Similarly to unfilled polymers, the dynamic mechanical properties of polymer/organoclay nanocomposites are sensitive to frequency and temperature, as well as to clay concentration. Richeton et al. (2005, “A Unified Model for Stiffness Modulus of Amorphous Polymers Across Transition Temperatures and Strain Rates,” Polymer, 46, pp. 8194–8201) has recently proposed a statistical model to describe the storage modulus variation of glassy polymers over a wide range of temperature and frequency. In the present work, we propose to extend this approach for the prediction of the stiffness of polymer composites by using two-phase composite homogenization methods. The phenomenological law developed by Takayanagi et al., 1966, J. Polym. Sci., 15, pp. 263–281 and the classical bounds proposed by Voigt, 1928, Wied. Ann., 33, pp. 573–587 and Reuss and Angew, 1929, Math. Mech., 29, pp. 9–49 models are used to compute the effective instantaneous moduli, which is then implemented in the Richeton model (Richeton et al., 2005, “A Unified Model for Stiffness Modulus of Amorphous Polymers Across Transition Temperatures and Strain Rates,” Polymer, 46, pp. 8194–8201). This adapted formulation has been successfully validated for PMMA/cloisites 20A and 30B nanocomposites. Indeed, good agreement has been obtained between the dynamic mechanical analysis data and the model predictions of poly(methyl-methacrylate)/organoclay nanocomposites.

References

References
1.
Chen
,
B.
, and
Evans
,
J. R. G.
, 2006, “
Elastic Moduli of Clay Platelets
,”
Scr. Mater.
,
54
(
9
), pp.
1581
1585
.
2.
Ginzburg
,
V. V.
,
Singh
,
C.
, and
Balazs
,
A. C.
, 2000, “
Theoritical Phase Diagrams of Polymer/Clay Composites: The Role of Grafted Orgaanic Modifiers,”
Macromolecules
,
33
, pp.
1089
1099
.
3.
Giannelis
,
E. P.
, 1996, “
Polymer Layered Silicate Nanocomposites
,”
Adv. Mater.
,
8
, pp.
29
35
.
4.
Chen
,
G.
, and
Qi
,
Z.
, 2000, “
Shear-Induced Ordered Structure in Polystyrene/Clay Nanocomposite
,”
J. Mater. Res.
,
15
, pp.
351
356
.
5.
Ma
,
J.
,
Qi
,
Z.
, and
Hu
,
Y
, 2001, “
Synthesis and Characterization of Polypropylene/Clay Nanocomposites
,”
J. Appl. Polym. Sci.
,
82
, pp.
3611
3617
.
6.
Lan
,
T.
, and
Pinnavaia
,
T. J.
, 1994, “
Clay-Reinforced Epoxy Nanocomposites
,”
Chem. Mater.
,
6
, pp.
2216
2219
.
7.
Kojima
,
Y.
,
Kawasumi
,
M.
,
Usuki
,
A.
,
Okada
,
A.
,
Fukushima
,
Y.
Kurachi
,
T.
, and
Kamigaito
,
O.
, 1993, “
Mechanical Properties of Nylon 6-Clay Hybrid
,”
J. Mater. Res.
,
8
, pp.
1185
1189
.
8.
Matadi
,
R.
,
Makradi
,
A.
,
Ahzi
,
S.
,
Sieffert
,
J. G.
,
Etienne
,
S.
,
Rush
D.
,
Vaudemont
,
R.
,
Muller
,
R.
, and
Bouquey
,
M.
, 2009, “
Preparation, Structural Characterization, and Thermomechanical Properties of Poly(Methyl Methacrylate)/Organoclay Nanocomposites by Melt Intercalation
,”
J. Nanosci. Nanotechnol.
,
9
, pp.
2923
2930
.
9.
Usuki
,
A.
,
Kojima
,
Y.
,
Kawasumi
,
M.
,
Okada
,
A.
,
Fukushima
,
Y.
,
Kurauchi
,
T.
, and
Kamigaito
,
O.
, 1993, “
Synthesis of Nylon 6-Clay Hybrid
,”
J. Mater. Res.
,
8
, pp.
1179
1184
.
10.
Liu
,
Y. J.
, and
Chen
,
X. L.
, 2003, “
Evaluations of the Effective Material Properties of Carbon Nanotube-Based Composites Using a Nanoscale Representative Volume Element
,”
Mech. Mater.
,
35
, pp.
69
81
.
11.
Chen
,
X. L.
, and
Liu
,
Y. J.
, 2004, “
Square Representative Volume Elements for Evaluating the Effective Material Properties of Carbon Nanotube-Based Composites
,”
Comput. Mater. Sci.
,
29
, pp.
1
11
.
12.
Liu
,
Y.
,
Nishimura
,
N.
, and
Otani
,
Y.
, 2005, “
Large-Scale Modeling of Carbon-Nanotube Composites by the Boundary Element Method Based on a Rigid-Inclusion Model
,”
Comput. Mater. Sci.
,
34
, pp.
173
187
.
13.
Van Workum
,
K.
, and
de Pablo
,
J. J.
, 2003, “
Computer Simulation of the Mechanical Properties of Amorphous Polymer Nanostructures
,”
Nano Lett.
,
3
, pp.
1405
1410
.
14.
Ospina
,
S. A.
,
Restrepo
,
J.
, and
Lopez
,
B. L.
, 2003, “
Deformation of Polyethylene: Monte Carlo Simulation
,”
Mater. Res. Innovations
,
7
, pp.
27
30
.
15.
Sheng
,
N.
,
Boyce
,
M. C.
, and
Parks
,
D. M.
, 2004, “
Multiscale Micromechanical Modeling of Polymer/Clay Nanocomposites and the Effective Clay Particle
,”
Polymer
,
45
, pp.
487
506
.
16.
Gates
,
T. M.
, and
Hinkley
,
J. A.
, 2003, “
Computational Materials: Modeling and Simulation of Nanostructured Materials and Systems
,”
NASA/TM–212163
.
17.
Odegard
,
G. M.
,
Gates
,
T. S.
,
Wise
,
K. E.
,
Park
,
C.
, and
Siochi
,
E. J.
, 2003, “
Constitutive Modeling of Nanotube-Reinforced Polymer Composites
,”
Compos. Sci. Technol.
,
63
, pp.
1671
1687
.
18.
Keller
,
T.
,
Tracy
,
C.
, and
Zhou
,
A.
, 2006, “
Structural Response of Liquid-Cooled GFRP Slabs Subjected to Fire---Part I: Material and Post-Fire Modeling
,”
Composites Part A
,
37
(
9
), pp.
1286
95
.
19.
Keller
,
T.
,
Tracy
,
C.
, and
Zhou
,
A.
, 2006, “
Structural Response of Liquid-Cooled GFRP Slabs Subjected to Fire - Part II: Thermo-Chemical and Thermo-Mechanical Modeling
,”
Composites Part A
,
37
(
9
), pp.
1296
308
.
20.
Drozdov
,
A. D.
, 2000, “
Viscoelastoplasticity of Amorphous Glassy Polymers
,”
Eur. Polym. J.
,
36
, pp.
2063
2074
.
21.
Mahieux
,
C. A.
, and
Reifsnider
,
K. L.
, 2001, “
Property Modeling Across Transition Temperatures in Polymers: A Robust Stiffness—Temperature Model
,”
Polymer
,
42
, pp.
3281
3291
.
22.
Mahieux
,
C. A.
, and
Reifsnider
,
K. L.
, 2002, “
Property Modeling Across Transition Temperatures in Polymers: Application to Thermoplastic Systems
,”
J. Mater. Sci.
,
37
, pp.
911
920
.
23.
Richeton
,
J.
,
Schlatter
,
G.
,
Vecchio
,
K. S.
,
Rémond
,
Y.
, and
Ahzi
,
S.
, 2005, “
A Unified Model for Stiffness Modulus of Amorphous Polymers Across Transition Temperatures and Strain Rates
,”
Polymer
,
46
, pp.
8194
8201
.
24.
Matadi
,
R.
,
Gueguen
,
O.
,
Ahzi
,
S.
,
Gracio
,
J.
, and
Ruch
,
D.
, 2010, “
Investigation of the Stiffness and Yield Behaviour of Melt-Intercalated Poly(Methyl Methacrylate)/Organoclay Nanocomposites: Characterisation and Modelling
,”
J. Nanosci. Nanotechnol
,
10
, pp.
2956
2961
.
25.
Takayanagi
,
M.
,
Harima
,
H.
, and
Iwata
,
Y.
, 1963, “
Viscoelastic Behaviour of Polymer Blends and Its Comparison With Model Experiments
,”
Memoirs of the Faculty of Engineering, Kyushu University
,
23
, pp.
1
13
.
26.
Voigt
,
W.
, 1889, “
Über die Beziehung zwischen den beiden Elastizitätskonstanten isotroper Körper
,”
Wied. Ann.
,
38
, pp.
573
587
.
27.
Reuss
,
A.
, 1929, “
Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle
,”
Z. Angew. Math. Mech.
,
9
, pp.
49
58
.
28.
Goyal
,
R. K.
,
Tiwari
,
A. N.
, and
Negi
,
Y. S.
, 2008, “
Microhardness of PEEK/Ceramic Micro- and Nanocomposites: Correlation With Halpin–Tsai Model
,”
Mater. Sci. Eng.
,
491
, pp.
230
236
.
29.
Wei
,
C. L.
,
Zhang
,
M. Q.
,
Rong
,
M. Z.
, and
Friedrich
,
K.
, 2002, “
Tensile Performance Improvement of Low Nanoparticles Filled-Polypropylene Composites
,”
Compos. Sci. Technol.
,
62
, pp.
1327
1340
.
30.
Mahieux
,
C. A.
, 1999, “
A Systematic Stiffness-Temperature Model for Polymers and Applications to the Prediction of Composite Behavior
,”
Ph.D. dissertation
,
Virginia Polytechnic Institute and State University; 1999. Blacksburg, VA 24061-0002
.
31.
Burdette
,
J. A.
, 2001, “
Fire Response of Loaded Composite Structures---Experiments and Modeling
,”
Master thesis
,
Virginia Polytechnic Institute and State University; 2001. Blacksburg, VA 24061-0002
.
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