an initial and progressive failure analysis for cryogenic composite fuel tank design

8/10/2019 An Initial and Progressive Failure Analysis for Cryogenic Composite Fuel Tank Design

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Journal of Composite

http://jcm.sagepub.com/content/41/21/2545The online version of this article can be found at:

DOI: 10.1177/0021998307076492

2007 41: 2545Journal of Composite MaterialsJaehyung Ju, Brent D. Pickle, Roger J. Morgan and J.N. Reddy

n Initial and Progressive Failure Analysis for Cryogenic Composite Fuel Tank Design

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An Initial and Progressive Failure Analysisfor Cryogenic Composite Fuel Tank Design

JAEHYUNGJU,* BRENTD. PICKLE, ROGER J. MORGAN ANDJ. N. REDDY

Department of Mechanical Engineering, Texas A&M University

College Station, TX 77843-3123, USA

ABSTRACT: Thermal residual stresses, internal pressure stresses, and acceleration

stresses during launch were evaluated and quantified for cryogenic composite fueltank design. Both failure initiation and progression of graphite/epoxy laminatesystem (IM7/977-2) [0/90/90/0/0/90]s and graphite/BMI laminate system(IM7/5250-4) [0/90/90/0/0/90]s were investigated using the non-isothermal classicallaminate and plate theory (CLPT) and the maximum stress failure criterion.The thermal residual stresses in the transverse direction are the dominant stresses oneach ply in the launch stage. After initial ply cracking, through-the-thicknesstemperature change of a laminate related to fuel leakage as well as a laminatestiffness matrix change was applied to the progressive failure analysis. The fuelleakage-based progressive analysis shows a higher number of initial ply crackingdoes not necessarily mean a higher chance of matrix cracking in all plies. Thegraphite/BMI laminate has such an advantage as transverse thermo-mechanical

resistance over the graphite/epoxy laminate at an initial exposure to253C and1500 kPa. In terms of complete laminate matrix cracking, however, the graphite/epoxy laminate is more resistant to transferring stresses to other plies than thegraphite/BMI laminate.

KEY WORDS: cryogenic composite fuel tank, progressive failure analysis,fuel leakage, IM7/977-2 (graphite/epoxy laminate system), IM7/5250-4 (graphite/BMI laminate system).

INTRODUCTION

FOR MORE THAN two decades, design and manufacturing of cryogenic composite fueltanks has been one of the most challenging technologies for achieving drastic weight

reduction of reusable launch vehicles (RLV) [1]. However, the development of the fuel

tank has not easily progressed. In July 1996, NASA and Lockheed Martin Corporation

and its industry partners entered into a cooperative agreement for the design,

development, and flight-testing of the X-33 RLV. But, a failure occurred during testing

of the X-33 prototype. An investigation teams study on the failure of the fuel tank

revealed the causes of the failure to be (i) inner face-sheet cracking which leads to

*Author to whom correspondence should be addressed. E-mail: [email protected] 18 appear in color online: http://jcm.sagepub.com

Journal ofCOMPOSITE MATERIALS, Vol. 41, No. 21/2007 2545

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permeation of liquid and gaseous hydrogen, (ii) high core pressure resulting from liquid

and gaseous hydrogen, (iii) reduced bond-line strength and toughness, and (iv)

manufacturing flaws and defects [2]. The wall of the X-33 fuel tank consists of two

layers of IM7/977-2, graphite/epoxy composite around a honeycombed Kevlar core.

The major cause of failure has been thought to be extensive transverse cracking of the

inside IM7/977-2 face-sheet. The cracking occurred due to a combination of mechanical

and thermal residual stresses as the tank was filled with cryogenic liquid hydrogen.

Interconnection of the cracks allows the hydrogen to infiltrate the honeycombed Kevlar

core. When the tank was subsequently emptied and temperatures began to rise, the cracks

closed and trapped the hydrogen between the two layers of IM7/977-2 laminate.

The hydrogen expanded as the temperature continued to increase, building up pressure in

the honeycombed Kevlar core until the outside layer of graphite/epoxy composite

ruptured. While the rupture was not directly caused by cracking, cracking was

the underlying reason why the failure occurred. Extensive cracking does also weaken

the laminate and can lead to an ultimate failure as well.

The program ran for 56 months with an overall cost of approximately $1.3 billion.The redesign of the fuel tank was proposed to cost about $100 million [3]. Therefore, it is

significant to develop more accurate analytical and numerical tools for cryogenic fuel tank

design to save time and cost. In order to detect the onset and extent of cracking in a

laminate, a stress analysis of each ply is required. While looking at the laminate from the

individual ply level, the onset of cracking will be determined by checking which ply

experiences cracking first. The extent of cracking will also be judged by counting failed

plies while applying loads.

Numerous studies on the design of composite pressure vessels subjected to internal and

external pressure have been conducted at room temperature [411]. Several stress analyses

for cryogenic fuel tank design have been performed [1220]. Glaessgen et al. presented theinitial ply level thermal and mechanical stress analyses to determine the causes of the X-33

liquid-hydrogen tank failure [14]. Abumeri et al. performed a finite element stress analysis

of IM7/977-2 laminate at253C. (423F) temperature, 207 kPa (30 psi) internal fuelpressure, and 2.53 g launch inertia force [15]. However, a detailed computational

algorithm was not given in either paper. Moreover, thermal gradients through the tank

skin were not considered in their studies. Instead, the same temperature assumption

through the thickness was made, which may give inaccurate stress results. Using

conventional damage mechanics, Mallick et al. showed damage evolution by deriving

modulus reduction as a function of crack density and applied stress in a filament wound

fuel tank laminate [/90/] [16]. But, they did not show ply level stress components. The

amount of the stresses applied on a composite by thermo-mechanical cycle, temperature,

acceleration induced force, and fuel pressure was addressed. However, detailed algorithms

and ply-by-ply stress analysis were not presented in their study.

In order to simulate damage propagation, a progressive failure analysis method is

required. Most progressive analyses check ply-cracking, update modulus reduction, and

use iterative decision making to cracking at applied load increments [2127]. The present

study suggests a new progressive failure analysis by changing through-the-thickness

temperatures associated with fuel leakage as well as equivalent laminate stiffness matrix,

whenever damaged plies are detected. Through-the-thickness temperatures are also

updated with an increasing number of failed plies and their connectivity at every step.

The equivalent laminate stiffness matrix is updated with an increasing number of damagedplies and lay-ups.

2546 J. JU ET AL.



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In this study, ply-by-ply failure analysis will be performed and used to determine the

state of cracking in IM7/977-2 (graphite/epoxy laminate system) and IM7/5250-4

(graphite/BMI laminate system) for [0/90/90/0/0/90]s lay-up. The scope of the study is

on the deterministic conceptual design approach for cryogenic composite tank

applications.

MATERIALS

The [0/90/90/0/0/90]slay-up of IM7/5250-4, provided by NASA Glenn Research Center

for our previous project for both experimental and theoretical analyses, was used in the

present analytical study. The lay-up is different from that of the liquid hydrogen composite

tank used in the X-33. In this study, the feasibility of IM7/5250-4 laminates for cryogenic

fuel tank design will be investigated by comparing damage analysis of IM7/5250-4

laminates to the analysis of IM7/977-2 laminates which were already used in the X-33 fuel

tank. The laminate thickness is 40 mm, which is approximately same as that of the X-33sandwich structure including inner face-sheet, core, and outer face-sheet. The thermal

and mechanical properties of IM7/977-2 and IM7/52504 lamina are shown in Tables 13

[2830].

STRESS ANALYSIS

The stress analysis of the cryogenic fuel tank at a launch stage will be divided into three

separate calculations: thermal residual stresses, stresses due to internal fuel pressure,

Table 2. Material property coefficients for IM7/977-2 carbon fiber/epoxy lamina (Vf 0.65)obtained from References [29,30]. Property (T) C0 C1T C2T2, T inC.Properties C0 C1 C2

Longitudinal tensile modulus, E11 (GPa) 180.63

Transverse tensile modulus, E22, E33 (GPa) 9.9424 0.0189 2.00E-05In-plane shear modulus, G12 (GPa) 6.1311 0.01 Poissons ratio v12, v13 0.33

Longitudinal thermal expansion coefficient, 11 (E-6/C) 0.1839 0.0001 1.00E-06Transverse thermal expansion coefficient, 22 (E-6/C) 23.055 0.0411

Transverse tensile strength, S22T(MPa) 72.84 0.0365 In-plane shear strength, S12 (MPa) 127.26 0.0548 Longitudinal tensile strength, S11T(MPa) 2953.03 Longitudinal compressive strength, S11C (MPa) 1447.67

Table 1. Thermal properties for IM7/977-2 and IM7/5250-4 laminas (Vf 0.65)obtained from Reference [28].

Properties IM7/977-2 IM7/5250-4

Specific heat, Cp (J/kgC) 942.0 812.5

Transverse thermal conductivity, k(W/mC) 0.464 0.540Density, (kg/m3) 1594.15 1571.60

Thermal diffusivity, (m2/s) 3.10E-07 4.10E-07

Failure Analysis for Cryogenic Composite Fuel Tank Design 2547



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and stresses caused by accelerated forces. A section of the tank wall will be approximated

by flat rectangular plates of 12 layer [0/90/90/0/0/90]sof IM7/977-2 and IM7/5250-4. The

flat plate approximation can be used because the radius of the cylindrical tank is large

enough, and a slight curvature in a small section of the tank wall can be neglected. The

plate will be oriented in a coordinate system as can be seen in Figure 1. As shown in

Figure 1, in the local laminate coordinate, the xy plane is the mid-plane of the laminate

and the positive z-direction is toward the outside of the tank along with the r-direction.

Total stresses applied on each lamina, k, are expressed as a summation of thermal,

pressure, and launch induced stresses, as shown in Equation (1). The three stress

components are assumed to be decoupled; therefore, the total stresses are expressed as a

linear combination of the three stresses.

Totalij k Tijk Pijk Lijk: 1

r

qt

Z

x

2(T): Transverse direction

1(F): Fiber direction

1 2 3

8.687 m

6 m

y

z

40 mm

Figure 1. Schematic of a cylindrical cryogenic composite fuel tank.

Table 3. Material property coefficients for IM7/5250-4 carbon fiber/BMI lamina (Vf 0.65)obtained from References [29,30]. Property (T) C0 C1T C2T2, T in C.

Properties C0 C1 C2

Longitudinal tensile modulus, E11 (GPa) 181.01

Transverse tensile modulus, E22, E33 (GPa) 11.158 0.0066 1.00E05In-plane shear modulus, G12 (GPa) 6.368 0.0129 Poissons ratio v12, v13 0.36

Longitudinal thermal expansion coefficient, 11 (E-6/C) 0.25

Transverse thermal expansion coefficient, 22 (E-6/C) 21.902 0.0307

Transverse tensile strength, S22T(MPa) 85.984 0.0815 0.0002In-plane shear strength, S12 (MPa) 100.42 0.105 Longitudinal tensile strength, S11T(MPa) 2959.2

Longitudinal compressive strength, S11C (MPa) 1450.70

2548 J. JU ET AL.



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7/25

resulting in thermal bending stresses. The temperature profiles in the laminate can be

described by the thermal diffusion equation:

@T

@t @

2T

@r2 3

where thermal diffusivity, k/Cp. A solution of Equation (3) is given inReference [32] as

Tr, t Ti T1 2ffiffiffi

pZ c

0

et2

dt T1 4

where c r=2ffiffiffi

p t [32]. Ti is the initial temperature, which is the laminate temperature

before fuel is filled. T1

is the fuel temperature. Thermal properties of IM7/977-2 and

IM7/5250-4 laminas are shown in Table 1 [28]. Based on the thermal properties and

Equation (4), temperature profiles as a function of time of IM7/977-2 and IM7/5250-4 at

20 and 40 mm, which are mid-and outer-surfaces, are shown in Figure 2. It takes more

than 600 h for mid-surface and the outer one to reach the LH2fuel temperature. According

to the final report of the X-33 liquid hydrogen tank, it took about 3 h for the composite

fuel tank to be filled with LH2and tested before the tank vent was initiated [2]. Therefore,

the 3-h period after the fuel filling is an interesting time frame in this study. Figure 3

shows temperature profiles through the thickness after the 3-h exposure to cryogenic fuel

on the inside laminate surface, r RI (z 0:5 N tply). Different thermal gradientsexist depending on laminates thermal diffusivities. Thermal gradients for IM7/977-2 and

IM7/5250-4, after the 3-h LH2 exposure on the inner surface, are 2.58 and 2.27C/mm,respectively (Figure 3). Through-the-thickness temperature profiles are applied to

250.00

200.00

150.00

100.00

50.00

0.00

50.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0

Time (h)

Temperature(C)

IM7/977-2 at 40mm

IM7/5250-4 at 40mm

IM7/977-2 at 20mm

IM7/5250-4 at 20mm

at 40mm

at 20mm

r

Thickness = 0mm Thickness = 40mm

Figure 2. Temperature profiles through thickness as a function of time when the inner surface is exposed

to LH2.

2550 J. JU ET AL.



8/25

determine T for each lamina in Equation (2), and accurate thermal residual stresses on

each lamina are obtained.

Internal Stresses Induced by Fuel Pressure

The internal pressure required to store the cryogenic fuel in the tank also causes

stresses in the wall of the fuel tank; stresses in the longitudinal and hoop directions.According to the ASME boiler and pressure vessel code, the applied longitudinal and

hoop stresses of isotropic materials by pressure, corresponding to Zand directions in

the global cylindrical coordinate (Figure 1), respectively, are defined as Equation (5)

and (6) [33].

PZZ P

R0=R1 215

and:

Pk

P 1 R0=rk2

R0=R1 21: 6

The axial stresses are all the same through the layers of a laminate wall; however, the

hoop stresses are shown as a distributed function ofr(k). Therefore, there exists a pressure

gradient through the hoop direction but the gradient is low enough to neglect.

For accurate computation in this study, the average hoop stress is calculated as:

P 1

RO RIZ RO

RIPk dr: 7

After 3 hours

260.00

210.00

160.00

110.000 5 10 15 20 25 30 35 40

Thickness (mm)

Temperature(C)

IM7/977-2 IM7/5250-4

r

Thickness= 0mm Thickness=40mm

Figure 3. Through-thickness temperatures after 3-h cryogenic exposure at the inner surface.




9/25

r(k) appears as the radius at the point in which the stress is being calculated. Ther-direction

in the global cylindrical coordinate is along the z-direction in the local laminate

coordinate. In this study, the points at which the hoop stress will be calculated are centers

of each lamina in the z-direction. From the flat rectangular plate approximation,pZZand

p

are rewritten as p

xx

and p

yy

, respectively.

Internal stresses of each lamina are different depending on their orientation. In order to

derive the individual lamina stresses, we need to start from the global stresses by pressures

applied on a laminate. Under the assumption that the pressure loading does not cause

bending, in-plane stresses on individual plies of a laminate by pressure can be expressed as:

fPijgkPxxPyyPxy

8; 8

where:

"0xx"0yy0xy"1xx"1yy1xy

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

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

P

A11 A12 A16A12 A22 A26A16 A26 A66

24

35 B11 B12 B16B12 B22 B26

B16 B26 B66

24

35

B11 B12 B16B12 B22 B26B16 B26 B66

24

35 D11 D12 D16D12 D22 D26

D16 D26 D66

24

35

26666664

37777775

1 NPxxNPyyNPxyMPxxMPxxMPxy

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

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

AijXNk1

Qkijzk1 zk

Bij1

2

XNk1

Qkijz2k1 z2k

Dij1

3

XNk1

Qkijz3k1 z3k

NP tply

N

Pxx

Pyy

0

8

>:

9

>=>;

MP

0

0

0

8>:

9>=>;

It should be noted that temperature gradients and temperature-dependent material

properties result in a [0/90/90/0/0/90]s laminate that is no longer symmetrical when faced

to the cryogenic fuel at one surface. Therefore, the extension-bending coupling stiffness,

Bij should be considered in the computation of the fuel pressure induced strains in

Equation (8). Therefore,f"1ijg is induced by the internal pressures even though momentresultants do not exist under the pressure loading.

2552 J. JU ET AL.



10/25

Stresses by Launch

The maximum applied load will occur at take off when the fuel tank is completely

full and the acceleration is the greatest. During take off, the fuel tank will experience

acceleration in both the axial and hoop directions, az and a. The in-plane stresses due to

the launch acceleration are:

LZZLLZ

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

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

L

A11 A12 A16

A12 A22 A26

A16 A26 A66

24 35 B11 B12 B16B12 B22 B26

B16 B26 B66

24 35B11 B12 B16

B12 B22 B26

B16 B26 B66

24

35 D11 D12 D16D12 D22 D26

D16 D26 D66

24

35

266666664

377777775

1 NLxx

NL

yy

NLxy

MLxxMLxxMLxy

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

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

AijXNk1

Qkijzk1 zk

Bij1

2XNk1

Qk

ijz2k1 z

2k

Dij 13

XNk1

Qkijz3k1 z3k

NL tply N

Lxx

Lyy

0

8>:

9>=>;

ML 0

0

0

8>:

9>=>;




11/25

While computing launch acceleration induced stresses, Bij are also considered because

the [0/90/90/0/0/90]s lay-up is not symmetric any more due to thermal gradients and

temperature dependent ply properties.

Failure Analysis Using Maximum Stress Criterion

The maximum stress failure criterion is applied to investigate ply level damage related

to transverse matrix cracking and longitudinal tensile and compressive failure:

Rk ijSij

k11

where ij

is the lamina stress applied and Sij

the lamina strength. If R(k) is equal to or

higher than 1, damage on ply k occurs.

Initial and Progressive Failure Model Depending on Failure Mechanism

For two decades, a number of progressive failure models of composite laminates

have been developed. The main concept of the progressive failure model is that non-

homogenous stresses within a composite structure give rise to a complicated failure

scenario. For example, when one ply experiences damage, subsequent plies may also

experience damage at the same load conditions due to redistribution of stresses, thusleading to overall reduction in laminate stiffness.

Conventional progressive models deal with the stiffness reduction caused by matrix

cracking as a function of microcrack densities, resulting in strength reduction of a

laminate [2127]. If transverse matrix cracking is encountered in layers,Q12,Q22, and Q66components that are in the layers stiffness matrix are reduced to be near zero, and

iterative computations are performed for updating Aij, Bij, and Dij. In this study, each

laminas thermal, pressure, and launch stresses are updated based on the updated Aij, Bij,

and Dij.

In addition to considering the updated laminas stiffness reduction, the fuel leakage

effect through the thickness direction is considered in modeling a progressive failure

model. Microscopic interface defects at an overlapping region of two matrix cracks in

adjacent layers have been assumed to provide the connecting path of fluid between

transverse matrix cracks [34,35]. The overlapping regions are thought to be attacked by

cryogenic fuel, resulting in complicated laminate modulus update and lamina stress

redistribution associated with local temperature changes. Inner surface plies, if cracked,

experience a through-the-thickness temperature change by cryogenic fuel leakage.

The crack induced temperature change also affects the thermal gradient over the rest of

plies. If cracking does not occur on inner surface plies, temperature and thermal gradient

changes are not expected (Figure 4).

Fuel leakage, due to the transverse matrix cracks in conjunction with inter-ply

delaminations resulting in an intersecting network of passages, has been an important issuefor designing cryogenic fuel tank. Some researchers have studied the leakage

2554 J. JU ET AL.



12/25

or permeation of cryogenic fuel through composite laminates by experiment or

modeling [3440].

The overall computational algorithm is shown in a flowchart (Figure 5). Thermal,

pressure, launch and total stresses are obtained in ply level based on temperature dependent

material properties and temperature distribution through the laminate thickness. Ply leveldamage is checked based on the failure criterion. The progressive failure analysis is

Tin, Interior Temperature,

= (Fuel Temperature)

Tout, Exterior Temperature

(a) Pressure, launch and thermal stresses as a function of failed plies

( )syP

eyP

(k)

(k)

(k) (k)

(k)

(k)

(k) (k)

(k)

(k)

(k)

(k)

[ ]Q=

( )syT

eyT[ ]Q=

( )syL

eyL[ ]Q=

( )sxP

exP[ ]Q=

( )sxT

exT[ ]Q=

( )sxL

exL[ ]Q=

z

q

Tin

Tin

TinTi

Tout

Tout Tout

(b) Ply temperature change as a function of number of failed plies and their connectivity

Cracking and interconnection: Thermal gradientupdate

Inside ply cracking: No thermal gradient update

Figure 4. Schematic of progressive failure analysis using temperature gradient change by crack

interconnection.




13/25


14/25

is assumed to be 253C and fuel mass 95,250 kg. Space vehicle mass (launch mass),ms, isassumed to be 129,250 kg. Internal fuel pressure is assumed to be under various conditions

from 65 to 1500 kPa. Diameter of the cylindrical fuel tank is set to be 6 m. A laminate

thickness of 40 mm and 12-layer oriented [0/90/90/0/0/90]sof the two different composites

were used for the stress analysis.

Figures 6 and 7 show thermal, pressure, and launch acceleration induced stresses of

IM7/977-2 and IM7/5250-4, respectively, in the principal material coordinate at253Cand 65, 132, 290, 600, 1000, and 1500 kPa (10, 20, 44, 91, 152, and 227 psi). Thermal

residual stresses in the fiber direction are compressive and those in the transverse direction

are tensile. Thermal residual stresses are dominant compared to pressure and launch

induced stress components at 65, 132 and 290 kPa in both the fiber and the transverse

directions. Thermal residual stresses in the transverse direction seem to be a leading source

causing ply damage due to the lower transverse ply strength than the longitudinal one.

Thermal residual stresses of IM7/977-2 plies are 6064 MPa in the transverse direction and62 to65 MPa in the fiber direction. The absolute value of thermal residual stresses of

(a)at 253C and 65 KPa (IM7/977-2)

Ply and direction (F-Fiber direction, T-Transverse direction)

F

T

(b)at 253Cand 132 KPa (IM7/977-2)


F

T

(c)at 253Cand 290KPa (IM7/977-2)


F

T

(d)at 253Cand 600 KPa (IM7/977-2)


F

T


(e)at 253Cand 1000 KPa (IM7/977-2)

F

T

(f)at 253Cand 1500 KPa (IM7/977-2)


Thermal Pressure LaunchThermal Pressure Launch

Thermal Pressure Launch

Thermal Pressure Launch Thermal Pressure Launch


F

T

70

20

30

80

130

180

230

1(F)

2(F)

3(F)

4(F)

5(F)

6(F)

7(F)

8(F)

9(F)

10(F)

11(F)

12(F)

1(T)

2(T)

3(T)

4(T)

5(T)

6(T)

7(T)

8(T)

9(T)

10(T)

11(T)

12(T)

1(F)

2(F)

3(F)

4(F)

5(F)

6(F)

7(F)

8(F)

9(F)

10(F)

11(F)

12(F)

1(T)

2(T)

3(T)

4(T)

5(T)

6(T)

7(T)

8(T)

9(T)

10(T)

11(T)

12(T)

1(F)

2(F)

3(F)

4(F)

5(F)

6(F)

7(F)

8(F)

9(F)

10(F)

11(F)

12(F)

1(T)

2(T)

3(T)

4(T)

5(T)

6(T)

7(T)

8(T)

9(T)

10(T)

11(T)

12(T)

1(F)

2(F)

3(F)

4(F)

5(F)

6(F)

7(F)

8(F)

9(F)

10(F)

11(F)

12(F)

1(T)

2(T)

3(T)

4(T)

5(T)

6(T)

7(T)

8(T)

9(T)

10(T)

11(T)

12(T)

1(F)

2(F)

3(F)

4(F)

5(F)

6(F)

7(F)

8(F)

9(F)

10(F)

11(F)

12(F)

1(T)

2(T)

3(T)

4(T)

5(T)

6(T)

7(T)

8(T)

9(T)

10(T)

11(T)

12(T)

S

tress(MPa)

70

20

30

80

130

180

230

S

tress(MPa)

70

20

30

80

130

180

230

Stress(MPa)

70

20

30

80

130

180

230

Stress(MPa)

70

20

30

80

130

180

230

Stress(MPa)

70

20

30

80

130

180

230

Stress(MPa)

Figure 6. Thermal, pressure, and launch induced stresses of IM7/977-2 [0/90/90/0/0/90]s in the fiber and

transverse directions at253C under various pressures.




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IM7/5250-4 are about 10 MPa higher in both fiber and transverse directions than those of

IM7/977-2, which are 7276 MPa in the transverse direction and

73 to

77 MPa in the

fiber direction. The ply 1 shows the highest thermal residual stress values in both the fiber

and the transverse directions, due to the direct cryogenic fuel contact. Thermal residual

stresses on plies gradually decrease when the location of the plies moves away from the

inside surface. In Bechel and Kims paper, after submerging both IM7/5250-4 [0/90]2sand

IM7/977-2 [0/90]2s of 5cm 5 cm 0.112 cm flat plates into LN2 and 1000 cryogeniccycles, interior plies of both plates have a less matrix crack density than ply 1 and 8, which

are exterior plies, indicating that there exists thermal gradients though the thickness of

the plates [30].

The thermal residual stress gradients of IM7/977-2 in the fiber and the transverse

directions are 0.08 and

0.09 MPa/mm, respectively. The magnitudes of IM7/5250-4

thermal residual stress gradients are a little higher than those of IM7/977-2, which are 0.10and0.11 MPa/mm in the fiber and the transverse directions, respectively.

(a)at 253C and 65 KPa (IM7/5250-4)

70

20

30

80

130

180

230

70

20

30

80

130

180

230

70

20

30

80

130

180

230

70

20

30

80

130

180

230

70

20

30

80

130

180

230

70

20

30

80

130

180

230

1(F)

2(F)

3(F)

4(F)

5(F)

6(F)

7(F)

8(F)

9(F)

10(F)

11(F)

12(F)

1(T)

2(T)

3(T)

4(T)

5(T)

6(T)

7(T)

8(T)

9(T)

10(T)

11(T)

12(T)

1(F)

2(F)

3(F)

4(F)

5(F)

6(F)

7(F)

8(F)

9(F)

10(F)

11(F)

12(F)

1(T)

2(T)

3(T)

4(T)

5(T)

6(T)

7(T)

8(T)

9(T)

10(T)

11(T)

12(T)

1(F)

2(F)

3(F)

4(F)

5(F)

6(F)

7(F)

8(F)

9(F)

10(F)

11(F)

12(F)

1(T)

2(T)

3(T)

4(T)

5(T)

6(T)

7(T)

8(T)

9(T)

10(T)

11(T)

12(T)

1(F)

2(F)

3(F)

4(F)

5(F)

6(F)

7(F)

8(F)

9(F)

10(F)

11(F)

12(F)

1(T)

2(T)

3(T)

4(T)

5(T)

6(T)

7(T)

8(T)

9(T)

10(T)

11(T)

12(T)

1(F)

2(F)

3(F)

4(F)

5(F)

6(F)

7(F)

8(F)

9(F)

10(F)

11(F)

12(F)

1(T)

2(T)

3(T)

4(T)

5(T)

6(T)

7(T)

8(T)

9(T)

10(T)

11(T)

12(T)

1(F)

2(F)

3(F)

4(F)

5(F)

6(F)

7(F)

8(F)

9(F)

10(F)

11(F)

12(F)

1(T)

2(T)

3(T)

4(T)

5(T)

6(T)

7(T)

8(T)

9(T)

10(T)

11(T)

12(T)


Stress(MPa)

Stress(MPa)

Stress(MPa)

Str

ess(MPa)

Stress(MPa)

Stress(MPa)







F

F

F

T

T

F

T

F

T

T

(b)at 253C and 132 KPa (IM7/5250-4)

Ply and direction(F-Fiber direction, T-Transverse direction)

(c)at 253C and 290 KPa (IM7/5250-4)


(d)at 253C and 600 KPa (IM7/5250-4)


(e)at 253C and 1000 KPa (IM7/5250-4)


F

T

(f)at 253C and 1500 KPa (IM7/5250-4)


F

T

F

T

Figure 7. Thermal, pressure, and launch induced stresses of IM7/5250-4 [0/90/90/0/0/90]s in the fiber and

transverse directions at253C under various pressures.

2558 J. JU ET AL.



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As internal fuel pressure increases, pressure stresses become dominant in the fiber

directions. Pressure induced stresses are higher in the fiber direction than those in the

transverse direction due to the higher lamina stiffness in the fiber direction. IM7/977-2 and

IM7/5250-4 have almost the same pressure stresses in the fiber direction due to the fiber

dominant modulus. Transverse pressure stresses of both laminates are low and similar in

both laminates. As the internal fuel pressure increases, the longitudinal directions loading

mode is changed from compression to tension. Pressure stresses begin to exceed thermal

residual stresses at 600 kPa in the fiber direction of 90 plies. At 600 kPa, tensile andcompressive stresses coexist in the fiber direction at IM7/977-2 laminate. Total stresses of

IM7/977-2 in the fiber direction experience tensile stresses at 1000 and 1500 kPa. In the

case of IM7/5250-4, all total stresses in the fiber direction start to be tensile at 1500 kPa

due to the relatively higher compressive thermal residual stresses than those of IM7/977-2.

Pressure stresses in the fiber direction of 90 plies are higher than those of 0 plies, becausehoop stresses in the global coordinate are applied in the fiber direction of 90 plies. On thecontrary, pressure stresses in the transverse direction of 0 plies are higher than those of

90 plies because hoop stresses in the global coordinate are also applied in the transversedirection of 0 plies.

Launch stresses are also higher in the fiber direction than in the transverse direction due

to the higher modulus in the fiber direction. But, the launch stresses are not high compared

to the thermal and pressure stresses. Launch stresses of 5.66.8 MPa are applied on both

laminate plies in the fiber direction, which are 63160% and 2.76.9% of pressure stresses

in the fiber direction at 65 and 1500 kPa internal pressures, respectively. Launch stresses

applied in the transverse direction are negligible, which are about 0.6 MPa.

Thermal residual stresses in the transverse direction contribute to about 80 to 98% of

the total stresses in both laminates, which means the thermal residual stress is the

dominant factor that should be critically considered for cryogenic composite fuel tankdesign.

Grenoble and Gates showed, in their experiment with IM7/977-2 [45/903/45/03]slaminates, higher leak rates at cryogenic temperature with increasing levels of uni-axial

tensile strain than at room temperature with the same levels of strains [36]. Their results

show that the thermal residual stresses at cryogenic temperature made an additional

contribution to matrix cracking compared with the mechanical loading at room

temperature.

Yokozeki et al. also showed that the thermal residual stress is a major reason causing

ply damage of a IM600/#133 carbon fiber/toughened epoxy system with [45/45/90]s,[45/

45/902]s, [902/

45/45]s, and [902/0/902]s lay-ups by investigating gas leakage data at

two conditions; room temperature and LN2temperature, under static mechanical loading

[40]. Their results exhibit higher leak rates under LN2 conditions than under room

temperature for all cases, indicating that gas leakage increases under cryogenic conditions

because of the increase of the leak path size due to the thermal residual strains, which is

exactly explained in the present study.

Cracking Conditions of Each Lamina under Different Loading Modes

Ply-by-ply total stress to strength ratio, (ij/Sij)(k), was computed and plotted in

Figure 8. Figure 8 shows transverse tensile stress to strength ratio, (22T/S22T)(k),longitudinal compressive stress to strength ratio, (11C/S11C)

(k), and longitudinal tensile




17/25


18/25


19/25

through the width direction and indicates a strong possibility of fuel leakage associated

with networking of the fully developed matrix cracks through the width direction.

At253C and 1500 kPa, for IM7/977-2, after two updates of equivalent laminatestiffness related to individual ply damage, six plies are left non-cracked. Combining

laminate temperature redistribution by fuel leakage with the updated laminate stiffness

matrix also did not show a distinctive change compared to the conventional progressive

failure model, leaving six plies undamaged (Tables 4 and 5).

IM7/5250-4 laminate originally has one ply transverse matrix cracking at253C and1500 kPa. Six updates of laminate stiffness matrix and iteration left three plies undamaged

using the conventional progressive failure model (Table 6). However, if the updated

laminate stiffness matrix is combined with thermal redistribution associated with the inner

surface matrix cracking-induced fuel leakage, all plies are transversely damaged as shownin Table 7.

Table 5. (r22T/S22T)(k) values of each layer of IM7/977-2 [0/90/90/0/0/90]s for progressive

failure analysis considering lamina stiffness reduction and fuel leakageat253C and 1500 kPa.

Number of iteration

Ply 0 1 2

1 1.001 (Failure)

2 0.940 0.990 0.981

3 0.944 0.992 0.986

4 1.011 (Failure) 5 1.012 (Failure)

6 0.947 0.990 0.992

7 0.945 0.986 0.991

8 1.007 (Failure)

9 1.003 (Failure)

10 0.934 0.969 0.982

11 0.928 0.961 0.977

12 0.984 1.034 (Failure)

Table 4. (r22T/S22T)(k) values of each layer of IM7/977-2 [0/90/90/0/0/90]s for progressive

failure analysis considering lamina stiffness reduction at253C and 1500 kPa.Number of iteration

Ply 0 1 2

1 1.001 (Failure)

2 0.940 0.995 0.986

3 0.944 0.995 0.989

4 1.011 (Failure)

5 1.012 (Failure)

6 0.947 0.989 0.991

7 0.945 0.985 0.990

8 1.007 (Failure)

9 1.003 (Failure)

10 0.934 0.964 0.977

11 0.928 0.955 0.971

12 0.984 1.028 (Failure)

2562 J. JU ET AL.



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Note that IM7/977-2 had a greater number of plies damaged in the matrix than

IM7/5250-4 at the initial damage stage, but IM7/977-2 had three plies un-cracked when

IM7/5250-4 plies were all cracked at the final stage at 253C and 1500 kPa. Plies 2 and 3seem to be crucial plies to determine whether the laminate will undergo complete laminate

damage or not. IM7/977-2 shows no transverse cracking on plies 2 and 3, resulting in no

direct thermal attack by fuel and no severe further damage transfer to other plies. On the

other hand, IM7/5250-4 experiences the transverse cracking on plies 2 and 3, after two and

three updates of laminate stiffness matrix and temperature redistribution, respectively.

A lower ply temperature of IM7/5250-4 than IM7/977-2 by a higher thermal conductivity

of IM7/5250-4 might contribute the higher thermal stress, resulting in matrix cracking inall plies.

Table 6. (r22T/S22T)(k) values of each layer of IM7/5250-4 [0/90/90/0/0/90]s

for progressive failure analysis considering lamina stiffnessreduction at253C and 1500 kPa.

Number of iteration

Ply 0 1 2 3 4 5 6

1 1.003 (Failure)

2 0.947 0.971 1.000 (Failure)

3 0.943 0.964 0.990 1.024 (Failure)

4 0.990 1.020 (Failure)

5 0.985 1.011 (Failure)

6 0.929 0.941 0.960 0.983 1.006 (Failure)

7 0.923 0.933 0.950 0.970 0.991 1.003 (Failure)

8 0.969 0.979 1.004 (Failure)

9 0.963 0.969 0.989 1.006 (Failure)

10 0.907 0.907 0.917 0.929 0.943 0.954 0.968

11 0.901 0.898 0.907 0.915 0.928 0.938 0.951

12 0.945 0.937 0.945 0.958 0.978 0.983 0.992

Table 7. (r22T/S22T)(k) values of each layer of IM7/5250-4 [0/90/90/0/0/90]s for

progressive failure analysis considering fuel leakage and lamina stiffnessreduction at253C and 1500 kPa.

Number of iteration

Ply 0 1 2 3 4 5

1 1.003 (Failure)

2 0.947 0.976 1.005 (Failure)

3 0.943 0.969 0.995 1.034 (Failure)

4 0.990 1.026 (Failure)

5 0.985 1.016 (Failure)

6 0.929 0.946 0.965 0.994 1.033 (Failure)

7 0.923 0.938 0.955 0.980 1.017 (Failure)

8 0.969 0.985 1.010 (Failure)

9 0.963 0.975 0.995 1.017 (Failure)

10 0.907 0.913 0.923 0.940 0.971 1.016 (Failure)

11 0.901 0.904 0.912 0.926 0.955 1.001 (Failure)

12 0.945 0.943 0.951 0.970 1.007 (Failure)




21/25

For R(k) values, (22T/S22T)(k) at253C and 1500 kPa of IM7/977-2 and IM7/5250-4

are between 0.9 and 1 (Tables 47), which means it is hard to say that plies are safe to

avoid the transverse matrix cracking against the thermal stresses applied on each ply.

Preventing the cryogenic temperature contact with the inside wall of the fuel tank could be

accomplished by insulating the laminate in order to minimize thermal residual stresses

on each ply. If the inner surface temperature of IM7/977-2 and IM7/5250-4 laminates can

be maintained to LN2 temperature which is196C, (22T/S22T)(k) at 1500 kPa of bothlaminates can be reduced to 0.750.8. Reducing thermal residual stresses using an electron-

beam curing is another way to alleviate the thermal stresses in the transverse direction of

the laminates. Assuming composites cured at room temperature using the electron-beam

curing, (22T/S22T)(k) of the IM7/977-2 and IM7/5250-4 laminates can be reduced to

0.430.51 and 0.380.47, respectively, which might be a potential benefit to the cryogenic

composite fuel tank design.

The initial stage of ply failure may cause an entire laminate failure by the fuel leakage

effect associated with crack connectivity. That was clearly shown in the case of IM7/5250-4

at253C and 1500 kPa. The fuel leakage problem could be resolved by using a liner,but there is still a trade-off between structural weight increase and protection of fuel

leakage.

It has been known that the transverse ply thickness plays a role in damage initiation and

progression. Generally, as the ply thickness decreases, the strain necessary to initiate

transverse matrix cracks increases and saturated transverse crack density decrease.

Bechel et al. showed about 1228% decrease of exterior plies crack density of IM7/5250-4

[0/90]2s after 1000 LN2 cryogenic cycles when the ply thickness decreased from 0.21 to

0.14 mm [30]. The present model, based on the classical laminate and plate theory, has the

limitation in predicting accurate ply matrix damage as a function of ply thickness.

CONCLUSIONS

An appropriate stress analysis was developed for cryogenic fuel tank design based on the

classical plate laminate theory using three key environmental conditions: (i) thermal

residual stress, (ii) internal fuel pressure, and (iii) acceleration during launch. Thermal

residual stresses applied on IM7/977-2 and IM7/5250-4 laminates are the most significant

source to determine initial ply transverse matrix cracking and complete laminate matrix

cracking. The thermal residual stresses are 8098% of the total stresses in the transverse

direction while internal pressure varies from 65 to 1500 kPa. Therefore, lowering the stress

free temperature, e.g., by using E-beam cured laminates, or protecting composite from

directly contacting cryogenic fuel by placing thermal protection layers will be the efficient

ways to reduce the total stresses. For accurate design, an exact measurement of CTE is

required as a function of temperature. Thermal residual stresses are very sensitive to CTE,

which might lead to imperfect designs if used with imprecise CTE.

Of the remaining stress sources, the stress by internal fuel pressure at 1500 kPa ranges

from 21 to 46% of the total stresses in the fiber direction depending on ply angles.

Lowering the internal pressure would reduce the total stress, but the pressure should be

determined based on the requirements for the design of fuel storages. The fuel pressure

itself does not seem to be a devastating factor for the cryogenic fuel tank design, compared

to the thermal residual stress. However, once cracks initiate, causing stiffness decreases inthese plies, the fuel pressure plays an important role in the progressive failure by raising

2564 J. JU ET AL.



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pressure stresses on undamaged plies. The acceleration induced launch stress ranges from 2

to 8% of the total stresses in the fiber direction. The launch stresses applied in the

transverse direction are negligible, which are about 0.6 MPa. This could be reduced by

lightening the whole weight of the launch vehicle structure.

A fuel leakage-based progressive failure analysis was suggested in this study.

An instantaneous temperature and temperature gradient updates caused by the fuel

leakage as well as laminate stiffness matrix updates affect significantly the progressive

failure behavior of laminates. For IM7/5250-4 at253C and 1500 kPa, the fuel leakagebased progressive analysis shows that an initial stage of the ply failure may cause a

complete laminate cracking, which cannot be shown using the conventional laminate

stiffness matrix update method.

NOMENCLATURE

Qkij plane stress reduced stiffness components ofkth lamina;i,j 1, 2, 6

xx, yy, xy coefficient of thermal expansion (CTE) of a lamina in the globalcoordinate consisting ofx and y directions

Totalij k total stress applied on kth laminaTijk thermal residual stress applied on kth laminaPijk pressure induced stress applied on kth laminaLijk launch induced stress applied on kth lamina

NTxx, NT

yy, NTxy in-plane thermal force resultants

NPxx, NP

yy, NPxy in-plane pressure force resultants

NLxx, NL

yy, NLxy in-plane launch force resultants

MT

xx, MT

yy, MT

xy moment resultants by thermal forcesMPxx, M

Pyy, M

Pxy moment resultants by pressure forces

MLxx, ML

yy, MLxy moment resultants by launch forcesN number of plies

"0xx , "0

yy , 0xy the membrane strains

"1xx , "1

yy , 1xy the flexural (bending) strains, known as the curvaturesT temperature of materials

T the difference between the operated temperature and the stress freetemperature of a laminate

P internal fuel pressureRO

outside radius of the fuel tank

RI inside radius of the fuel tankaZZ, a launch acceleration to Z and directions in the global cylindrical

coordinate

AZZ, A cross-sectional area to Zand directions in the global cylindricalcoordinate

ms mass of the space vehiclet time

tply lamina thicknessk thermal conductivity (W/mC)

Cp

specific heat (kJ/kgC)

density (kg/m3) thermal diffusivity (m2/s)




23/25

Subscript T, C tensile, compressiveSuperscriptT,P,L thermal, pressure, launch

ACKNOWLEDGMENTS

This research was kindly funded by Dr Charles Lee of the Air Force Scientific Office

of Research (AFSOR) and the Advanced Technology Program sponsored by the State

of Texas.

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2568 J. JU ET AL.
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an initial and progressive failure analysis for cryogenic composite fuel tank design

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