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FLUID STRUCTURE INTERACTION ON
COMPOSITE STRUCTURES: EXPERIMENTAL &
NUMERICAL STUDIES
Y. W. Kwon
Distinguished Professor
Dept. of Mech. & Aero. Engineering
Naval Postgraduate School
Monterey, California, USA
Multiphysics Conference, December 13-14, 2012
2
Overview
• Introduction
• Objectives
• Experimental Impact Study
• Effect of Nanomaterials (CNT/CNF)
• Computational Modeling and Simulation
• Conclusions
3
Introduction
• Increasing use of composite materials for
naval applications
– Surface ship hull structures
– Superstructures, Sonar domes, etc.
• Polymer composite materials are much lighter
than metals
– Sandwich structures even lighter than standard
laminated composite structures
• The fluid effects are important on sandwich
and/or laminated polymer composite
structures because of their low densities.
4
Objectives
• To understand and predict the effects of Fluid-Structure Interaction (FSI) on dynamic response and failure of laminated or sandwich polymer composite structures when in contact with water
• To conduct experimental study to measure the effect of FSI on laminated or sandwich composite structures
• To study the effect of locally distributed CNT & CNF on the interface strength under FSI
• To develop multiphysics based computational techniques for FSI
Experimental Impact Study
5
• In order to evaluate the FSI effects on
composites, the same impact loading conditions
are applied to the same composite structure,
either immersed in water (called wet structure)
or in air (called dry structure) without causing
damage.
• The same impact loading conditions are applied
to composite structures causing damage under
dry and wet structures.
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Impact Conditions
6
• (A): Air-backed dry impact => Dry impact (Baseline)
• (B): Air-backed wet impact
• (C): Water-backed wet impact
• (D): Water-backed dry impact
• Impact on the top surface of the plate
(A) (B) (C) (D)
Clamped
Plate
Air
surrounding
Clamped
Plate
Water
surrounding
Clamped
Plate
Water
surrounding
Air
Water
surrounding
Air
Clamped
Plate
Impact Testing Equipment
• Free fall impact machine
• Anechoic water tank
8 8
Vacuum Assisted Resin Transfer Molding
(VARTM)
Source: NSWC-CD
• Schematic of VARTM
9 9 9
VARTM Technique
9
Water-Backed Dry Impact
• Impact force comparison between dry and wet case
no damage damage for wet damage for both
(15 cm) (20 cm) (50 cm)
0 50 100 150 200 250 300 350 400 450 -200
0
200
400
600
800
1000
1200
Time, msec
Forc
e, N
Dry Wet
0 50 100 150 200 250 300 350 400 450 -200
0
200
400
600
800
1000
1200
1400
1600
1800
Time, msec
Forc
e, N
Dry Wet
0 50 100 150 200 250 300 350 400 450
0
500
1000
1500
2000
2500
3000
3500
Time, msec F
orc
e, N
Dry Wet
Water-Backed Dry Impact
• Damage growth along with the drop height
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0
0.5
1
1.5
2
2.5
0 10 20 30 40 50 60 70 80
Del
amin
atio
n, c
m
Drop Height, cm
Measured Damage as Function of Drop Height
Sample 1 - Dry
Sample 2 - Dry
Sample 3 - Wet
Sample 4 - Wet
Water-Backed Dry Impact
• Normal strains at gage #2 (no damage)
0 50 100 150 200 250 300 350 400 450 -1.5
-1
-0.5
0
0.5
1
Time, msec
X-S
train
, 1000 m
icro
str
ain
Dry Wet
y x
y
1
2 3 4
0 50 100 150 200 250 300 350 400 450 -1.5
-1
-0.5
0
0.5
1
1.5
Time, msec
Y-S
train
, 1000 m
icro
str
ain
Dry Wet
Water-Backed Dry Impact
• Normal strains along x-axis at gage #2
0 50 100 150 200 250 300 350 400 450 -1.5
-1
-0.5
0
0.5
1 15.24cm (6in) Drop Height
Time, msec
Str
ain
, 1000 m
icro
str
ain
Dry Wet
0 100 200 300 400 500 600 700 -4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1 76.20cm (30in) Drop Height
Time, msec
Str
ain
, 1000 m
icro
str
ain
Dry Wet
Water-Backed Dry Impact
• Normal strains along x-axis at gage #3
0 50 100 150 200 250 300 350 400 450 -1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 15.24cm (6in) Drop Height
Time, msec
Str
ain
, 1000 m
icro
str
ain
Dry Wet
0 100 200 300 400 500 600 700 -3
-2
-1
0
1
2
3 71.12cm (28in) Drop Height
Time, msec
Str
ain
, 1000 m
icro
str
ain
Dry Wet
Water-backed Wet Impact
• Strain-y at gage #4 vs. drop height
15
0 20 40 60 80 100-0.5
0
0.5
1
Time (msec)
milli
stra
in
(a) Drop Height: 55.9cm
wet
dry
0 20 40 60 80 100-0.5
0
0.5
1
Time (msec)
milli
stra
in
(b) Drop Height: 61.0cm
wet
dry
0 20 40 60 80 100-1
-0.5
0
0.5
1
Time (msec)
milli
stra
in
(c) Drop Height: 71.1cm
wet
dry
0 20 40 60 80 100-1
-0.5
0
0.5
1
1.5
Time (msec)
milli
stra
in
(d) Drop Height: 76.2cm
wet
dry
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Dry & Wet Impact on E-glass Plate
16 -1500
-1000
-500
0
500
1000
1500
2000
2500
3000
0 20 40 60 80
Fo
rce (
N)
Time (mS)
Wet Impact at 14"
2771.041899
-1000
0
1000
2000
3000
4000
5000
0 10 20 30 40 50 60 70 80
Fo
rce (
N)
Time (mS)
Dry Impact at 14”
17
FSI Effect on Composite Plate
• Natural Frequency
17
T (sec) ωd (rad/sec)
Dry ε2x 0.010 645.758
ε1x 0.010 657.592
ε2y 0.010 655.875
ε1y 0.010 655.875
Water-backed wet ε2x 0.034 187.463
ε1x 0.033 189.442
ε2y 0.033 189.442
ε1y 0.033 189.157
Air backed wet ε2x 0.026 241.660 ε1x 0.026 242.471
ε2y 0.026 242.004
ε1y 0.025 247.244
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FSI Effect on Composite Plate
• Added Virtual Mass Increment Factor b
b
1
dw
Wet ωn
(rad/sec)
Dry ωn
(rad/sec)
β factor
Water-backed ε2x 173.3422 615.6221 11.61
ε1x 176.6594 661.6360 13.03
ε2y 179.1838 633.4428 11.50
ε1y 173.2472 614.7481 11.59
Air-backed ε3x 223.4895 615.6221 6.59
ε1x 238.2935 661.6360 6.71
ε2y 226.9937 633.4428 6.79
ε1y 226.8572 614.7481 6.34
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E-glass Sandwich Composites
• ¼” Balsa core
• 2-3 plies 6 oz E-glass skin
• Derakane 530A vinyl ester resin
• 1” beams
20
Progressive Impact on E-glass
Sandwich Beam
20
Impact Test
Specimen
Drop Height (mm) Failure
Site 355.6 406.4 457.2 558.8 609.6 660.4
Fo
rce
(N
)
Wet Test #1 805 869 885* - - - Mid-span
Wet Test #2 916 1030 1090* - - - Mid-span
Avg. Wet
test 861 950 988
Dry Test #1 720 767 792 912 1032* Boundary
Dry Test #2 829 892 905 934 990 1010* Boundary
Avg. Dry
Test 774 830 849 923 1011 1010
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Failure of Sandwich Beam
21
Dry Impact
Failure
Wet Impact
Failure
Carbon Fiber Composite Beam
• Pre-cracked beam, 300 mm x 25 mm
• Clamped at both ends
• Impact to the top center
• Strain gage attached to the bottom center
22
With or Without
CNT or CNF
Pre-crack
110 mm
Pristine and Functionalized CNTs
23
SEM showing comparison Dispersion
Functionalized MWNT Pristine CNT
Pristine and Functionalized CNT
24
SEM showing comparison Dispersion
Functionalized MWNT Pristine CNT
25
Interface Strength with CNT
25
• Comparison of two concentrations of CNT – 7.5g/m2 and the
11.5g/m2 resulted in strength increase over the non-reinforced composite joints
– 7.5g/m2 provided the greatest strength increase (10.6%)
– Standard deviation shows no overlap between the results of the non-reinforced and 7.5g/m2 concentration level
Phase 2 Results
0.00g/m^2 7.5g/m^2 11.5g/m^2100.00
110.00
120.00
130.00
140.00
150.00
160.00
170.00
180.00
190.00
Surface Area Concentration
Maxim
um
Stress (
MP
a)
26
Interface Strength with CNT
26
• Failure Stress – All five trials were used for stress data analysis
– 3 types of MWCNT provided a strength increase greater than 11%
– Best based on strength increase and smallest standard deviation.
• D = 30 +/-15nm, L = 5-20 microns, Purity > 95%
Phase 3 Results: Average Maximum Stress (all-data)
No CNT SWCNT MWCNT-A MWCNT-B MWCNT-C MWCNT-D MWCNT-E MWCNT-F120
125
130
135
140
145
150
155
160
165
170
Static Three-Point Bending Load
27
Interface Cracks under Dry Impact
Without CNT With CNT
28
29 29
Interface Crack Growth w/o CNT
30 30
Interface Crack Growth w/ CNT
31 31 31
Mode II Crack Propagation
• Non-reinforced
Crack grows from initial
crack tip
• CNT reinforced
Crack begins away from
initial crack site and
connects to initial crack
32 32
Mode II Results
• CNT reinforcement results in 30.5% increase in Mode II critical energy release rate (calculated via compliance method)
Mode II Average Values
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
No
rmal
ized
GII
Resin Only
CNT
Dry Beam with and without CNT
• w/o CNT w/ CNT
33
Broken resin
Pre-Crack
end
of
crack
Broken carbon fibers
Pre-crack
Failure under Dry Impact
34
• CNTs-reinforced failed at higher impact energy
• No significant improvement for CNFs-reinforced samples
over non-reinforced samples
• Failure defined as crack growth to the center of the beam
90cm height
CNTs-reinforced 9.5mm (no failure at this impact height)
CNFs-reinforced 66% failure, 10mm for non-failure
samples
Non-reinforced 66% failure, 12mm for non-failure
samples
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Water-backed air impact on beams
0 50 100 150 200 250 300 350-200
0
200
400
600
800
1000
Time, msec
Forc
e,
N
Impact Force, CNT Reinforced Sample
60cm
75cm
90cm
Impact force w/o CNT Impact force w/ CNT
0 50 100 150 200 250 300 350-200
0
200
400
600
800
1000
1200
Time, msec
Forc
e,
N
Impact Force, Non-Reinforced Sample
60cm
75cm
90cm
36
Water-backed air impact on beams
36
Strain w/o CNT Strain w/ CNT
0 50 100 150 200 250 300 350 0
1
2
3
4
5
6
7
Time, msec
Str
ain
, 1000 m
icro
str
ain
Strain Data, CNT Reinforced Sample
60cm 75cm 90cm
0 50 100 150 200 250 300 350 0
1
2
3
4
5
6
7
8
Time, msec
Str
ain
, 1000 m
icro
str
ain
Strain Data, Non-Reinforced Sample
60cm 75cm 90cm
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Computational Model
• Developed 2-D and 3-D models
• Structure: CG- or DG-FEM
• Fluid: FEM, LBM, CA
• Fluid-Structure Interaction
• Fluid analysis is the major
computational cost.
Water 0 500 1000 15000
2
4
6
8
10
12
No. of Elements
CP
U R
atio
of F
EA
to
CA
Solid-like Shell Element
• Shell element with displacement DOFs and no
rotational DOFs
• Easy to model multiple layers through thickness
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1 2
3
4
5 6
7 8
CG & DG Formulations
• Continuous Galerkin (CG) as well as
Discontinuous Galerkin (DG) formulations were
used.
• DG is useful to model failure along element
interface such as delamination.
39
CG & DG Formulations
• Effect of resin layers in numerical modeling
40
Five layer plate model
core
skin
resin
Static Bending of Laminated Plate
• 0/90/0 layers
Transv. Shear Stress Diff. of w/ & w/o resin layer
41
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Norm. Shear Stress
No
rm. T
hic
kn
ess A
xis
Analy. Sol.
FEM Soln.
-0.4 -0.2 0 0.2 0.4 0.6 0.8 1-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Normalized Stress Difference
No
rm.
Th
ickn
ess
Axi
s
Bending Stress
Shear Stress
Dynamics of Sandwich Plate
• Comparison between with and without
resin layers
42
0 0.05 0.1 0.150
0.2
0.4
0.6
0.8
1x 10
-3
Time (sec)
Dis
pla
ce
me
nt
(m)
Without Resin Layer
With Resin Layer
0 0.05 0.1 0.15-2.2
-2
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2x 10
6
Time (sec)
Str
ess
(P
a)
Without Resin Layer
With Resin Layer
Dynamics of Sandwich Cylinder
• Comparison between with and without
resin layers
43
0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15-1
-0.5
0
0.5
1
1.5x 10
-7
Time (sec)
Dis
pla
ce
me
nt
(m)
Without Resin Layer
With Resin Layer
0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15-4
-3
-2
-1
0
1
2
3
4x 10
5
Time (sec)
Str
ess a
t ce
nte
r (P
a)
Without Resin Layer
With Resin Layer
Delamination Model
44
• CG: Reduced modulus of resin layer
• DG: Separation of resin/skin interface
Partial (tangential) disconnection
Full (both normal and tangential) disconnection
Disconnection Model with DG
45
• Full Disconnection • Partial Disconnection
Full Disconnection with DG
46
Partial DIsconnection with DG
47
48
Reduced Modulus with CG
49
Delamination in Composite
Materials • Comparison of three different models
Undamaged Full
Disconnection
Partial
Disconnection
Reduced
Modulus
Max. stress
Location
Max stress
Location
Max stress
Location
Max stress
Location
Skin center center zone edge center
Core center center zone edge center
Resin top center center zone edge zone edge
Resin
bottom
center center zone edge zone edge
50
Fluid Medium
• Fluid Domain: FEM, CA, LBM
FEM Domain
CA or LBM
Domain
51
CA Rule for 2-D Wave Equation
( ) ( ) ( ) ( ) 2 ( )( )
2
e w n s cc
r t r t r t r t r tr t t
3-D Wave Equation
• CA rule for 3-D
ϕ(C,t+1)=(ϕ(N,t)+ϕ(S,t)+ϕ(E,t)+ϕ(W,t)+ϕ(F,t)+ϕ(B,t)
-3ϕ(C,t-1))/3
• Time Scale Factor (TSF)
52
3TSF =dx 3
c
TSF =dx 3
3c
TSF =dx
c 3= dt
Comparison of CA and FEM
53
54
Coupling FE & CA Models
• Comparison FE inside CA vs. CA alone
55
Lattice Boltzmann Method
• Classical LBM (CLBM)
• : probability of finding a particle
at lattice site and time t, which moves
along the i-th lattice direction with the
local particle velocity .
• FE-Based LBM (FELBM)
),,1,0( ) ),((),(),( nitxftxfttxexf iiii
),( txfi
x
ie
0~1
fffe
t
f
56
Lid-Driven Cavity
Backward Step
57
1x
S
Cylindrical Obstacle
58
Strouhal No. for Vortex Shedding
Frequency
FSI Model
59
LBM computations on GPU, structural dynamics on
CPU.
Increase performance by:
Maximize overlap of independent calculations
Maximize use of computational resources
FSI Result
60
FSI : 2D Lid-Driven Cavity
61
FSI : 2D Lid-Driven Cavity
62
FSI results
• Comparison with and without FSI
63
0 0.002 0.004 0.006 0.008 0.01
-6
-4
-2
0x 10
-4 baseline plate displacement
time (s)
dis
pla
ce
me
nt
(m)
dry
wet
0 0.002 0.004 0.006 0.008 0.01-7
-6
-5
-4
-3
-2
-1
x 10-4 double density plate displacement
time (s)
dis
pla
ce
me
nt
(m)
dry
wet
Modeling Validation of Wet Plate
• Comparison between exp. and num. results
64
0 0.005 0.01-1
-0.5
0
0.5
y gage 1
time (s)
1000
s
tra
in
calculated
measured
0 0.005 0.01-1.5
-1
-0.5
0
0.5
x gage 2
time (s)
1000
s
tra
in
calculated
measured
Conclusions
• It is essential to include the FSI effect for design and
analysis of polymer composite structures which are in
contacted with water.
• FSI effect is non-uniform over the composite plate. It is
sensitive to boundary conditions.
• Local CNT-reinforcement in a resin interface layer in
carbon fiber beams enhanced the fracture toughness
significantly.
• Developed Displacement-based shell elements, CA,
LBM, FEM, and their coupling tecjniques for FSI.
65
Thank you for your attention!
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