hydrostatic pressure burst test and pressure cycling test of … pdf... · 2006-05-24 · test...

WHEC 16 / 13-16 June 2006 – Lyon France

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Hydrostatic Pressure Burst Test and Pressure Cycling Test

of Compressed Hydrogen Tanks

Toshihiko OOIa, Takafumi IIJIMAa, Koichi OSHINOa, Hiroyuki MITSUISHIa, Shogo WATANABEa

aJapan Automobile Research Institute 1328-23 Takaheta, Osaka, Shirosato, Ibaraki 311-4316, Japan, [email protected]

ABSTRACT: Compressed hydrogen tanks for fuel cell vehicles require sufficient strength to prevent bursting, and also require fatigue strength to resist repeated fills and releases. To clarify the bursting characteristics of two tank types (type 3 and type 4), hydrostatic pressure burst tests were conducted. The burst pressure of every tank demonstrated a two to three times higher than the minimum required burst pressure. The expansion ratios and strain differences between the two types of tanks were dependent on the material properties and fiber volume fraction of each tank. Pressure cycling tests of type 3 tanks with initial flaws were continued until leak before burst (LBB). The tank life decreased in accordance with the increasing depth of the initial flaw. When the initial flaws were greater than 0.1 mm, LBB occurred at the initial flaw position. The tank life was correctly estimated from striation spacing at the fracture surface of LBB. The maximum depth of allowable defects of the type 3 tank used in this study was from 0.10 mm to 0.15 mm.

KEYWORDS : Fuel Cell Vehicle, Pressure Burst Test, Pressure Cycling, Compressed Hydrogen Tank, Leak Before Burst

1, Introduction Almost every fuel cell vehicle (FCV) presently used on public roads utilizes onboard compressed hydrogen tanks for hydrogen fuel. The compressed hydrogen tank is also a major choice of onboard tanks for future FCV's. Anti-burst strength to resist high pressure and fatigue strength to protect against failure caused by repeated refuels are necessary characteristics for these tanks. This study investigates the bursting characteristics of two types of compressed hydrogen tanks by conducting hydrostatic pressure burst tests: type 3 tank (fully wrapped composite tanks with metal liners) and type 4 tank (fully wrapped composite tanks with non-metallic liners). Since the fatigue strength of the non-metallic liner is greater than the metal liner, the relation between the depth of an internal flaw artificially induced in the aluminum alloy liner of the type 3 tank as a fatigue sensitive site and the life of the tank were examined by performing pressure cycling tests until leak before burst (LBB) 1) conditions were satisfied. Both tests were performed based on Japanese regulation JARI S 001 (2004). 2)

2. Procedures 2.1 Test Tank Specifications for the tanks tested in this study are listed in Table 1. The type 3 metal liner is made of aluminum alloy (A6061-T6), and the type 4 liner is made of high density polyethylene (HDPE). The tank liners are wrapped with carbon fiber reinforced plastics (CFRP). 2.2 Hydrostatic Burst Test Test conditions of the hydrostatic burst test are presented in Table 2, and the schematic diagram of the apparatus for the burst test is shown in Fig. 1. Test tanks were prepared on a closed, dry pit floor. A pressure sensor was installed on the tank side of the pressure line to correctly measure the pressure of the tanks. Pressurization rate was held at no lager than 300 kPa/sec over 80% of the minimum required burst pressure (78.75 MPa). Tank pressure and strains


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generated at the tank surface were monitored during the test. Strain gauges were mounted on the external surface of the CFRP layer.

Table 1 Specifications of Test Tanks

3.2

7.2

MinimumBurst Pressure

(FP×2.25※2)[MPa]

VH3 Tank(Type3※3)KHK　Approved

VH4 Tank(Type4※4)ANSI/IAS NGV2-1998

Thickness of Liner(Cylindrical Part)

[MPa]

Tank TypeSpecification

FP※1

[MPa]Volume

[L]

Diameter× Length

[mm]

78.75

35 65 φ400×840 78.75

35 34 φ280×830

※1 FP：Filling Pressure ※3 Liner Material：A6061-T6 ※2 2.25：Stress Ratio ※4 Liner Material：High Density Polyethylene（HDPE）

Table 2 Conditions of Burst Test Test Place Dry Pit

Rate of Pressurizationover Minimum Burst Pressure×80%(≒60MPa) ≦300kPa/sec

Layout of Pressure Measurement Sensor Tank Side Pressure Line

Type of Pressure Measurement Sensor Strain Gauge Type，Measurable Range：200MPa

Sampling Rate 10Hz

Test Tank

ＭHydraulicUnit

Pressure Sensor(Control)

ContorolUnit

Test Pit

300MPaIntensifier

High Pressure HoseControl valve

Pressure Sensor(Measurement)

Test TankTest Tank

ＭHydraulicUnit

Pressure Sensor(Control)

ContorolUnitContorolUnit

Test Pit

300MPaIntensifier

High Pressure HoseControl valve

Pressure Sensor(Measurement)

Fig.1 Schematic Diagram of Apparatus for Burst Test


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2.3 Pressure Cycling Test to Assess the Size of Allowable Defect Sizes of internal flaws artificially induced in the aluminum alloy liner are listed in Table 3, and the intensifier and layout of the pressure cycling test is illustrated in Fig. 2. Test conditions are described in Table 4. Tests were continued until LBB conditions were satisfied. Pressure and strains were also monitored the same as for the hydrostatic pressure test to confirm the possibility of detecting a sign just before LBB and/or burst. Details of tank investigations after LBB are given in Table 5. Striation marks3) appearing at the fracture surface of LBB were observed, and the spacing of the marks were measured to estimate the life of a type 3 tank.

Table 3 Dimensions of Initial Flaw

250.30 0.30-B

250.30 0.30-A

250.20 0.20-B

250.20 0.20-A

250.15 0.15-C

250.15 0.15-B

250.15 0.15-A

250.10 0.10-C

250.10 0.10-B

250.10 0.10-A

Length [mm]Depth [mm]

Dimensions of Initial FlawTank ＃

250.30 0.30-B

250.30 0.30-A

250.20 0.20-B

250.20 0.20-A

250.15 0.15-C

250.15 0.15-B

250.15 0.15-A

250.10 0.10-C

250.10 0.10-B

250.10 0.10-A

Length [mm]Depth [mm]

Dimensions of Initial FlawTank ＃

CFRP Layer Aluminum Alloy Liner

Initial Flaw

Tail End Plug

Cylindrical Part

Dome

120MPa Intensifier

Test Tanks

High Pressure Hose

120MPa Intensifier

Test Tanks

High Pressure Hose

Fig. 2 Intensifier and Layout of Pressure Cycling Test

Table 4 Conditions of Pressure Cycling Test

10HzPressure, StrainMeasurement

Leak before BurstTermination

4 cycles/minFrequency

over 44 MPa (≒ FP×125％)Maximum Pressure

under 1 MPaMinimum Pressure

Test Conditions

Deionized WaterFluid (Medium)

Dry PitTest Place

10HzPressure, StrainMeasurement

Leak before BurstTermination

4 cycles/minFrequency

over 44 MPa (≒ FP×125％)Maximum Pressure

under 1 MPaMinimum Pressure

Test Conditions

Deionized WaterFluid (Medium)

Dry PitTest Place


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Table 5 Detail of Investigations

Observe by Scanning Electron MicroscopeFracture Surface of LBB

①Fix Sample by Resin, ②Polish※1,③Etch※2,④Observe by Optical MicroscopeCross Section of LBB

Measure along Circumference by MicrometerLiner Thickness

Measure by Laser MicroscopeDepth of Initial Flaw

①Clean Liner, ②Spray Penetrant,③Remove Penetrant after 15min, ④DevelopLBB Position

MethodsItems

Observe by Scanning Electron MicroscopeFracture Surface of LBB

①Fix Sample by Resin, ②Polish※1,③Etch※2,④Observe by Optical MicroscopeCross Section of LBB

Measure along Circumference by MicrometerLiner Thickness

Measure by Laser MicroscopeDepth of Initial Flaw

①Clean Liner, ②Spray Penetrant,③Remove Penetrant after 15min, ④DevelopLBB Position

MethodsItems

※1 Polish：＃800 → ＃1200 → ＃2400 → Diamond Paste (3 µm) → Diamond Paste (1 µm) → SiO2 0.06 µm ※2 Etch：Immerse in 90% H2O-5%HNO3-3%HCl-2%HF for 30 sec to 60 sec → Wash by Water. 3. Results and Discussions 3.1 Bursting Characteristics of Tanks The results of burst test are summarized in Table 6.

Table 6 Results of Burst Test

60MPa＞ 60MPa≦ Number of Stroke[time]

Discharge※2

[cc]a-1 121.0 3.46 1,360 285 6.3 3,100a-2 117.0 3.34 1,380 292 6 2,958b-1 94.8 2.71 1,136 460 13 6,409b-2 95.5 2.73 1,240 460 13 6,409

Rate of Pressurization[kPa/sec] Movement of the IntensifierBurst

Pressure[MPa]

Stress Ratio※1

(2.25)Tank

#

※1 Stress Ratio = Burst Pressure [MPa]/FP [MPa] (FP = 35.0 MPa) ※2 Discharge [cc] = Discharge of Intensifier/Stroke [cc/time]×Number of Stroke [time] (Discharge of Intensifier/Stroke = 493 cc) 3.1.1 Burst of Type 3 Tanks Fig. 3 illustrates the situation in the dry pit after the burst of a type 3 tank. The aluminum alloy liner was divided into two parts, the top dome and the rest, in the thickness transition area between the cylindrical part and dome. The CFRP layer was separated from the liner and was scattered all over the pit. A diagram of pressure and strain vs. time of a type 3 tank (a-1) is presented in Fig. 4. The resulting pressurization rates were 1360 kPa/sec (a-1) and 1380 kPa/sec (a-2) up to 60 MPa, and 285 kPa/sec (a-1) and 292 kPa/sec (a-2) at pressures above 60 MPa. The burst pressures were nearly 120 MPa. The stress ratios (burst pressure/filling pressure) were nearly 3.4 and fully cleared the minimum required burst pressure. At above 60 MPa, axial strains at the cylindrical part increased rapidly and strain gauges exceeded their measurable range. Additionally, at 80 to 90 MPa, all gauges except the axial gauge at the dome exceeded the measurable range. However, circumferential strains increased linearly with the pressure until bursting. The maximum strain at the end of the dome was about 7,000 µε in the axial direction and about 3,500 µε in the circumferential direction. Strains generated at the dome were smaller than strains in the cylindrical part. 3.1.2 Burst of Type 4 Tanks The results in the dry pit after the burst of a type 4 tank are illustrated in Fig. 5. The CFRP layer was completely separated from its plastic liner, and the liner was divided along its bead weld. Also, the boss of the top end was separated from the liner. The pressure and strain vs. time diagram of a type 4 tank (b-1) is depicted in Fig. 6. Pressurization rates reached 1136 kPa/sec (b-1) and 1240 kPa/sec (b-2) up to 60 MPa, and 460 kPa/sec at pressures above 60 MPa. The burst pressures were 94.8 MPa (b-1) and 95.5 MPa (b-2). The stress ratios were 2.71 (b-1) and 2.73 (b-2). These values also cleared the minimum required burst pressure. Since almost all strain gauges exceeded their measurable range at about 60 MPa, only strains at


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the dome were monitored until bursting. The maximum strain at the end of the dome was about 4,500 µε in the axial direction and about 1,200 µε in the circumferential direction. Similar to the type 3 tank, strains generated at the dome were smaller than those in the cylindrical area.

Top Side Dome

CFRP Layer

Aluminum Alloy Liner(Cylindrical Part + Tail Side Dome)

Top Side Dome

CFRP Layer

Aluminum Alloy Liner(Cylindrical Part + Tail Side Dome)

Plastic Liner(Cylindrical Part + Top Side Dome)

CFRP Layer

Tail Side Dome

Plastic Liner(Cylindrical Part + Top Side Dome)

CFRP Layer

Tail Side Dome

Fig. 3 Situation after Burst of Type 3 Tank (a-1) Fig. 5 Situation after Burst of Type 4 Tank (b-1)

0

50

100

150

0.0 60.0 120.0 180.0 240.0 300.0 360.0

Time　[sec]

Pressure　[MPa]

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000Strain　[με]

Pressure

①A

①C②A②C

③Dome A

③Dome C

④A

④C⑤A

⑤C

BurstPressure121 .0ＭPa

Axial

Circumfere

i l

③Dome CircumferentialA：Axial

C：Circumferential

③Dome Axial

Minimum Required

Burst Pressure

78.75MPa

0

50

100

150

0.0 60.0 120.0 180.0 240.0 300.0 360.0

Time　[sec]

Pressure　[MPa]

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

Strain　[με]

Pressure

①A

①C

②A

②C

③Dome A

③Dome C

④A

④C

⑤A

⑤C

Burst

Pressu re

94 .8ＭPa

③Dome Circumferential

A：Axial

C：Circumferential

③Dome Axial

Minimum RequiredBurst Pressure

78.75MPa

Fig. 4 Pressure, Strain vs. Time during Burst Test Fig. 6 Pressure, Strain vs. Time during Burst Test

of Type 3 tank (a-1) of Type 4 tank (b-1) 3.1.3 Comparison of Type 3 Tanks and Type 4 Tanks Both types of tank cleared the minimum required burst pressure, confirming that these tanks possessed enough anti-burst strength for commercial use. The expansion ratios of the tanks just before burst were calculated by equation (1),4), 5) and the results are presented in Table 7. K = －V ・∆p / ∆V (1) K：Bulk Modulus of Water [GPa] V：Volume of Tank (Water Capacity) [cm3] ∆p：Pressure Difference by Compression [GPa] (Burst Pressure) ∆V：Volume Difference by Compression [cm3] Here, the minus sign (－) in equation (1) simply means that the volume of the tank decreases in accordance with increased pressure, so it is possible to delete the sign. ∆V = V・∆p / K (2) V2 is the total amount of water discharge by intensifier until burst and is equal to [number of stroke × water discharge per stroke (493 cm3)]. V3 is [V2－∆V]. The expansion ratio just before burst is equal to V3 / V. The expansion ratio was nearly 4% for type 3 tanks and nearly 5.7% for type 4 tanks. The strain generated in the cylindrical part of type 4 tanks was about twice that of type 3 tanks under equal pressure. The differences between type 3 and type 4 tanks, both in the expansion ratio and the strain in the cylindrical parts, were thought to depend on liner material (type 3 tank: aluminum alloy, type 4 tank: HDPE) and structure of the CFRP layer, e.g. winding pattern and fiber volume fraction. 6)


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Table 7 Calculated Results of Expansion Ratio

a-1 0.121 1,672 3,106 1,434 4.2a-2 0.117 1,617 2,958 1,341 3.9b-1 0.0948 2,703 6,409 3,706 5.7b-2 0.0955 2,723 6,409 3,686 5.7

V2

[cc]V3

[cc]ER※3

[％]

2.28※2 65,000

Tank＃

K[GPa]

V[cc]

2.46※1 34,000

∆P[GPa]

∆V[cc]

※1 Average Bulk Modulus of Water(1 to 150 MPa) ※2 Average Bulk Modulus of Water(1 to 100 MPa) ※3 Expansion Ratio 3.2 LBB Characteristics of Type 3 Tanks with Initial Flaw 3.2.1 LBB Cycles and Positions The condition of LBB is indicated in Fig. 7. The relation between the depth of the initial flaw and LBB cycles is given in Fig. 8. The tank’s life decreased with increasing depth of the initial flaw. When the depth of the initial flaw was under 0.10 mm, LBB sometimes occurs at none initial flaw sites of the liner. However, for initial flaws exceeding 0.10 mm in depth, cracks initiated along the initial flaw and propagated to the external surface of the liner.

Leak Water

0.10-A , 14748cycles

Leak WaterLeak Water

0.10-A , 14748cycles Depth of Initial Flaw [mm]

0

5000

10000

15000

20000

25000

30000

35000

40000

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

LBB[cycles]

● LBB at Initial Flaw Site

○ LBB at None Initial Flaw Site

Depth of Initial Flaw [mm]

0

5000

10000

15000

20000

25000

30000

35000

40000

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

LBB[cycles]



0

5000

10000

15000

20000

25000

30000

35000

40000

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

LBB[cycles]



Fig. 7 Situation of LBB Fig. 8 LBB Cycles vs. Depth of Initial Flaw

3.2.2 Strain Characteristics during Pressure Cycling Pressure and strain vs. time during the initial 10 cycles is plotted in Fig. 9, and strain vs. pressure is plotted in Fig. 10. Since strains were completely synchronized to pressure, both in axial and circumferential directions, strain measurements were quick and responsive and pressure cycling was conducted in the elastic region. The maximum strain of this type 3 tank (0.15-B) was 1,700 µε axially and 3,100 µε circumferentially, making the axial/circumferential strain ratio almost 0.5, which indicated a good agreement with theoretical axial/circumferential ratio of generated stress in the pressurized thin cylinder.7)

0

10

20

30

40

50

0 15 30 45 60 75 90 105 120 135 150

Time　[sec]

Pressure　[MPa]

0

1000

2000

3000

4000

5000

Strain　[με]

CircumferentialAxialPressure

0

10

20

30

40

50

0 15 30 45 60 75 90 105 120 135 150

Time　[sec]

Pressure　[MPa]

0

1000

2000

3000

4000

5000

Strain　[με]

CircumferentialAxialPressure

0

1000

2000

3000

4000

0 5 10 15 20 25 30 35 40 45

Pressure　 [MPa]

Strain　[με]

Axial

Circumferential

Fig. 9 Pressure, Strain vs. Time Fig. 10 Strain vs. Pressure

during Pressure Cycling during Pressure Cycling (1 to 10 cycle, 0.15-B, Cylindrical Part) (1 to 10 cycle, 0.15-B, Cylindrical Part)


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The relation between the number of cycles and strain/pressure ratios (strain amplitude/pressure amplitude) is indicated in Fig. 11. Although the strain/pressure ratio in the circumferential direction was almost constant until LBB, it rose rapidly just before a break of the strain gauges in the axial direction. A hoop winding (wound in a circumferential direction) of CFRP covered the outside surface of this tank. We considered that it would be easy to generate cracks along the interface of the fiber and resin parallel to the winding direction by pressure cycling, breaking the strain gauges in the axial direction. Therefore, strain measurements were influenced by the surface condition of the tank, i.e. composite structure of the carbon fiber and resin and winding direction of the carbon fiber, making it difficult to detect any signs just before LBB and/or burst by monitoring strain during the pressure cycling test.

0

20

40

60

80

100

0 5000 10000 15000

Cycle　[times]

Strain／Pressure

[με／ＭＰa]

Axial

CircumferentialBreak of Strain Gauge

LBB

0

20

40

60

80

100

0 5000 10000 15000

Cycle　[times]

Strain／Pressure

[με／ＭＰa]

Axial

CircumferentialBreak of Strain GaugeBreak of Strain Gauge

LBBLBB

Fig. 11 Strain/Pressure vs. Cycle during Test

(0.15-A, Cylindrical Part) 3.2.3 Depth of Initial Flaw and Liner Thickness Depth fluctuations of the initial flaws are depicted in Fig. 12. The depths of the initial flaws were stable in the axial direction, but in comparison with other tanks an initial flaw of 0.10-A was approximately 25 µm deeper than that of 0.10-B and 0.10C. This seemed to be one reason LBB did not occur at the initial flaw sites in 0.10-B and 0.10-C.

0

50

100

150

200

0 5 10 15 20 25

Distance from Flaw Edge [mm]

Depth of Initial Flaw [μm]

0.15-A

0.15-B

0.15-C0

50

100

150

200

0 5 10 15 20 25


Depth of Initial Flaw [μm]

0.15-A

0.15-B

0.15-C0

50

100

150

200

0 5 10 15 20 25


Depth of Initial Flaw [μm」

0.10-A

0.10-B

0.10-C0

50

100

150

200

0 5 10 15 20 25


Depth of Initial Flaw [μm」

0.10-A

0.10-B

0.10-C

0ｍｍ

25ｍｍ

Depth ofInitial Flaw

Distance fromFlaw Edge

Circumferential

Axial

Thickness Direction

Fig.12 Depth Fluctuations of Initial Flaw


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Liner thickness at the initial flaw sites, their neighbors, and LBB positions (LBB occurred at none-initial flaw sites) are presented in Fig. 13. Variation of liner thickness among tanks sometimes exceeded 0.10 mm, especially in the tanks with a 0.10 mm initial flaw; where it was larger than the initial flaw depth. This was thought to influence to LBB position and life.

Circumferential

Axial

Thickness Direction

Initial Flaw SiteNeighbor

of Initial Flaw

2600

2800

3000

3200

3400

0.10-A 0.10-B 0.10-C 0.15-A 0.15-B 0.15-C 0.20-A 0.20-B 0.30-A 0.30-B

Tank #

Liner Thickness　[μm]

Initial Flaw Site

Neighbor of Initial Flaw

LBB Position (None Initial Flaw Site)

6828μm

Fig. 13 Liner Thickness of Test Tank

Circumferential fluctuations of liner thickness are illustrated in Fig. 14. Since the maximum difference of liner thickness in 0.10-C was over 0.20 mm, liner thickness at the initial flaw site was 3.2 mm, which was thicker than its thinnest part. This was also thought to influence LBB characteristics. According to Figs. 12 to 14, LBB characteristics of type 3 tanks depended on the depth of the initial flaw and the liner thickness variations, particularly for shallower flaws. Since LBB sometimes occurred at the none-initial flaw site in the case of a 0.10 mm initial flaw, it is considered that the maximum depth of allowable defects in this tank might exceed 0.1 mm.

0deg.

180deg.

90deg.270deg.

Initial Flaw Liner Thickness

3.0

3.1

3.2

3.3

3.4

0 90 180 270 360

Angle from Initial Flaw 　[degree]

Liner Thichness　[mm]

0.10-B

0.10-C

Initial Flaw

Difference of Thicknessbetween Initial Flaw Siteand The Thinnest Site

Depth of Initial Flaw

Fig. 14 Circumferential Fluctuations of Liner Thickness

3.2.4 Crack Propagation Characteristics at LBB Position of Tanks Cross sections of the liner after LBB at the initial flaw site are presented in Fig. 15. Cracks initiated from the bottom of the initial flaw and penetrated to the external surface of the liner. In 70% to 90 % of liner thickness, cracks zigzagged across crystal grains of the liner. At the final stage of propagation, cracks inclined at 45 degrees. Fracture surfaces of a liner after LBB at the initial flaw site are illustrated in Fig. 16. Greater than 500 µm from the internal surface of the liner, stripe marks at right angles to the thickness direction clearly appeared at the fracture surface of LBB, particularly for LBB at the initial flaw site. These were striation marks characteristic of fatigue fractures.3) Since striation marks were evidence of crack propagation by pressure cycling, each stripe corresponded to one cycle, and with deeper cracks the striation spacing became wider. Figs. 15 and 16 confirmed that LBB was caused by pressure cycles at the fatigue sensitive site of the liner, as in the bottom of the initial flaw.


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1ｍｍ

0.1ｍｍ

Circumferential

ThicknessDirection

Crack

≒45deg

①1500μm above Initial Flaw

①

Initial Flaw

②②500μm above Initial Flaw

External Surface

Fig. 15 Cross section of Liner after LBB (0.30-A, Initial Flaw Site)

Axial

ThicknessDirection

①3000μm above Initial Flaw

②1500μm above Initial Flaw

③500μm above Initial Flaw

InitialFlaw

①

②

③

External Surface

Fig. 16 Fracture Surface of Liner after LBB (0.30-A, Initial Flaw Site)


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3.2.5 Estimating the Life of a Tank The relation between striation spacing appearing at the fracture surface of LBB and the depth of the initial flaw is illustrated in Fig. 17. This relation was approximated by equation (3). y = a1・xn (3) y：Striation Spacing [m] x：Propagated Depth of Crack [m] a1, n：Coefficients (a1 = 0.0124, n = 1.4716)

1.E-08

1.E-07

1.E-06

1.E-05

0.0001 0.001 0.01

Propagated Depth of Crack ：x　[m]

Striation Spacing ：y　[m]

□ Initial Flaw 0.30ｍｍ◇ Initial Flaw 0.20ｍｍ○ Initial Flaw 0.15ｍｍ△ Initial Flaw 0.10ｍｍ― Regression Line

Fig. 17 Striation Spacing vs. Propagated Depth of Crack

The stress intensity factor range (∆K) was calculated by equation (4) 8). K = Mσ・ (πa)0.5 ∆K = M∆σ・ (πa)0.5 (4) ∆σ：Stress Amplitude [MPa] (∆σ = 210 MPa = 70 GPa × 3,000 µε) 70 GPa：Bulk Modulus of Aluminum 3,000 µε：Circumferential Strain at 35 MPa a：Propagated Depth of Crack [m] M：Correlation Factor for Surface (M = 1.12 in Surface Crack) The relation between striation spacing and ∆K calculated by equation (4) is illustrated in Fig. 18. This relation was approximated by equation (5). y = A・(∆K)m (5) y：Striation Spacing [m] ∆K：Stress Intensity Factor Range [MPa・m0.5] A, m：Materials Coefficients (A = 2×10－10, m = 2.9431)

1.E-08

1.E-07

1.E-06

1.E-05

10 100

Stress Intensity Factor Range ：ΔK　[MPa・m0.5]

Striation Spacing ：y　[m]

□ Initial Flaw 0.30ｍｍ◇ Initial Flaw 0.20ｍｍ○ Initial Flaw 0.15ｍｍ△ Initial Flaw 0.10ｍｍ― Regression Line

Fig. 18 Striation Spacing vs. Stress Intensity Factor Range


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The fatigue life of a metallic structure with planar flaw is indicated in equation (27) in section 8 of British Standard (BS) 7910 (1999),9) and is transformed to equation (6).

2/mmm

12/mi

12/mf

2/mmm

a

a Y)(A)m2()aa(2

=)a(Y)(A

da=N

f

i πσ∆πσ∆ －

－＋－＋－

∫ (6)

N：Fatigue Life [time] (Repeated Number of Pressure Cycles until LBB) ai：Initial Flaw Size [m] af：Final Flaw Size [m], (af = 0.003 m) ∆σ：Stress Amplitude [MPa], (∆σ = 210MPa) Y：Correlation Factor for Surface (Y = 1.12 same as M in equation (2) ) A, m：Materials Coefficients (A = 2×10－10, m = 2.9431) The number of pressure cycles until LBB was also calculated by dividing the total crack length by the crack propagation distance per cycle. If a crack propagates through the shortest path, the life of the tank is as indicated in equation (7). Accounting for the zigzag of an actual crack propagation path, the life of the tank is indicated in equation (8). Here, k1 and k2 are zigzag coefficients that represent the ratios of actual crack length/the shortest length, and k1 is 1.2 and k2 is 1.5 (k1：deeper than 0.0002m, k2：up to 0.0002m) from cross sectional observations of LBB position.

1)n(axx

=dxa

x=

xadx

=y

dx=Y

1

1ni

1nf

1

nx

xn

1

x

x

x

x1

f

i

f

i

f

i＋－

－

・

＋－＋－－

∫∫∫ (7)

Y1：Repeated Number of Pressure Cycles [time] xi：Initial Flaw Size [m] xf：Final Flaw Size [m] a1, n：Coefficients (a1 = 0.0124, n = 1.4716)

)1n(axkx)kk(+xk

=y

dxk+

ydx

k=Y1

1ni2

1n1i12

1nf1

x

x2

x

x12

1i

i

f

1+i＋－

－－＋－＋－＋

＋－＋

∫∫ (8)

Y2：Repeat Number of Pressure Cycling [time] xi：Initial Flaw Size [m] xi+1：Initial Flaw Size＋0.0002 [m] xf：Final Flaw Size [m] a1, n：Coefficients (a1 = 0.0124, n = 1.4716) k1, k2： Zigzag Coefficients (k1 = 1.2, k2 = 1.5) Calculated results of equation (6), (7), and (8) are plotted in Fig. 19. Equation (6) agreed well with the actual LBB, proving that this equation correctly estimates the life of a compressed hydrogen tank with a thin cylindrical shape. On the other hand, equation (8) indicated better agreement with actual LBB than equation (7). Although life estimation accuracy improved by reflecting the zigzag of the crack propagation path, results were varied depending on evaluation of the zigzag coefficients. Further investigations are necessary to establish the proper equation for the repeated number of pressure cycles until LBB. Therefore, equation (6) is thought to be the most suitable estimation. From equation (6), a tank with an initial flaw less than 0.13 mm is able to exceed 11,250 cycles. One of three tanks with an initial flaw of 0.15 mm actually broke before 11,250 cycles. Consequently, for the type 3 tank used in this study, the maximum allowable depth of a defect to complete 11,250 cycles of 44 MPa without LBB was between 0.10 mm and 0.15 mm.


12/12

0

5000

10000

15000

0 0.0002 0.0004 0.0006 0.0008 0.001

Depth of Initial Flaw　[m]

LBB　[cycles]

N　Equation (6)Y1　Equation (7)Y2　Equation (8)ＬＢＢ test results

0.15mm

11,250cycles(7)

(8)(6)

Fig. 19 LBB Cycle vs. Depth of Initial Flaw

4. Summary The followings were obtained by performing a hydrostatic pressure burst test and pressure cycling test of compressed hydrogen tanks for a fuel cell vehicle (FCV). (1) The burst pressure was nearly 120 MPa and the stress ratio (burst pressure/filling pressure) was almost

3.4 for type 3 tanks. The burst pressure was almost 95 MPa and the stress ratio was nearly 2.7 for type 4 tanks. Both tanks used in this study exceeded the minimum required burst pressure defined in JARI S 001 (2004), confirming that these tanks had sufficient anti-burst strength for commercial use.

(2) The expansion ratio of the tanks just before burst was almost 4% for type 3 tanks and was almost 5.7%

for type 4 tanks. Under equal pressure, the strain generated in the cylindrical part of the type 4 tanks was about twice that of the type 3 tanks. The differences between the type 3 and type 4 tanks used in this study, both in expansion ratio and strain in the cylindrical parts, depended on liner material and the structure of the carbon fiber reinforced plastics (CFRP) layer.

(3) Tank life decreased with increased depth of the initial flaw. When the depth of initial flaw was under 0.10

mm, sometimes leak before burst (LBB) did not occur at the initial flaw sites of the liner. (4) Striation marks clearly appeared at the fracture surface of LBB, especially when LBB occurred at the

initial flaw site, confirming that LBB was caused by pressure cycles at fatigue sensitive sites. The tank life was correctly estimated by applying material coefficients (A, m) obtained from striation spacing observed at the fracture surface of LBB, to the equation proposed in British Standard (BS) 7910 (1999).

This study was supported by New Energy and Industrial Technology Development Organization of Japan (NEDO) under a research program "Development for Safe Utilization and Infrastructure of Hydrogen". References: 1) JARI S 001 (2004) 2) KHK : Investigation Report of Aluminum Alloy Tank for SCUBA, (2002), p.23 3) JIM :Kinzoku Binran 6th edition, Maruzen, (2000), p.339 4) JSME : JSME Mechanical Engineers' Handbook A5 : Fluid Mechanics, Maruzen, (1990), p.5 - 6 5) S. Sano, M. Arie : Suirikigaku oyobi Suiriki Kikai, Kogaku Tosho, (1962), p.4 6) H. Fukuda, G. Ben : Fukugo Zairyo no Rikigaku Josetu, Kokon Shoin, (1989), p.18 - 23 7) K. Onishi : JIS ni motozuku KIkai Sekkei Seizu Binran 6th edition, Rikogaku Sha, (1990), p.4 - 12 8) H. Kobayashi : Hakai Rikigaku, Kyoritu Shuppan, (1993), p.81 9) British Standard (BS) 7910 : 1999, p.42

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