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Research Papers

Incorporating Density and Temperature in the Stretched Exponential Model for Predicting Stress Relaxation Behavior of Polymer Foams

[+] Author and Article Information
Bipul Barua

School of Aerospace and
Mechanical Engineering,
University of Oklahoma,
Norman, OK 73019
e-mail: bipul@ou.edu

Mrinal C. Saha

Mem. ASME
School of Aerospace and
Mechanical Engineering,
University of Oklahoma,
Norman, OK 73019
e-mail: msaha@ou.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received October 16, 2014; final manuscript received August 6, 2015; published online September 24, 2015. Assoc. Editor: Georges Cailletaud.

J. Eng. Mater. Technol 138(1), 011001 (Sep 24, 2015) (7 pages) Paper No: MATS-14-1196; doi: 10.1115/1.4031426 History: Received October 16, 2014; Revised August 06, 2015

This paper discusses an approach to incorporate density and temperature terms in the well-known stretched exponential (SE) model for predicting the stress relaxation behavior of polymer foams. We have developed this approach for closed-cell polyurethane foams (PUFs) and verified using experimental data for accuracy. The SE model was first examined using short-term experimental data to predict long-term stress relaxation behavior of PU solid (PUS). The corresponding model parameters were then extracted for PUS and two PUFs with different densities (PU404 and PU415) at three different test temperatures. Finally, an expression was developed in conjunction with the modified Gibson–Ashby relationship and the Arrhenius equation and validated for other foam density (PU420) and test temperatures. The predictions were found to be reasonably good with more than 90% accuracy.

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Figures

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Fig. 1

Tensile stress relaxation of (a) PUS, (b) PU415 foam, and (c) PU404 foam at different temperatures

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Fig. 2

SE model prediction of the stress relaxation behavior of PUS at 298 K using different amounts of experimental data

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Fig. 3

Comparison of the predicted (solid lines) and experimental stress relaxation behavior for (a) PUS, (b) PU415 foam, and (c) PU404 foam at different temperatures. The SE model prediction is based on the experimental data up to 1528 s.

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Fig. 4

Normalized initial stress relaxation modulus, Eof/Eos, of PUF as a function of relative density along with the curve-fitting of Eq. (3)

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Fig. 5

Temperature dependency of (a) initial modulus, (b) constants Cs, and (c) relaxation time for PUS and PUFs

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Fig. 6

Experimental and predicted stress relaxation behavior of PU404 foam and PU415 foam at (a) 318 K and (b) 348 K. Solid lines are the predicted curves.

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Fig. 7

Experimental and predicted stress relaxation behavior of PU420 foam at (a) 298 K, (b) 318 K, (c) 333 K, (d) 348 K, and (e) 363 K. Solid lines are the predicted curves.

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