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Research Papers

Viscoelastic Response of Closed-Cell Polyurethane Foams From Half Hour-Long Creep Tests: Identification of Lomnitz Behavior

[+] Author and Article Information
Christian Pichler

Material Technology Innsbruck,
University of Innsbruck,
Innsbruck A-6020, Austria
e-mail: christian.pichler@uibk.ac.at

Marcus Maier

Material Technology Innsbruck,
University of Innsbruck,
Innsbruck A-6020, Austria
e-mail: marcus.maier@uibk.ac.at

Roman Lackner

Professor
Material Technology Innsbruck,
University of Innsbruck,
Innsbruck A-6020, Austria
e-mail: roman.lackner@uibk.ac.at

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received May 2, 2018; final manuscript received July 2, 2018; published online September 17, 2018. Assoc. Editor: Anastasia Muliana.

J. Eng. Mater. Technol 141(2), 021001 (Sep 17, 2018) (12 pages) Paper No: MATS-18-1126; doi: 10.1115/1.4040831 History: Received May 02, 2018; Revised July 02, 2018

In this paper, a protocol for interpretation of static creep tests on closed-cell polyurethane foams is defined, considering the influence of a finite loading duration when identifying creep compliance parameters. Experiments were conducted at isothermal conditions with temperatures ranging from 20 to 120 °C. The experimental results indicate Lomnitz, i.e., logarithmic-type creep behavior. We discuss uniqueness of the backcalculated parameters. Furthermore, the viscoelastic material parameters obtained were verified in independent experiments: elastic compliance by ultrasonic wave velocity measurements, viscous material parameters by relaxation tests.

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Figures

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Fig. 1

(a) Prescribed stress history, (b) ramp compliance in a creep test with J̃=ε(t)/σ0, and (c) ramp compliance rate indicating logarithmic-type behavior (foam A, see Sec. 2)

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Fig. 2

(a) Relaxation function for Lomnitz material [18,19], (b) expected relaxation function for foam A (see Sec. 2) with material parameters identified in creep experiment in this paper (see Fig. 6); inlay shows relaxation data for polyurethane [24] (sample PU-46 in Fig. 4 [24])

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Fig. 3

(a)–(d) Measured ramp compliance for t > t0 in creep tests conducted at various temperatures, foam A and (e) ramp compliance rates indicating logarithmic-type behavior for low temperature with slope of −1 and combined logarithmic/Maxwellian behavior for temperatures T ≥ 90 °C, note: experiments for temperatures 30, 50, and 70 °C coincide with 20 °C measurement and were omitted in figure

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Fig. 4

Uniqueness of parameter identification scheme as regards J log dev and E when τlog is set constant (corresponding to 20 °C measurement in Fig. 3)

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Fig. 5

Nonuniqueness of parameter identification scheme as regards E and τlog (corresponding to 20 °C measurement in Fig. 3)

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Fig. 6

Arrhenius plot of backcalculated material parameters for foam A: (a) Lomnitz parameters and (b) Scott–Blair parameters, compare 1/E to J(t = 0.1 s)

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Fig. 7

Close-up of measured ramp compliance at the transition from loading to dwelling phase, J̃(t=t0) is marked

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Fig. 8

Uniqueness of parameter identification scheme as regards JPLdev and nPL (corresponding to 20 °C measurement in Fig. 3)

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Fig. 9

Elastic compliance 1/E versus power-law quasi-instantaneous compliance J(t) at (a) t = 0.1 s and (b) t = 0.01 s

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Fig. 10

Arrhenius plot of backcalculated material parameters for foam B: (a) Lomnitz parameters and (b) Scott–Blair parameters, compare 1/E to J(t = 0.1 s)

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Fig. 11

Arrhenius plot of backcalculated material parameters for foam C: (a) Lomnitz parameters and (b) Scott–Blair parameters, compare 1/E to J(t = 0.1 s)

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Fig. 12

Arrhenius plot of (a) elastic compliance and (b) Lomnitz creep parameters of closed cell polyurethane foams

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Fig. 13

Determination of elastic properties of foams A and B by ultrasonic measurements

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Fig. 14

Expected relaxation behavior of foam A with material parameters as determined in Sec. 3.1, see also Table 2

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Fig. 15

Backcalculation of material parameters from 30 h relaxation experiment on foam A conducted at T = 30 °C: E = 19.0 MPa and J log dev=0.0022 MPa−1

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Fig. 16

Illustration of Boltzmann superposition principle for creep test, logarithmic type creep behavior, σ0 = 1 MPa, t0 = 100 s; material parameters E = 25 MPa, J log dev=0.03 MPa−1, τlog = 1 s: (a) stress history and (b) strain history

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Fig. 17

Smooth transition from Maxwellian to Lomnitz-type creep behavior via nlog in Jeffreys–Lomnitz creep law; material parameters E = 25 MPa, J log dev=0.03 MPa−1, τlog = 1 s

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