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Analysis of intermetallic swelling on the behavior of a hybrid solutionfor compressed hydrogen storage Part I: Analytical modeling

Abdelkader Hocine a,b, * , David Chapelle b , Lamine M. Boubakar b , Ali Benamar c, Abderrezak Bezazi da University Hassiba Benbouali, BP. 151, Chlef 02000, Algeriab Institute FEMTO-ST, Dept. LMARC, 24, Epitaphe street, 25000 Besanon, Francec ENSET, Department of Mechanical Engineering, BP. 1523, Oran 31000, Algeriad University 08 Mai 1945, BP. 401, Guelma 24000, Algeria

a r t i c l e i n f o

Article history:Received 25 September 2009Accepted 23 November 2009Available online 27 November 2009

Keywords:LaminatesIntermetallicsFailure analysis

a b s t r a c t

This study focuses on the mechanical response of a hybrid solution dedicated to gaseous hydrogen stor-age. This solution is made of a carbon/epoxy composite overwrapped on a metal liner rst coated withintermetallic material. The composite helps to reinforce the structure, while the liner prevents it fromany leakage. In case of deciency, the intermetallic material behaves as a sponge and interrupts the leak-age by absorption and micro-cracks reduction. This hybrid solution or this specic use of intermetallicmaterial has never been presented before. The laminate composite is anisotropic, whereas the liner isan elasticplastic material. The intermetallic is purely thermo elastic and its study is limited to itsmechanical contribution. Using these hypotheses, the suggested analytical model provides an exact solu-tion for stresses and strains on thecylindrical section of the hybrid solution submitted to thermomechan-ical static loading and hydrogen leakage. The swelling effect of the intermetallic on the behavior of thestructure is then investigated.

Crown Copyright 2009 Published by Elsevier Ltd. All rights reserved.

1. Introduction

Hydrogen is considered as one of the more promising energyvectors of the future. It can be used as a fuel in many applications.However, this requires several technological hurdles to be cleared,especially the one concerning its storage. Storage must offer a highdegree of safety as well as allowing ease of use in terms of energydensity and dynamics of fuel storage and controlled release.

The use of composite materials is an extremely interestingalternative to metallic materials in the construction of tanks. In-deed, these materials are characterized by their lightness, rigidity,good fatigue strength, and corrosion resistance when their compo-nents are not metallic [1] . Thin or thick walled tanks are widelyused in several branches of engineering, such as the storage of compressed hydrogen, liqueed and compressed natural gas [2,3] .

The choice of material for the liner is crucial whenever the ves-sel is designed to contain gas under high pressure, to prevent forinstance the diffusion through the wall, or when it is designed tocontain liquid under severe temperature conditions. The over-wrapped composite aims to ensure the mechanical strength. This

storage can provide several advantages: it ensures a perfect partic-ipation between the liner and the composite hull, it uses the over-all resistance of the ber in tension and it allows reaching weightsaving up to 50% in comparison with all metal vessels [4,5] .

In many metals, the hydrogen embrittlement decreases drasti-cally the failure strength. Experimental observations [6,7] and the-oretical calculations [810] have demonstrated that dissolution of hydrogen atoms increases the dislocation mobility and promotehighly localized plastic processes, which eventually lead to ductilerupture. In the case of hydrogen storage, the embrittlement phe-nomenon can be responsible of the formation of cracks in the alu-minum liner and can lead to micro-leaks.

Based on previous works, Chapelle and Perreux [11] developedan analytical procedure to predict the behavior of the cylindricalsection of a type 3 vessel for hydrogen storage applications. Theanisotropic plastic ow of the liner and the damage for the com-posite were taken into account. Hocine et al. [12] present an exper-imental, analytical and FEMsimulation investigation of a hydrogenstorage vessel of type 3. The suggested analytical model providesan exact solution for stresses and strains on the cylindrical sectionof the vessel solution submitted to mechanical static loading. Someanalytical results are compared with experimental and the niteelement solutions, a good correlation is observed.

The present study concerns the development of an improvedhigh pressure hydrogen storage vessel ( Fig. 1 ). In this solution, ahydrogen absorbing intermetallic between the aluminum liner

0261-3069/$ - see front matter Crown Copyright 2009 Published by Elsevier Ltd. All rights reserved.doi: 10.1016/j.matdes.2009.11.048

* Corresponding author. Address: University Hassiba Benbouali, BP. 151, Chlef 02000, Algeria. Tel./fax: +213 27 72 28 77.

E-mail addresses: [email protected] (A. Hocine), [email protected] (D. Chapelle), [email protected] (L.M. Boubakar), [email protected] (A. Benamar), [email protected] (A. Bezazi).

Materials and Design 31 (2010) 24352443

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and the carbon ber/epoxy resin composite is integrated. Even if this solution has been previously mentioned by Janot et al. [13] ,the present study is fully original because it focuses on mechanicalaspect of this hybrid structure. The role of the intermetallic is notto absorb the whole hydrogen stored in the high pressure tank as itmay be used in other hybrid storage [1416] . Here, the intermetal-lic material aims to capture small leaks of hydrogen coming frommicro-cracks, as those occurring due to plastic deformations inthe aluminum liner. Moreover, controlling the evolution of intrin-sic physical properties of this material, conductivity for instance,may allow following the global integrity of the storage vessel. Oncethe leakage has occurred and absorption has taken place, theseproperties are supposed to be affected and, depending on the mag-nitude of the shift, an active control could prevent the storagemedium from being used again.

Criteria on which the metal hydride is selected for a hydrogenstorage medium are strongly dependent on the application.According to literature, ZrFe compounds are interesting candidates[17] forour application. What is to be emphasized, when looking atthe properties of the Zr 3Fe alloy, is its excellent kinetics of absorp-tion, very low equilibrium pressure, good oxidation resistance andirreversibility.

The effect of the intermetallic swelling on the behavior of theliner and composite, while leakage of hydrogen is occurring, is tobe investigated. Here, the intermetallic layer undergoes an homo-geneous swelling all along the structure. Moreover, based onexperimental observations and crystallographic considerations[18,19] , attention is paid on two different scenarios: the rst oneassumes an isotropic swelling of the intermetallic while theabsorption is occurring (called AIS for After Isotropic Swelling),

whereas in the second one (called AITS for After Isotropic Trans-verse Swelling), a transverse anisotropy is introduced. This secondscenario should happen while a textured intermetallic material isintegrated. Then the expansion is oriented according to the averagecrystal orientation. The two mechanical responses of these scenar-ios are compared to the results obtained when no leakage is hap-pening; this state is called (BS), for Before Swelling.

When hydrogen reacts with the intermetallic, it occupies crys-tallographic intersticial sites within the cell leading to a swellingof the intermetallic (see Fig. 2 ). According to [13] , the metallicpowder can expand 20% of its initial volume. If the swelling effectis not taken into account, it may generate stress. The estimation of this stress is given by analogy between a material inating byabsorption of hydrogen and a material dilating while subjectedto a variation in temperature. An analysis of the stresses and thedisplacements through the walls thickness is presented. This mod-el analysis is based on the three-dimensional (3-D) anisotropicelasticity for the composite, and on the Hill criterion which allowsintroducing the plastic ow of the liner. This analysis aims to studythe inuence of the intermetallic component on the mechanical re-sponse of a type 3 hydrogen vessel and to assess the ability of theintermetallic to have a positive effect on the crack closure.

2. Analysis procedure

2.1. Stress and strain analysis

Considering a hybrid storage solution consisting of a metallicliner, an intermediate intermetallic layer and a multilayered com-posite made of a polymer matrix reinforced with long bers (seeFig. 2 ), the general stressstrain relationship for each k-th compo-

Nomenclature

Cylinder reference marks z, h, r circumferential direction radial directionr kij and e

kij (i, j = z , h, r ) layer stress and strain tensor compo-nents

r 0 and r a inner and outer radius respectively hybrid solution

Composite reference marksCc stiffness tensorCc ij ; i; j z ; h ; r u winding angle according to z directionr xU , r 0 xU ; r yU ; r 0 yU ; r yxU tensile and compressive strengths and

plane shear strengthF 11 , F 22 , F 66 , F 12 , F 1 and F 2 classical TsaiWu parameters

Liner reference marksS Le and S

L p elastic and plastic fourth order compliance tensors

respectivelyF , G, H , L, M , N parameters characterizing the anisotropy of the

material called Hill coefcientsr 0 yield stress

Intermetallic reference marksS I e elastic fourth order compliance tensorsD T temperature increase for expansion (thermal analogy)a I thermal expansion coefcients tensorE I , mI and GI Young modulus, Poisson coefcient and shear mod-

ulus

Fig. 1. Hybrid solution.

Hydrogen

Adsorption

Absorption

Stress

Intermetallic Hybride

Swelling

Fig. 2. Swelling of the intermetallic by hydrogen absorption.

2436 A. Hocine et al. / Materials and Design 31 (2010) 24352443



nent submitted to an axisymmetric thermomechanical loading isgiven by:

r z

r h

r r

shr

s zr

s z h

8>>>>>>>>>>>>>>>>>>>>>>>>>:

9>>>>>>>>>>>>>=>>>>>>>>>>>>>;

k

C 11 C12 C13 0 0 C16

C 12 C22 C23 0 0 C26

C 13 C23 C33 0 0 C36

0 0 0 C44 C45 0

0 0 0 C45 C55 0

C 16 C26 C36 0 0 C66

266666666666664

377777777777775

k e z a z D T

eh a hD T

er a r D T

chr

c zr

c z h

8>>>>>>>>>>>>>>>>>>>>>>>>>:

9>>>>>>>>>>>>>=>>>>>>>>>>>>>;

k

1

where z , h, r represent a cylindrical co-ordinate system, a z , ah, a r thecorresponding thermal expansion coefcients and D T a tempera-ture deviation from the reference one.

In this study, the thermal loading will only concern the interme-tallic layer. A thermal analogy is used in order to model the inter-metallic volume expansion following the hydrogen absorption.

In the particular case of an axisymmetric loading, the local bal-ance equations becomes in each k-th component:

dr kr dr

r kr r khr

0 2

The radius r is such as r 0 6 r 6 r a, where r 0 and r a are the struc-ture inner and outer radius respectively (see Fig. 3 ). The straindis-placement relationships are:

ekr dU kr

dr ; ekh

U kr r ; e

k z

dU k z dz e0

ck z h dU kh

dz c0 r ; ck zr 0 ; ckhr

dU khdr

U khr

8>:

3

Assuming an elasticplastic behavior for the liner, the incre-mental total strain tensor e is linked to the incremental Cauchytrue stress tensor r such as:

de dee de p S Le S L p dr 4

where S Le and S L p represent the elastic and plastic fourth order com-

pliance tensors respectively.Considering an isotropic plastic ow of the aluminum liner, the

Hills criterion is used to dene the plastic yield function:

F r zz r hh2 Gr hh r rr

2 H r rr r zz 2 2 Lr 2hr 2 M r

2 zr

2 N r 2 z h r20 5

F , G, H , L, M , N , called Hill coefcients, are parameters which charac-terize the anisotropy of the material. The Hill coefcients are deter-mined from tensile yield strength along the direction of orthotropy(F , G and H ) and yield strength of pure shear along the three planesof orthotropic symmetry ( L, M and N ) [20] . These parameters arestrongly dependent on the process used to manufacture thealuminum.

The yield stress r 0 is updated following the Hollomon-typehardening law:

r r 0 ge pd 6

Parameters g and d are given in Table 1 [11,12] .The plastic evolution laws are classically derived assuming a

normal ow within the context of an associated plasticity. In thiscase, the plastic fourth order compliance tensor is given by:

S LP Q

r 20 l 0_e p7

where l 0_eP represents the slope of the hardening law and:

Q

g21 g1 g2 g1 g3 Lg1 r hr M g1 r zr N g1 r z h



2 Lg1 r hr 2 Lg2 r hr 2 Lg3 r hr 2 L2 r 2hr 2 LM r hr r zr 2 LN r hr r z h

2 M g1 r zr 2 M g2 r zr 2 M g3 r zr 2 LM r hr r zr 2 M 2 r 2 zr 2 MN r z hr zr

2 N g1 r z h 2 N g2 r z h 2 N g3 r z h 2 LN r hr r z h 2 MN r zr r z h 2 N 2 r 2 z h

0BBBBBBBBBBBBBB@

1CCCCCCCCCCCCCCA8

where

g1 H Gr zz H r hh Gr rr g2 H F r hh H r zz F r rr

g3 F Gr rr Gr zz F r hh

8>:

9

Assuming an isotropic elastic behavior for the intermetalliclayer, the fourth order compliance tensor is of the following form:

S I e

S I 11 S I 12 S

I 13 0 0 0

S I 12 S I 22 S

I 23 0 0 0

S I 13 S I 23 S

I 33 0 0 0

0 0 0 S I 2323 0 0

0 0 0 0 S I 1313 0

0 0 0 0 0 S I 1212

0BBBBBBBBBB@

1CCCCCCCCCCA

10

with

S I 11 S I 22 S I 33 1E I

; S I 23 S I 12 S I 13 mI

E I ; S I 2323 S I 1313 S I 1212 1

GI

11

E I , mI and GI being respectively the intermetallic Young modulus,Poisson coefcient and shear modulus.

In order to account for the expansion phenomena following thehydrogen absorption, the incremental strain tensor is computed byconsidering a thermal loading:

deI S I edr a I D T 12

a I being the thermal expansion coefcients tensor.The considered composite material is composed of an organic

matrix reinforced with long bers. With respect to the local cylin-

drical co-ordinates system, the fourth order stiffness tensor is of the following form:

Fig. 3. Stress state in cylindrical part of hybrid solution.

A. Hocine et al. / Materials and Design 31 (2010) 24352443 2437



C c

C c 11 Cc 12 C

c 13 0 0 C

c 16

C c 12 Cc 22 C

c 23 0 0 C

c 26

C c 13 Cc 23 C

c 33 0 0 C

c 36

0 0 0 Cc 44 Cc 45 0

0 0 0 Cc 45 Cc 55 0

C c 16 Cc 26 C

c 36 0 0 C

c 66

2666666664

3777777775

13

In order to assess the strength of the composite, the TsaiWu crite-rion is introduced:

F 11 r k x 2

F 22 r k y 2

F 66 r k yx 2

2 F 12 r k y r k x F 1 r k x F 2 r k y 6 1 14

with

F 11 1

r xU r 0 xU ; F 22

1

r yU r 0 yU ; F 66

1

r 2 yxU ;

F 1 1

r xU 1

r 0 xU ; F 2

1

r yU 1

r 0 yU ; F 12

1

2

1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir xU r 0 xU r yU r 0 yU q 15

F 11 , F 22 , F 66 , F 12 , F 1 and F 2 are the classical TsaiWu parameterswhich depend on the composite material tensile and compressivestrengths, r xU , r yU , r 0 xU ; r 0 yU in the bers direction, the transverseone and in the layer plane shear strength r yxU .

2.2. Problem formulation

Substituting the expression of radial and hoop stresses derivedfrom Eq. (1) into Eq. (2) and using Eq. (3) , the following differentialequation is obtained:

d2 U kr dr 2

1

r dU kr

dr

N k1r 2

U kr N k2 e0 N k3 D T h i

1

r N k4 c0 16

where

N k1 C k22C k33

N k2 C k12 C

k13

C k33N k3

K k3 K k2

C k33N k4

C k26 2 C k36

C k33

a k2 N k2

1 N k1a k3

N k31 N k1

a k4 N k4

4 N k117

and

K k1 ak z C k11 akh C k12 a kr C k13




8>>>>>>>>>>>>>>>:

18

The solution of Eq. (16) depends on the value b k ffiffiffiffiffiffiffiffi N k1q .For b (k) = 1:

U kr Dkr E k=r

r ln r 2 N

k2 e0 N k3 DT a k4 c0 r 2 19

For b (k) = 2:

U kr Dkr b

k E kr b

k ak2 e0 ak3 DT r N

k4

2 c0 r 2 ln r 20

For b (k) 1(or 2):

U kr Dkr b

k E kr b

k ak2 e0 ak3 DT r a k4 c0 r 2 21

D(k)

, E (k)

, c0 and e0 being integration constants. The superscript k issuch as k e [1, w], where w = nL + nC + 1. The computation of the

liner plastic behavior is performed progressively by dividing itsthickness into nL sub-layers. nC is the number of composite layers.

2.3. Boundary and continuity conditions

The continuity of the radial displacements gives:

8k 2 1 ; w 1 ; U k r kext U k 1 r kext 22 The continuity of the radial stresses gives:

8k 2 1 ; w 1 ; r kr r kext r k 1 ext r kext r 1 r r 0 p0r wr r a 0

8>>>:

23

The axial equilibrium condition for the solution with closed endeffect can be expressed as:

2 p Xw

k1Z

r k

r k 1r k z r rdr pr

20 p0 24

The zero torsion condition is:

2 p Xw

k1Z

r k

r k 1 s z hr r 2 dr 0 25

2.4. Solution procedure

The problem formulated in the previous sections is solved forthe AITS (Isotropic Transverse Swelling) and AIS (Isotropic Swell-

ing) scenarios in order to assess the effect of the intermetallicexpansion simultaneously on the liner and on the composite whilethe tank is submitted to an internal pressure. An analysis of theliner upper surface and the composite lower surface stress statesis performed. The considered internal pressure is limited to40 MPa to keep the intermetallic behavior purely elastic. The inter-nal radius of the liner is of 33 mm and its thickness of 2 mm. Forthis analysis, Hills criterion introduced to account the liner plasticow is reduced to the von Mises criterion. The thickness of theintermetallic is of 0.2 mm when each composite layer has a thick-ness of 0.27 mm. The solutions are obtained by using the MATLABnumerical code. All the results are represented as functions of thefollowing non-dimensional ratio R:

R r r 0r a r 0

26

The liner thickness corresponds to R values varying from 0 to 0.306.From 0.306 to 0.337, the intermetallic thickness is recovered.

Tables 13 respectively present the material properties of a car-bon/epoxy composite, an aluminum liner and a Zr 3Fe intermetallic.The used composite stacking sequences are presented in Table 4 .

3. Discussions of results

3.1. Storage solution mechanical response for an internal pressure of 40 MPa

3.1.1. Radial displacement

Four different stacking sequences have been studied: Seq1[50] 8 , Seq2 [50] 7 + [90] 2 , Seq3 [60] 8 and Seq4 [60] 7 + [90] 2 .




The variation of radial displacements U r for the considered stackingsequences is shown in Fig. 4 . A similar trend for all the sequences isobserved andmaximum displacements are recorded at the internalwall. Starting from the internal wall, the displacement value de-creases gradually to a minimum at the external wall. The use of two 90 winding angle layers allows the radial displacement tobe reduced similarly for Seq2 or Seq4. Finally, the radial displace-ment decreases when a 60 winding angle is used, and this effectis intensied when the stacking sequence includes two circumfer-ential layers.

3.1.2. Stress and strain analysisAs shown in Fig. 5 , it can be veried that the hoop and axial

stresses are discontinuous through the tank thickness when differ-

ent materials are used. Fig. 5 shows that the intermetallic thermo-mechanical behavior generates a maximal hoop and axial stressesfor 0.306 6 R 6 0.337. The use of a 90 winding angle modies thestress distribution through the thickness. The more relevant effectsare an increase of the axial stress level on the liner, and a decreaseof the hoop stress level on the composite.

Fig. 6 shows the axial and hoop strain variation through thethickness. Depending on the strain component, these variationsare linear, constant or with a varying slope from one layer toanother.

These rst semi-analytical results present the thermomechani-cal response of a multilayer composite coated on an intermetalliclayer and a closed aluminum liner submitted to an internal pres-sure of 40 MPa. The result analysis shows that the behavior of

the considered hybrid storage solution strongly depends on thestacking sequence of the composite part.

3.2. Analysis of the intermetallic swelling

The effect of the intermetallic thermomechanical swelling onthe liner and on the composite behaviors is investigated in this sec-

tion by considering two stacking sequences: Seq3: [60] 8 andSeq4: [60] 7 + [90] 2 . For each sequence, two behavior assumptions

Table 2

Liner properties.

E L (GPa) mL r 0 (MPa) r r (MPa) g (MPa) d

Al 6060 72 0.25 200 250 310 0.09

Table 3

Intermetallic properties.

E I (GPa) mI a I (10 5 C 1)

Zr3Fe 122.5 0.33 0.66

Table 4

Different stacking sequences of the hybrid solution.

Sequence Winding angle

Seq1 [50] 8Seq2 [50] 7 + [90] 2Seq3 [60] 8Seq4 [60] 7 + [90] 2

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

R

R a d i a l d i s p

l a c e m e n

t ( m m

)

Seq1Seq2Seq3Seq4

Fig. 4. Radial displacement through the thickness.

Table 1

Composite properties.

E x (GPa) E y (GPa) G xy (GPa) m yx r LU (MPa) r 0LU (MPa) r TU (MPa) r 0TU (MPa) r TLU (MPa)

C/E 141.6 10.7 3.88 0.26 1500 1500 50 250 70

0 0.2 0.4 0.6 0.8 1150

250

350

450

550

R

H o o p s

t r e s s

[ M P a

]

Seq1Seq2Seq3

Seq4

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250

300

R

A x i a

l s t r e s s

[ M P a

]

Seq1Seq2Seq3Seq4

Fig. 5. Hoop and axial stress through the thickness.




are considered for the intermetallic which is rstly pre-stressed byan internal pressure: an isotropic thermomechanical swelling (AIS)and an isotropic transverse thermomechanical swelling (AITS).

3.2.1. The intermetallic radial displacement The intermetallic thermomechanical loading is used by choos-

ing a difference in temperature corresponding to a volume varia-tion of 2%. This volume variation can reach nearly 20% when thehydride absorption is complete, but here it is limited to 2% withthe aim of not obtaining stresses without any physical meaning.Fig. 7 shows the radial displacement distribution through thethickness. The obtained radial dilatation with the AIS scenario is0.4% higher than the AITS one. This phenomenon induces a highstress level on both the liner and the composite part as shown inFig. 8 .

3.2.2. Stress and strain analysis 3.2.2.1. Axial and hoop stresses. The observed axial and hoop stres-ses general trend before leakage and for AIS and AITS scenarios re-mains the same for the considered stacking sequences. Hence, onlyresults for Seq3 are then discussed.

Fig. 9 shows the axial stress distribution through the thickness.For each thermomechanical swelling, the intermetallic acts on thecomposite part by applying an axial stress, even if magnitudeappears more important for the AIS scenario. At the opposite,dependingon the scenario the swelling of the intermetallic induceson the liner part once, in case of AIS scenario, an increase of 64%

compare with the state BS (before leakage), or a decrease, in caseof AITS of 39%.

Fig. 10 shows the hoop stress variation through the thickness.An increase of the hoop stress is also observed on the compositepart for the AITS and AIS scenarios. However, the hoop stress levelfor the AITS scenario is 20% higher than the one for the AIS on theliner.

Depending on the liner micro-cracks orientation, the stressstateobtained by the previous modelings can lead to crack openingor closure. An optimal stress state associated with the local hydro-gen absorption capability of the intermetallic layer can lead nallyto a smart storage solution.

3.2.2.2. Radial stress. Fig. 11 shows the radial stress evolutionthrough the thickness. This evolution is linear in each constitutivepart. When a swelling is present, the radial stress level is higher onthe liner outer surface than on the composite inner surface.

For the considered stacking sequences (Seq3 and Seq4), the AITSscenario leads to a decrease of the radial stress level on the liner.For the AIS scenario, the radial stress level increases on thecomposite. This could have a positive effect on the cracks by clos-ing them.

Table 5 gives the equivalent stresses and strains on the linerfollowing the previous modelings. When the AITS scenario is used,the increase of both equivalent stress and strain is weak. This

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5x 10

-3

R

H o o p s

t r a

i n

Seq1Seq2Seq3Seq4

0 0.2 0.4 0.6 0.8 1-2

-1

0

1

2x 10

-3

R

A x i a

l s t r a

i n

Seq1Seq2Seq3Seq4

Fig. 6. Hoop and axial strains through the thickness distribution.

0 0.2 0.4 0.6 0.8 10.725

0.7275

0.73

0.7325

R

R a

d i a l d i s p

l a c e m e n

t ( m m

)

A.I.S A.I.T.S

Fig. 7. Radial displacement through the thickness of intermetallic.

0 0.2 0.4 0.6 0.8 10.04

0.06

0.08

0.1

0.12

0.14

R

R a

d i a l d i s p

l a c e m e n

t ( m m

)

Seq3-B.SSeq3-A.I.SSeq4-B.SSeq4-A.I.SSeq3-A.I.T.SSeq4.A.I.T.S

Fig. 8. Radial displacement through the thickness for Seq3 and Seq4, Before

Swelling (BS), After Isotropic Swelling (AIS) and After Isotropic Transverse Swelling(AITS).




induces non-signicant closure effect on a crack whatever its ori-entation is.

3.2.2.3. Axial and hoop strains. The evolution of the axial and the

hoop strains through the thickness are shown Fig. 12 for Seq3. Thisevolution is rather the same than for Seq4.

On the liner and for both consideredstacking sequences, the ax-ial strain increases for the AIS scenario whereas it decreases for theAITS scenario. On the other hand, an increase of the hoop strainlevel is observed on the composite part. The presence of circumfer-

ential layers in the stacking sequences reduces the hoop strain le-vel and increase the axial strain one.

0 0.2 0.4 0.6 0.8 1-1700

-1400

-1100

-800

-500

-200

100

400

R

A x i a l s

t r e s s

[ M P a

]

Seq3-B.SSeq3-A.I.SSeq3-A.I.T.S

0 0.0767 0.1534 0.2301 0.306750

70

90

110

130

150

170

190

R (Liner)

A x i a

l s t r e s s

[ M P a ] Seq3-B.S

Seq3-A.I.SSeq3-A.I.T.S

0.3374 0.4797 0.6219 0.7642 0.9064 170

80

90

100

110

120

130

140

R (Composite)

A x i a

l s t r e s s

[ M P a

]


(a) Distribution of axial stress throughthe thickness of hybrid solution

(b ) Zoom of distribution of axial stress through

the thickness of liner part (0 R 0.306).

(c) Zoom of distribution of axial stress through

the thickness of composite part (0.337 R 1).

Fig. 9. Axial stress through the thickness for Seq3, Before Swelling (BS), AfterIsotropic Swelling (AIS) and After Isotropic Transverse Swelling (AITS).

0 0.2 0.4 0.6 0.8 1-1800

-1200

-600

0

600

R

H o o p s t r e s s

[ M P a

]


(a) Distribution of hoop stress through the thickness of hybrid solution.

0 0.0767 0.1534 0.2301 0.3067140

160

180

200

R (Liner)

H o o p s

t r e s s

[ M P a ]


(b) Zoom of distribution of hoop stress through the thickness of liner part (0 R 0.306).

0.3374 0.4796 0.6219 0.7641 0.9064 1150

200

250

300

350

R (composite)

H o o p s t r e s s

[ M P a

]


(c) Zoom of distribution of hoop stress through the thickness of composite part (0.337 R 1).

Fig. 10. Hoop stress through the thickness for Seq3, Before Swelling (BS), AfterIsotropic Swelling (AIS) and After Isotropic Transverse Swelling (AITS).




3.2.2.4. Radial strain. Fig. 13 shows the radial strain evolutionthrough the thickness. Considering the stacking sequence Seq3which gives similar results to that of the stacking sequence Seq4,the intermetallic thermomechanical swelling leads to an increaseof the compressive stress, both on the liner and the composite.

The computed axial and hoop strains are not so convenient. Theintermetallic swelling tends to increase the strains and so tends toopen the cracks. The only positive inuence seems to happen forthe AITS scenario. In this case, a decrease of the axial strain is ob-served with the expansion of the intermetallic. So, if the crack isoriented along the circumferential direction, this decrease couldlead to its closure. Otherwise, for both scenarios, the opening of the crack is expected.

4. Conclusions and perspectives

This paper presents an analytical modeling of a hybrid solutionfor hydrogen storage made of an aluminum liner coated with anintermetallic, itself overwrapped by lament winding. Thisapproach is completely original as far as the analysis focuses onthe mechanical response of this peculiar structure which purposeis to secure the hydrogen storage medium. Different sequences of

the multilayer composite are investigated. This analysis allowspredicting the effect of the intermetallic swelling on the mechani-

cal response both of the liner and the composite while leakage of hydrogen is occurring. Present results in terms of stresses, strainsand displacement through the thickness, are discussed for two sce-narios, After Isotropic Swelling (AIS) and After Isotropic TransverseSwelling (AITS), and are compared with the state before leakage,Before Swelling (BS).

The rst part is devoted to the mechanical response of four dif-ferent stacking sequences: [50] 8 , [50] 7 + [90] 2 , [60] 8 and

[60] 7 + [90] 2 when no leakage happens. This analysis shows thatthe behavior of this hybrid solution strongly depends on the stack-

0 0.2 0.4 0.6 0.8 1-40

-30

-20

-10

0

R

R a

d i a l s t r e s s

[ M P a

]

Seq3-B.S.Seq3-A.I.T.SSeq3-A.I.S

0 0.2 0.4 0.6 0.8 1-40

-30

-20

-10

0

R

R a

d i a l s t r e s s

[ M P a

]


Fig. 11. Radial stress through the thickness Before Swelling (BS), After IsotropicSwelling (AIS) and After Isotropic Transverse Swelling (AITS) for Seq3 and Seq4.

Table 5

Equivalent stress and strain for Seq3.

Scenario BS AIS AITS

Equivalent stress (MPa) 198.86 206.57 201.49Equivalent strain (%) 0.33 0.64 0.40

0 0.2 0.4 0.6 0.8 10

1

2

3

4

5 x 10

-3

R

A x i a l s t r a

i n


0 0.2 0.4 0.6 0.8 11.5

2

2.5

3

3.5

4 x 10

-3

R

H o o p s t r a

i n


Fig. 12. Axial and hoop strains through the thickness for Seq3, Before Swelling (BS),After Isotropic Swelling (AIS) and After Isotropic Transverse Swelling (AITS).

0 0.2 0.4 0.6 0.8 1-7

0

7

14

21 x 10

-3

R

R a

d i a l s t r a

i n


Fig. 13. Radial strain through the thickness for Seq3, Before Swelling (BS), AfterIsotropic Swelling (AIS) and After Isotropic Transverse Swelling (AITS).




ing sequences of the composite. Finally, the different results de-crease with the 60 winding angle and the effect are ampliedwhen this stacking sequence is modied in order to have two cir-cumferential layers.

Thesecond part focuses on the analysis of intermetallic swellingon the behavior of a hybrid solution. The intermetallic swelling hasa signicant inuence on the mechanical behavior of the hybridsolution.

Results clearly show that the swelling of intermetallic inducesits crushing on the liner and the composite. According to the re-sults obtained for radial strain and stress, the liner and the com-posite are subjected to an increase of the compression statewhatever swelling scenario is.

Cracks initiated during the pressure loading will tend to openmore, except in case of the AITS scenario if additionally the crackis circumferentially oriented. The increase of the radial compres-sion is also expected to have a positive inuence on the cracksclosure.

Authors are fully aware of the limits of such an analysis; itmeans the global swelling of the intermetallic, and the elasticbehavior of this intermetallic. However, this study gives some pe-culiar informations on the structure response and on the potentialof such a material when used to secure hydrogen storage media. Ina forthcoming paper, we will consider a nite element method tomake it possible to see more in details the effect of the local swell-ing on a crack initiated in the liner.

References

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Analysis-of-intermetallic-swelling-on-the-behavior-of-a-hybrid-solution-for-compressed-hydrogen-storage-â€“-Part-I-Analytical-modeling_2010_Materials-&-Design