The damping responses of the nanocomposites with different nano-inclusions were conducted by using the forced vibration technique. The damping performances of the sandwich structure embedded with particulate nanocomposites as core materials were also characterized in the study. The conventional micromechanical model was employed to predict the damping responses of the nanocomposites. The dominant energy dissipation mechanism during the vibration tests were characterized through FEM analysis. Based on the forgoing investigation, several conclusions were addressed.
1. Apparently, the rubber particles can dramatically improve the damping responses of the nanocomposites as well as the corresponding sandwich structures. However, the flexural stiffness of the nanocomposites can be deduced by the inclusion of the rubber particles. It is interesting to mention that the damping properties can be improved by the silica nanoparticles, which is not quite coincided with the prediction from the micromechanical model. The mechanism resulting in the enhancement of the damping property of silica nanoparticles need to be further studied. In addition, it was found that the hybrid inclusion system (10wt%
silica nanoparticles and 10wt% CTBN rubber particles) can demonstrate good damping properties without scarifying its flexural stiffness. The hybrid concept can be employed in the future design of composite materials.
2. Based on the FEM analysis, the dominant energy dissipation mechanism for cantilever-type nanocomposites samples is extension mode. However, once the nanocomposites were embedded as core materials in the sandwich structures, the dominant energy dissipation mode is becoming mixed mode (including the extension and shear modes).
When the thickness ratio of the core to the face sheet is decreasing, the energy dissipation is mostly controlled by the shear mode. In our current design of sandwich structure, both extension and shear modes occur. Although the dominant modes in cantilever-type sample and sandwich structures is different, experimental results demonstrate that the hybrid
nanocomposites still exhibit superior damping responses than other cases.
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Appendix A: Stoichiometric Calculation
Silica/epoxy nanocomposite: Stoichiometric calculation & manufacturing processes
DGEBA，EEW = 187(g/equiv)… x F400 + DGEBA
F400，EEW = 295 (g/equiv) (40%SiO2)… y H-100，AHEW = 45 (g/equiv)… u
Mechanical stir 200 rpm, 5 min Calculation example:
Let SiO2 contain 10wt%
Which means a = 10wt%
If DGEBA = x = 10 grams Sonication
10 min Such that
u/45 = x/187 + y/295 0.4y/(0.6y+u+x) = a
Degasification 20 min, RT Thus
y = 3.820 grams (F400) u = 2.989 grams (H-100)
Adding H-100
Mechanical stir 200 rpm, 10 min
Degasification 30 min
Molding
CTBN/epoxy nanocomposite: Stoichiometric calculation & manufacturing processes
DGEBA，EEW=187(g/equiv)… x
CTBN，EEW=1775 (g/equiv)… z DGEBA + CTBN
H-100，AHEW=45 (g/equiv)… u Calculation example:
Mechanical stir 200 rpm, 80℃, 6 hr Let CTBN contain 10wt%
Which means: a = 10wt%
If DGEBA = x = 10 grams
Such that Degasification
20 min, 80℃
x/187 + z/1775 = u/45 z/(x+u) = a
Adding H-100 Thus
z = 1.244 grams (CTBN) u = 2.438 grams (H-100)
Mechanical stir 200 rpm, 10 min
Degasification 30 min
Molding
Silica/CTBN/epoxy nanocomposite: Stoichiometric calculation & manufacturing processes
DGEBA，EEW=187(g/equiv)… x F400 + DGEBA
F400，EEW=295 (g/equiv) (40%SiO2)… y CTBN，EEW=1775 (g/equiv)… z
H-100，AHEW=45 (g/equiv)… u
Mechanical stir 200 rpm, 5 min Calculation example:
Let silica contain 10wt% and
CTBN contain 10wt% Sonication
Mechanical stir 200 rpm, 10 min
Degasification 30 min
Molding
Appendix B: The source code of the Mori-Tanaka micromechanical model
This source code of Mori-Tanaka micromechanical model is only validated in spherical inclusions.
If the inclusions of the nanocomposite is not the particle shape, this source code should be modified and characterize here.
In the input zone, following material properties should be given by the user.
Em: Young’s modulus of the matrix vm: Poisson’s ratio of the matrix Ep: Young’s modulus of the particle vp: Poisson’s ratio of the particle c1: volume fraction of the particle
clear all
% c1=0+i*0.01; % 20 wt% => c2 = 0.1124 c3 = 1-c1; % volume fraction of matrix
v = vm;
%--- Eshelby for isotropic spherical ---%
% Se: Eshelby Tensor %
cm21 = cm12 ;
%--- --- --- ---%
I = eye(6) ; ICm = inv(Cm) ;
%--- A^(Eshelby) equation calculation: ---%
T = I + Se*ICm*(Cp-Cm) ;
Tp = inv(T) ; % A^(Eshelby) equation
%---%
%--- Mori-Tanaka standard form calculation: ---%
A = (c3*I+c1*Tp) ; IA = inv(A) ;
Cmor = (c3*Cm + c1*Cp*Tp)*IA ; % c1 volume fraction of particle
%---%
Dmor = inv(Cmor) ;
elastic = 1/(Dmor(1,1)) % Young's modulus of the composites
%tplot(i,1)=c1;
%tplot(i,2)=elastic;
%end
Em = Gm*(2*(vm+1)) ;
vmor = elastic/Cmor(6,6)/2-1 ;
%--- --- The End --- ---%
Table 3.1 Comparison results of loss factor by two types of FRF.
FRF 1st Loss factor 2nd Loss factor
Mobility 2.78 % 3.04 %
Receptance 2.80 % 3.08 %
Table 4.1 Natural frequency and loss factor raw data of the particulate nanocomposite vibrating in the first mode.
Specimen Natural frequency (Hz)
Silica(10wt%)_1 24.75 3.47
Silica(10wt%)_2 25.44 3.65
Silica(10wt%)_3 25.06 3.41
CTBN(10wt%)_1 24.25 3.18
Silica(10wt%)+CTBN(10wt%)_1 24.88 3.90 Silica(10wt%)+CTBN(10wt%)_2 24.44 3.89 Silica(10wt%)+CTBN(10wt%)_3 24.19 3.84
CSR(10wt%)_1 24.38 3.44
CSR(10wt%)_2 24.56 3.49
CSR(10wt%)_3 24.94 3.65
Silica(10wt%)+CSR(10wt%)_1 24.69 4.19
Silica(10wt%)+CSR(10wt%)_2 24.44 4.17
Silica(10wt%)+CSR(10wt%)_3 24.94 4.24
Clay(2.5wt%)_1 24.13 3.45
Clay(2.5wt%)_2 24.44 3.41
Clay(2.5wt%)_3 24.75 3.43
Table 4.2 Natural frequency and loss factor raw data of the particulate nanocomposite vibrating in the second mode.
Specimen Natural frequency (Hz)
Loss factor (%)
Neat_1 154.4 2.87
Neat_2 155.3 2.96
Neat_3 156.4 2.94
Silica(10wt%)_1 157.5 3.26
Silica(10wt%)_2 156.9 3.27
Silica(10wt%)_3 156.5 3.20
CTBN(10wt%)_1 153.8 3.68
CTBN(10wt%)_2 152.8 3.58
CTBN(10wt%)_3 153.8 3.52
CTBN(30wt%)_1 154.5 3.91
CTBN(30wt%)_2 153.9 3.86
CTBN(30wt%)_3 156.4 3.87
Silica(10wt%)+CTBN(10wt%)_1 154.8 3.58 Silica(10wt%)+CTBN(10wt%)_2 156.4 3.49 Silica(10wt%)+CTBN(10wt%)_3 159.5 3.56
CSR(10wt%)_1 153.6 3.80
CSR(10wt%)_2 154.9 3.64
CSR(10wt%)_3 153.6 3.75
Silica(10wt%)+CSR(10wt%)_1 156.6 3.48
Silica(10wt%)+CSR(10wt%)_2 155.0 3.43
Silica(10wt%)+CSR(10wt%)_3 156.8 3.50
Clay(2.5wt%)_1 155.3 3.48
Clay(2.5wt%)_2 157.9 3.53
Clay(2.5wt%)_3 157.1 3.51
Table 4.3 Natural frequency and loss factor of the particulate nanocomposites vibrating in the
Silica(10wt%) 25.08 3.51±0.12 18.98
CTBN(10wt%) 24.65 3.12±0.06 5.76
CTBN(30wt%) 24.42 4.40±0.18 49.15
Silica(10wt%)+CTBN(10wt%) 24.50 3.88±0.03 31.53
CSR(10wt%) 24.63 3.53±0.15 19.66
Silica(10wt%)+CSR(10wt%) 24.69 4.20±0.04 42.37
Clay(2.5wt%) 24.44 3.43±0.01 16.27
Table 4.4 Natural frequency and loss factor of the particulate nanocomposites vibrating in the second mode.
Silica(10wt%) 156.97 3.24±0.03 10.96
CTBN(10wt%) 153.47 3.59±0.08 22.95
CTBN(30wt%) 154.90 3.88±0.02 32.88
Silica(10wt%)+CTBN(10wt%) 156.90 3.54±0.04 21.23
CSR(10wt%) 154.03 3.73±0.08 27.73
Silica(10wt%)+CSR(10wt%) 156.13 3.47±0.04 18.84
Clay(2.5wt%) 156.77 3.51±0.04 20.21
Table 4.5 Flexural modulus of the particulate nanocomposites determined by the experimental results in first mode.
Sample Modulus E
(GPa)
Increment (%)
Neat 2.884 -
Silica(10wt%) 3.136 8.74
CTBN(10wt%) 2.385 -17.30
CTBN(30wt%) 1.353 -53.09
Silica(10wt%)+CTBN(10wt%) 2.731 -5.31
CSR(10wt%) 2.474 -14.22
Silica(10wt%)+CSR(10wt%) 2.794 -3.12
Clay(2.5wt%) 2.959 2.60
Table 4.6 Flexural modulus of the particulate nanocomposites determined by the experimental results in second mode.
Sample Modulus E
(GPa)
Increment (%)
Neat 2.971 -
Silica(10wt%) 3.238 8.99
CTBN(10wt%) 2.453 -17.44
CTBN(30wt%) 1.379 -53.58
Silica(10wt%)+CTBN(10wt%) 2.850 -4.07
CSR(10wt%) 2.564 -13.69
Silica(10wt%)+CSR(10wt%) 2.837 -4.51
Clay(2.5wt%) 3.044 2.46
Table 4.7 Loss factor of the particulate nanocomposites at 25Hz in the DMA test.
Silica(10wt%)+CTBN(10wt%) 25 3.64 62.50
CSR(10wt%) 25 3.09 37.95
Silica(10wt%)+CSR(10wt%) 25 3.81 70.09
Clay(2.5wt%) 25 3.02 34.82
Table 4.8 Loss factor of the particulate nanocomposites at 150Hz in the DMA test.
Specimen
Silica(10wt%)+CTBN(10wt%) 150 6.11±0.05 20.99
CSR(10wt%) 150 5.96±0.08 18.01
Silica(10wt%)+CSR(10wt%) 150 5.69±0.05 12.67
Clay(2.5wt%) 150 5.78±0.07 14.46
Table 4.9 Natural frequency and loss factor raw data of the sandwich nanocomposite structure vibrating in the first mode.
Specimen Natural frequency (Hz)
Loss factor (%)
Neat_1 150.5 3.04
Neat_2 150.9 3.13
Neat_3 151.0 3.09
Silica(10wt%)_1 150.9 3.13
Silica(10wt%)_2 151.1 3.28
Silica(10wt%)_3 151.9 3.18
CTBN(10wt%)_1 151.9 3.38
CTBN(10wt%)_2 152.9 3.44
CTBN(10wt%)_3 151.6 3.60
CTBN(30wt%)_1 153.0 3.90
CTBN(30wt%)_2 152.8 3.99
CTBN(30wt%)_3 152.1 3.81
Silica(10wt%)+CTBN(10wt%)_1 152.9 3.64 Silica(10wt%)+CTBN(10wt%)_2 151.8 3.65 Silica(10wt%)+CTBN(10wt%)_3 152.5 3.67
CSR(10wt%)_1 152.5 3.64
CSR(10wt%)_2 151.8 3.57
CSR(10wt%)_3 152.5 3.66
Silica(10wt%)+CSR(10wt%)_1 152.6 3.53
Silica(10wt%)+CSR(10wt%)_2 152.6 3.51
Silica(10wt%)+CSR(10wt%)_3 152.1 3.55
Clay(2.5wt%)_1 152.9 3.53
Clay(2.5wt%)_2 151.5 3.58
Clay(2.5wt%)_3 150.5 3.56
Table 4.10 Natural frequency and loss factor raw data of the sandwich nanocomposite structure vibrating in the first mode.
Specimen
Silica(10wt%) 151.30 3.19±0.07 3.24
CTBN(10wt%) 152.13 3.47±0.11 12.30
CTBN(30wt%) 152.63 3.90±0.09 26.21
Silica(10wt%)+CTBN(10wt%) 152.40 3.65±0.02 18.12
CSR(10wt%) 152.27 3.62±0.05 17.15
Silica(10wt%)+CSR(10wt%) 152.43 3.53±0.02 14.24
Clay(2.5wt%) 151.63 3.56±0.03 15.21
Table 4.11 Effective flexural modulus of the sandwich nanocomposite structures via the vibrating results in the first mode.
Sample Modulus E
(GPa)
Increment (%)
Neat 103.99 -
Silica(10wt%) 106.67 2.58
CTBN(10wt%) 101.73 -2.17
CTBN(30wt%) 99.19 -4.62
Silica(10wt%)+CTBN(10wt%) 102.81 -1.13
CSR(10wt%) 102.56 -1.14
Silica(10wt%)+CSR(10wt%) 103.16 -0.80
Clay(2.5wt%) 104.94 0.91
Table 4.12 Material properties for micromechanics model [26, 28].
Property Epoxy Silica Particle
Elasticity(GPa) 2.971 + 0.0868i 70
Poisson’s ratio 0.35 + 0.00012i 0.2
Table 4.13 Simulation results of silica/epoxy nanocomposite through micromechanics model.
Storage modulus
(GPa)
Loss factor (%)
Increment of Loss factor
(%)
Neat epoxy 2.971 2.92 -
Silica(10wt%) 3.331 2.89 - 1.027
Silica(20wt%) 3.686 2.87 - 1.171
Table 4.14 Material properties for neat epoxy plate [28,39].
Mechanical property Epoxy Young’s modulus (GPa) 3.16
Density (Kg/m3) 1135.7 Poisson’s ratio 0.35
ψxx (%) 13.19
ψxy (%) 15.08
Table 4.15 First two mode results of epoxy plate through FEM modal analysis.
Natural frequency
(Hz) Ezx / Exx ΔEzx / ΔExx
Mode I 25.134 0.00272 0.00311
Mode II 157.34 0.00468 0.00535
Table 4.16 Results of epoxy rod in the DMA test through FEM static analysis.
Ezx / Exx ΔEzx / ΔExx
Epoxy 0.0857 0.0979
Table 4.17 Material properties for CFRP lamina [40].
Mechanical property Value
Ex (GPa) 138
Ey (GPa) 8.5
Gxy (GPa) 7.3
Density(g/cm3) 1580
Poisson’s ratio νxy 0.44
Table 4.18 First mode results of the sandwich structure with epoxy layer interleaved through modal analysis.
f
c D
D Natural frequency (Hz) Ezx / Exx ΔEzx / ΔExx
0.25 59.092 Hz 15.898 18.169
0.50 66.293 Hz 5.355 6.120
1.00 79.973 Hz 2.249 2.570
2.00 104.41 Hz 1.109 1.267
4.00 144.64 Hz 0.739 0.845
4.30 150.06 Hz 0.718 0.821
Mixture solution Mixture solution
Fig 2.1 Mechanical stirrer.
Mixture solution Mixture solution
Fig 2.2 Misonix sonicator 3000.
Fig 2.3 Curing process of particulate/epoxy nanocomposite.
Thermocouple
Temperature controller Thermocouple
Temperature controller
Fig 2.4 Temperature controller and thermocouple.
0o 0o 0o
0o 0o 0o
unidirectional graphite/epoxy prepreg
Core material :
particulate nanocomposites 0o
0o 0o
0o 0o 0o 0o 0o 0o
0o 0o 0o
unidirectional graphite/epoxy prepreg
Core material :
particulate nanocomposites
Fig 2.5 Stacking sequence of the sandwich nanocomposite structure.
pump Vacuum
Fig 2.6 Hot press machine.
Backing tray
Fig 2.7 Stacking sequence of the assisted materials and nanocomposite laminates for fabricating sandwich nanocomposite structure.
A B C D
Fig 2.8 Optical microscope images of thickness in sandwich specimen in 100 magnification.
185 mm
1.55 mm 0.375 mm
0.375 mm length
thickness
185 mm
1.55 mm 0.375 mm
0.375 mm length
thickness length thickness
Fig 2.9 Schematic of the nanocomposite sandwich structure.
(a) (b)
Fig 2.10 TEM images of 10 wt% silica/epoxy nanocomposites: (a) in 50000 magnification (b) in 100000 magnification [28].
2 μm 2 μm 2 μm
1 μm 1 μm 1 μm
(a) (b)
Fig 2.11 TEM images of 10 wt% CTBN/epoxy nanocomposites: (a) in 8000 magnification (b) in 15000 magnification.
(a) (b)
Fig 2.12 TEM images of 30 wt% CTBN/epoxy nanocomposites: (a) in 6000 magnification (b) in 15000 magnification.
(a) (b)
Fig 2.13 TEM images of 10 wt%-10wt% silica/CTBN/epoxy nanocomposites: (a) in 20000 magnification (b) in 50000 magnification.
2 μm 2 μm
2 μm 1 μm1 μm
1 μm
(a) (b)
Fig 2.14 TEM images of 10 wt% CS ep y n ocR/ ox an om sipo tes a) 8000: ( in magnification (b) in 15000 magnification.
(a) (b)
Fig 2.15 TEM images of 10 wt%-10wt% silica/CSR/epoxy nanocomposites: (a) in 20000 magnification (b) in 50000 magnification [29].
(a) (b)
Fig 2.16 TEM images of 10 wt% organoclay/epoxy nanocomposites: (a) in 6000 magnification (b) in 20000 magnification.
signal
OROS FFT analyzer computer 4000series
OROS FFT analyzer computer 4000series Fig 3.1 Experimental equipment for vibration test.
Fig 3.2 Input (shaker) spectrum of epoxy resin at a time of vibration test.
Fig 3.3 Output (laser vibrometer) spectrum of epoxy resin at a time of vibration test.
(a) (b)
Fig 3.4 Input (shaker) spectrum of epoxy resin at an interval time of vibration test: (a) before (b) after enhancement procedure.
(a) (b)
Fig 3.5 Output (laser vibrometer) spectrum of epoxy resin at an interval time of vibration test:
(a) before (b) after enhancement procedure.
Fig 3.6 Illustration of the half-power bandwidth method for measuring damping.
Fig 3.7 Integration result of output (laser vibrometer) spectrum of epoxy resin at a time of vibration test.
Fig 3.8 Applied stress and measured strain in a time history during the test [35].
40 mm 56 mm
3 mm
D = 0.05sin(ωt) mm 40 mm
56 mm
3 mm
D = 0.05sin(ωt) mm
Fig 3.9 Boundary condition and dimension of the test specimen applied in the DMA test.
Fig 3.10 Apparatus feature of Perkin-Elmer Instruments dynamic mechanical analyzer 8000 (DMA 8000).
4.20
Fig 4.1 Loss factor of the particulate nanocomposite vibrating in the first mode.
3.24
Fig 4.2 Loss factor of the particulate nanocomposite vibrating in the Second mode.
2.88
Fig 4.3 Flexural modulus of the nanocomposite determined from the vibrating results in the first mode.
Fig 4.4 Flexural modulus of the nanocomposite determined from the vibrating results in the second mode.
0.00
Fig 4.5 Comparison results of the loss factor of different nanocomposites in the DMA test with varying frequencies.
5.69 5.78
Fig 4.6 DMA results of loss factor in the particulate nanocomposite at 150Hz.
3.53 3.56
Fig 4.7 Loss factor of the sandwich nanocomposite structure vibrating in the first mode.
106.7
Fig 4.8 Flexural modulus of sandwich nanocomposite structure calculated from the vibrating results in the first mode.
Z
X Y
Z
X Y
Z
X Y
Fig 4.9 Schematic of the epoxy plate with the clamped-free boundary condition.
Z
X Y
Z
X Y
Z
X Y
(a)
Z
X Y
Z
X Y
Z
X Y
(b)
Fig 4.10 First two bending mode shapes of epoxy plate under clamped-free boundary condition (a) First mode (b) Second mode.
0.05 mm
Z
X Y
0.05 mm 0.05 mm
Z
X Y
Z
X Y
Fig 4.11 Schematic of the epoxy rod with the fixed-fixed boundary condition, and applied displacement boundary condition.
Z
X Y
Z
X Y
Z
X Y
Fig 4.12 Deformation of epoxy specimen under fixed-fixed boundary condition in the DMA test.
Dc Df
Df
x z Dc
Df
Df
x z x
z
Damping layer Unidirectional
laminates
Z
X Y
Damping layer Unidirectional
laminates
Z
X Y
Z
X Y
Fig 4.13 Schematic of the sandwich structure with the clamped-free boundary condition.