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Determination of the autofrettage pressure and estimation

of material failures of a Type III hydrogen pressure vessel

by using finite element analysis

Dae-Sung Son, Jin-Ho Hong, Seung-Hwan Chang*

School of Mechanical Engineering, Chung-Ang University 221, Huksuk-Dong, Dongjak-Gu, Seoul 156-756, Republic of Korea

a r t i c l e i n f o

Article history:

Received 29 February 2012

Received in revised form

11 June 2012

Accepted 13 June 2012

Available online 12 July 2012

Keywords:

Type III hydrogen pressure vessels

Autofrettage pressure

Winding angle

Failure criterion

a b s t r a c t

The autofrettage process of a Type III hydrogen pressure vessel for fuel cell vehicles with

preset winding pattern was simulated by finite element analysis (FEA). For a precise finite

element analysis, the ply based modeling technique was used for the composite layers;

a contour function was derived for the fibers at the dome part to determine the exact

winding angle; and the exact composite thickness was also considered. In order to deter-

mine the most appropriate autofrettage pressure, stress analysis of the pressure vessel

according to its internal pressure was carried out with consideration of the international

regulations about pressure vessel design. The minimum stress ratio, the permanent

volumetric expansion and the generated residual stress were investigated, and the failure

of the pressure vessel under minimum burst pressure was predicted by application of

various failure criteria of anisotropic composites.

Copyright ª 2012, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rightsreserved.

1. Introduction

Hydrogen gas produces no harmful byproducts when it burns,

so it has received much attention as a source of eco-friendly

energy [1,2]. To utilize hydrogen as a fuel source, various

storage methods have been developed. Among these

methods, the most commercialized method has been to

charge hydrogen gas in a pressure vessel at a high pressure.

One of the promising industrial fields to use hydrogen is theautomobile industry. But low energy density of hydrogen gas

has been the main reason for its low competitiveness against

existing fuels such as gasoline; therefore, high capacity

(70 MPa) pressure vessels are in demand for commercializa-

tion of hydrogen gas. To design a high capacity (70 MPa)

pressure vessel, a new material is essential, and fibrous

composites such as the carbon/epoxy composite is considered

one of the promising materials for fabricating Type III and

Type IV pressure vessels [3]. These pressure vessels are made

by the filament winding process, in which the liner is

completely wound by filaments at various winding angles. In

the filament winding process, various design factors such as

the winding pattern greatly affect the vessel performance.

Various algorithms to optimize these design factors were

studied [4e6]. Investigations on the performance of Type III

and Type IV pressure vesselsaccording to the design factors of

the filament winding process were also carried out. Camaraet al. [7] and Biea et al. [8] investigated the fatigue behavior of

composite pressure vessels by using a statistical method and

continuum damage mechanics, and they estimated the

fatigue life of the pressure vessels for various conditions. Liu

et al. [9e11] formulated an estimation method for the property

degradation of composites according to the generated stresses

in pressure vessels and then, applied this estimating method

to FEA to predict the failure-inducing pressure. Hu et al. [12]

* Corresponding author. Tel.: þ82 2 820 5354; fax: þ82 2 814 9476.E-mail address: [email protected] (S.-H. Chang).

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investigated the failure of pressure vesselscausedby cracks in

the liner with consideration of the autofrettage process.

Tomioka et al. [13] investigated the failure strength of a pres-

sure vessel according to the environmental temperature by an

experimental approach. Unlike the Type IV pressure vessels,

the Type III pressure vessel undergoes the autofrettage

process to enhance its fatigue characteristics [14]. The auto-

frettage process generates tensile residual stress in thecomposite layers and compressive residual stress in the liner

because the excessive internal pressure (autofrettage pres-

sure) makes the liner yield. Therefore, when service pressure

is applied to the vessel, a low level tensile stress is generated

in the material, which enhances fatigue strength. The

performance of the autofrettage process is affected by the

radius of the vessel, the composite thickness and modulus,

plastic behavior of the liner, the magnitude of the autofrettage

pressure, and so on [15]. Therefore, the autofrettage pressure

should be determined by considering the shape of the pres-

sure vessel and the winding pattern of the carbon fibers.

In this paper, vessel performance according to the auto-

frettage pressure was investigated with consideration of international regulations to determine the appropriate auto-

frettage pressure for a Type III hydrogen pressure vessel with

a pre-set winding pattern. The important factors for accurate

finite element analysis of the autofrettage process are the

consideration of the anisotropic property of the composites

and the information about the liner’s plastic behavior. Even

a slight variation of these factors may generate a big differ-

ence in the analysis result because of the involvement of non-

linear plastic deformation and the interaction of stress

distributions in the two materials. Therefore, the composite

layer has to be modeled precisely, and the exact non-linear

stressestrain relationship of the liner is needed. In this

paper, the ply based modeling technique [16], which canprovide the exact stress distribution for the composite layer,

and the exact stressestrain relationship for an aluminum

liner were used for the finite element analysis. With this

modeling technique, the stresses in orthotropic directions in

every single composite layer were calculated accurately. The

variable winding angles and composite thickness at the dome

part were also considered through a contour function of the

fibers. To determine the most appropriate autofrettage pres-

sure, four major conditions from the international regulations

on the Type III pressure vessel design were applied.

2. Modeling

2.1. Geometry and material properties of the pressure

vessel

The Type III hydrogen pressure vessel with capacities of

70 MPa and 113 L was investigated and its shape and

geometric details are shown in Fig. 1. It is composed of

a port, an aluminum liner and composite layers. The

aluminum liner was fabricated by deep drawing and ironing

processes so it has a single port, as shown in Fig. 1. At the

opposite part of the port, a knob was formed to support

filaments during the filament winding process. To simulate

the actual service condition of the vessel, the port was filled

with a solid object and a tie condition was imposed on the

interface of the boss and the liner. A simple contact condi-

tion was imposed on the interface between the liner and the

composite layers because these two parts are combined by

filaments in tension and bonded by excessive resins, which

is expected to be very weak [16]. The surface contact func-

tion provided by ABAQUS 6.9-1 was used to define contact

surfaces and impose friction coefficient on the interface. Innormal direction at the interface a hard contact, which is

a general contact condition, was applied and the friction

coefficient of 0.4 [17] was imposed on the interface in

tangential direction. For a precise stress analysis with

reduced computation time, only the small axisymmetric

part (5) of the pressure vessel was modeled by using surface

symmetric condition in the hoop direction. An 8 node 3D

rectangular element (C3R8R) was used for the modeling, and

a layup tool supplied by ABAQUS 6.9-1 was used for the ply

based modeling [16] of the composite laminate. The port and

the liner were made of aluminum (6061-T6), and the ortho-

tropic property of the carbon/epoxy composite laminate

(MR60H-24K/epoxy, Grafil Inc., USA) was used for themodeling of the composite layers. This prepreg had the

same type of carbon fiber and fiber volume fraction (65%) as

the filament winding structure. The material properties

used in the finite element analysis are listed in Table 1.

As mentioned, one of the most important factors for esti-

mating the appropriate autofrettage pressure was the plastic

behavior of the liner. Therefore, the non-linear stressestrain

relationship of an aluminum 6061-T6 [18] was used in the

analysis. The composite laminate was composed of 132

windings (plies) with various winding angles (a hoop winding

(90), high helical windings (80, 75, 65) and helical windings

(30, 25, 23, 21, 18, 15, 13)). The details of the winding

patterns were not specified for company confidentiality.Because of the nature of the filament winding process, the

winding angle (J) contains simultaneously the positive (þJ)

and the negative (J) ply angles with respectto the axial axis,

so the balanced stacking sequence was used in the analysis.

Material degradation of the composite layers due to

temperature rise was not considered in this paper because the

generated temperature during fueling was expected not to

exceed 100 C [19] and the composite layers maintain its

original material property in this temperature condition [20].

2.2. Composite modeling

If a composite laminate is thin enough, the ply basedmodeling and the laminate based modeling techniques give

almost the same results [21]. But for thick composite struc-

tures such as a Type III hydrogen pressure vessel (70 MPa

class), the ply based modeling technique provides much more

precise stress distribution [16]; therefore, the ply based

modeling technique was used for the accurate stress analysis

of the autofrettage process in this study. In the ply based

modeling technique, every single winding layer (ply) of the

pressure vessel was modeled by using the composite layup

tool provided by ABAQUS 6.9-1, and the variations of the

winding angle and thickness at the dome part were also

considered. To apply the variation of the winding angle of the

carbon filaments at thedome part to the finite element model,








the fiber angle (a) was defined as the angle between the

meridian line and the fiber, which varies with the angular

position (F) and winding angle (J), as shown in Fig. 2a. It was

assumed that fibers did not slip and they traveled the shortest

path during the winding process. When the distance from an

arbitrary point D on the surface of the dome to thecentral axis

is ri the position of the point D can be expressed by (ricos A, risinA, f (ri)) where the function f (ri) is defined by the dome geom-

etry. The fiber angle (a) between a fiber direction ð F!0

Þ and the

derivative of the meridian line ðV !0

Þ can be expressed by eq. (1).

And the angular position (F) and the length of ri have the

relationship of eq. (2);

a ¼ tan1 ri f 0ðriÞ f ðriÞ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ f f 0ðriÞg

2q ffiffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi ffiffi

ricot2J f f ðriÞg2

q (1)

tan F ¼ f ðriÞ

ri(2)

By combining the eqs. (1) and (2), the fiber angle (a) can be

expressed as a function of the angular position (F) [16].Therefore, once the winding angle (J) is known, the fiber angle

(a) at an arbitrary angular position (F) can be identified. The

variation of the fiber angle of helical windings (80, 75, 65, 30,

25, 23, 21, 18, 15, 13) was calculated, as shown in Fig. 2b.

Thehoop winding (90) was not carried out atthe dome part. To

consider the thickness variation along the angular position,

a prototype of the pressure vessel was cut and the actual

composite thickness of the dome part wasmeasured, as shown

in Fig. 3a. At the dome part, there was no hoop winding, which

occupied a large portion of the winding angles at the cylinder

part, and the fiber density increased along the angular position

(see Fig. 3b); therefore, the total composite thickness at the

dome part increased overall along the angular position. The

initial decrease of the composite thickness was caused by the

absence of hoop winding and the small areal coverage of the

high helical winding fibers (80, 75, 65), which covered around

20 of the angular position, as shown in Fig. 2b.

To estimate a single ply thickness, it was assumed that the

composite thickness variation at the dome part did not

correlate with the winding angle. After considering thecoverage area of each fiber for different winding angles, the

single ply thickness was calculated, as shown in Fig. 3a. To

apply this thickness variation to the finite element model,

additional balanced plies were added to the existing

composite laminate, as shown in Fig. 3b, and this method

helped to simulate the actual winding pattern and the shape

of the dome part. And for realizing a more accurate winding

angle, the local coordinate system of each finite element was

used to align the fiber direction along the actual winding

direction. The additional modeling details are described in the

preliminary study [16].

3. Determination of the autofrettagepressure

3.1. Conditions for determining autofrettage pressure

Among many international regulations on the design of

pressure vessels, the compressed gaseous hydrogen regula-

tion [22], which was proposed by European Integrated

Hydrogen Project e Phase II (EIHP-II), and the ISO 15869:2009

[23] were considered in the determination of the appropriate

autofrettage pressure of a Type III hydrogen pressure vessel.

The important conditions for determining autofrettage pres-

sure are as follows;

Fig. 1 e Finite element model of a Type III hydrogen pressure vessel.

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 e n e r g y 3 7 ( 2 0 1 2 ) 1 2 7 7 1 e1 2 7 8 1 12773







Narayanaswami et al. [27] proved that the most accurate

failure prediction can be obtained when the inter-stress

strength tensor F12 becomes zero or the value of Hoffman’s

suggestion. Because the value of F12 in Hoffman’s suggestion

depends on the fiber directional strength (Xt, Xc), the value of

F12 becomes very low, almost zero, as shown in Fig. 5. In this

paper, the material failure of the composite part was esti-

mated for the four failure criteria (maximum stress and

strain criteria, Tsai-Wu failure criterion, Hoffman failure

criterion), and the results were compared.

4. Analysis results

4.1. Permanent volumetric expansion

The permanent volume expansion (r) presented in [Condition

2] in the previous chapter is defined as the ratio of the

permanent volume change to the total volume change under

the test pressure condition after the autofrettage process, and

is expressed by the following relation;

Fig. 2e

Determination of fiber angle and areal coverage according to the angular position; (a) schematic diagram for definingthe fiber angle according to dome geometry, (b) variations of fiber angle according to the angular position and helical

winding angle.








stress at the service pressure. The minimum burst pressure

was 164.5 MPa, which was 2.35 times the service pressure

(70 MPa) as defined in ’EIHP-II’ [22]. The stress ratios decreased

as the autofrettage pressure increased, as shown in Fig. 6b.

This decrease was due to the fact that the fiber stress under

service pressure increased with the autofrettage pressure

because higher autofrettage pressures generated higher levels

of tensile residual stress in the composite layers. But the fiberstress under the minimum burst pressure was seldom

affected by the level of autofrettage pressure because of the

relatively low level of the residual stress compared to the total

fiber stress. When the autofrettage pressures are in the ranges

of 105e107 MPa, the minimum stress ratio becomes higher

than 2.35, which satisfies [Condition 3].

4.3. Failure prediction under the minimum burst

pressure

The Type III hydrogen pressure vessel should be safe under

the minimum burst pressure (164.5 MPa) based on the regu-

lation ([Condition 4]). Therefore, the possibility of any failures

both in the aluminum liner and the composite layers was

investigated by using finite element analysis. The four failure

criteria were used to estimate any material failures in the

composite layers. First, the stresses of the aluminum liner

under various pressure conditions were plotted against the

autofrettage pressure in Fig. 6b. The aluminum liner stresses

decreased as the autofrettage pressure increased under the

service pressure condition but they showed little change

under the minimum burst pressure condition. The maximum

stress (314.9 MPa) generated in the aluminum liner was lower

than the ultimate strength (333.72 MPa) of the aluminum liner,

so the liner will not fracture.

To estimate the failure of the composite layers of the

pressure vessel, the case of 107 MPa autofrettage pressure

amongst 105 MPa, 106 MPa and 107 MPa, which satisfied the

Pressure

Step

Autofrettage

Pressure

Zero

Pressure-1(0MPa)

Service

Pressure(70MPa)

Test

Pressure(105MPa)

Zero

Pressure-2(0MPa)

Pressure

Step

Autofrettage

Pressure

Zero

Pressure(0MPa)

Service

Pressure(70MPa)

Test

Pressure(105MPa)

Minimum Burst

Pressure(164.5MPa)

a

b

Fig. 4 e

Loading histories for determining (a) permanent volumetric expansion, (b) the minimum stress ratio and

material failure.

Fig. 5 e

Comparison of various failure criteria.








[Condition 3], was investigated. Once the pressure vessel thatexperienced 107 MPa autofrettage pressure remained safe, the

other cases were considered to be theoretically safe because

higher autofrettage pressures generate higher residual

stresses in the composite layer of the pressure vessel. But the

generated fiber stress according to the autofrettage pressure

was almost uniform, as shown in Fig. 6b, so the failure

behavior of the composite layers was expected to be the same

for the other autofrettage pressure conditions.

To estimate the failure of the composite layers, the

maximum stress criterion was applied to the stress analysis

result. The failure index, defined as the ratio of the generated

stress to the material strength in each orthogonal direction, as

expressed in eq. (3), was plotted against characterized length(x /L), as shown in Fig. 7. The characterized length (x /L) is

defined as the ratio of the contour path (x) of the pressure

vessel surface to the axial perimeter (L),as shown in Fig. 1. The

yellow surfaces in Figs. 7e9 represent failure surfaces. The

calculation result showed that the generated fiber stress and

in-plane shear stress were much lower levels than their cor-

responding strengths, so material failure was not predicted.

On the otherhand, it showed almost a failure index of unity in

the transverse direction, which means the hoop winding and

helical windings of the composite laminate may fail by the

transverse tensile stress if the internal pressure increases due

to an abnormal situation such as a sudden temperature rise

during fuel injection [19]. The maximum strain criterion

produced the similar result to the maximum stress criterion

(see Fig. 8) but it predicted a safer condition, especially in the

transverse direction. This safe condition was due to the

Poisson’s ratio, which correlate the strains in other directions;

as a result, the Poisson’s ratio effect reduced the strains in the

transverse direction, which is more realistic.

In order to estimate the material failure more precisely,

second order failure criteria were also applied. For the case of

the Tsai-Wu criterion, the inter-stress strength tensor F12 wasset to be zero for the precise prediction of brittle failure under

the tensile stress condition [27]. The failure index expressed

by the left hand side of eq. (6) was calculated as shown in

Fig. 9a. The result was similar to the failure index distribution

of the in-plane transverse stress for the maximum stress

criterion, and this similarity explains why the transverse

tensile stress is the most harmful factor that leads to material

failure of this composite structure. The maximum failure

index of 0.786 is predicted at the outermost center part of the

cylinder of the helical windings. This result was similar to the

results of Hoffman’s criterion (Fig. 9b), because in this crite-

rion the inter-stress strength tensor is mainly related to the

very high fiber directional strengths, which make the strength

Fig. 6 e Results of stress analysis for determining (a) the

permanent volumetric expansion, (b) the minimum stress

ratio at composite layer.

Fig. 7 e The maximum stress criterion under the loading

condition of 107 MPa; (a) fiber direction, (b) in-plane

transverse direction, (c) in-plane shear.








tensor very low, comparable to zero. Both of the two criteria

predict a sharp rise of stresses at the border between the dome

and the cylinder parts as shown in Fig. 9. This stress distri-

bution may cause problems under a fatigue loading condition;

therefore, a special design consideration such as winding

pattern changes needs to be taken into account.

The failure analysis of the Type III hydrogen pressure

vessel with an autofrettage pressure of 107 MPa proved the

safety of the vessel without any material failures. It was also

proved that this autofrettage pressure satisfied all the condi-tions of a safe design of a Type III hydrogen pressure vessel.

5. Discussions

In order to determine the autofrettage pressure of a Type III

pressure vessel, the four design conditions should be satisfied

and the generated stresses need to be low for high fatigue life.

First, the range of appropriate autofrettage pressures which

satisfied the four design conditions for the current pressure

vessel with a pre-set winding pattern were estimated

(105 MPae107 MPa). The most appropriate autofrettage pres-

sure should be determined in this range by using the stress

analysis results. First, to enhance the fatigue characteristics,

a low rate of permanent volume expansion was preferable

based on [Condition 2]. Second, as the minimum stress ratio

increased, the composite layers became safer, but it raised

stresses in the liner. The preferable autofrettage pressure

should make the minimum stress ratio exceed the allowable

value of 2.35 slightly, and should minimize the liner’s stress

based on [Condition 3] because fibrous composites have goodfatigue characteristics. As a result, the autofrettage pressure

that guaranteed structural safety and the lowest permanent

volume expansion (see Fig. 6a), made the minimum stress

ratio exceed 2.35, and generated the lowest stress in the liner

was found to be 107 MPa, as shown in Fig. 6b.

A simple contact surface condition rather than a perfect

bonding condition at the interface was used to estimate the

stress distribution of a pressure vessel during autofrettage

process.

Based on the measurement of the bonding strength of

a carbon/epoxy composite-aluminum single lap joint [28] and

preliminary experimental investigation the level of bonding

strength of a carbon/epoxy composite-aluminum single lap joint is below 15 MPa but the analyzed bonding stress of the

Type III hydrogen pressure vessel at the interface is higher

than 17 MPa for the case of perfect bonding condition, which

represents the bonding layer fails during the autofrettage

process. Therefore, the perfect bonding condition is not able

to represent the actual behavior of the interface during the

autofrettage process.

In order to check the effect of the friction coefficient at the

interface the lower level of friction coefficient (0.25) was also

applied and the result was compared with the case of the

higher friction coefficient (0.4) which was used for estimating

the stress distribution of the pressure vessel. The lower level

of friction coefficient (0.25) generated almost the same stress

Fig. 8 e

The maximum strain criterion under the loadingcondition of 107 MPa; (a) fiber direction, (b) in-plane

transverse direction, (c) in-plane shear.

Fig. 9 e The second order failure criteria of orthotropic

materials; (a) Tsai-Wu criterion, (b) Hoffman criterion.








distribution as the case of 0.4 friction coefficient in all the

materials under the loading history.

It seemed a friction coefficient within moderate range

seldom affected the stress distribution.

On the other hand, for the case of the perfect bonding

condition, it generated higher stress in the liner and the

composite layers under the service condition after the auto-

frettage process. This was caused by the fact that this condi-tion did not allow any relative motion between the composite

layers and the aluminum liner at the interface.As a result, the

perfect bonding condition generated 15 MPa and 20 MPa

higher stresses in the cylinder part and in the dome part of the

liner, respectively than those of the case of surface contact

condition and this may affect the determination of the auto-

frettage pressure.

For more reliable design of the pressure vessel some more

design consideration needs to be investigated.

The temperature dependence on vessel mechanical

performance was not considered in this paper. Based on the

analysis result of temperature rise during the hydrogen

fueling process [19] it was expected that the temperaturewould rise to around 100 C when the pressure vessel was

filling from empty to 70 MPa. The mechanical properties of the

carbon/epoxy composite used in this paper maintains its

original value until the service temperature of 100 C [20],

which represent the calculation results of the material

behavior and the autofrettage pressure are reliable. But the

temperature may rise over 100 C for unexpected circum-

stances, therefore it is needed to investigate the temperature

effect on the behavior of the pressure vessel including the

determination of the autofrettage pressure, which is a part of

our future work.

The stressestrain relationship of the aluminum liner

affects much the determination of the autofrettage pressurebecause of the non-linear behavior of the aluminum liner. If

the yield stress increases by 5% with Young’s modulus

unchanged the liner stress under the service condition after

the autofrettage process will increase by 3.3%. But, if the yield

stress decreases by 5% the liner stress decreases by 10.9%

under the same condition. This represents the exact non-

linear relationship of the stressestrain curve is essential to

determine the appropriate autofrettage pressure. On the other

hand, the variation of Young’s modulus does not affect much

the stress distribution in the liner, which represents the

moderate changes of Young’s modulus does not contribute to

the changes of the autofrettage pressure.

6. Conclusions

In this paper the appropriate autofrettage pressure for a Type

III hydrogen pressure vessel for fuel cell vehicles with a preset

winding pattern was determined by stress analysis with

consideration of the related international regulations.

Because the effect of the level of autofrettage pressure on

stress generation in materials and service life of a vessel is

great, the stress was accurately calculated by finite element

analysis. To calculate the stress distribution accurately in the

composite layers and the aluminum liner according to the

level of autofrettage pressure, the ply based modeling

technique for the composite layers was carried out to model

the pressure vessel. To estimate the changes in stress distri-

butions in the materials ofthe pressure vessel such as those of

the generated residual stresses after the autofrettage process,

which induces yielding of the liner, a non-linear stressestrain

relationship was considered. Moreover, to calculate the exact

winding angle at the dome parts, a contour function was

derived for the fibers, and by using this, the exact arealcoverage of a fiber at a certain winding angle was accurately

estimated. And the thickness variation of the composite

layers at the dome part was also considered by measuring the

actual composite thickness after cutting the vessel prototype.

From the analysis results, it wasfound that as the autofrettage

pressure increased, the permanent volumetric expansion

decreased and the compressive residual stress in a liner

increased, which enhanced the structural performance of the

pressure vessel. To determine the most appropriate auto-

frettage pressure of the Type III hydrogen pressure vessel, the

four conditions ([Condition 1]e[Condition 4]) proposed by

European Integrated Hydrogen Project e Phase II and ISO

15869:2009 were considered. The appropriate autofrettagepressure was determined to be 107 MPa.

The modeling technique and the process to determine the

autofrettage pressure presented in this paper can be utilized

in theoptimal design of a Type III pressure vessel to determine

the optimal winding pattern and liner shape.

Acknowledgments

This research was supported by the Chung-Ang University

Excellent Student Scholarship and partly by the research

program of “Estimation of the material property for FCV Type

III Hydrogen Storage Vessel (70 MPa)” through Ministry of

Knowledge and Economy of Korea.

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