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
.
You do not currently have access to this content.