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.
Issue Section:
Research Papers
References
1.
Mainardi
, F.
, and Spada
, G.
, 2011
, “Creep, Relaxation and Viscosity Properties for Basis Fractional Models in Rheology
,” Eur. Phys. J. Spec. Top.
, 193
(1
), pp. 133
–160
.2.
Bazant
, Z. P.
, and Prasannan
, S.
, 1989
, “Solidification Theory for Concrete Creep—I: Formulation
,” ASCE J. Eng. Mech.
, 115
(8
), pp. 1691
–1703
.3.
Bažant
, Z. P.
, Hauggard
, A. B.
, Baweja
, S.
, and Ulm
, F.-J.
, 1997
, “Microprestress Solidification Theory for Concrete Creep—Part I: Aging and Drying Effects
,” ASCE J. Eng. Mech.
, 123
(11
), pp. 1188
–1194
.4.
Acker
, P.
, and Ulm
, F.-J.
, 2001
, “Creep and Shrinkage of Concrete: Physical Origins and Practical Measurements
,” Nucl. Eng. Des.
, 203
(2–3
), pp. 148
–158
.5.
Pichler
, C.
, Lackner
, R.
, and Mang
, H. A.
, 2008
, “Multiscale Model for Creep of Shotcrete—From Logarithmic-Type Viscous Behavior of CSH at the μm-Scale to Macroscopic Tunnel Analysis
,” J. Adv. Concrete Technol.
, 6
(1
), pp. 91
–110
.6.
Pichler
, C.
, and Lackner
, R.
, 2009
, “Identification of Logarithmic-Type Creep of Calcium-Silicate-Hydrates by Means of Nanoindentation
,” Strain
, 45
(1
), pp. 17
–25
.7.
Lomnitz
, C.
, 1956
, “Creep Measurements in Igneous Rocks
,” J. Geol.
, 64
(5
), pp. 473
–479
.8.
Lomnitz
, C.
, 1957
, “Linear Dissipation in Solids
,” J. Appl. Phys.
, 28
(2
), pp. 201
–205
.9.
Lomnitz
, C.
, 1962
, “Application of Logarithmic Creep Law to Stress Wave Attenuation in Solid Earth
,” J. Geophys. Res.
, 67
(1
), pp. 365
–367
.10.
Pandey
, V.
, and Holm
, S.
, 2016
, “Linking the Fractional Derivative and the Lomnitz Creep Law to Non-Newtonian Time-Varying Viscosity
,” Phys. Rev. E
, 94
(3
), p. 032606
.11.
Buckingham
, M. J.
, 2000
, “Wave Propagation, Stress Relaxation, and Grain-to-Grain Shearing in Saturated, Unconsolidated Marine Sediments
,” J. Acoust. Soc. Am.
, 108
(6
), pp. 2796
–2815
.12.
Davis
, M.
, and Thompson
, N.
, 1950
, “Creep in a Precipitation-Hardened Alloy
,” Proc. Phys. Soc. London, B
, 63
(11
), pp. 847
–860
. 371),13.
Wyatt
, O. H.
, 1953
, “Transient Creep in Pure Metals
,” Proc. Phys. Soc. London, B
, 66
(6
), pp. 459
–480
.14.
Nabarro
, F. R. N.
, 2001
, “The Time Constant of Logarithmic Creep and Relaxation
,” Mater. Sci. Eng. A
, 309–310
, pp. 227
–228
.15.
Nabarro
, F. R. N.
, 2001
, Creep Mechanism in Crystalline Solids, 2nd ed., Elsevier, Amsterdam, The Netherlands, pp. 1788
–1795
.16.
Savitzky
, A.
, and Golay
, M. J. E.
, 1964
, “Smoothing and Differentiation of Data by Simplified Least Squares Procedures
,” Anal. Chem.
, 36
(8
), pp. 1627
–1639
.17.
Press
, H. P.
, Flannery
, B. P.
, Teukolsky
, S. A.
, and Vetterling
, W. T.
, 1992
, Numerical Recipes in Fortran 77: The Art of Scientific Computing
, 2nd ed., Cambridge University Press
, Cambridge, UK.18.
Mainardi
, F.
, and Spada
, G.
, 2012
, “On the Viscoelastic Characterization of the Jeffreys-Lomnitz Law of Creep
,” Rheol. Acta
, 51
(9
), pp. 783
–791
.19.
Garra
, R.
, Mainardi
, F.
, and Spada
, G.
, 2017
, “A Generalization of the Lomnitz Logarithmic Creep Law Via Hadamard Fractional Calculus
,” Chaos, Solitons Fractals
, 102
, pp. 333
–338
.20.
Moreland
, J. C.
, Wilkes
, G. L.
, and Turner
, R. B.
, 1994
, “Viscoelastic Behavior of Flexible Slabstock Polyurethane Foams - Dependence on Temperature and Relative Humidity—I: Tensile and Compression Stress (Load) Relaxation
,” J. Appl. Polym. Sci.
, 52
(4
), pp. 549
–568
.21.
Moreland
, J. C.
, Wilkes
, G. L.
, and Turner
, R. B.
, 1994
, “Viscoelastic Behavior of Flexible Slabstock Polyurethane Foams as a Function of Temperature and Relative Humidity—II: Compressive Creep Behavior
,” J. Appl. Polym. Sci.
, 52
(4
), pp. 569
–576
.22.
Zhu
, H. X.
, and Mills
, N. J.
, 1999
, “Modelling the Creep of Open-Cell Polymer Foams
,” J. Mech. Phys. Solids
, 47
(7
), pp. 1437
–1457
.23.
Tobushi
, H.
, Hayashi
, S.
, Endo
, M.
, and Shimada
, D.
, 2002
, “Creep and Stress Relaxation of Polyurethane-Shape Memory Polymer Foam
,” Trans. Jpn. Soc. Mech. Eng. Ser. A
, 68
(676
), pp. 1788
–1793
(in Japanese).24.
Xia
, H.
, Song
, M.
, Zhang
, Z.
, and Richardson
, M.
, 2007
, “Microphase Separation, Stress Relaxation, and Creep Behavior of Polyurethane Nanocomposites
,” J. Appl. Polym. Sci.
, 103
(5
), pp. 2992
–3002
.25.
Kanyanta
, V.
, and Ivankovic
, A.
, 2010
, “Mechanical Characterisation of Polyurethane Elastomer for Biomedical Applications
,” J. Mech. Behav. Biomed. Mater.
, 3
(1
), pp. 51
–62
.26.
Stehfest
, H.
, 1970
, “Algorithm 368: Numerical Inversion of Laplace Transforms
,” Commun. ACM
, 13
, pp. 47
–49
.27.
White
, S. W.
, Kim
, S. K.
, Bajaj
, A. K.
, Davies
, P.
, Showers
, D. K.
, and Liedtke
, P. E.
, 2000
, “Experimental Techniques and Identification of Nonlinear and Viscoelastic Properties of Flexible Polyurethane Foam
,” Nonlinear Dyn.
, 22
(3
), pp. 281
–313
.28.
Singh
, R.
, Davies
, P.
, and Bajaj
, A. K.
, 2003
, “Identification of Nonlinear and Viscoelastic Properties of Flexible Polyurethane Foam
,” Nonlinear Dyn.
, 34
(3/4
), pp. 319
–346
.29.
Deng
, R.
, Davies
, P.
, and Bajaj
, A. K.
, 2004
, “A Case Study on the Use of Fractional Derivatives: The Low-Frequency Viscoelastic Uni-Directional Behavior of Polyurethane Foam
,” Nonlinear Dyn.
, 38
(1–4
), pp. 247
–265
.30.
Deng
, R.
, Davies
, P.
, and Bajaj
, A. K.
, 2006
, “A Nonlinear Fractional Derivative Model for Large Uni-Axial Deformation Behavior of Polyurethane Foam
,” Signal Process.
, 86
(10
), pp. 2728
–2743
.31.
Deng
, R.
, Davies
, P.
, and Bajaj
, A. K.
, 2003
, “Flexible Polyurethane Foam Modelling and Identification of Viscoelastic Parameters for Automotive Seating Applications
,” J. Sound Vib.
, 262
(3
), pp. 391
–417
.32.
Azizi
, Y.
, Davies
, P.
, and Bajaj
, A. K.
, 2016
, “Identification of Nonlinear Viscoelastic Models of Flexible Polyurethane Foam From Uniaxial Compression Data
,” ASME J. Eng. Mater. Technol.
, 138
(2
), p. 021008
.33.
Dzierza
, W.
, 1982
, “Stress–Relaxation Properties of Segmented Polyurethane Rubbers
,” J. Appl. Polym. Sci.
, 27
(5
), pp. 1487
–1499
.34.
Nitta
, K.-H.
, and Suzuki
, K.
, 1999
, “Prediction of Stress–Relaxation Behavior in High Density Polyethylene Solids
,” Macromol. Theory Simul.
, 8
(3
), pp. 254
–259
.35.
Slonimsky
, G. L.
, 1967
, “Laws of Mechanical Relaxation Processes in Polymers
,” J. Polym. Sci., Part C
, 16
(3
), pp. 1667
–1672
.36.
Ortiz
, C.
, Ober
, C. K.
, and Kramer
, E. J.
, 1998
, “Stress Relaxation of a Main–Chain, Smectic, Polydomain Liquid Crystalline Elastomer
,” Polymer
, 39
(16
), pp. 3713
–3718
.37.
Barua
, B.
, and Saha
, M. C.
, 2011
, “Tensile Stress Relaxation Behavior of Thermosetting Polyurethane Solid and Foams: Experiment and Model Prediction
,” ASME J. Eng. Mater. Technol.
, 133
(4
), p. 041007
.38.
Barua
, B.
, and Saha
, M. C.
, 2016
, “Incorporating Density and Temperature in the Stretched Exponential Model for Predicting Stress Relaxation Behavior of Polymer Foams
,” ASME J. Eng. Mater. Technol.
, 138
(1
), p. 011001
.39.
Kaushiva
, B. D.
, Dounis
, D. V.
, and Wilkes
, G. L.
, 2000
, “Influences of Copolymer Polyol on Structural and Viscoelastic Properties in Molded Flexible Polyurethane Foams
,” J. Appl. Polym. Sci.
, 78
(4
), pp. 766
–786
.40.
Nutting
, P. G.
, 1921
, “A New General Law of Deformation
,” J. Franklin Inst.
, 191
(5
), pp. 679
–685
.41.
Scott Blair
, G. W.
, and Reiner
, M.
, 1951
, “The Rheological Law Underlying the Nutting Equation
,” Appl. Sci. Res.
, 2
(1
), p. 225
.42.
Marquardt
, D. W.
, 1963
, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters
,” J. Soc. Ind. Appl. Math.
, 11
(2
), pp. 431
–441
.43.
Love
, A. E. H.
, 1959
, A Treatise of the Mathematical Theory of Elasticity
, 4th ed., Cambridge University Press
, Cambridge, UK.44.
Warfield
, R. W.
, and Barnet
, F. R.
, 1972
, “Elastic Constants of Bulk Polymers
,” Naval Ordnance Laboratory, White Oak, Silver Spring, MD, Report No. NOLTR 71-227.45.
Widdle
, R. D.
, Jr., Bajaj
, A. K.
, and Davies
, P.
, 2008
, “Measurement of the Poisson's Ratio of Flexible Polyurethane Foam and Its Influence on a Uniaxial Compression Model
,” Int. J. Eng. Sci.
, 46
(1
), pp. 31
–49
.46.
Nitta
, K.-H.
, and Yamaguchi
, M.
, 1998
, “A Constitutive Equation for Nonlinear Stress–Strain Curves of Crystalline Polymers
,” J. Mater. Sci.
, 33
(4
), pp. 1015
–1021
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