. Technol., 69, pp. 59–61.
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.
Yeoh,  O. H., 1993, “Some forms of the strain energy function for rubber,” Rubber Chem. Technol., 66, pp. 754–771.
Yeoh,  O. H., 1990, “Characterization of elastic properties of carbon-black-filled rubber vulcanizates,” Rubber Chem. Technol., 63, pp. 792–805.
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Rivlin,  R. S., 1992, “The Elasticity of Rubber,” Rubber Chem. Technol., 65, pp. G51–G66.
Mullins,  L., 1969, “Softening of Rubber by Deformation,” Rubber Chem. Technol., 42, pp. 339–362.
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Ahmadi, H. R., Gough, J., Muhr, A. H., and Thomas, A. G., 1999, “Bi-axial experimental techniques highlighting the limitations of a strain-energy description of rubber,” Constitutive Models for Rubber, A. Dorfmann and A. Muhr, eds., A. A. Balkema, Netherlands.
Mullins,  L., 1947, “Studies in the absorption of energy by rubber. I. Introductory Survey,” J. Rubber Research, 16, pp. 180–185.
Bueche,  F., 1962, “Mullins Effect and Rubber-Filler Interaction,” Rubber Chem. Technol., 35, pp. 259–273.
Derham,  C. J., and Thomas,  A. G., 1977, “Creep of rubber under repeated stressing,” Rubber Chem. Technol., 50, pp. 397–402.
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Bergstrom,  J. S., and Boyce,  M. C., 2000, “Large strain time-dependent behavior of filled elastomers,” Mech. Mater., 32, pp. 627–644.
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Mars, W. V., and Fatemi, A., 2003, “Fatigue Crack Nucleation and Growth in Filled Natural Rubber,” J. Fatigue Fract. Eng. Mater. Struct., 26 , pp. 779–789.
Mars,  W. V., and Fatemi,  A., 2003, “A Phenomenological Model for the Effect of R ratio on Fatigue of Strain Crystallizing Rubber,” Rubber Chem. Technol., 76(5), pp. 1241–1258.
Mars,  W. V., and Fatemi,  A., 2003, “A Novel Specimen for Investigating Mechanical Behavior of Elastomers under Multiaxial Loading Conditions,” Journal of Experimental Mechanics, 44 (1).
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Figures

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Simple tension, planar tension, and equibiaxial tension test specimens, with corresponding stretch and stress states
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Section view of axial/torsion test specimen
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Axial-torsion loading path designations. δ=displacement,θ=twist.
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Axial-torsion experimental matrix in terms of peak axial and shear engineering strains
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Axial-torsion experimental matrix in terms of peak principal engineering strains
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Monotonic stress-strain curves in simple tension, planar tension, and equibiaxial tension
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Cyclically stable stress-strain curves in progressively increasing simple tension (a), planar tension (b), and equibiaxial tension (c), and comparison of best-fit Neo-Hookean model to curves in simple and equibiaxial tension (d)
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Axial and shear engineering stress amplitude evolution with cycles for R=0, proportional loading with 3.9°/mm, path D
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Cyclically stabilized axial and shear stress-strain curves under R=0, proportioning loading with 3.9°/mm, path D. For comparison, the pure axial, pure torsion, and proportional monotonic stress-strain curves are superimposed.
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Axial and shear engineering stress amplitude evolution with cycles, path H
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Cyclically stabilized axial and shear stress-strain curves for path H. For comparison, the pure axial, pure torsion, and proportional monotonic stress-strain curves are superimposed.
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Combined axial-torsion strain and stress paths associated with phase angles of ϕ=0 deg (path D), ϕ=45 deg (path G), ϕ=90 deg (path H) and ϕ=180 deg (path I).
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Evolution of axial-torsion stress paths for phase angles of ϕ=0 deg (path D), ϕ=45 deg (path G), ϕ=90 deg (path H), and ϕ=180 deg (path I).
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Effect of strain component phase difference on stabilized axial and shear stress-strain curves. ϕ=0 deg for path D, ϕ=90 deg for path H, and ϕ=180 deg for path I.
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Shear engineering stress amplitude evolution with cycles, showing the effect of an initial overload in path B (specimens 180 and 181). The evolution of the no-overload case is also shown (specimen 183). Following the initial overload, all tests were run at the same displacement amplitude.

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