U.S. DOT ANALYSIS OF COMPOSITE HYDROGEN STORAGE CYLINDERS UNDER TRANSIENT THERMAL LOADS J. Hu, S....

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ANALYSIS OF COMPOSITE HYDROGEN STORAGE ANALYSIS OF COMPOSITE HYDROGEN STORAGE CYLINDERS UNDER TRANSIENT THERMAL LOADSCYLINDERS UNDER TRANSIENT THERMAL LOADS

J. Hu , S. Sundararaman and K. Chandrashekhara J. Hu , S. Sundararaman and K. Chandrashekhara Department of Mechanical and Aerospace EngineeringDepartment of Mechanical and Aerospace Engineering

University of Missouri – RollaUniversity of Missouri – Rolla

William ChernicoffWilliam Chernicoff US Department of TransportationUS Department of Transportation

Washington, DC 20509Washington, DC 20509

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OutlineOutline

• Background

• Finite Element Model

• Resin Reaction Model

• Failure Criterion

• Temperature Dependent Material Model

• Sub-laminate Model

• Results

• Conclusion

http://campus.umr.edu/

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BackgroundBackground

Composite Cylinder WallComposite Cylinder Wall The inner liner of the cylinder serves as a The inner liner of the cylinder serves as a

hydrogen gas permeation barrierhydrogen gas permeation barrier A filament-wound, carbon/epoxy A filament-wound, carbon/epoxy

composite laminate provides the desired composite laminate provides the desired pressure load bearing capacitypressure load bearing capacity

A glass/epoxy layer provides impact and A glass/epoxy layer provides impact and damage resistancedamage resistance

Carbon/Epoxy

Carbon/Epoxy

Carbon/Epoxy

Carbon/Epoxy

Aluminum liner

Glass/Epoxy

Major loading bearing component

Filament wound Composite Storage Cylinder


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• Gas filling process

• Environmental temperature change

• Exposure to fire

Thermal loading

Pressure loading (Settled)• 34.5 MPa to 70 MPa

Hydrogen storage cylinders

Bonfire test

Background (Contd.)Background (Contd.)


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Finite Element ModelFinite Element Model

The finite element equation for a double curved composite shell

e e e e e eTM K F F

1 2

Te u v w where

is mass matrix

is stiffness matrix

is mechanical force loading

is thermal force loading

eM eK

eF

eTF

o1 2 1 2 1 1 21

u( , , , ) = (1 + ) ( , , ) + ( , , )uR

t t t

o1 2 1 2 2 1 22

v( , , , ) = (1 + ) ( , , ) + ( , , )vR

t t t

o1 2 1 2w ( , , , ) = ( , , )wt t

2

1 R2

R1

Displacement field for a doubly curved shell


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Finite Element Model (Contd.)Finite Element Model (Contd.)The heat conduction equation can be expressed as

[ ]{ } [ ]{ } { }T T TC T K T H

[ ] n mT

V

C cN N dV[ ] n m

T

V

K N k N dV [ ] n n

T s r

S V

H N q dS N q dV

where

c,k

sq

rq

and are thermal conductivity, specific heat and density respectively

and are surface heat flux and heat due to resin reaction and flow.

Finite element model for transient thermo-mechanical analysis can be written as

0 0 00

0 00 0 { }0

ee e ee ee

T

T T T

KM F F

TC K HT


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Implementation SchemeImplementation Scheme

Thermal loading

Mechanical loading

Failure theory

Initialization

Compute stress and temperature

Compute material modulus, density,and thermal conductivity

Material strength

Resin reaction model

Density

Failure type

Stress

Failure typeStrength

Pressure

Temperature

Temperature

Reaction heat

Heat flux


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Resin Reaction ModelResin Reaction Model

( / )e AE RTAt

Reaction kinetic equation (Arrhenius’s law) is:

- Pre-exponential factor

- Density

- Gas constant

- Activation energy

- Temperature

A

T

AER

where

- Timet


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Resin Reaction Model (Contd.)Resin Reaction Model (Contd.)

w

z

g tm dz

t

Gas mass flux at any spatial location

- Wall thickness of composite

- Distance from hot facez

wt

Heat of resin decomposition and gas mass flux can be written as

( ) ( )r g pg pg p

Tq m C Q C C T T

z t

where

where- Specific heat of gas

- Specific heat of composite

- Ambient temperature

- Heat of decomposition

pgC

pC

Q

T


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Resin Reaction Model (Contd.)Resin Reaction Model (Contd.)Parameters of resin reaction model used in present study

PropertyProperty ValuesValues

Pre-exponential factor (A)Pre-exponential factor (A) 500.0500.0

Activation energy (EActivation energy (EAA)) 6.05×106.05×104 4 J/molJ/mol

Gas constant (R)Gas constant (R) 8.314 J/mol/K8.314 J/mol/K

Specific heat of gas (CSpecific heat of gas (Cpgpg)) 2386.5 J/Kg/K2386.5 J/Kg/K

Specific heat of composite (CSpecific heat of composite (Cpp)) 1066.0 J/Kg/K1066.0 J/Kg/K

Heat of decomposition (Q)Heat of decomposition (Q) 3.5×103.5×105 5 J/KgJ/Kg

Ambient temperature (TAmbient temperature (T∞∞)) 2020°°CC


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Failure CriterionFailure Criterion

Hashin’s criterion (for progressive failure model)

22 33 0

2 2 2 222 33 12 13 23 22 33

2 2mtt S

T LT

IF F

Matrix tensile or shear cracking

22 33 0

22 2 2 2

22 33 12 13 23 22 3322 33 2 2

11

2 4

cT

mc c S S ST LT LT LT

FI

F F F F

Matrix compressive or shear cracking

, , , andt c t c SL L T T LTF F F F Fwhere are longitudinal tensile strength, longitudinal compressive

strength, transverse tensile strength, transverse compressive strength and shear strength of unidirectional ply respectively. For a two-dimensional analysis with transverse shear deformation, is taken as zero.33


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Failure criterion Failure criterion (Contd.)(Contd.)

11 0

2

2 21112 132

1ft t S

L LT

IF F

11 0

11fc c

L

IF

Fiber tensile failure

Fiber compressive failure


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Failure criterion Failure criterion (Contd.)(Contd.)

Material degradation parameters considered are (S. C. Tan, 1991):

2 2 2d TE D E 12 4 12

d TG D G 23 4 23d TG D G

2 4 0.2T TD D

Matrix tensile or shear cracking:

and where

2 2 2d cE D E 12 4 12

d cG D G23 4 23d cG D G 2 4 0.4c cD D

Matrix compressive or shear cracking:

and where

1 1 1d TE D E 1 0.07TD

Fiber tensile failure:

where

1 1 1d cE D E 1 0.14cD

Fiber compressive failure:

where


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Temperature Dependent Material ModelTemperature Dependent Material Model

Mechanical and thermal properties of fiber reinforced composites vary significantly with temperature. Hyperbolic tan (tanh) function (A. G. Gibson et. al., 2006) is used to fit the test data for temperature dependent material model.

P(T) tanh2 2

U R U Rg

P P P Pk T T C

where, P(T) - temperature dependent material property

PU - the unrelaxed (low temperature) value of that property

PR - the relaxed (high temperature) value of that property

k - constant describing the breath of the distribution

T - temperature

Tg - mechanically determined glass transition temperature

C - constant


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Temperature Dependent Material Model (Contd.)Temperature Dependent Material Model (Contd.)

Curve fitting test data for transverse and shear moduli


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Longitudinal modulus and strengthLongitudinal direction PU PR K C Tg (oC)

Modulus (GPa) 133.35 111 0.0064 1 100

Strength(MPa)

Tensile 133.35 111 0.0064 1070/127 100

Compressive 133.35 10.7 0.0150 1070/127 100

Transverse modulus and strengthTransverse direction PU PR K C Tg (oC)

Modulus (GPa) 9.135 0.1 0.022 1 100

Strength(MPa)

Tensile 9.135 0.1 0.022 40/8.7 100

Compressive 9.135 0.1 0.022 170/8.7 100

Shear modulus and strength

Shear properties PU PR K C Tg (oC)

Modulus (GPa) 4.515 0.045 0.02 1 100

Strength (MPa) 4.515 0.045 0.02 70/4.3 100

The curve fitting parameters for carbon/epoxy are:


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Temperature (°C) 0 20 70 95 120 170

Cp(KJ/Kg/°C) 0.8 0.86 1.08 1.28 1.4 1.5


Experimental thermal data for carbon/epoxy (G. Kalogiannakis et. al., 2004 ):

Temperature (°C) 20 40 60 80 100 120 140

1 (10-6/ °C) 1.47 0.97 0.77 0.81 1.09 1.61 2.37

2 (10-6/ °C) 29.2 29.5 33.2 40.0 50.2 63.6 80.4

Longitudinal Thermal Conductivity K11= 6.5 W/m/°C

Transverse Thermal Conductivity K22 = 0.65 W/m/°C K33 = 0.65 W/m/°C


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E1 (GPa) E2 (GPa) G12= G13 (GPa) G23(GPa) 12 1 (1/°C) 2 (1/°C)

55 16 7.6 5.0 0.28 6.3 x 10 -6 32 x 10 -6

Strengths (MPa) 1620 690 40 140 60

tLF c

LF tTF C

LF SLTF


Mechanical properties of S-glass/epoxy

Mechanical and thermal properties of Aluminum 6061-T6

Elastic Modulus, EElastic Modulus, E Poisson’s ratio, Poisson’s ratio, Yield strength, Yield strength, yy (1/°C)

70 GPa70 GPa 0.330.33 455 MPa455 MPa 24.3 x 1024.3 x 10-6-6

DensityDensity Heat capacityHeat capacity Heat conductivityHeat conductivity

2700 Kg/m2700 Kg/m33 1000 J/g/K1000 J/g/K 250 W/m/K250 W/m/K

As thermal conductivity and specific heat of glass/epoxy are very close to those of carbon/epoxy, the same values are taken for glass/epoxy.


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Sublaminate ModelSublaminate Model

Each sublaminate consists of several lamina


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Sublaminate ModelSublaminate Model (Contd.)(Contd.)Sublaminate homogenization:• In-plane strains and the interlaminar stresses through the thickness are constant.

The lamina stress-strain relationship is:

where are sub matrices of global stiffness matrix

Partially inverting equation (1) and averaging the in-plane stresses and interlaminar strains:

ooo oio

ioi iii

C C

C C

, andoo oi iiC C C

the terms in are constant through the laminate

(1)

o o

Ti i

A B

B D

(2)

1

1

Nk

ook t k

tA C

t

1

1

Nk

oo oik t k

tB C C

t

1

1

Nk

oi oo oi iik t k

tD C C C C

t

where

andkt is the thickness of each lamina tt is the total thickness of the sublaminate


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Sublaminate Model (Contd.)Sublaminate Model (Contd.)

Partially inverting Eq. (2) , yields

1 1

1 1

o o

T Ti i

A A B

B A B A B D

Equivalent stiffness of the homogenized sublaminate is

1 1

1 1eq T T

A A BQ

B A B A B D

Equivalent engineering properties can be retrieved by inverting Eq. (4)

(3)

(4)


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ResultsResultsTo evaluate the heat transfer model with resin reaction, a simple case is compared with the results available in literature.

Hot face

Cold face

Cold face temperature variation with time is plotted and compared for a composite panel heated at hot face

0 200 400 600 800 1000200

400

600

800

1000

1200

1400

Time (second)

Tem

pera

ture

(K

elvi

n)

Hot faceCold face-ABAQUSCold face-literature


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ResultsResults (Contd.) (Contd.)Modeling

1/8 of cylinder (diameter 0.44 m) is modeled in ABAQUS

A fine mesh is used at the heat source (diameter 0.06 m )

Symmetric boundary conditions are applied

Thermal Load

75,000 Watt/m2 flux acts on the center circle to simulate the localized fire attack

Mechanical Load

Internal pressure is applied on the cylinder

Model mesh

Boundary conditions


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ResultsResults (Contd.) (Contd.)

Sublaminate technique is used to model the composite cylinder wall

The model is implemented in ABQUS FEA code by user subroutine

S8RT doubly curved shell element

Outer surface

Inner surfaceDimensionsThickness of aluminum liner: 2.54 mmThickness of each hoop sublaminate: 5.8 mmThickness of each helical sublaminate: 3.6 mmThickness of protection layer (S-glass/epoxy) : 4 mm


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Temperature DistributionTemperature Distribution

Temperature of various locations in thickness direction at the heat source

Inner surface of sublaminate 1

Outer surface of sublaminate 4



Outer surface of S-glass/epoxy sublaminate


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Temperature DistributionTemperature Distribution

Temperature distribution along the path

path

0 0.02 0.04 0.06 0.08 0.10

100

200

300

400

500

600

700

Distance along path (Time=100s)

Tem

pera

ture

(o C

)

Inner surface of sublaminate 1Inner surface of sublaminate 4Outer surface of sublaminate 5Outer surface of sublaminate 6Outer surface of S-glass/epoxy

0 0.02 0.04 0.06 0.08 0.10

100

200

300

400

500

600

700

800


Tem

pera

ture

(o C

)


0 0.02 0.04 0.06 0.08 0.10

100

200

300

400

500

600

700

800


Tem

pera

ture

(o C

)



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Residual Resin ContentResidual Resin Content

Residual resin content varies with time at different locations in thickness direction at the heat source

S-glass/epoxy Sublaminate

Sublaminate 6

Sublaminate 5

Sublaminate 4

Sublaminate 1


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path

Density change along path

Residual Resin ContentResidual Resin Content

0 0.02 0.04 0.06 0.08 0.1

0

20

40

60

80

100


Res

idua

l res

in p

erce

ntag

e (%

)

Sublaminate 1Sublaminate 4Sublaminate 5Sublaminate 6S-glass/epoxy

0 0.02 0.04 0.06 0.08 0.1

0

20

40

60

80

100


Res

idua

l res

in p

erce

ntag

e (%

)


0 0.02 0.04 0.06 0.08 0.1

0

20

40

60

80

100


Res

idua

l res

in p

erce

ntag

e (%

)



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Resin Depletion in Sublaminate 6Resin Depletion in Sublaminate 6


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Stress Distribution in LinerStress Distribution in Liner

Stress distribution in liner (1000 second )

path

Stress distribution along path

0 0.02 0.04 0.06 0.08 0.11.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

Distance along path

Mis

es S

tres

s (1

00 M

Pa)

Time 1secTime 100secTime 500secTime 1000sec


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Stress Distribution in Sublaminate 6 (Hoop layer)Stress Distribution in Sublaminate 6 (Hoop layer)

Longitudinal stress distribution in sublaminate 6 (1000 sec )

path


0 0.02 0.04 0.06 0.08 0.13.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5

Distance along path

S11

(10

0 M

Pa)


Transverse stress distribution in sublaminate 6 (1000 sec )

Shear stress distribution in sublaminate 6 (1000 sec )


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Stress Distribution in Sublaminate 5 (Helical Layer)Stress Distribution in Sublaminate 5 (Helical Layer)

Longitudinal stress distribution in sublaminate 5 (1000 sec )

path


Transverse stress distribution in sublaminate 5 (1000 sec )

Shear stress distribution in sublaminate 5 (1000 sec )

0 0.02 0.04 0.06 0.08 0.12

2.5

3

3.5

4

4.5

Distance along path

S11

(10

0 M

Pa)



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Composite Cylinder FailureComposite Cylinder FailureTime

= 1 Sec

SL1 SL2 SL3 SL4 SL5 SL6

34.5 MPa 0 0 0 0 0 0

48 MPa 0 0 0 0 0 0

69 MPa 1 1 1 1 1 1

86 MPa 1 1 1 1 1 1

Time = 1000 Sec

SL1 SL2 SL3 SL4 SL5 SL6

34.5 MPa 0 0 1 0 1 1

48 MPa 1 1 1 1 1 1

69 MPa 1 1 1 1 1 1

86 MPa 2 2 2 2 2 2

SL – sublaminate, 0 – no failure, 1 – matrix failure, 2 – fiber break

For a pressure of 34.5 MPa, no failure occurs due to mechanical load. Matrix failure occurs during fire exposure in the layers close to the heat source (sublaminates 5 and 6).

For a pressure of 48 MPa, no failure occurs due to mechanical load. Matrix failure occurs during fire exposure in the all the layers.

For a pressure of 69 MPa, matrix failure occurs due to mechanical load.

For a pressure of 86 MPa, matrix failure occurs due to mechanical load. Fiber break occurs due to localized heat source.


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Matrix Failure Process in Sublamiate 5 (34.5 MPa pressure)Matrix Failure Process in Sublamiate 5 (34.5 MPa pressure)


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Fiber Break Process in Sublamiate 6 (86 MPa pressure)Fiber Break Process in Sublamiate 6 (86 MPa pressure)


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ConclusionsConclusions

A comprehensive finite element model is developed accounting for temperature dependent material properties, resin reaction and progressive failure model.

Under localized fire exposure, the temperature of outermost layer increases rapidly around the heat source, however, the temperature increase in the cylinder inner layers and adjacent area is not significant.

Under localized fire exposure, resin is depleted quickly in the outermost layers and very slowly in inner layers. The resin depleted area may cause fiber breakage during the cool down process which may be a safety concern.

For lower internal pressures, localized fire exposure cause matrix failure in and around the regions of the heat source.

Under high internal pressures, localized fire exposure initiates fiber breakage and may cause overall failure of the cylinder.


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Continuing EffortsContinuing Efforts

Continued refinement of the model – Continued refinement of the model – evaluation of heat transfer to a PRD and evaluation of heat transfer to a PRD and other safety devicesother safety devices

Comparison to physical testComparison to physical test NHTSANHTSA OtherOther


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Thank you

K. [email protected]

http://www.umr.edu/~chandra/

William [email protected]

http://hydrogen.dot.gov


U.S. DOT ANALYSIS OF COMPOSITE HYDROGEN STORAGE CYLINDERS UNDER TRANSIENT THERMAL LOADS J. Hu, S....

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