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.

6

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

11

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

16

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

18

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

19

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

21

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

35

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

37

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

38

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!

66