The stress relaxation behavior of a Twaron CT709® fabric/natural rubber composite under a uniaxial constant strain is studied using three viscoelasticity models with different levels of complexity and a newly developed para-rheological model. The three viscoelasticity models employed are a one-term generalized Maxwell model (comprising one Maxwell element and an additional spring in parallel), a two-term generalized Maxwell model (including two Maxwell elements and an additional spring in parallel), and a four-parameter Burgers model. The values of the parameters involved in each model are extracted from the experimental data obtained in this study. The stress relaxation tests reveal that the stress starts to decay exponentially for a short duration and then continues to decrease linearly with time. It is found that the initial relaxation response of the composite is predicted fairly well by all of the four models, while the long-time stress relaxation behavior is more accurately predicted by the para-rheological model. The accuracy of each model in describing the stress relaxation behavior of the composite is quantitatively compared.
1.
Matveev
, V. S.
, and Budnitskii
, G. A.
, 1996, “Materials for Protection From Ballistic Injury
,” Fibre Chem.
, 27
, pp. 147
–149
.2.
Lim
, C. T.
, Shim
, V. P. W.
, and Ng
, Y. H.
, 2003, “Finite-Element Modeling of the Ballistic Impact of Fabric Armor
,” Int. J. Impact Eng.
0734-743X, 28
, pp. 13
–31
.3.
Tan
, V. B. C.
, Zeng
, X. S.
, and Shim
, V. P. W.
, 2008, “Characterization and Constitutive Modeling of Aramid Fibers at High Strain Rates
,” Int. J. Impact Eng.
0734-743X, 35
, pp. 1303
–1313
.4.
Rao
, M. P.
, Duan
, Y.
, Keefe
, M.
, Powers
, B. M.
, and Bogetti
, T. A.
, 2009, “Modeling the Effects of Yarn Material Properties and Friction on the Ballistic Impact of a Plain-Weave Fabric
,” Compos. Struct.
0263-8223, 89
, pp. 556
–566
.5.
Gauthier
, C.
, Pelletier
, J. M.
, David
, L.
, Vigier
, G.
, and Perez
, J.
, 2000, “Relaxation of Non-Crystalline Solids Under Mechanical Stress
,” J. Non-Cryst. Solids
0022-3093, 274
, pp. 181
–187
.6.
Brinson
, H. F.
, and Brinson
, L. C.
, 2008, Polymer Engineering Science and Viscoelasticity: An Introduction
, Springer
, New York
.7.
Bjork
, F.
, and Stenberg
, B.
, 1990, “Stress Relaxation of a Nitrile Rubber Surrounded by an Oil That Increases the Network Density
,” Polymer
0032-3861, 31
, pp. 1649
–1657
.8.
Ortiz
, C.
, Kim
, R.
, Rodighiero
, E.
, Ober
, C. K.
, and Kramer
, E. J.
, 1998, “Deformation of a Polydomain, Liquid Crystalline Epoxy-Based Thermoset
,” Macromolecules
0024-9297, 31
, pp. 4074
–4088
.9.
Doi
, M.
, and Takimoto
, J.
, 2003, “Molecular Modelling of Entanglement
,” Philos. Trans. R. Soc. London, Ser. A
0962-8428, 361
, pp. 641
–652
.10.
Sperling
, L. H.
, 2006, Introduction to Physical Polymer Science
, 4th ed., Wiley
, New York
.11.
Grassia
, P.
, and Hinch
, E. J.
, 1996, “Computer Simulations of Polymer Chain Relaxation via Brownian Motion
,” J. Fluid Mech.
0022-1120, 308
, pp. 255
–288
.12.
Illers
, K. H.
, Kilian
, H. G.
, and Kosfeld
, R.
, 1961, “Physical Properties of High Polymers
,” Annu. Rev. Phys. Chem.
0066-426X, 12
, pp. 49
–82
.13.
Patel
, M.
, Morrell
, P. R.
, and Murphy
, J. J.
, 2005, “Continuous and Intermittent Stress Relaxation Studies on Foamed Polysiloxane Rubber
,” Polym. Degrad. Stab.
0141-3910, 87
, pp. 201
–206
.14.
Munch
, E.
, Pelletier
, J. M.
, Sixou
, B.
, and Vigier
, G.
, 2006, “Molecular Mobility of Crosslinked Elastomers Stretched Above Tg
,” Polymer
0032-3861, 47
, pp. 3477
–3485
.15.
Tobolsky
, A. V.
, and Aklonis
, J. J.
, 1964, “A Molecular Theory for Viscoelastic Behavior of Amorphous Polymers
,” J. Phys. Chem.
0022-3654, 68
, pp. 1970
–1973
.16.
Rouse
, P. E.
, Jr., 1953, “A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers
,” J. Chem. Phys.
0021-9606, 21
, pp. 1272
–1280
.17.
Ramirez
, J.
, Sukumaran
, S. K.
, and Likhtman
, A. E.
, 2007, “Significance of Cross Correlations in the Stress Relaxation of Polymer Melts
,” J. Chem. Phys.
0021-9606, 126
, p. 244904
.18.
Konyali
, H.
, Menceloglu
, Y.
, and Erman
, B.
, 2008, “Long Time Stress Relaxation of Amorphous Networks Under Uniaxial Tension: The Dynamic Constrained Junction Model
,” Polymer
0032-3861, 49
, pp. 1056
–1065
.19.
Abadi
, M. T.
, 2009, “Micromechanical Analysis of Stress Relaxation Response of Fiber-Reinforced Polymers
,” Compos. Sci. Technol.
0266-3538, 69
, pp. 1286
–1292
.20.
Biot
, M. A.
, 1954, “Theory of Stress-Strain Relations in Anisotropic Viscoelastic and Relaxation Phenomena
,” J. Appl. Phys.
0021-8979, 25
, pp. 1385
–1391
.21.
Bartenev
, G. M.
, Kucherskii
, A. M.
, and Radayeva
, G. I.
, 1981, “Relaxation Processes in Elastomers at Low Strains From the Data of Relaxation Spectrometry, Stress-Strain and Thermomechanical Curves
,” Polym. Sci. U.S.S.R.
0032-3950, 23
, pp. 313
–322
.22.
D’Amore
, A.
, Caputo
, F.
, Grassia
, L.
, and Zarrelli
, M.
, 2006, “Numerical Evaluation of Structural Relaxation-Induced Stresses in Amorphous Polymers
,” Composites, Part A
1359-835X, 37
, pp. 556
–564
.23.
Machiraju
, C.
, Phan
, A. -V.
, Pearsall
, A. W.
, and Madanagopal
, S.
, 2006, “Viscoelastic Studies of Human Subscapularis Tendon: Relaxation Test and a Wiechert Model
,” Comput. Methods Programs Biomed.
0169-2607, 83
, pp. 29
–33
.24.
Meera
, A. P.
, Said
, S.
, Grohens
, Y.
, Luyt
, A. S.
, and Thomas
, S.
, 2009, “Tensile Stress Relaxation Studies of TiO2 and Nanosilica Filled Natural Rubber Composites
,” Ind. Eng. Chem. Res.
0888-5885, 48
, pp. 3410
–3416
.25.
ASTM Standard E328-02, 2008, Standard Test Methods for Stress Relaxation Tests for Materials and Structures,
ASTM International
, West Conshohocken, PA
.26.
Slonimskii
, G. L.
, and Rogovina
, L. Z.
, 1964, “Determination of the Mechanical Characteristics of a Polymeric Material by Stress Relaxation at Constant Deformation
,” Polym. Sci. U.S.S.R.
0032-3950, 6
, pp. 684
–688
.27.
Spontak
, R. J.
, Roberge
, R. L.
, Vratsanos
, M. S.
, and Starner
, W. E.
, 2000, “Model Acrylate-Terminated Urethane Blends in Toughened Epoxies: A Morphology and Stress Relaxation Study
,” Polymer
0032-3861, 41
, pp. 6341
–6349
.28.
Alger
, M. S. M.
, 1997, Polymer Science Dictionary
, 2nd ed., Chapman & Hall
, London
.29.
Torvik
, P. J.
, and Bagley
, R. L.
, 1984, “On the Appearance of the Fractional Derivative in the Behavior of Real Materials
,” ASME J. Appl. Mech.
0021-8936, 51
, pp. 294
–298
.30.
Pritz
, T.
, 2003, “Five-Parameter Fractional Derivative Model for Polymeric Damping Materials
,” J. Sound Vib.
0022-460X, 265
, pp. 935
–952
.31.
David
, N. V.
, Gao
, X. -L.
, and Zheng
, J. Q.
, 2010, Supplemental notes on derivations (17 pages, electronically available upon request).32.
Gerdeen
, J. C.
, Lord
, H. W.
, and Rorrer
, R. A. L.
, 2006, Engineering Design With Polymers and Composites
, CRC
, Boca Raton, FL
.33.
David
, N. V.
, Gao
, X. -L.
, and Zheng
, J. Q.
, 2010, “Constitutive Behavior of a Twaron®/Natural Rubber Composite
,” Mech. Adv. Mater. Struct.
, 17
, pp. 246
–259
.34.
David
, N. V.
, Gao
, X. -L.
, and Zheng
, J. Q.
, 2009, “Modeling of Viscoelastic Behavior of Ballistic Fabrics at Low and High Strain Rates
,” Int. J. Multiscale Comp. Eng.
1543-1649, 7
, pp. 295
–308
.35.
Treloar
, L. R. G.
, 1944, “Stress-Strain Data for Vulcanised Rubber Under Various Types of Deformation
,” Trans. Faraday Soc.
0014-7672, 40
, pp. 59
–70
.36.
Hamza
, S. S.
, El-sabbagh
, S.
, and Shokr
, F.
, 2008, “Elastic Behavior of NR/IIR Rubber Blend Loaded With Different Compatibilizers
,” Int. J. Polym. Mater.
0091-4037, 57
, pp. 203
–215
.37.
Ramorino
, G.
, Bignotti
, F.
, Pandini
, S.
, and Ricco
, T.
, 2009, “Mechanical Reinforcement in Natural Rubber/Organoclay Nanocomposites
,” Compos. Sci. Technol.
0266-3538, 69
, pp. 1206
–1211
.38.
Joseph
, S. H.
, 2005, “A Method for Modelling the Nonlinear Viscoelastic Response of Polymers
,” Mech. Time-Depend. Mater.
1385-2000, 9
, pp. 35
–69
.39.
Maity
, J.
, Jacob
, C.
, Das
, C. K.
, Alam
, S.
, and Singh
, R. P.
, 2008, “Direct Fluorination of Twaron Fiber and the Mechanical, Thermal and Crystallization Behaviour of Short Twaron Fiber Reinforced Polypropylene Composites
,” Composites, Part A
1359-835X, 39
, pp. 825
–833
.40.
Wang
, Z. D.
, and Zhao
, X. X.
, 2008, “Modeling and Characterization of Viscoelasticity of PI/SiO2 Nanocomposite Films Under Constant and Fatigue Loading
,” Mater. Sci. Eng., A
0921-5093, 486
, pp. 517
–527
.41.
Findik
, F.
, Yilmaz
, R.
, and Koksal
, T.
, 2004, “Investigation of Mechanical and Physical Properties of Several Industrial Rubbers
,” Mater. Des.
0264-1275, 25
, pp. 269
–276
.42.
Hummel
, S. R.
, Hossain
, K.
, and Hayes
, G. T.
, 2001, “Biaxial Stress Relaxation of High Impact Polystyrene (HIPS) Above the Glass Transition Temperature
,” Polym. Eng. Sci.
0032-3888, 41
, pp. 566
–574
.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.
