Research Papers

Constitutive Behavior and Temperature Effects in NR and SBR Under Variable Amplitude and Multiaxial Loading Conditions

[+] Author and Article Information
Ryan J. Harbour1

Mechanical, Industrial and Manufacturing Engineering Department, The University of Toledo, 2801 West Bancroft Street, Toledo, OH 43606

Ali Fatemi2

Mechanical, Industrial and Manufacturing Engineering Department, The University of Toledo, 2801 West Bancroft Street, Toledo, OH 43606afatemi@eng.utoledo.edu

Will V. Mars

Research Department, Cooper Tire and Rubber Company, 701 Lima Avenue, Findlay, OH 45840wvmars@coopertire.com


Present address: Goodyear Tire and Rubber Company.


Corresponding author.

J. Eng. Mater. Technol 130(1), 011005 (Dec 21, 2007) (11 pages) doi:10.1115/1.2806276 History: Received December 12, 2006; Revised September 07, 2007; Published December 21, 2007

Knowledge of the stress response of a material to the applied deformations is necessary for many engineering analysis and applications. This paper addresses the observed effects of load sequencing, Mullins effect, and multiaxial loading on the constitutive behavior of rubber under variable amplitude conditions for a series of experiments using multiaxial ring test specimens. Two filled rubber materials were used and compared in this study; natural rubber, which strain crystallizes, and styrene butadiene rubber (SBR), which does not. A pseudoelastic approach is used to model the cyclic stress-strain response for both materials. The implications of inelasticity when using hyperelastic material models are also discussed. Based on temperature results for the multiaxial ring specimen obtained via a thermal imaging system for SBR, a model capable of accurately predicting surface temperature for the multiaxial ring specimen as a function of hysteresis area and test frequency has been developed.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

The general design of the multiaxial ring test specimen with a rubber ring bonded between two steel mounting rings

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Figure 2

Variable amplitude displacement path sequence designations for multilevel (Paths F and G), multiaxial (Paths H and I), and random (Path J) tests

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Figure 3

Fits of the modified neo-Hookean material model using the Ogden–Roxburgh damage parameter to typical stable stress-strain loops (128th cycle) from multiple axial tests for (left) NR and (right) SBR. This model accounts for the Mullins effect based on the cyclic loading causing damage to the material. Table 2 presents the material parameters for the model.

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Figure 4

Illustration of differences between maximum stress levels for constant amplitude tests and similar cycles applied as the lower peak strain cycles in multiaxial test Path F in NR

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Figure 5

Cyclically stable stress-strain curves for torsion cycles from Path H in SBR plotted with the stress-strain curve for a corresponding constant amplitude test

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Figure 6

Stress-strain curves for the random test Path J in NR plotted with stable constant amplitude stress-strain loops for comparison: (left) axial and (right) shear

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Figure 7

Comparison of stable stress-strain loops in NR and SBR for (left) a pure axial test with a 100% peak axial strain and (right) a fully reversed torsion test with a 60% shear strain amplitude

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Figure 8

Comparison of hysteresis energy per cycle for NR and SBR as a function of loading strain energy density per cycle for all test Paths A–I. SBR has higher hysteresis as evident by the larger area between loading and unloading stress-strain curves.

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Figure 9

Cyclically stable stress-strain curves in NR for (left) torsion with Rθ=0 and (right) fully reversed torsion

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Figure 10

Maximum steady-state surface temperature for a SBR multiaxial ring specimen under constant amplitude loading conditions

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Figure 11

Temperature profile in the axial direction for fully reversed torsion with a 75% shear strain amplitude at 1Hz and the test specimen cross section

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Figure 12

Maximum steady-state temperature for test signals with a 75% shear strain amplitude at 1Hz for torsion and a 75% peak axial strain at 1Hz for axial

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Figure 13

Dissipation rate as a function of surface temperature in SBR for a multiaxial ring specimen. The dissipation rate is calculated as the hysteresis area per second.



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