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Optimization of carbon fiber usage in Type 4hydrogen storage tanks for fuel cell automobiles

H.S. Roh, T.Q. Hua*, R.K. Ahluwalia

Argonne National Laboratory, Argonne, IL 60439, USA

a r t i c l e i n f o

Article history:

Received 25 February 2013

Received in revised form

20 June 2013

Accepted 5 July 2013

Available online 14 August 2013

Keywords:

Finite element analysis

Type IV composite pressure vessels

Hydrogen storage

* Corresponding author. Argonne National La252 3296.

E-mail address: hua@anl.gov (T.Q. Hua).0360-3199/$ e see front matter Copyright ªhttp://dx.doi.org/10.1016/j.ijhydene.2013.07.0

a b s t r a c t

Finite element (FE) analysis of a filament wound 700-bar compressed hydrogen storage

Type 4 tank is presented. Construction of the FE model was derived from an initial netting

analysis to determine the optimal dome shape, winding angle, and helical and hoop layer

thicknesses. The FE model was then used to predict the performance of the composite tank

subject to the operating requirements and design assumptions, and to provide guidance for

design optimization. Variation of the winding angle and helical layer thickness in the dome

section was incorporated in the FE model. The analysis was used to determine the mini-

mum helical and hoop layer thicknesses needed to assure structural integrity of the tank.

The analysis also examined the use of “doilies” to reinforce the dome and the boss sections

of the tanks to reduce the number of helical layers wound around the cylindrical section of

the tank. The results of the FE analyses showed that the use of doilies reduces the stresses

near the dome end but the stresses at the tank shoulder are not affected. A new integrated

end-cap design is proposed to reinforce the dome section. With the integrated end-cap, FE

analysis showed that the high stress points shift from the dome to the cylindrical section of

the tank.

Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

1. Introduction (DOE’s) Controlled Hydrogen Fleet and Infrastructure Valida-

With the depletion of fossil fuels and increasing concerns of

their hazardous effects on the environment, hydrogen has

emerged as an attractive alternative fuel for use in trans-

portation. Hydrogen can be stored onboard the vehicles as

compressed gas, cryo-compressed liquid, or in advanced

storage materials, such as chemical hydrides, metal hydrides,

or sorbents. Compressed hydrogen storage in Type 3 (metal-

lined) and Type 4 (polymer-lined) tanks provides a near-term

pathway to fuel cell vehicle commercialization because

physical storage as a compressed gas is well understood, and

it has been demonstrated in the U.S. Department of Energy’s

boratory, 9700 S Cass Av

2013, Hydrogen Energy P16

tion and Demonstration Project (also referred to as the

National Fuel Cell Electric Vehicle, FCEV, Learning Demon-

stration) [1].

A recent study of 350- and 700-bar H2 storage tanks [2] has

shown that the carbon fibereepoxy composite needed to pro-

vide the structural strength for these fuel tanks is the highest

contributor to the total storage system cost, accounting for

>70% of the total system cost. Therefore, reducing the amount

of carbon fiber usage is one of themajor Department of Energy

(DOE) initiatives in physical hydrogen storage system devel-

opment. This can be accomplished by a combination of

optimal geometric tank design and improvement in filament

enue, Argonne, IL 60439, USA. Tel.: þ1 (630) 252 7753; fax: þ1 (630)

ublications, LLC. Published by Elsevier Ltd. All rights reserved.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 2 7 9 5e1 2 8 0 212796

winding technique, as well as a lower cost carbon fiber. Fila-

ment winding is a widely practiced technique for high perfor-

mance composite structures, such as pressure vessels, fuel

tanks, pipes, and rocket motor cases. Winding patterns vary,

however, depending on the tank geometry, themanufacturing

process, fiber layout, machine accuracy, and cost. Since

filament-wound composite pressure vessels aremore prone to

fail in their dome sections, the dome shape and fiber winding

over the dome are important considerations in the overall

structural integrity of the storage tank.

A geodesic (i.e., isotensoid) winding design [3], in which

all fibers are uniformly stressed and display no shearing or

bending stiffness, has a minimum mass of the carbon fiber

composite for a given cylinder diameter and storage pres-

sure. An isotensoid dome is, therefore, regarded as the

optimal shape for a filament wound dome. Geodesic path

for fiber layout used in netting analysis [4,5] is commonly

used in the initial design of pressure vessels. This is fol-

lowed by finite element (FE) analysis to simulate the me-

chanical behavior of vessel in fine details. Kabir [6]

conducted a numerical analysis of filament wound pressure

vessels with over-wrapped metallic liners with plastic

behavior (Type 3 tanks). Results of 3-Dimensional (3-D) FE

analyses showed that the metallic liner produces a

remarkable drop in the principal on-axis stresses in both

the helical and the hoop wound layers of the fibereepoxy

composite. Park [7] studied possible variations in winding

angles considering a semi-geodesic path equation, and

performed 3-D FE analyses to predict the behavior of fila-

ment wound structures incorporating continuous change of

fiber angles over the dome region. The FE results matched

well with the experimental data from strain gages attached

to the outer surface of the tank. Ahluwalia [8] and Hua [9]

assessed the performance and cost of cryo-compressed

and compressed hydrogen storage tank systems and

compared them to the DOE 2010, 2015, and ultimate targets

for automotive applications.

Table 1 e Design parameters.

Tank parameters Unit Values

Recoverable H2 kg 1.4e5.6

Empty pressure MPa 2

Service pressure MPa 70

Length-to-diameter 1.5e3.7

Liner material HDPE

Design safety factor 2.25

Burst pressure MPa 158

Failure location Cylinder

Translation efficiency % 87

Fiber strength variability % 90

Winding efficiency % 80

T700 fiber strength MPa 4900

Composite strength MPa 2550

Fiber volume fraction 0.6

Composite density kg/m3 1800

E1, E2, E3 GPa 135, 9.66, 9.66

G12, G13, G23 GPa 5.86, 5.86, 3.46

n12, n13, n23 0.25, 0.25, 0.41

In conventional filamentwinding of Type 4 tanks, the high-

density polyethylene (HDPE) liner is fully wrapped with car-

bon fiber composites in both helical and hoop directions. He-

lical layers are wound from end to end to bear the axial

stresses and protect the dome, while hoop layers are wound

only in the cylindrical section to carry the hoop stresses not

carried by the helical layers. In this paper, we identify the

most vulnerable failure points in a Type 4 700-bar H2 storage

tank, and propose methods to reinforce the tank using a

reduced amount of carbon fiber as compared to conventional

filament winding techniques.

2. Methodology

2.1. Configuration of compressed hydrogen storagetanks

This study addresses the design of compressed hydrogen

storage tanks with operating pressures of 70 MPa, suitable for

high-volume manufacturing for automotive applications, in

particular fuel cell vehicles. The analyses are for Type 4

hydrogen storage tanks wrapped with carbon fiber and

capable of storing 1.4e5.6 kg usable hydrogen. Using a safety

factor of 2.25, the tanks are designed for a minimum burst

pressure of 158 MPa. The carbon fiber is assumed to be Toray

T700S, which has a manufacturer-listed tensile strength of

4900 MPa. The fiber-resin composite, with 60% fiber by vol-

ume, has a manufactured-listed tensile strength of 2550 MPa.

The allowable stress for design purposes is lower by two fac-

tors. One is the fiber manufacturing factor to account for

variability in fiber quality due to high volume manufacturing

and another is the tank manufacturing factor to account for

variations in the winding process and conditions. We adopt a

manufacturing variability factor of 90%, and a winding effi-

ciency of 80% in this study. The design parameters and ma-

terial properties are listed in Table 1.

Comments

Single/dual

Type 4 tank

Ratio of composite strength to fiber strength normalized to 60% fiber

volume

Fiber variability due to high volume manufacturing

Include effects of composite thickness, winding tension

Toray

Toray

Toray

Fig. 1 e Schematic of Type 4 compressed hydrogen storage tank.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 2 7 9 5e1 2 8 0 2 12797

Fig. 1 shows a schematic drawing of a storage tank that is

1400 mm in length and 465 mm in diameter, which can store

5.6 kg of usable hydrogen (5.8 kg total) at 70 MPa [10]. A fiber

winding angle of 15� was used for the helical layers, while

angles close to 90� were used for the hoop layers. To help

squeeze out excessive resin during the winding process,

the helical and hoop layers were wound alternately over the

liner.

2.2. Design procedures

A flowchart of the analysis process is shown in Fig. 2. Input

parameters, such as service pressure, amount of recoverable

hydrogen, are used to determine the minimum internal vol-

ume of the storage tank. The length-to-diameter ratio is

chosen to fit the tank within the available space in the auto-

mobile, in which the storage system (including balance-of-

plants) will be installed.

After determining tank’s internal dimensions, i.e., length,

diameter, and the dome shape, netting analysis [11] is used to

estimate the helical and hoop layer thicknesses in the cylin-

drical portion of the tank required for the burst pressure as a

design load. Using results obtained from the netting analysis,

Fig. 2 e Flowchart for design and analysis proce

3-D FE analysis is conducted using ABAQUS [12] with the

Wound Composite Modeler extension [13]. The helical and

hoop layer thicknesses are increased until the fiber stresses in

both layers are less than the allowable stresses.

To reduce the total usage of carbon fiber, the dome section,

known to be the weakest portion of the tank, is reinforced

using doily layers which are “strips” of carbon fiber (CF) placed

strategically in the dome for local reinforcement. As shown in

Fig. 3, the doilies are inserted between helical layers over the

dome in order to provide extra strength in the circumferential

direction. One method for inserting the doily layer is to over-

wrap it with the woven cloth, while the othermethod involves

winding it with the fibers. Using either method, the dome is

reinforced along the longitudinal direction as well as the

circumferential direction. It is noted that fiber directions of

the doily in this studywere chosen to be close to 90� in order to

reduce the stresses in the helical layers. The advantage of

adding doilies is that the helical layer thickness can be

reduced without compromising the target stress ratio. As a

result, the total amount of CF usage is also reduced. Addi-

tionally, we propose a new integrated end-cap design that

could also reduce carbon fiber usage relative to conventional

filament winding method.

ss of compressed hydrogen storage tanks.

Fig. 3 e Doilies for local reinforcement of the dome.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 2 7 9 5e1 2 8 0 212798

3. Mathematical and numerical analysis

3.1. Netting analysis

Netting analysis is a preliminary sizing step to estimate the

thicknesses of the helical and hoop layers for given pressure

load, safety factor, and composite strength. To simplify this

procedure, it is assumed that the resin does not contribute to

carrying any part of the load. For a cylinder with a unit length

subjected to an inner pressure p (see Fig. 4 for an explanation

of the various parameters), force equilibrium along axial and

hoop directions gives,

axial : sf ;atacos2að2pRÞ ¼ p

�pR2

�(1)

hoop : sf ;atasin2aþ sf ;90t90 ¼ pR (2)

From Eqs. (1) and (2), the thicknesses of the helical layers

and the hoop layers can be obtained as

ta ¼ pR=�2sf ;acos

2a�

(3)

t90 ¼ pR�2� tan2a

���2sf ;90

�(4)

where R is the tank radius, sf,a and sf,90 are design allowable

stress of fiber in the helical layer and the hoop layer,

respectively.

Fig. 4 e Circular cylindrical storage tank: left, cylinder su

3.2. FE modeling

FE analyses were performed using ABAQUS 6.11 with the

Wound Composite Modeler extension. The geometry of the

tank determined in the previous section was used to create

the FE model. First, the FE model was set up with only helical

and hoop windings, i.e., without any special extra dome

reinforcement, considered as a base case. The results of this

analysis were subsequently compared with the results of a

model that incorporates doilies for dome reinforcement.

When doilies are used in themodel, they are inserted between

the helical layers. In view of the symmetry, axial symmetric

boundary conditions were applied at the mid-plane cross

section of the cylinder through the Z-plane, and cyclic

boundary conditionswere assigned in the q-direction on the 5�

azimuthal strip. The opening end of the tank was allowed to

translate along the Z-direction. Material properties such as

tensile strength, Young’smodulus, Poisson’s ratio are listed in

Table 1.

The helical layer thickness and winding angle were varied

element by element in the dome section. The FE model was

created using 3-D elements provided in ABAQUS. To ensure

convergence, four elements in the azimuthal circumferential

direction and 10 to 16 elements through the cylinder thickness

direction were used.

3.3. Wound Composite Modeler

The Wound Composite Modeler extension was used to auto-

matically generate FE models of filament wound pressure

vessels. The Wound Composite Modeler requires geometric

parameters, such as type of dome, cylinder diameter, and

winding layout of helical and hoop windings, to define the

geometry of the tank in the cylindrical and dome portions. The

Wound Composite Modeler also calculates the change of fiber

angles over the dome (Fig. 5) and applies it to the FE model.

3.4. Results and discussions

FE analyses were performed on filament wound storage tanks

with and without special dome reinforcement techniques,

which include the use of doilies or an integrated end-cap. In

this paper, the FE models for the various cases are identified

from themodel name. For example, V145-DY-30modelmeans

that it has the inner volume of 145 L, the dome is reinforced by

doily layers, and the last two digits,�30 indicates the length to

bject to inner pressure P; right, helical fiber element.

Fig. 5 e Variation of helical angle in the dome section.

0 200 400 600 800

0

1

2

helical layer

90o hoop winding Variable hoop winding

Stre

ss a

long

fibe

r dire

cito

n, G

Pa

Distance, mm

hoop layer

CL

Fig. 6 e Fiber stress distribution in helical and hoop layers

of 145L model with different hoop winding patterns.

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diameter ratio times ten of the hydrogen storage tank model.

Other notations include ND (no doilies) and EC (end cap).

Table 2 summarizes the results for various models that are

discussed in this section.

3.4.1. Hoop winding angleThe case V145-ND-30a represents a base case with only he-

lical and hoop windings for a tank that holds 5.6 kg usable

hydrogen. The helical and hoop thicknesses are 18.5 mm and

19.6 mm, respectively. The total composite weight of the

tank is 107.4 kg. Fig. 6 shows the upper/lower bound stress

profiles at the helical and hoop layers determined by FE

analysis. In this baseline design where the hoop angle is 90�,the stress decreases from inner to outer layers, and the

stress at the innermost layer is 33% higher than that in the

outermost layer. Our analysis showed that the stress distri-

bution could be made more uniform across the layers by

varying the fiber angle from 75� at the innermost layer,

increasing to 90� at the outermost layer. The more uniform

stress distribution in case V145-ND-30b results in smaller

hoop layer thicknesses of 17.6 mm. The amount of CF usage

is reduced to 102 kg.

Table 2 e Geometry and weight of the composite for different

FE model H2, kg L/D ID, mm

Helical

V36-DY-30 1.4 3.0 246 9.0

V52-DY-25 2.0 2.5 300 11.0

V73-DY-30 2.8 3.0 310 11.3

V104-DY-16 4.0 1.6 378 15.5

V145-ND-15 5.6 1.5 521 22.4

V145-DY-15 5.6 1.5 521 17.8

V145-ND-30a 5.6 3.0 391 18.5

V145-ND-30b 5.6 3.0 391 18.5

V145-DY-30 5.6 3.0 391 14.3

V145-EC-30 5.6 3.0 391 14.3

3.4.2. L/D ratioTanks that fit within the available space onboard a vehicle

typically have length-to-diameter ratio between w1.5 and

w4.0. For the same volume of 145 L, analysis was carried out

for a tank with a smaller L/D ratio of 1.5 and compared with

case V145-ND-30b described above. The results of the analysis

showed only a small difference in the amount of composite

needed, 103.6 kg for L/D of 1.5 versus 102.0 kg for L/D of 3.0.

3.4.3. Doilies for reinforcing the dome regionsTo reinforce a pressure vessel for aerospace applications, the

use of doilies has been suggested by Dorsch [14]. James [15]

reported that the use of wafer reinforcement increased the

calculated burst pressure by 17% compared to a model

without the reinforcement. However, since the winding angle

decreases rapidly with increasing radial distance from the

boss, the wafer’s outer edge fibers approach perpendicularity

to the polar fibers, resulting in a severe stiffness discontinuity.

This high angular orientation between wafer and polar fibers

also causes strain incompatibilities, which may lead to

delamination and premature vessel failure.

models.

Thickness, mm CF composite weight, kg

Hoop Doily End-cap

11.1 4.5 No 23.1

13.3 5.0 No 33.3

14.0 5.5 No 46.0

20.0 6.0 No 68.0

23.5 e No 103.6

23.5 6.5 No 93.1

19.6 e No 107.4

17.6 e No 102.0

17.6 5.5 No 91.0

17.6 e 5.0 92.6

0

30

60

90

120

w/o Doilyw/ Doily

93.1 91.0

3.0

102.0

Wei

ght o

f CF

Com

posi

te, k

g

L/D Ratio

103.6

1.5

Fig. 8 e Comparison of composite usage for models with or

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 2 7 9 5e1 2 8 0 212800

In order to investigate the effect of local reinforcement

with a 5e6 mm thick doily on the stress distribution in the

helical layer in the dome, the doily was inserted between the

helical layers in the dome section, and the calculated stresses

were compared to the stresses without the doily, for L/D ratios

of 1.5 and 3.0. Fig. 7 shows the upper/lower bound stress dis-

tributions in the helical and hoop layers with and without the

doily. For both L/D ratios of 1.5 and 3, the results show that

tanks with the doily have a greater stress reduction in the

dome region than the tanks without the doily. Consequently,

local reinforcement using a doily can help to reduce the

thickness of the helical layer. The stresses in the helical and

hoop layers increase slightly in the cylindrical section of the

tank because of the reduced helical thickness but are within

the design allowable stress. Fig. 8 shows a comparison of the

resulting composite weight for the designs with andwithout a

doily. Using the doily reduces the weight of the total

(a)

(b)

0 150 300 450 600

0

1

2

doily

helical layer

L/D = 1.5 w/o w/

Stre

ss a

long

fibe

r dire

cito

n, G

Pa

Distance, mm

hoop layer

CL

0 200 400 600 800

0

1

2

doily

helical layer

L/D = 3.0 w/o w/

Stre

ss a

long

fibe

r dire

cito

n, G

Pa

Distance, mm

hoop layer

CL

Fig. 7 e Fiber stress distribution in the helical and hoop

layers (a) L/D [ 1.5 with and without doily (b) L/D [ 3.0

with and without doily.

without doily.

composite needed from 102e103.6 kg to 91e93.1 kg for tanks

of L/D of 1.5e3, respectively, for a weight saving of nearly 10%.

3.4.4. Storage size effectUnder a fixed operating pressure of the tank, the amount of

recoverable H2 into the tank solely depends on tank sizes. This

study designed compressed hydrogen tanks in various sizes

and compared composite weights required for those tank

sizes. For service pressure of 70 MPa, Fig. 9 shows the relation

of the design weight of the composite using a doily to the

tank’s storage capacity for hydrogen. It is seen that the

amount of composite materials required is nearly linearly

proportional to the hydrogen carrying capacity.

3.4.5. Integrated end-capWe developed and analyzed the Integrated End Cap Vessel

(IECV) concept (Fig. 10) for Type 4 compressed hydrogen

storage tanks. The end caps are first fabricated separately by

0 1 2 3 4 5 60

20

40

60

80

100

L/D > 2.0 L/D < 2.0

Wei

ght o

f CF

Com

posi

te, k

g

Amount of Usable H2 in Tank

Fig. 9 e Relation between composite usage and H2 storage

capacity.

Fig. 10 e Integrated end-cap for local reinforcement of the

dome.

(a)

(b)

0 150 300 450 600 750

0

1

2

Hoop layer upper bound lower boundHelical layer upper bound lower boundEnd-cap

Stre

ss a

long

fibe

r dire

cito

n, G

Pa

Distance, mm

End Cap : 30 deg fiber angles

CL

0 150 300 450 600 750

0

1

2

Hoop layer upper bound lower boundHelical layer upper bound lower boundEnd-cap

End Cap : 60 deg fiber angles

Stre

ss a

long

fibe

r dire

cito

n, G

Pa

Distance, mm

CL

Fig. 11 e Fiber stress distribution in helical and hoop

layers: (a) with end-cap using 30� fiber angle, (b) with end-

cap using 60� fiber angle.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 8 ( 2 0 1 3 ) 1 2 7 9 5e1 2 8 0 2 12801

Resin Transfer Molding (RTM) and are made of the same car-

bon fiber (T700S) and resin material that is used in the tank

overwrap. The tensile strength of end cap is assumed to be

75% of the fiber strength used in helical and hoop layers. The

end caps are then integrated with the HDPE liner and the

aluminum boss using the blow molding method. Finally, the

tank is reinforced by conventional helical and hoopwinding of

the fibers. In this design, the inner pressure is carried by the

end cap as well as the helical layer in the dome, so that the

amount of helical windings needed is less than that in a

conventional tank that is reinforced by filament wound fibers

only. Fig. 10 shows a sectional view of a 5-mm-thick end-cap.

To investigate the effect of fiber angles in the end-cap on fiber

stresses in the helical and hoop layers, end capswith�30� and�60� fiber angles were modeled.

Fig. 11 plots the stresses along the fiber direction in helical

and hoop layer of V145-ECwith end-cap of�30� and�60� fiberangle. Our FE analysis shows that the stress in the composite

is reduced at the shoulder as well as near the boss flange. The

peak stress is moved from the dome section (in filament

wound tank) to the cylindrical section of the tank. For the end-

caps with �30� fiber angles, it is seen that stresses in hoop

layer tend to increase around the junction of the cylinder and

the dome. This happens because the end-caps with �30� fiberangles do not have enough stiffness to resist the deformation

in radial direction. With end-cap of �60� fiber angle, however,

stresses in the hoop layers around the junction are seen to

decrease, while reducing stresses in the helical layers at the

dome. In addition, it is seen that the fiber stresses in the end-

cap region are evenly distributed. Fig. 12 shows the shear

stresses at the layer interface for the end-cap with �60� fiber

angles (V145-EC-30). The shear stresses are well distributed

over the dome ranging from30 to 80MPa. Similar to the tensile

stress distribution across the layers, the shear stress is highest

at the innermost interface between the end-cap and the first

helical layer, and decreases at the outer layer interfaces. The

weight of the composite with the end-cap was 92.6 kg, which

is a little heavier than the model with the doily, 91 kg, partly

due to the lower tensile strength assumed for the end-caps.

0 100 200 300 400 500 600 700 800-400

-300

-200

-100

0

100

200

dome

Interface 1st 2nd 3rd

Shea

r stre

ss, M

Pa

Distance, mm

cylinder

Fig. 12 e Shear stresses distribution at fiber layer interfaces

with end-cap using ±60� fiber angles.

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4. Conclusions

This study dealt with the design and analysis of Type 4 fila-

ment wound compressed hydrogen storage tanks for fuel cell

vehicles. The focus of the analysis was on only the carbon

fibereepoxy composite used in overwrap windings to provide

the structural strength for the compressed gas tankeHDPE

liner, outer protection, if any, boss, or other balance-of-plant

in the total hydrogen storage system were not included in

the analyses discussed in this paper. The configuration of the

composite was determined for various tank volumes and

thicknesses of helical and hoop layers were calculated using

netting analysis for preliminary sizing. The effects of three

main parameters on the stress distributions in the composite

were analyzed: (1) the hoop winding angle, (2) use of a rein-

forcing doily in the dome region, and (3) use of an integrated

end-cap. The main findings are summarized below.

� Changing the hoopwinding angle in the various hoop layers

led to w5% reduction of the composite needed to meet the

same design requirements.

� In the investigation of the effect of tank L/D ratio on com-

posite weight for 5.6 kg recoverable H2 storage capacity

tanks, the results of the analysis for L/D of 1.5 and 3.0

showed only a small difference in the amount of composite

needed, 103.6 kg versus 102.0 kg, respectively.

� Usingadoily inthedomesectionreduced thestressesnear the

opening end of the tank, but the doily did not help to reduce

the stresses over the shoulder section which was not rein-

forced by the doily. Also, using the doily reduces theweight of

the total composite needed from 102e103.6 kg to 91e93.1 kg.

� The composite weight needed for satisfying design re-

quirements increases linearlywith the capacity of storedH2.

� In the IECV design, the stress in the dome is reduced sub-

stantially and is lower than the stress in the cylindrical

section. It was shown that using the end-cap could reduce

the required thickness of helical layer and result in com-

posite weight-saving by about 10%.

Acknowledgments

This work was supported by the U.S. Department of Energy’s

Office of Energy Efficiency and Renewable Energy. Ms. Grace

Ordaz of the Office of Fuel Cell Technologies was the Tech-

nology Development Manager for this study. Argonne Na-

tional Laboratory, a U.S. Department of Energy Office of

Science laboratory, is operated by UChicago Argonne, LLC,

under Contract No. DE-AC02-06CH11357.

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