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

Materials and Design 31 (2010) 2435–2443

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Analysis of intermetallic swelling on the behavior of a hybrid solution for compressed hydrogen storage – Part I: Analytical modeling Abdelkader Hocine a,b,*, David Chapelle b, Lamine M. Boubakar b, Ali Benamar c, Abderrezak Bezazi d a

University Hassiba Benbouali, BP. 151, Chlef 02000, Algeria Institute FEMTO-ST, Dept. LMARC, 24, Epitaphe street, 25000 Besançon, France c ENSET, Department of Mechanical Engineering, BP. 1523, Oran 31000, Algeria d University 08 Mai 1945, BP. 401, Guelma 24000, Algeria b

a r t i c l e

i n f o

Article history: Received 25 September 2009 Accepted 23 November 2009 Available online 27 November 2009 Keywords: Laminates Intermetallics Failure analysis

a b s t r a c t This study focuses on the mechanical response of a hybrid solution dedicated to gaseous hydrogen storage. This solution is made of a carbon/epoxy composite overwrapped on a metal liner first coated with intermetallic material. The composite helps to reinforce the structure, while the liner prevents it from any leakage. In case of deficiency, the intermetallic material behaves as a sponge and interrupts the leakage by absorption and micro-cracks reduction. This hybrid solution or this specific use of intermetallic material has never been presented before. The laminate composite is anisotropic, whereas the liner is an elastic–plastic material. The intermetallic is purely thermo elastic and its study is limited to its mechanical contribution. Using these hypotheses, the suggested analytical model provides an exact solution for stresses and strains on the cylindrical section of the hybrid solution submitted to thermomechanical static loading and hydrogen leakage. The swelling effect of the intermetallic on the behavior of the structure is then investigated. Crown Copyright Ó 2009 Published by Elsevier Ltd. All rights reserved.

1. Introduction Hydrogen is considered as one of the more promising energy vectors 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 high degree of safety as well as allowing ease of use in terms of energy density and dynamics of fuel storage and controlled release. The use of composite materials is an extremely interesting alternative to metallic materials in the construction of tanks. Indeed, these materials are characterized by their lightness, rigidity, good fatigue strength, and corrosion resistance when their components are not metallic [1]. Thin or thick walled tanks are widely used in several branches of engineering, such as the storage of compressed hydrogen, liquefied and compressed natural gas [2,3]. The choice of material for the liner is crucial whenever the vessel is designed to contain gas under high pressure, to prevent for instance the diffusion through the wall, or when it is designed to contain liquid under severe temperature conditions. The overwrapped composite aims to ensure the mechanical strength. This

* 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).

storage can provide several advantages: it ensures a perfect participation between the liner and the composite hull, it uses the overall resistance of the fiber in tension and it allows reaching weight saving up to 50% in comparison with all metal vessels [4,5]. In many metals, the hydrogen embrittlement decreases drastically the failure strength. Experimental observations [6,7] and theoretical calculations [8–10] have demonstrated that dissolution of hydrogen atoms increases the dislocation mobility and promote highly localized plastic processes, which eventually lead to ductile rupture. In the case of hydrogen storage, the embrittlement phenomenon can be responsible of the formation of cracks in the aluminum liner and can lead to micro-leaks. Based on previous works, Chapelle and Perreux [11] developed an analytical procedure to predict the behavior of the cylindrical section of a type 3 vessel for hydrogen storage applications. The anisotropic plastic flow of the liner and the damage for the composite were taken into account. Hocine et al. [12] present an experimental, analytical and FEM simulation investigation of a hydrogen storage vessel of type 3. The suggested analytical model provides an exact solution for stresses and strains on the cylindrical section of the vessel solution submitted to mechanical static loading. Some analytical results are compared with experimental and the finite element solutions, a good correlation is observed. The present study concerns the development of an improved high pressure hydrogen storage vessel (Fig. 1). In this solution, a hydrogen absorbing intermetallic between the aluminum liner

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

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A. Hocine et al. / Materials and Design 31 (2010) 2435–2443

Nomenclature Cylinder reference marks z, h, r circumferential direction radial direction ðkÞ rðkÞ and eij (i, j = z, h, r) layer stress and strain tensor compoij nents r0 and ra inner and outer radius respectively hybrid solution Composite reference marks stiffness tensor Cc Ccij ; ði; j ¼ z; h; rÞu winding angle according to z direction rxU, r0xU ; ryU ; r0yU ; ryxU tensile and compressive strengths and plane shear strength F11, F22, F66, F12, F1 and F2 classical Tsai–Wu parameters

and the carbon fiber/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 mechanical aspect of this hybrid structure. The role of the intermetallic is not to absorb the whole hydrogen stored in the high pressure tank as it may be used in other hybrid storage [14–16]. Here, the intermetallic material aims to capture small leaks of hydrogen coming from micro-cracks, as those occurring due to plastic deformations in the aluminum liner. Moreover, controlling the evolution of intrinsic physical properties of this material, conductivity for instance, may allow following the global integrity of the storage vessel. Once the leakage has occurred and absorption has taken place, these properties are supposed to be affected and, depending on the magnitude of the shift, an active control could prevent the storage medium from being used again. Criteria on which the metal hydride is selected for a hydrogen storage medium are strongly dependent on the application. According to literature, ZrFe compounds are interesting candidates [17] for our application. What is to be emphasized, when looking at the properties of the Zr3Fe alloy, is its excellent kinetics of absorption, very low equilibrium pressure, good oxidation resistance and irreversibility. The effect of the intermetallic swelling on the behavior of the liner and composite, while leakage of hydrogen is occurring, is to be investigated. Here, the intermetallic layer undergoes an homogeneous swelling all along the structure. Moreover, based on experimental observations and crystallographic considerations [18,19], attention is paid on two different scenarios: the first one assumes an isotropic swelling of the intermetallic while the absorption is occurring (called AIS for After Isotropic Swelling),

Liner reference marks SLe and SLp elastic and plastic fourth order compliance tensors respectively F, G, H, L, M, N parameters characterizing the anisotropy of the material called Hill coefficients r0 yield stress Intermetallic reference marks elastic fourth order compliance tensors SIe DT temperature increase for expansion (thermal analogy) aI thermal expansion coefficients tensor EI, mI and GI Young modulus, Poisson coefficient and shear modulus

whereas in the second one (called AITS for After Isotropic Transverse Swelling), a transverse anisotropy is introduced. This second scenario should happen while a textured intermetallic material is integrated. Then the expansion is oriented according to the average crystal orientation. The two mechanical responses of these scenarios are compared to the results obtained when no leakage is happening; this state is called (BS), for Before Swelling. When hydrogen reacts with the intermetallic, it occupies crystallographic intersticial sites within the cell leading to a swelling of the intermetallic (see Fig. 2). According to [13], the metallic powder can expand 20% of its initial volume. If the swelling effect is not taken into account, it may generate stress. The estimation of this stress is given by analogy between a material inflating by absorption of hydrogen and a material dilating while subjected to a variation in temperature. An analysis of the stresses and the displacements through the wall’s thickness is presented. This model analysis is based on the three-dimensional (3-D) anisotropic elasticity for the composite, and on the Hill criterion which allows introducing the plastic flow of the liner. This analysis aims to study the influence of the intermetallic component on the mechanical response of a type 3 hydrogen vessel and to assess the ability of the intermetallic 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 metallic liner, an intermediate intermetallic layer and a multilayered composite made of a polymer matrix reinforced with long fibers (see Fig. 2), the general stress–strain relationship for each k-th compo-

Hybride

Intermetallic

Adsorption Swelling Hydrogen Absorption

Stress Fig. 1. Hybrid solution.

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

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A. Hocine et al. / Materials and Design 31 (2010) 2435–2443

nent submitted to an axisymmetric thermomechanical loading is given by:

8 ðkÞ rz 9 > > > > > > > > > > > > > r > > > > h> > > > > > > > = r

> > > shr > > > > > > > > > > > > > > > s > > zr > > > > > > ; :

2

C11

6 6C 6 12 6 6 6 C13 6 ¼6 6 0 6 6 6 6 0 4

szh

C16

C12

C13

0

0

C22

C23

0

0

C23

C33

0

0

0

0

C44

C45

0

0

C45

C55

C26

C36

0

0

3ðkÞ 8 ðkÞ ez  az DT 9 > > > > > > 7 > > > > > eh  ah DT > > C26 7 7 > > > > > > 7 > > > > 7 > > = C36 7 < er  ar DT > 7 7 > > 7 > chr 0 7 > > > > > > 7 > > > > 7 > > > > > 7 c 0 5 > > zr > > > > > > ; : czh C66 C16

ð1Þ where z, h, r represent a cylindrical co-ordinate system, az, ah, ar the corresponding thermal expansion coefficients and DT a temperature deviation from the reference one. In this study, the thermal loading will only concern the intermetallic layer. A thermal analogy is used in order to model the intermetallic volume expansion following the hydrogen absorption. In the particular case of an axisymmetric loading, the local balance equations becomes in each k-th component: ðkÞ

ðkÞ

ðkÞ

drr rr  rh þ ¼0 dr r

ð2Þ

The radius r is such as r0 6 r 6 ra, where r0 and ra are the structure inner and outer radius respectively (see Fig. 3). The strain–displacement relationships are:

8 ðkÞ dU r > < eðkÞ r ¼ dr ; > :

ðkÞ zh

c ¼

ðkÞ

dU h dz

ðkÞ

ðkÞ

¼ c0 r;

ðkÞ hr

c ¼ 0; c ¼

ðkÞ

dU h dr

ðkÞ



  de ¼ dee þ dep ¼ SLe þ SLp dr

ð4Þ

Fðrzz  rhh Þ2 þ Gðrhh  rrr Þ2 þ Hðrrr  rzz Þ2 þ 2Lr2hr þ 2M r2zr 2 0

þ 2Nr ¼ r

ð5Þ

F, G, H, L, M, N, called Hill coefficients, are parameters which characterize the anisotropy of the material. The Hill coefficients are determined from tensile yield strength along the direction of orthotropy (F, G and H) and yield strength of pure shear along the three planes of orthotropic symmetry (L, M and N) [20]. These parameters are strongly dependent on the process used to manufacture the aluminum. The yield stress r0 is updated following the Hollomon-type hardening law:

r ¼ r0 ¼ gðep Þd

ð6Þ

Parameters g and d are given in Table 1 [11,12]. The plastic evolution laws are classically derived assuming a normal flow within the context of an associated plasticity. In this case, the plastic fourth order compliance tensor is given by:

Q 0 ð _ pÞ

rl e

where

2 0

g1 g2

Lg1 rhr

g1 g3

Mg1 rzr

l0 ðe_ P Þ represents the slope of the hardening law and:

N g1 rzh

1

B C B g g g22 g2 g3 Lg2 rhr Mg2 rzr N g2 rzh C B C 1 2 B C B C 2 B g1 g3 C g g g L g r M g r N g r hr zr zh 2 3 3 3 3 3 B C C Q ¼B B C 2 2 B 2Lg1 rhr 2Lg2 rhr 2Lg3 rhr 2L rhr 2LMrhr rzr 2LN rhr rzh C B C B C B C 2 2 B 2M g1 rzr 2M g2 rzr 2Mg3 rzr 2LM rhr rzr 2M rzr 2MN rzh rzr C @ A 2N 2 r2zh ð8Þ

where

where SLe and SLp represent the elastic and plastic fourth order compliance tensors respectively. Considering an isotropic plastic flow of the aluminum liner, the Hill’s criterion is used to define the plastic yield function:

SLP ¼

g21

ð3Þ

Uh r

Assuming an elastic–plastic behavior for the liner, the incremental total strain tensor e is linked to the incremental Cauchy true stress tensor r such as:

2 zh

0

2Ng1 rzh 2Ng2 rzh 2Ng3 rzh 2LNrhr rzh 2MN rzr rzh

dU z Ur eðkÞ eðkÞ z ¼ dz ¼ e0 h ¼ r ; ðkÞ zr

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

ð7Þ

8 g ¼ ðH þ GÞrzz  Hrhh  Grrr > < 1 g2 ¼ ðH þ FÞrhh  Hrzz  F rrr > : g3 ¼ ðF þ GÞrrr  Grzz  F rhh

ð9Þ

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

0

SI11 B I BS B 12 B I B S13 I Se ¼ B B B 0 B B 0 @ 0

SI12

SI13

0

0

SI22

SI23

0

0

SI23

SI33

0

0

0

0

SI2323

0

0

0

0

SI1313

0

0

0

0

0

1

C 0 C C C 0 C C C 0 C C 0 C A

ð10Þ

SI1212

with

 1 mI 1 SI11 ¼ SI22 ¼ SI33 ¼ I ; SI23 ¼ SI12 ¼ SI13 ¼ I ; SI2323 ¼ SI1313 ¼ SI1212 ¼ I E E G ð11Þ EI, mI and GI being respectively the intermetallic Young modulus, Poisson coefficient and shear modulus. In order to account for the expansion phenomena following the hydrogen absorption, the incremental strain tensor is computed by considering a thermal loading:

deI ¼ SIe dr þ aI DT

ð12Þ

aI being the thermal expansion coefficients tensor. The considered composite material is composed of an organic matrix reinforced with long fibers. With respect to the local cylindrical co-ordinates system, the fourth order stiffness tensor is of the following form:

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A. Hocine et al. / Materials and Design 31 (2010) 2435–2443

2

Cc11 6 Cc 6 12 6 c 6 C13 Cc ¼ 6 6 0 6 6 4 0

Cc12

Cc13

Cc22 Cc23

Cc23 Cc33

0

Cc16

0

0

0

0 Cc44

0 Cc45

Cc26 Cc36

0 0

0

Cc45

Cc55

Cc16

Cc26

Cc36

0

0

0

3

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

7 7 7 7 7 0 7 7 7 0 5

ð13Þ

Cc66

 The continuity of the radial displacements gives:

In order to assess the strength of the composite, the Tsai–Wu criterion is introduced:

F 11



 ðkÞ 2

rx

þ F 22



rðkÞ y

2

þ F 66



rðkÞ yx

2

ð14Þ

1

F1 ¼

1

rxU



F 22 ¼

;

1

r0xU

F2 ¼

;

1

ryU r0yU 1

ryU



F 66 ¼

;

1

r0yU

1

r2yxU

F 12 ¼ 

;

1 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 rxU r0 ryU r0 xU

yU

F11, F22, F66, F12, F1 and F2 are the classical Tsai–Wu parameters which depend on the composite material tensile and compressive strengths, rxU, ryU, r0xU ; r0yU in the fibers direction, the transverse one and in the layer plane shear strength ryxU.

Substituting the expression of radial and hoop stresses derived from Eq. (1) into Eq. (2) and using Eq. (3), the following differential equation is obtained:

dr

2

ðkÞ

ðkÞ

ðkÞ

aðkÞ 2 ¼

ðkÞ

C 22

ðkÞ

N2 ¼

ðkÞ

C 33

ðkÞ N2 ðkÞ

1  N1

ðkÞ

C 12  C 13

ðkÞ

ðkÞ

N3 ¼

ðkÞ

C 33

aðkÞ 3 ¼

ðkÞ N3 ðkÞ

1  N1

ðkÞ

K3  K2

aðkÞ 4 ¼

ðkÞ

C 33

ðkÞ

ðkÞ

N4 ¼

ðkÞ

C 26  2C 36 ðkÞ

C 33

ðkÞ N4 ðkÞ

4  N1

ð17Þ and

8 ðkÞ ðkÞ ðkÞ ðkÞ ðkÞ ðkÞ ðkÞ > > > K 1 ¼ az C 11 þ ah C 12 þ ar C 13 > > > > > K ðkÞ ¼ aðkÞ C ðkÞ þ aðkÞ C ðkÞ þ aðkÞ C ðkÞ < r z h 2 21 22 23 > ðkÞ ðkÞ ðkÞ ðkÞ ðkÞ ðkÞ ðkÞ > > K 3 ¼ az C 31 þ ah C 32 þ ar C 33 > > > > > : ðkÞ ðkÞ ðkÞ ðkÞ ðkÞ ðkÞ ðkÞ K 4 ¼ az C 61 þ ah C 62 þ ar C 63 The solution of Eq. (16) depends on the value bðkÞ For b(k) = 1: ðkÞ ðkÞ U ðkÞ r ¼ D r þ E =r þ

ð18Þ

qffiffiffiffiffiffiffiffi ðkÞ ¼ N1 .

ð19Þ

For b(k) = 2: ðkÞ   N ðkÞ ðkÞ ðkÞ ðkÞ bðkÞ U ðkÞ þ EðkÞ r b þ a2 e0 þ a3 DT r þ 4 c0 r 2 lnðrÞ r ¼ D r 2

ð20Þ

(k)

(k)

ðkÞ

 ð23Þ

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

2p

w Z X k¼1

rk

rk1

2 rðkÞ z ðrÞrdr ¼ pr 0 p0

ð24Þ



2p

 ðkÞ ðkÞ ðkÞ þ a2 e0 þ a3 DT r þ a4 c0 r 2

w Z X k¼1

r ðkÞ

szh ðrÞr2 dr ¼ 0

ð25Þ

rðk1Þ

The problem formulated in the previous sections is solved for the AITS (Isotropic Transverse Swelling) and AIS (Isotropic Swelling) scenarios in order to assess the effect of the intermetallic expansion simultaneously on the liner and on the composite while the tank is submitted to an internal pressure. An analysis of the liner upper surface and the composite lower surface stress states is performed. The considered internal pressure is limited to 40 MPa to keep the intermetallic behavior purely elastic. The internal radius of the liner is of 33 mm and its thickness of 2 mm. For this analysis, Hill’s criterion introduced to account the liner plastic flow is reduced to the von Mises criterion. The thickness of the intermetallic is of 0.2 mm when each composite layer has a thickness of 0.27 mm. The solutions are obtained by using the MATLAB numerical code. All the results are represented as functions of the following non-dimensional ratio R:

r  r0 ra  r0

ð26Þ

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 1–3 respectively present the material properties of a carbon/epoxy composite, an aluminum liner and a Zr3Fe 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

For b(k) – 1(or 2): ðkÞ

rr ðr0 Þ ¼ p0 > > : ðwÞ rr ðra Þ ¼ 0

R¼

 r lnðrÞ  ðkÞ ðkÞ ðkÞ N 2 e0 þ N 3 DT þ a4 c0 r 2 2

ðkÞ b U ðkÞ þ EðkÞ r b r ¼ D r



ð16Þ

where

N1 ¼



2.4. Solution procedure

h i1 N 1 dU r ðkÞ ðkÞ ðkÞ þ N4 c0  12 U ðkÞ r ¼ N 2 e0 þ N 3 DT r dr r r ðkÞ

þ



ðkÞ ðkþ1Þ ðkÞ rðkÞ r ext ¼ rext r ext r

 The zero torsion condition is:

2.2. Problem formulation

2

ð22Þ

 The continuity of the radial stresses gives:

ð1Þ

;

ð15Þ

d U ðkÞ r

    ðkÞ ðkÞ U ðkÞ r ext ¼ U ðkþ1Þ r ext

8 > > < 8k 2 ½1; w  1;

with

rxU r0xU

8k 2 ½1; w  1;

ðkÞ ðkÞ þ 2F 12 rðkÞ y rx þ F 1 rx

þ F 2 rðkÞ 6 1 y

F 11 ¼

2.3. Boundary and continuity conditions

ð21Þ

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

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.

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A. Hocine et al. / Materials and Design 31 (2010) 2435–2443 Table 1 Composite properties. Ey (GPa)

Gxy (GPa)

myx

rLU (MPa)

r0LU (MPa)

rTU (MPa)

r0TU (MPa)

rTLU (MPa)

141.6

10.7

3.88

0.26

1500

1500

50

250

70

3.1.2. Stress and strain analysis As shown in Fig. 5, it can be verified that the hoop and axial stresses are discontinuous through the tank thickness when different materials are used. Fig. 5 shows that the intermetallic thermomechanical behavior generates a maximal hoop and axial stresses for 0.306 6 R 6 0.337. The use of a 90° winding angle modifies the stress distribution through the thickness. The more relevant effects are an increase of the axial stress level on the liner, and a decrease of the hoop stress level on the composite. Fig. 6 shows the axial and hoop strain variation through the thickness. Depending on the strain component, these variations are linear, constant or with a varying slope from one layer to another. These first semi-analytical results present the thermomechanical response of a multilayer composite coated on an intermetallic layer and a closed aluminum liner submitted to an internal pressure of 40 MPa. The result analysis shows that the behavior of the considered hybrid storage solution strongly depends on the stacking sequence of the composite part. 3.2. Analysis of the intermetallic swelling The effect of the intermetallic thermomechanical swelling on the liner and on the composite behaviors is investigated in this sec-

tion by considering two stacking sequences: Seq3: [±60]8 and Seq4: [±60]7 + [90]2. For each sequence, two behavior assumptions

0.2

Radial displacement (mm)

The variation of radial displacements Ur for the considered stacking sequences is shown in Fig. 4. A similar trend for all the sequences is observed and maximum displacements are recorded at the internal wall. Starting from the internal wall, the displacement value decreases gradually to a minimum at the external wall. The use of two 90° winding angle layers allows the radial displacement to be reduced similarly for Seq2 or Seq4. Finally, the radial displacement decreases when a 60° winding angle is used, and this effect is intensified when the stacking sequence includes two circumferential layers.

0.1

mL

r0 (MPa)

rr (MPa)

g (MPa)

d

72

0.25

200

250

310

0.09

0

0.2

0.4

0.6

0.8

550

Seq1 Seq2 Seq3 Seq4

450

350

250

0

0.2

0.4

0.6

0.8

300

mI

aI (105 C1)

122.5

0.33

0.66

Table 4 Different stacking sequences of the hybrid solution.

Axial stress [MPa]

Zr3Fe

EI (GPa)

1

R

Seq1 Seq2 Seq3 Seq4

250 Table 3 Intermetallic properties.

1

Fig. 4. Radial displacement through the thickness.

150

EL (GPa)

Seq1 Seq2 Seq3 Seq4

0.05

R

Table 2 Liner properties.

Al 6060

0.15

0

Hoop stress [MPa]

C/E

Ex (GPa)

200 150 100 50

Sequence

Winding angle

Seq1 Seq2 Seq3 Seq4

[±50]8 [±50]7 + [90]2 [±60]8 [±60]7 + [90]2

0

0

0.2

0.4

0.6

0.8

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

1

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A. Hocine et al. / Materials and Design 31 (2010) 2435–2443

are considered for the intermetallic which is firstly pre-stressed by an 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 choosing a difference in temperature corresponding to a volume variation of 2%. This volume variation can reach nearly 20% when the hydride absorption is complete, but here it is limited to 2% with the aim of not obtaining stresses without any physical meaning. Fig. 7 shows the radial displacement distribution through the thickness. The obtained radial dilatation with the AIS scenario is 0.4% higher than the AITS one. This phenomenon induces a high stress level on both the liner and the composite part as shown in Fig. 8.

-3

5

x 10

4

Hoop strain

3.2.2.2. Radial stress. Fig. 11 shows the radial stress evolution through the thickness. This evolution is linear in each constitutive part. When a swelling is present, the radial stress level is higher on the liner outer surface than on the composite inner surface. For the considered stacking sequences (Seq3 and Seq4), the AITS scenario leads to a decrease of the radial stress level on the liner. For the AIS scenario, the radial stress level increases on the composite. This could have a positive effect on the cracks by closing them. Table 5 gives the equivalent stresses and strains on the liner following the previous modelings. When the AITS scenario is used, the increase of both equivalent stress and strain is weak. This

0.7325

Radial displacement (mm)

3.2.2. Stress and strain analysis 3.2.2.1. Axial and hoop stresses. The observed axial and hoop stresses general trend before leakage and for AIS and AITS scenarios remains the same for the considered stacking sequences. Hence, only results for Seq3 are then discussed. Fig. 9 shows the axial stress distribution through the thickness. For each thermomechanical swelling, the intermetallic acts on the composite part by applying an axial stress, even if magnitude appears more important for the AIS scenario. At the opposite, depending on the scenario the swelling of the intermetallic induces on the liner part once, in case of AIS scenario, an increase of 64%

compare with the state BS (before leakage), or a decrease, in case of AITS of 39%. Fig. 10 shows the hoop stress variation through the thickness. An increase of the hoop stress is also observed on the composite part for the AITS and AIS scenarios. However, the hoop stress level for the AITS scenario is 20% higher than the one for the AIS on the liner. Depending on the liner micro-cracks orientation, the stress state obtained by the previous modelings can lead to crack opening or closure. An optimal stress state associated with the local hydrogen absorption capability of the intermetallic layer can lead finally to a smart storage solution.

3

2

0.7275

0.725

Seq1 Seq2 Seq3 Seq4

1

0

0.73

0

0.2

A.I.S A.I.T.S 0

0.2

0.4

0.6

0.8

1

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

0.4

0.6

0.8

1

R

0.14

-3

x 10

Radial displacement (mm)

2

Axial strain

1

0

Seq1 Seq2 Seq3 Seq4

-1

-2

0

0.2

0.4

0.6

0.8

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

0.12

0.1

0.08 Seq3-B.S Seq3-A.I.S Seq4-B.S Seq4-A.I.S Seq3-A.I.T.S Seq4.A.I.T.S

0.06

0.04

0

0.2

0.4

0.6

0.8

1

R 1 Fig. 8. Radial displacement through the thickness for Seq3 and Seq4, Before Swelling (BS), After Isotropic Swelling (AIS) and After Isotropic Transverse Swelling (AITS).

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A. Hocine et al. / Materials and Design 31 (2010) 2435–2443

400

600

Hoop stress [MPa]

Axial stress [MPa]

100 -200 -500 -800 -1100 Seq3-B.S Seq3-A.I.S Seq3-A.I.T.S

-1400 -1700

0

0.2

0.4

0.6

0.8

0

-600

-1200

-1800 1

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

0

0.2

R

0.4

0.6

0.8

1

R

(a) Distribution of axial stress through the thickness of hybrid solution

(a) Distribution of hoop stress through the thickness of hybrid solution. 200

190

Hoop stress [MPa]

Axial stress [MPa]

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

150 130 110 90

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

160

70 50

0

0.0767

0.1534

0.2301

140

0.3067

0

0.0767

0.1534

0.2301

R (Liner)

R (Liner)

(b) Zoom of distribution of axial stress through

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

the thickness of liner part (0 ≤ R ≤ 0.306). 350

140

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

Hoop stress [MPa]

Axial stress [MPa]

130 120 110

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

100 90

0.3067

300

250

200

80 70 0.3374

0.4797

0.6219

0.7642

0.9064

1

R (Composite)

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

induces non-significant closure effect on a crack whatever its orientation 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. This evolution is rather the same than for Seq4.

150 0.3374

0.4796

0.6219

0.7641

0.9064

1

R (composite)

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

On the liner and for both considered stacking sequences, the axial strain increases for the AIS scenario whereas it decreases for the AITS scenario. On the other hand, an increase of the hoop strain level is observed on the composite part. The presence of circumferential layers in the stacking sequences reduces the hoop strain level and increase the axial strain one.

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A. Hocine et al. / Materials and Design 31 (2010) 2435–2443 -3

5

-10

-20

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

3

2

-30

-40

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

0

0.2

0.4

0.6

0.8

1

0

1

R

0.2

0.4

0.6

0.8

1

-3

4 -10

x 10

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

Hoop strain

3.5

-20

-30

-40

0

R

0

Radial stress [MPa]

x 10

4

Axial strain

Radial stress [MPa]

0

Seq4-B.S Seq4-A.I.S Seq4-A.I.T.S

0

0.2

0.4

0.6

0.8

3

2.5

2 1

1.5

R

0

0.2

0.4

0.6

0.8

1

R

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

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

Table 5 Equivalent stress and strain for Seq3.

-3

Scenario

BS

AIS

AITS

Equivalent stress (MPa) Equivalent strain (%)

198.86 0.33

206.57 0.64

201.49 0.40

21

x 10

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

4. Conclusions and perspectives This paper presents an analytical modeling of a hybrid solution for hydrogen storage made of an aluminum liner coated with an intermetallic, itself overwrapped by filament winding. This approach is completely original as far as the analysis focuses on the mechanical response of this peculiar structure which purpose is to secure the hydrogen storage medium. Different sequences of the multilayer composite are investigated. This analysis allows predicting the effect of the intermetallic swelling on the mechani-

Radial strain

14

3.2.2.4. Radial strain. Fig. 13 shows the radial strain evolution through the thickness. Considering the stacking sequence Seq3 which gives similar results to that of the stacking sequence Seq4, the intermetallic thermomechanical swelling leads to an increase of the compressive stress, both on the liner and the composite. The computed axial and hoop strains are not so convenient. The intermetallic swelling tends to increase the strains and so tends to open the cracks. The only positive influence seems to happen for the AITS scenario. In this case, a decrease of the axial strain is observed with the expansion of the intermetallic. So, if the crack is oriented along the circumferential direction, this decrease could lead to its closure. Otherwise, for both scenarios, the opening of the crack is expected.

7

0

-7

0

0.2

0.4

0.6

0.8

1

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

cal response both of the liner and the composite while leakage of hydrogen is occurring. Present results in terms of stresses, strains and displacement through the thickness, are discussed for two scenarios, After Isotropic Swelling (AIS) and After Isotropic Transverse Swelling (AITS), and are compared with the state before leakage, Before Swelling (BS). The first part is devoted to the mechanical response of four different stacking sequences: [±50]8, [±50]7 + [90]2, [±60]8 and [±60]7 + [90]2 when no leakage happens. This analysis shows that the behavior of this hybrid solution strongly depends on the stack-

A. Hocine et al. / Materials and Design 31 (2010) 2435–2443

ing sequences of the composite. Finally, the different results decrease with the 60° winding angle and the effect are amplified when this stacking sequence is modified in order to have two circumferential layers. The second part focuses on the analysis of intermetallic swelling on the behavior of a hybrid solution. The intermetallic swelling has a significant influence on the mechanical behavior of the hybrid solution. Results clearly show that the swelling of intermetallic induces its crushing on the liner and the composite. According to the results obtained for radial strain and stress, the liner and the composite are subjected to an increase of the compression state whatever swelling scenario is. Cracks initiated during the pressure loading will tend to open more, except in case of the AITS scenario if additionally the crack is circumferentially oriented. The increase of the radial compression is also expected to have a positive influence on the cracks closure. Authors are fully aware of the limits of such an analysis; it means the global swelling of the intermetallic, and the elastic behavior of this intermetallic. However, this study gives some peculiar informations on the structure response and on the potential of such a material when used to secure hydrogen storage media. In a forthcoming paper, we will consider a finite element method to make it possible to see more in details the effect of the local swelling on a crack initiated in the liner. References [1] Liang CC, Chen HW, Wang CH. Optimum design of dome contour for filamentwound composite pressure vessels based on a shape factor. J Compos Struct 2002;58(4):469–82. [2] Verijenco VE, Adali S, Tabakov PY. Stress distribution in continuously heterogeneous thick laminated pressure vessels. J Compos Struct 2001;54(2– 3):371–7. [3] Vasiliev VV, Krinakov AA, Razin AF. New generation of filament-wound composite pressure vessels for commercial applications. J Compos Struct 2003;62(3–4):449–59.

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