Pappu L.N. Murthy

Glenn Research Center, Cleveland, Ohio

Reliability of COPVs Accounting for 

Margin of Safety on Design Burst 

NASA/TM—2012-217638

August 2012
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Pappu L.N. Murthy

Glenn Research Center, Cleveland, Ohio

Reliability of COPVs Accounting for 

Margin of Safety on Design Burst 

NASA/TM—2012-217638

August 2012

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

The author wishes to acknowledge the sponsorship provided by the NASA Engineering Safety Center for the Independent Technical 

Assessment of safety of the Kevlar and Carbon COPVs onboard the orbiter and the International Space Station The author would 

also like to acknowledge the technical advice, review and support of Dr. Lorie Grimes-Ledesma the lead for the NESC CPV WG 

(Composite Pressure Vessel Working Group).

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only. Their usage does not constitute an official endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2012-217638 1

Reliability of COPVs Accounting for 

Margin of Safety on Design Burst

Pappu L.N. Murthy

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

In this paper, the stress rupture reliability of Carbon/Epoxy Composite Overwrapped Pressure Vessels 

(COPVs) is examined utilizing the classic Phoenix model and accounting for the differences between the 

design and the actual burst pressure, and the liner contribution effects. Stress rupture life primarily 

depends upon the fiber stress ratio which is defined as the ratio of stress in fibers at the maximum 

expected operating pressure to actual delivered fiber strength. The actual delivered fiber strength is 

calculated using the actual burst pressures of vessels established through burst tests. However, during the 

design phase the actual burst pressure is generally not known and to estimate the reliability of the vessels 

calculations are usually performed based upon the design burst pressure only. Since the design burst is 

lower than the actual burst, this process yields a much higher value for the stress ratio and consequently a 

conservative estimate for the reliability. Other complications arise due to the fact that the actual burst 

pressure and the liner contributions have inherent variability and therefore must be treated as random 

variables in order to compute the stress rupture reliability. Furthermore, the model parameters, which 

have to be established based on stress rupture tests of subscale vessels or coupons, have significant 

variability as well due to limited available data and hence must be properly accounted for. In this work an 

assessment of reliability of COPVs including both parameter uncertainties and physical variability 

inherent in liner and overwrap material behavior is made and estimates are provided in terms of degree of 

uncertainty in the actual burst pressure and the liner load sharing.

Nomenclature

F lifetime distribution function

DBP design burst pressure

ABP actual burst pressure

MEOP maximum expected operating pressure

BF burst factor

ABF actual burst factor

Ply liner share of pressure yield

Plmeop liner share of pressure at MEOP

s stress ratio

sBF stress ratio based on burst factor

sa actual stress ratio

σ fiber stress

σref fiber stress at burst pressure

t time in hours

tref characteristic time corresponding to σref

ρ power-law coefficient for stress

β lifetime shape parameter

η variable that captures uncertainty in burst pressure

λ variable that captures yield strength variability

Θ ratio of liner support at MEOP to burst pressure
NASA/TM—2012-217638 2

Introduction

Composite overwrapped pressure vessels are used for storing high pressure gases on board spacecraft 

such as the Orbiter, the International Space Station, and the Crew Exploration and Launch vehicles

MPCV (multipurpose crew vehicle) and SLV (space launch vehicle) being developed under current 

NASA programs. The primary reason for using COPVs for these applications is due to the substantial 

weight savings they offer compared to all metallic pressure vessels. For example, on the Space Shuttle 

Orbiter, replacement of all metallic pressure vessels with Kevlar COPVs resulted in a total weight savings 

of about 30 percent of all metallic tanks weight. Mass critical space applications such as the Ares and 

Orion vehicles are currently being planned to use as many COPVs as possible in place of all-metallic 

pressure vessels to minimize the overall mass of the vehicle. Furthermore, robotic missions such as earth 

orbiting satellites or deep space missions to outer planets are usually much more mass critical, since any 

mass saved allows additional science instruments to be added. For these missions, mass savings of up to 

50 percent can be realized through the use of COPVs.

COPVs are a mature technology, with a very successful use history at NASA. However, the stress 

rupture failure mode is not very well understood; therefore leading to significant conservatism and thus 

less weight savings. This composite failure mode is important to understand because the consequence of a 

failure is catastrophic. Since overwraps are subjected to sustained loads during long periods of a mission, 

the failure mode due to stress rupture is an added concern for the mission risk management. 

Stress rupture life primarily depends upon the fiber stress ratio which is defined as the ratio of stress 

in fibers at the maximum expected operating pressure to actual delivered fiber strength. Since a COPV 

consists of a metallic liner (which minimizes permeability) overwrapped with composite, the delivered 

fiber strength is calculated analytically by removing the influence of the liner to provide the composite 

response at the pressure level of interest. Several other factors also influence the COPV stress rupture and 

detailed discussion of these can be found in References 1 and 2. The actual delivered fiber strength is 

calculated using the actual burst pressures of the vessels established through burst tests. These vessels are 

usually designed to a design burst factor of 2.0, however, launch vehicles and deep space mission vehicles 

sometimes use a more aggressive burst factor of 1.5. One reason to design with a higher burst factor is to 

minimize the stress rupture risk without unduly penalizing the mission performance. In general, the higher 

the burst factor, the lower the fiber stresses in the overwrap, thereby minimizing the stress rupture risk.

COPV manufacturers however design the vessels such that the actual burst pressures are significantly 

higher than the design burst pressure, often as high as 5 to 10 percent.

In the current paper the stress rupture life reliability as a function of the burst factor and the margin of 

safety are computationally simulated utilizing the classic Phoenix model of stress rupture that was used 

for Orbiter reliability calculations. Furthermore, stress ratio dependency on several fundamental variables 

and their uncertainties in them are examined in detail. For this purpose the variability of burst strength, 

variability in liner yield strength and variability in operating pressure are considered as random variables.

Methodology

Current carbon composite overwrapped pressure vessels are typically designed to operate with a 

safety factor equivalent to a Burst Factor of 2.0. The Burst Factor (BF) is defined as the ratio of the design 

burst pressure (DBP) to the maximum expected operating pressure (MEOP). The design burst is the 

pressure at which the manufacturer by actual test must demonstrate that the COPV is stable with no 

abnormal consequences during the qualification process. Following successful demonstration of the DBP, 

usually the test is continued by increasing the pressure until an actual burst occurs to demonstrate 

additional margin. It is not uncommon for the manufacturer to over design the vessel by 5 to 10 percent so 

that a successful qualification test is assured. According to the definition the burst factor is expressed as

DBP BF

MEOP = (1)
NASA/TM—2012-217638 3

At the maximum expected operating pressures (MEOP), an estimate of the fiber stress ratio in the 

overwrap based on design Burst Factor is given by

1

BF s

BF = (2)

Two factors that contribute to the conservatism of Equation (2) must be considered to arrive at the actual 

fiber stress ratio. The first factor concerns with the actual burst pressure, ABP that must be used to 

calculate the fiber stress ratio as opposed to the design burst pressure (DBP). ABP is usually significantly 

higher than DBP. The actual burst strength may be expressed as

ABP DBP = +η (1 ) (3)

η is the “margin of safety” on DBP. The actual burst factor is therefore given by

ABF BF = +η (1 ) (4)

The actual burst strength of typical COPVs is a random variable with a mean value and a coefficient of 

variation. To account for this here η is considered as a random variable with a lognormal distribution. The 

mean value is usually around 0.1 to 0.15 (assuming that the actual burst strength is 10 to 15 percent

higher than the design burst). The coefficient of variation is around 5 percent (typical for carbon). The 

actual stress ratio accounting only for the ABP is given by

1

(1 )

or

(1 ) BF

s

BF

s s

= + η

= +η

(5)

From Equation (5) it can be seen that the stress ratio, s, is a random variable and is less than sBF since η is 

always a positive quantity. In reality, it is quite possible to have ABP less than DBP, for small η values 

with large scatter in burst strength however, in the current formulation using a lognormal distribution for 

η this possibility is eliminated. 

The second factor affecting the stress ratio, concerns the load carrying contributions of the liner. It 

should be noted that in the above equation the liner contributions are neglected. Typically, the COPVs 

used for space applications are designed such that the liner carries 10 to 20 percent load at MEOP and 

therefore the fiber stress ratio needs to be adjusted to take this into account. For example if the liner 

support pressure at MEOP is Plmeop and the liner support pressure at yield is Ply, then the actual stress 

ratio, sa at MEOP is given by

( )

( )

( )

{ }

or

(1 )

l meop

a

ly

l meop

a

ly

MEOP P

s

ABP P

MEOP P

s

DBP P

− = −

− = +η −

(6)

Equations (5) and (6) must be combined to calculate a more accurate value for the stress ratio. It 

should be noted that, the manufacturer’s autofrettage cycle induces compressive and tensile residual 

stresses in the liner and overwrap, respectively, which introduce additional complications in the stress 
NASA/TM—2012-217638 4

ratio estimation process. In the current work however, these issues are completely neglected and only the 

“margin of safety” on DBP included. 

Stress Rupture Life Reliability: Phoenix Classic Model

It is customary to utilize a Weibull statistics based approach to fit the stress rupture life data, in this 

case the original Lawrence Livermore National Laboratories (LLNL) test data (Ref. 1) were fitted with 

this approach. There are a number of models presented in the literature, with a comparison of advantages 

and disadvantages discussed in Reference 3. Herein the Phoenix Classic model is used. The so-called 

classic model was originally pioneered by Coleman (Ref. 4) in the late 1950s and further developed by 

Phoenix and colleagues (Refs. 5 to 9) over the past 27 years. More recently this model has undergone a 

thorough review during two independent technical reviews and assessments sponsored by the NASA 

NESC (NASA Engineering Safety Center) (Refs. 1 and 2). As mentioned above, the model is based on a 

Weibull distribution framework for strength and lifetime with the embodiment of a power law to describe 

damage in a composite versus stress level. Derivation of the model is available in references (Refs. 4 and

7) where the power-law in stress level (with temperature dependence) is derived from thermally-activated 

chain scission using a Morse potential as a model (Refs. 7). In the simplest setting of constant stress 

applied quickly and maintained over a long time period, the basic equation for the model is given by

( | ) 1 exp ( )

ref

t Ft s s

t

β

ρ

          =− −               

(7)

where F(ts) represents the probability of failure at time t. In the above equation the quantity (s = σop/σref)

is the ratio of fiber stress at operating pressure to fiber stress at burst pressure (stress ratio), t is time, tref is 

a reference time, ρ is the power law exponent, and β is the Weibull shape parameter for lifetime. The 

value for σref is determined from the flight COPV burst tests and stress analysis of the COPV. The model 

is shown for a single stress level over time, but for more general time histories a memory integral is used 

to accumulate damage (similar to Miner’s rule for fatigue) at different stress levels.

Illustrative Example

The Classic Model parameters that are appropriate for a representative carbon fiber, T1000G

composite are given by (Ref. 2)

Classic Model

114

0.22

0.001 hr ref t

ρ =

β =

=

(8)

The stress ratio used in the following calculations is based on Equation (5). The uncertainties associated 

with the model parameters are those for a “Hi-Variability” case. The “High variability” assumption means 

that the uncertainty associated with the model parameters used are those uncertainties that can be 

substantiated based on the small fiber strands database that currently exists. The associated coefficients of 

variation (cov) are given by
NASA/TM—2012-217638 5

Classic Model Variabilities

cov 25%; cov 30%

cov 30%;

ref ρ = t =

β =

(9)

For illustration purposes lognormal marginal distributions for all parameters are assumed. In addition 

to these, an additional random variable to account for the actual burst strength variability is introduced 

with the random variable η. It should be mentioned that since the stress ratio is assumed random (by 

virtue of the burst strength variability), this can complicate the uncertainty related to parameter 

distributions. Consequently, a Bayesian framework is employed although Bayes theorem is not relied on 

for computing a posterior distribution of the parameters. The distributions are all assumed to be 

independent with no correlations among them, even though it is acknowledged in reality they should be 

multivariate dependent variables. Ten thousand Monte-Carlo simulations of reliability using Equation (7)

are performed and the results are shown in Figure 1. Here, the point estimate, mean and 95 percent

confidence limit for reliability are plotted versus “margin of safety” varying from 0.01 to 0.2. Note, 

however, the simulation shows that although the margin of safety inherent in the simulation of a 

manufacturer’s design does provide much higher point estimates of reliability, due to the high variability

in model parameters, similar gains are not realized for the mean and 95 percent confidence reliability 

estimates; wherein no more than half a nine in reliability can be realized.

The actual stress ratio and the upper bound 95 percent confidence stress ratios are shown in Figure 2

versus margin of safety on DBP. If A-Basis values are required then the 99 percentile value has to be used 

instead of 95 percentile on stress ratio. Assuming that a typical range for the actual burst strength of 

COPVs have a margin of safety between 10 and 15 percent with a coefficient of variation of 5 percent, the 

actual stress ratio lies between 0.43 to 0.46 for a design burst factor of 2.0 as shown in the figure. 

Together Figure 1 and Figure 2 provide quick and useful estimates of operating stress ratio and 

preliminary reliability estimates for COPVs during the design stage, including typical uncertainties in 

various parameters.

Figure 1.—Reliability measures for a typical carbon COPV as a function of margin of safety 

on design burst pressure (DBP). Almost two nines of reliability can be gained for point 

“margin of safety” equal to 0.2 as compared to 0.01 as seen in the figure.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 2

3

4

5

6

7

8

9

Margin of Safety on DBP

Reliability in # of Nines

Point

Mean

95% CL

Design Burst Strength PLN, 11/4/2011

T1000G COPV at 50%

Nominal s.r based on

Burst factor 2.0

Typical Range for

Actual Burst Strength

COV = 5%
NASA/TM—2012-217638 6

Figure 2.—Actual stress ratio estimates at MEOP for a typical carbon COPV as a function of margin 

of safety on design burst pressure (DBP).

Sensitivity Analysis

The stress ratio used in the above calculations is based on Equation (5) which only has one random 

variable, the ABP of the vessel. However, as already mentioned, the stress ratio depends on other 

important variables where uncertainties do exist. Here an attempt is made to perform a sensitivity analysis 

on the stress ratio considering uncertainties in liner support at operating pressure and burst pressure. The 

results from such a sensitivity analysis can help quantify the uncertainty in the stress ratio which may 

arise due to its functional relationship to the aforementioned random variables and rank them in the order 

of importance. The steps to perform such an analysis involve, 1) formulating the stress ratio in terms of all 

the fundamental variables, 2) identifying the ones which are uncertain, and 3) provide information 

pertaining to their distribution statistics. Equation (6) for the stress ratio may be modified to include 

various independent variables in the following manner:

( )

{ (1 ) }

l meop

a

ly

P

s

DBP P

μ− λ = +η − λ (10)

where μ is the operating pressure, with a mean of MEOP and is assumed to be distributed normally. λ is a 

random variable that captures the variability in yield strength of the liner material which is also assumed 

to be normally distributed with a mean of 1. Thus we have the stress ratio expressed as a function of three 

fundamental random variables μ, λ and η. Variability in the geometry of the vessel, etc., are not 

considered explicitly in this preliminary analysis. However, these are indirectly accounted for in the 

variability of burst strength. Basically the aleatory variability in operating conditions (operating 

pressures), liner yield strength and the vessel burst, have been considered.

In Equation (10) it should be noted that Ply and Plmeop are related by the following inequality

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.4

0.41

0.42

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.5

Margin of Safety on DBP

Actual Stress Ratio

Typical Range for actual

Burst strength COV = 5%

Mean and Point values for

Actual stress ratio

95% confidence Upper

bound stress ratio

PLN 12/30/2008

A-Basis Stress Ratio

bound stress ratio
NASA/TM—2012-217638 7

P P ly lmeop ≥ (11)

Let us introduce a new parameter the liner participation factor, Θ, defined as the ratio of liner support at 

MEOP to liner support at burst; that is

ly

lmeop

P

P

 

Θ =      

(12)

Furthermore, by substituting Equation (12) into Equation (10) the following expression for the stress ratio

is obtained:

( )

{ (1 ) }

ly

a

ly

P

s

DBP P

μ−Θ λ = +η − λ (13)

For plastically operating liners Θ is equal to 1 by definition and for all other cases is between 0 and 1, 

typically 0 << Θ ≤ 1.

The above equation can be used to study the sensitivity of stress ratio to various fundamental 

variables.

Trade Studies

The effect of liner support at MEOP and liner support at yield on the stress ratio has been studied for 

a range of liner supports at MEOP varying from 5 to 30 percent and for Θ = 0.8. For this exercise it has 

been assumed that the liner is elastic at MEOP and plastic at burst. Figure 3 shows the variability in stress 

ratio for a family of liner support values at MEOP varying from 5 to 30 percent and for a constant liner 

support at yield of 1.25 times the liner support at MEOP. The 99 percentile value (analogous to A-Basis) 

for stress ratio varies from 0.45 to 0.5 while the mean values range from 0.38 to 0.445.

Figure 4 shows the Point, 95 and 99 percentile values of stress ratio as a function of liner support at 

MEOP. 

Figure 3.—Normal plots of stress ratios for a range of liner support at MEOP.

0.3 0.35 0.4 0.45 0.5 0.55

0.003

0.01

0.02

0.05

0.10

0.25

0.50

0.75

0.90

0.95

0.98

0.99

0.997

Stress Ratio

Probability

PLN, 11/10/2011

25%

20%

15%

10%

5%

30%

Liner Support at MEOP = 5% - 30% of MEOP pressure

Liner Support at Burst = (1.25 x Liner Support at MEOP)

Design Burst Factor = 2.0

Liner Support

at MEOP
NASA/TM—2012-217638 8

Figure 4.—Liner support versus stress ratio for a vessel designed for a burst factor of 2.0.

Figure 5.—Scatter plots showing the sensitivity of the fundamental variables on the stress ratio.

Stress Ratio Sensitivities

As seen from Equation (10) the stress ratio is a function of three fundamental variables; the pressure 

at MEOP, the variability in liner yield strength and the variability in the actual burst strength. In Figure 5

plots of each fundamental variable versus the stress ratio are shown. As can be seen from the figure, the 

pressure at MEOP has a strong influence on the stress ratio, which is to be expected. The other two 

variables have minimal effect on the stress ratio. The magnitude of the correlation coefficient between the 

variable and stress ratio gives a measure of the sensitivity and is shown in a Bar plot in Figure 6.

0.05 0.1 0.15 0.2 0.25 0.3 0.38

0.4

0.42

0.44

0.46

0.48

0.5

Liner Support at MEOP

Stress Ratio

99%

95%

Point

PLN, 11/10/2011

Liner support at Meop 5% - 30% 

Liner support at Burst = 1.25* L. S. at MEOP

Design Burst Factor 2.0

Variability:

Yield strength 3%

Burst 5%

MEOP 5%
NASA/TM—2012-217638 9

Figure 6.—Stress ratio sensitivities.

Figure 7.—Scatter plots showing the sensitivity of the fundamental variables on the stress 

rupture life reliability.

Stress Rupture Life Reliability Sensitivities

With the aid of Equations (7) and (13) the influence of various random variables on stress rupture life 

reliability can be evaluated. The results are shown in Figure 7 and Figure 8.

As can be seen from Figure 7, the model parameters (β, ρ and tref) appear to be more strongly 

influencing the reliability compared to the other parameters like margin of safety, yield strength and MEOP.

The magnitudes of these correlations can be seen more clearly in Figure 8 where the correlations are shown 

in bar chart format side by side. Among the non-model variables the MEOP appears to have the strongest 

1 2 3 -0.2

0

0.2

0.4

0.6

0.8

1

1.2

Margin of

Safety

MEOP

variability Yield Strength

variability

PLN, 11/10/2011
NASA/TM—2012-217638 10

Figure 8.—Sensitivities of various fundamental random variables on the stress rupture 

life reliability.

influence on stress rupture life reliability. However, when comparing all variables, the model parameters by 

far have the most influence on the stress rupture life reliability. From these preliminary results it can be 

concluded that it is important to have a good set of data to establish model parameters with tight bounds, as 

these appear to control the reliability more significantly compared to the other parameters.

Concluding Remarks

In this short paper the issue of unknown burst strength of a COPV during the design stage and how 

that affects the operating stress ratio and consequently the stress rupture life reliability evaluations of the 

vessel are addressed. Usually only the operating pressures and the design burst pressure are known during 

the preliminary COPV design stage. Herein we attempted to include randomness in the burst pressure and 

operating pressure along with variability in yield strength and a formal assessment of their influence on

stress ratio and the stress rupture reliability were made. The sensitivity of various fundamental variables 

on the stress ratio as well as the stress rupture life reliability is assessed. As is expected the operating 

pressure has the greatest influence on stress ratio followed by the yield strength of the liner and burst 

strength margin of safety. The computations were made with the assumption that the liner is elastically 

responding at MEOP and its support at yield is about 25 percent higher than at MEOP. Furthermore, the 

sensitivity of the fundamental random variables on the stress rupture life reliability is also evaluated and 

the results show significantly more influence of stress rupture model parameters on the reliability as 

compared to the other parameters. Although, the simulations are performed for a single set of liner 

support, assessment for other combinations of liner support at MEOP and liner support at burst can be 

made with the given equations in a straight forward manner. The methodology developed herein can be of 

great use during the preliminary stages of COPV development for a specific mission.

1 2 3 4 5 6 -0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

Fundamental Random Variables

sensitivity

Margin of

Safety

Yield

Strength

β t

ref ρ

Influence of Fundamental

Random variables on the Stress

Rupture Life Reliability

MEOP

PLN, 11/14/2011
NASA/TM—2012-217638 11

References

1. Orbiter Kevlar/Epoxy Composite Overwrapped Pressure Vessel Flight Rationale Technical 

Assessment Report, Vol. I and II, NASA NESC Report RP-07-34, April 12, 2007.

2. Shelf Life Phenomenon and Stress Rupture Life of Carbon/Epoxy Composite Overwrapped Pressure 

Vessels (COPVs) Technical Consultation Report, Vol. I and II, NASA NESC Report RP-06-83, 

September 14, 2006.

3. Lorie Grimes-Ledesma, Murthy, P.L.N., Phoenix, S.L., and Ronald Glaser, “A Comparison of 

Various Stress Rupture Life Models for Orbiter Composite Pressure vessels and Confidence 

Intervals”, NASA/TM- 2007-214808.

4. Coleman, B.D. “Statistics and Time Dependence of Mechanical Breakdown in Fibers,” Journal of 

Applied Physics, 29 (1958): 968.

5. Wu, H.F., S.L. Phoenix, and P. Schwartz, P. “Temperature Dependence of Lifetime Statistics for 

Single Kevlar49 Filaments in Creep-Rupture,” Journal of Materials Science, 23 (1988):1851.

6. Phoenix, S.L., and E.M. Wu. “Statistics for the Time Dependent Failure of Kevlar-49/Epoxy 

Composites: Micromechanical Modeling and Data Interpretation.” IUTAM Symposium on Mechanics 

of Composite Materials,

7. Phoenix, S.L. “Statistical Modeling of the Time and Temperature Dependent Failure of Fibrous 

Composites.” Proceedings of the 9th US National Congress of Applied Mechanics, Book no. H00228, 

ASME, NY (1982): 219.

8. Phoenix, S.L. “The Asymptotic Time to Failure of a Mechanical System of Parallel Members,” SIAM 

Journal on Applied Mathematics, 34 (1978): 227.

9. Phoenix, S.L. “Stochastic Strength and Fatigue of Fiber Bundles,” International Journal of Fracture, 

14 (1978): 327.
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5f. WORK UNIT NUMBER

WBS 869021.03.03.02.01 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-18283 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2012-217638 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Category: 24 

Available electronically at http://www.sti.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

In this paper, the stress rupture reliability of Carbon/Epoxy Composite Overwrapped Pressure Vessels (COPVs) is examined utilizing the classic Phoenix model and accounting 

for the differences between the design and the actual burst pressure, and the liner contribution effects. Stress rupture life primarily depends upon the fiber stress ratio which is 

defined as the ratio of stress in fibers at the maximum expected operating pressure to actual delivered fiber strength. The actual delivered fiber strength is calculated using the 

actual burst pressures of vessels established through burst tests. However, during the design phase the actual burst pressure is generally not known and to estimate the 

reliability of the vessels calculations are usually performed based upon the design burst pressure only. Since the design burst is lower than the actual burst, this process yields a 

much higher value for the stress ratio and consequently a conservative estimate for the reliability. Other complications arise due to the fact that the actual burst pressure and the 

liner contributions have inherent variability and therefore must be treated as random variables in order to compute the stress rupture reliability. Furthermore, the model 

parameters, which have to be established based on stress rupture tests of subscale vessels or coupons, have significant variability as well due to limited available data and hence 

must be properly accounted for. In this work an assessment of reliability of COPVs including both parameter uncertainties and physical variability inherent in liner and 

overwrap material behavior is made and estimates are provided in terms of degree of uncertainty in the actual burst pressure and the liner load sharing. 

15. SUBJECT TERMS

Composite overwrapped pressure vessels; Stress rupture; Weibull statistics; Stress rupture life; Liner load sharing; Burst pressure; 

Operating pressure; Fiber strength; Pressurization rate; Power law; Confidence intervals; Reliability statistics 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

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UU 

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18 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

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