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Experimentally Evaluating Equilibrium Stress in Uniaxial Tests

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Abstract

Many models use the equilibrium stress, also sometimes known as the back stress, in characterizing the response of both polymeric and non-polymeric materials. We study the characteristics of the equilibrium and show that the tangent modulus and local Poisson’s ratio at equilibrium both are rate independent for common modeling assumptions. This fact is used to propose a method based on uniaxial tension or compression to measure the equilibrium stress, and the associated point’s tangent modulus and local Poisson’s ratio. The method is based on cyclic loading and identification of similar states with vastly different loading rates. The method is used to characterize the equilibrium stress in glassy polycarbonate, and the results are studied in regard to the possible error for such a measurement. The method is faster than most other proposed methods for calculating the equilibrium stress, and provides additional measurements of parameters at equilibrium that are normally not obtained.

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Notes

  1. There can be a difference between the equilibrium stress and the term in a model called the back stress. In particular this occurs when the plastic flow is selected to be materially constrained, such as is the case for the standard assumption of incompressible plastic flow. The difference is similar to the indeterminacy introduced by material constraints on the stress and can easily be evaluated. To avoid the potential confusion between the two, in the following we focus on the stress at equilibrium and denote it as the equilibrium stress or back stress.

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Acknowledgment

The research reported in this article was partially supported by the U.S. Army Research Laboratory (ARL) under the RMAC-RTP Cooperative Agreement No. W911NF-04-2-0011.

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Authors and Affiliations

  1. Department of Engineering Mechanics, University of Nebraska–Lincoln, Lincoln, NE, 68588-0526, USA

    A. Goel, K. Strabala, M. Negahban & R. Feng

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  1. A. Goel
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  2. K. Strabala
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  3. M. Negahban
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  4. R. Feng
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Correspondence to M. Negahban.

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Goel, A., Strabala, K., Negahban, M. et al. Experimentally Evaluating Equilibrium Stress in Uniaxial Tests. Exp Mech 50, 709–716 (2010). https://doi.org/10.1007/s11340-009-9268-z

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  • DOI: https://doi.org/10.1007/s11340-009-9268-z

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