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EFFECT OF STRAIN ON THE GAS PERMEABILITY
OF COMPOSITE LAMINATES
JAMES VANPELT III
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
James VanPelt III
To my family, friends, and instructors who have shown me the path to follow to achieve such a
I would like to thank Dr. Bhavani V. Sankar for allowing me to complete my Master of
Science through his gracious intellectual and financial support. He has supported my endeavors
with his availability, patience, and encouragement. Much of the advice he has given me not only
helped me to complete my research activities, but will help me in my employment and personal
future. I would also like to thank Dr. Kaushik Mallick for his professional expertise that has
provided the base from which my research has grown.
Many thanks are extended to the Center of Advanced Composites family. Dr. Ifju, through
his generosity, has allowed me to use his equipment in the Experimental Stress/Analysis lab. Dr.
Jenkins has given me encouragement and many useful new developmental ideas to aid in my
testing. Thank you to my colleagues who have assisted me in both my academic and research
achievements. Without them, there would remain many unsolved problems.
I would like to acknowledge my family who has provided the emotional and financial
foundation from which I have been able to build upon. Thank you to my friends outside of
engineering who have kept me grounded and have helped to diversify my life. Finally, I thank
God for giving me the health and environment that has been so vital in my success at the
University of Florida.
TABLE OF CONTENTS
ACKNOWLEDGMENTS .............. ...............4.....
LIST OF TABLES ........._.._.. .....___ ...............7...
LIST OF FIGURES .............. ...............8.....
AB S TRAC T ............._. .......... ..............._ 10...
1 INTRODUCTION ................. ...............12.......... ......
Composite Materials............... ...............1
Aerospace Applications .................. ..... .......... ... .. ....... .............1
Literature Revi ew/Previ ou s Work on P erm eab ility Te sti ng ................. .......... .............1 3
Standard Test Method for Determining Gas Permeability .............. ...............14....
Permeability Apparatus .............. ...............14....
Calculating Permeability .............. ...............15....
Testing Specimens ................ ...............16.................
Testing Adapted for Strain............... ...............17.
2 FINITE ELEMENT MODELING................ ...............2
Motivation for Modeling .............. ...............22....
Strain Gage Placement............... ...............2
Test Area Deflection ................. ... ........ ...............23......
Exploring Alternative Specimen Geometries .............. ...............23....
3 PERMEABILITY INVESTIGATION ................. ......... ...............32......
Initial Permeability Testing Criteria ................ ...............32................
Permeability and Time............... ...............32..
Permeability and Upstream Pressure ................. ...............33................
Permeability and Gas Selection ................. ...............34................
Uncertainty Analysis .............. ...............34....
4 STRENGTH TESTING................ ...............42
Grouping the Specimens ................. ...............42........... ....
Failure Testing .................. .......... ...............42.......
Inverse Dog Bone Failure ................. ...............42........... ...
Rectangular Strip Failure............... ...............43
Strain Through the Thickness ................. ...............44................
Permeability and Strain............... ...............45.
5 CONCLUSIONS AND FUTURE WORK ................. ...............53........... ...
A MATLAB CODE FOR PERMEABILITY .............. ...............54....
B MATLAB CODE FOR FALCO ................. ...............56........... ...
LIST OF REFERENCES ................. ...............60........... ....
BIOGRAPHICAL SKETCH .............. ...............61....
LIST OF TABLES
2-1 Material properties used in the FE analysis. ............. ...............25.....
3-1 Permeability versus time. Helium gas, 30 psi, fiberglass. ................ .......................36
3-2 Permeability versus time. Nitrogen gas, 30 psi, fiberglass. ................ ......................37
3-3 Permeability versus time. Helium gas, multiple upstream pressures, [0/0/90/90]s. .........38
3-4 Error used in uncertainty analysis............... ...............38
LIST OF FIGURES
1-1 X-33 (Courtesy: Sukjoo Choi ). ............. ...............18.....
1-2 Damage progression. A) Micro-cracks. B) Transverse cracks. C) Delamination. D)
Debonding of the face sheet. (Courtesy: Sukj oo Choi ) ................. ............ .........18
1-3 Volumetric permeability determination method (Courtesy: ASTM D1434-82 )........19
1-4 Permeability testing apparatus (Courtesy: Sukjoo Choi ). ................... ...............1
1-5 Specimen/chamber interface (Courtesy: Sukj oo Choi ) ................. ............ .........20
1-6 Curing cycle. .............. ...............20....
1-7 Mechanical grip and specimen interaction. ............. ...............21.....
1-8 Modified test setup............... ...............21.
2-1 Strain in the 2-direction of a [0/0/90/90]s specimen subj ected to 100 pounds of
tension. .............. ...............26....
2-2 Stress in the 12-direction of a [0/0/90/90]s specimen subj ected to 100 pounds of
tension. .............. ...............27....
2-3 Deflection of 0.001313 in. due to an upstream pressure of 10 psi ................. ................28
2-4 Deflection of 0.01313 in. due to an upstream pressure of 100 psi............... ..................29
2-5 New specimen geometry ................. ...............30................
2-6 Deflection due to upstream pressures and clearance allowed ................. ........._._ .....30
2-7 New geometry specimen deflection. A) Isometric view. B) Side view. ................... .......31
3-1 Slug position versus time. Helium gas, 30 psi, fiberglass. ............. .....................3
3-2 Permeability versus time. Helium gas, 30 psi, fiberglass. ................ ................ ...._39
3-3 Slug position versus time. Nitrogen gas, 30 psi, fiberglass of thickness 0.5 mm.............39
3-4 Permeability versus time. Nitrogen gas, 30 psi, fiberglass. ................ ......................40
3-5 Slug movement versus time interval. Helium gas, multiple pressures, [0/0/90/90]s. .......40
3-6 Permeability versus time interval. Helium gas, multiple pressures, [0/0/90/90]s. ...........41
3-7 Error bars associated with helium gas, 30 psi, and fiberglass. ............. .....................4
4-1 Inverse dog bone specimen failure. ............. ...............46.....
4-2 Failed inverse dog bone specimen. ............. ...............46.....
4-3 Load versus strain curve for inverse dog bone specimen [0/90/0/90]s. ..........................47
4-4 Stress versus strain curve for inverse dog bone specimen [0/90/0/90]s. ...........................47
4-5 Failure on the front side of the specimen. ....._ .....___ ........_.__ .........4
4-6 Failure on the back side of specimen. .............. ...............48....
4-7 six strain through the thickness from the FE analysis at 100 psi upstream pressure. ........49
4-8 six strain through the thickness from the FE analysis at 50 psi upstream pressure. ..........49
4-9 811, 822, and Yl2 through the thickness from the laminate analysis program FALCO.
Only axial load is assumed to act on the specimen. No upstream pressure is used..........50
4-10 Logarithmic permeability versus strain for [90/+6/-6/90] laminate............... ................5
4-11 Logarithmic permeability versus time. 0.3389% strain, [90/+6/-6/90], 50 psi
upstream pressure for specimen #144............... ...............51..
4-12 Grip assembly for permeability versus strain measurements. ................... ...............5
4-13 Side view of assembly for permeability versus strain measurements............... ...............5
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
EFFECT OF STRAIN ON THE GAS PERMEABILITY OF COMPOSITE LAMINATES
James VanPelt III
Chair: Bhavani Sankar
Cochair: Peter Ifju
Major: Aerospace Engineering
Because of their excellent mechanical and thermal properties, fiber reinforced composite
materials are good candidates for various gas storage systems in space vehicles. However, micro-
cracking and delamination in these materials could lead to gas permeation and catastrophic
failure of the system. The purpose of this research is to investigate various factors including the
applied strains that affect the gas permeability. An experimental procedure has been developed
according to ASTM D1434-82 standards. In order to simulate the loads induced by launch and
landing of the vehicle, the composite specimens are subj ected to a given load during the gas
Permeability values tended to converge after at least 15 minutes of test duration. Due to
higher molecular weight, Nitrogen permeated at a slower rate than Helium. Permeability did not
depend on upstream pressure when the specimens were not loaded. To test the permeability of
the specimens under load, the gas permeation test setup and the laminate were oriented in such a
manner that desired load could be applied to the specimen in the material testing machine. A
new geometry of specimen was developed such that there was a seamless integration between
machinery and specimens. Finite element modeling proved that the newly developed geometry
would allow for accurate permeability measurements. Finally, an uncertainty analysis was
performed to identify various sources of errors. The maj or source of error stemmed from length
measurements taken with calipers or rulers.
Composites consist of two or more separate materials combined in a macroscopic
structural unit. They can be made from a combination of metals, polymers, or ceramics.
Structural composites made from polymers reinforced with fibers, such as glass and graphite,
have proven to be very effective. This is due to the fact that the composite materials are much
stronger and stiffer in fiber form than they are in bulk form. With a higher modulus and a lower
density, these fibers can lead to a great improvement in strength-to-weight ratio. Properties like
this have lead composites to be used greatly in the aerospace industry .
The next generation of reusable launch vehicles (RLV) will require new and innovative
materials to reduce the cost of launching payloads into orbit from $10,000 per pound to $1,000.
One maj or issue of concern is using these fiber-reinforced composites to make durable,
lightweight, cryogenic propellant tanks. Various gas storage systems contribute to almost half
the dry weight of space vehicles. Using these materials in tank applications is very challenging
but promising in reducing the weight of future space vehicles .
X-33 Demonstrator: The sandwich liquid hydrogen (LH2) tank of the X-33
Demonstrator (Figure 1-1) was ground tested in 1999. When micro-cracking of the composite
inner skin occurred, the tank failed. Initially, the tank is filled with cryogenic fuels at extremely
low temperatures. This causes the material to shrink. Gas created by the evaporation of the LH2
caused the composite tank to rupture due to the micro-cracking associated with material
shrinkage . There are also various stresses imposed on the tank when the vehicle is launched
and then during reentry and landing. Figure 1-2  shows how the cryogenic fuel can leak
through micro-cracks induced by these stresses. When the micro-cracks develop, they provide a
pathway for the gas to leak through the specimen. The example in Figure 1-2 is a [0/90/0] layup.
The goal of this research is to measure how much gas permeates through specimens of various
orientations and understand various factors that affect the permeability measurements.
Literature Review/Previous Work on Permeability Testing
There have been many ongoing tests in the past investigating the permeability of various
materials in cryogenic storage applications. Some tests explored how the addition of polymer
films to the composite laminate would decrease the permeability of the testing material. Several
commercially available and LaRC films exhibited lower permeability than the composite panels
tested which would imply adding these films to the panels would lower the permeability of the
tank . Other film research was performed with films that were preconditioned. This consisted
of combinations of elevated temperature, cryogenic temperature, and moisture for extended
periods of time. It was shown that the preconditioning of the films had no significant effect on
permeability. On of the films, Tedlar, possessed the best barrier properties, allowing the least
amount of He gas to permeate .
Permeability tests were also conducted on sandwich core materials containing a Hexcel
HRP or DuPont Korex core with graphite/epoxy facesheets. These panels were subj ected to
static and dynamic shear loads. Permeability increased instantaneously when catastrophic failure
occurred (failure occurred at the bondline). Also, as the number of cycles increased during the
tests, permeability increased for the Korex core . A tetra-axial test was also performed on a
Bismaleimide (BMI) based graphite fiber composite material. Permeability was seen to increase
right before catastrophic failure occurred. It was also found that due to creep, permeability s a
time dependent parameter .
The effect of impact testing and the permeability' s dependence on upstream pressure (post-
impact) has also been explored. For post-impact testing, the permeability has a non-linear
dependence on the upstream pressure. An increase in pressure results in a more substantial
increase in permeability. These tests were conducted using a bubble-type leak detector that
corresponded with the qualitative permeability measurements .
Combining cryogenic applications with tensile loading on carbon fiber laminates was also
the focus of previous research. Significant leakage was observed under liquid Nitrogen testing
conditions when a tensile load was applied. When compared to the leakage at room temperature
at the same tensile load, permeability only varied slightly. There remained some mechanical
effect of the cryogenic storage condition that affected the permeability of the material .
Standard Test Method for Determining Gas Permeability
In order to measure the amount of gas that permeates through a specimen, a volumetric
determination method was developed based on ASTM D1434 standards . This method can
be seen in Figure 1-3. A specimen to be tested is placed in between an upstream and a
downstream chamber. The downstream chamber is open to atmospheric pressure. Any gas that
permeates through the specimen is indicated by a volume change in gas. This volume manifests
itself in the movement of a liquid slug downstream of the permeating gas.
The permeability apparatus used is shown in Figure 1-4. Gas enters from the tank through
the upstream gas inlet tube. The precision pressure regulator then adjusts the upstream pressure
of the gas entering the upstream chamber. Upstream pressure is measured with a P-303A
pressure transducer from Omega Engineering Inc. An outlet valve is located in the upstream
chamber to purge the system of any excess atmospheric gas before the test is conducted. Usually
the system was allowed to purge for five minutes before testing began. Gas then permeates
through the specimen when this outlet valve is closed. A close-up of this interaction is shown in
Figure 1-5. A greased gasket/O-ring interface is used as well as a 300-pound compressive force
so that no permeating gas might escape before entering the capillary tube.
Downstream of the specimen is a capillary tube with isopropyl alcohol dyed with pen ink.
Because differences in the liquid used for the slug were non-existent, alcohol was chosen for
testing due to its ease of cleaning. The capillary tube was allowed to rest on the surface of a
ruler. No differences were found placing the tube at various angles however. Also, the length of
the slug was proven to be a non-factor in volumetric determination of permeating gas . The
movement of the slug in the capillary tube is a result of how much gas has permeated through the
Permeability calculations begin with observing how far the slug moves along the capillary
tube in a certain amount of time. This is measured by placing the capillary tube along a ruler and
using a stopwatch to record time intervals. The meniscus of one side of the slug is used for
ob servati on. The internal area of the capillary tube (ac ) is known, so the volumetric flow rate
(Vy) of the gas can be calculated as shown in Equation 1-1.
V, = a (1-1)
Next, the gas transmission rate (GTR) is calculated as a function of ambient pressure (po )
ambient temperature (T), the universal gas constant (R), testing area of the specimen (A), and
volumetric flow rate (Vy,) in Equation 1-2. Ambient pressure is recorded with a 2113A
barometric pressure sensor from Pasco Scientific. The universal gas constant
is 8.3143 x 103 L Pa/mol K and ambient temperature is assumed to be 300 K.
GTR = Pof(1-2)
The permeance (P), in Equation 1-3, is calculated by knowing the upstream pressure (p)
and GTR. Permeability (P ) is the permeance multiplied with the thickness (t) of the specimen,
as shown in Equation 1-4.
P= P-t (1-4)
Units for permeability are mol s/m Pa. The logarithm of permeability is taken and will be
used in the rest of this document for greater ease in comparing results. It should be noted that the
logarithmic permeability is usually a negative number, and hence higher the magnitude (absolute
value) of the log of permeability, the less permeable the material is.
Various testing samples were fabricated using graphite/epoxy prepregs in an autoclave.
The layers were configured in specific orientations and then cured. Prepregs used for initial
samples were from Torayca and were product number T800HB-12K-40B. The curing cycle for
these specimens involved constant atmospheric pressure and a vacuum of -30 in. Hg. First, the
specimens were heated to 225 and held for one hour. Then, they were raised to 35007 and
held for four and a half hours before returning to room temperature. This temperature
distribution is outlined in Figure 1-6.
Specimens were then cut in an inverse dog bone shape (Figure 1-7). This shape resulted
from the grip and testing area constraints. The specimen was required to be cut so that it could
be centered within the mechanical grips used for loading the specimen while being wide enough
in the body to accommodate the testing area of the gasket. Fiberglass tabs were adhered to the
tips with a hysol epoxy. It will be shown later why the specimen must fit into the grip.
Testing Adapted for Strain
To allow for permeability testing while the specimen is undergoing a load, the prior setup,
shown in Figure 1-4, had to be modified. Instead of using the MTI machine as a source for the
300 pounds of compressive force, it had to now be used to apply external load to the specimen.
In order to accomplish this, a bracket was designed to hold the upstream and downstream
chambers horizontally as shown in Figure 1-8. A torque wrench was used to tighten the brackets
around the specimen providing the clamping force required for no gas to escape.
Strain in the specimen was measured using a 120 0Z uniaxial Vishay Micro-Measurements
strain gage. Load was measured using a 25,000 pound load cell. The MTI machine is rated up
to 30,000 pounds and the grips' capacity is 30,000 pounds. A LabVIEW program monitors load
versus strain for various testing situations. Permeability is still calculated as before. All data
sensors were monitored in the same fashion as previously explained.
Fiue11 -3 Cuts:SkjoCo 4)
D)ur Debodin ofth ac het (Courtesy: Sukjoo Choi ).
Figure 1-3. Volumetric permeability determination method (Courtesy: ASTM D1434-82 ).
Figure 1-4. Permeability testing apparatus (Courtesy: Sukjoo Choi ).
Figure 1-5. Specimen/chamber interface (Courtesy: Sukj oo Choi ).
0 100 200 300 400 500 600
Figure 1-6. Curing cycle.
Figure 1-7. Mechanical grip and specimen interaction.
Figure 1-8. Modified test setup.
FINITE ELEMENT MODELING
Motivation for Modeling
Due to the unique geometry of the specimen used in this research, a finite element analysis
was performed to investigate any maj or stress concentrations that might affect permeability
results. The fillets of radii of about 10 mm were cut into the specimen so that available grips
could be used without reducing the testing width of the testing area. There was also the question
of where to place the strain gage if these fillets might cause some adverse stress gradients. Also,
the deflection of the specimen due to the upstream pressure was investigated. There was concern
that the deflection might be too much for the system to handle. All finite element modeling was
performed using the commercial software Abaqus with material properties outlined in Table 2-1.
Strain Gage Placement
Initially, the specimens used were inverse dog bone shaped. This gave rise to the question
of where a suitable location for the strain gage would be. The strain gage cannot be placed over
the center of the specimen where testing occurs because it would be difficult to attach wires to
the specimen. Furthermore, placing a strain gage at the center of the testing area would interfere
with the permeating gas through the specimen. A model of the entire specimen was made to
investigate regions of similar strain. In this case, the model was of a [0/0/90/90]s layup. In
Abaqus, linear/quadratic elements with four nodes per element and three degrees of freedom per
node were used. The resulting strain in the 2-direction from applying 100 pounds is shown in
Figure 2-1. The strain in the 2-direction was found to be the only significant value of strain
From this model, it was determined that the strain gage could be placed anywhere along
the centerline of the specimen. For ease of testing, the gage was placed about one inch below the
fiberglass tab. This location should provide an accurate representation of the strain measured
across the testing area of the specimen without any upstream pressure applied.
In order to increase the accuracy of the FE model, a quarter-sized model was analyzed
using the same type of elements noted previously. Significant stress concentrations appeared in
the corner as more shear stresses developed. This is shown in Figure 2-2. The stress
concentrations were localized enough to confirm the validity of the strain gage placement.
Test Area Deflection
When the [0/0/90/90]s specimen is subj ected to an upstream pressure, it will undergo some
deflection. A circular plate of diameter equal to that of the O-ring was analyzed with finite
elements. The plate was assumed to be on pinned support around the edges. For this analysis, 3-
D shell elements were used. S4R elements with four degrees of freedom per node were
subjected to pressures ranging from 10 to 100 psi. Figures 2-3 and 2-4 show the deflection
dependence on upstream pressure. Based on the results, the deflection dependence on upstream
pressure is a linear relationship. For a clamped condition, the maximum deflection from Abaqus
was 0.003539 in. The deflection due to all ranges of upstream pressures was very small and was
regarded as negligible for having any permeability interference.
Exploring Alternative Specimen Geometries
When fabricating the specimens had to be completed cheaper and faster to suit the testing
constraints, a new geometry was explored. The inverse dog bone shape is influenced by two
parameters: the grip width and the testing area. Grip width cannot change, for these grips have
the strength required for pulling the specimen to large strain levels. Testing area, however, can
change. The testing area is the area created by the radius of the gasket. By substituting an O-
ring for the gasket, the cross sectional area of testing is reduced. This would get rid of the
inverse dog bone shape and allow rectangular strips to be easily fabricated with a shear. A
picture of the new specimen geometry is shown in Figure 2-5.
New specimens cut to this geometry were four and six layer laminates. Strain field across
the specimen is now assumed to be uniform because of the uniform loading and the rectangular
geometry of the new specimens. However, due to the smaller thickness, a new deflection
analysis was performed. The thought was that a less thick specimen would deflect more and
possibly cover up and obstruct the permeating gas pathway to the capillary tube.
Abaqus Modeling of Deflection on New Geometry: Downstream of the specimen, there
is an outlet pathway that the permeating gas follows to get to the capillary tube. The clearance
between an un-deformed specimen and this hole is 0.035 in. A finite element model, created
with eight node shell elements with six degrees of freedom per node, shows that the deformation
due to 80 and 100 psi exceeds the given clearance of 0.03 5 in. This is shown graphically in
Figure 2-6. All tests conducted with the new geometry were to not exceed 50 psi in order to
avoid the excessive deflection that would obstruct the permeability measurements.
Shown in Figure 2-7 is a four layer specimen subj ected to a tensile load of 1000 pounds
and to 100 psi upstream pressure across the testing area. The conj ecture here is that the
deformation causes the specimen to interact with the inside of the downstream chamber, causing
some possible blocking of the outlet to the capillary tube. Two solutions exist; to obtain a
thicker O-ring, or to use 50 psi as the upstream pressure for all tests with the new specimen.
Choosing 50 psi upstream pressure was the choice made for further studies.
Table 2-1. Material properties used in the FE analysis.
El (psi) 2.00152x107 6.20x106
E2 (psi) 1.30534x107 1.29x106
E3 (psi) 1.30534x106
nul2 0.3 0.27
Gl2 (psi) 1.00076x106 6.50x105
Gl3 (psi) 1.00076x106
G23 (psi) 519793
SNEG, (fraction = -1.0), Layer =1
(Ae. Crit.: 75%)
ODE: Job-1.odb ABAQUS/STANDARD Viersion 6.5-5 Wed
Increment 1: Step Time = 1.000
Primary Viar: S 2
Deformed Var: U Defornatilon Scale Factor: +3.104e+03
F:09 Eastern Standard Time 2006
Figure 2-1. Strain in the 2-direction of a [0/0/90/90]s specimen subjected to 100 pounds of
SNEG, (fractlon = -1.0), Layer =1
(8e. Crit.: 75%)
Figure 2-2. Stress in the 12-direction of a [0/0/90/90]s specimen subjected to 100 pounds of
Figure 2-3. Deflection of 0.001313 in. due to an upstream pressure of 10 psi.
Figure 2-4. Deflection of 0.01313 in. due to an upstream pressure of 100 psi.
* \ .*~. *
--- -~ -..-~nsnffn
Figure 2-5. New specimen geometry
Current clearance allowed by o-ring
Figure 2-6. Deflection due to upstream pressures and clearance allowed.
Figure 2-7. New geometry specimen deflection. A) Isometric view. B) Side view.
Initial Permeability Testing Criteria
To begin the experimental permeability testing, the inverse dog bone shape and fiberglass
specimens were used to verify certain parameters that would be used later for the rectangular
specimens. Three investigations were performed at no strain level. A relationship between
permeability and time was established. Dependence of permeability on upstream pressure was
recorded. Finally, the impact of gas selection on permeability was explored. Before any test was
completed, a control was initiated. This control was an aluminum plate. The aluminum plate
was inserted in the permeability testing apparatus. No slug movement was noted. This verified
no leaks existed in the system and that all testing could proceed as planned.
Permeability and Time
An investigation of permeability and time was performed using a fiberglass specimen, the
same material used on the tabs. Tests were performed with both helium and nitrogen gas at an
upstream pressure of 30 psi. The idea was to see if permeability values leveled out at a certain
time after testing was initiated.
For helium gas, the tests were allowed to run for 30 minutes. The position of the slug was
recorded every five minutes. This gave six intervals of slug movement and thus six intervals of
permeability calculations. Table 3-1 shows the values obtained from this test. The highlighted
section of the table illustrates the intervals were permeability converged. Average permeability
and the standard deviation are dually noted. Figure 3-1 outlines the slug position versus time,
while Figure 3-2 shows the permeability versus time. Again, the logarithm of permeability is
taken for ease of comparison.
The same analysis was performed using Nitrogen as the permeating gas. Initially, the tests
were allowed to run for 30 minutes. One Einal test was allowed to run for 60 minutes because it
was expected that nitrogen would take longer to permeate due to its larger atomic size. Table 3-2
shows results from this test. Slug movement and permeability for this test began to converge
after 30 minutes of testing as shown in Figures 3-3 and 3-4.
The conclusion that can be made from this analysis is that the data obtained during the first
20 minutes of the testing duration should be disregarded. Gas was still turned on and slug
movement monitored, but only permeability values after 20 minutes were averaged together to
Permeability and Upstream Pressure
It has already been noted that using the inverse dog bone specimens is acceptable up to 100
psi. The next step was to determine if permeability depended on upstream pressure. The
precision pressure regulator would only allow up to 60 psi upstream pressure. So, tests were
performed at 10, 50, and 60 psi. The specimen used in this case was a [0/0/90/90]s inverse dog
bone shaped laminate. Helium gas was used in all cases and was allowed to permeate for 30
minutes. Based on the permeability versus time analysis performed, all permeability values are
the average over the Einal 15 minutes of the test.
It was found that in an unstrained condition, permeability does not depend on upstream
pressure. Figure 3-5 shows the slug movement versus time for the three upstream pressures.
There is good convergence after the first 15 minutes. Figure 3-6 shows the permeability versus
time in each case. It appears at first glance that there is a large discrepancy in permeability data.
This difference is attributed to a slug movement differential of less than 0.5 mm. This data is
shown in Table 3-3. Such a small difference could be attributed to eye sight error in reading the
Based on the tested results, it is concluded that permeability does not depend on upstream
pressure in a non loaded case. For future testing with the dog bone shaped specimen, 30 psi was
selected as the upstream pressure. Rectangular specimens were tested at an upstream pressure of
50 psi. Both of these values are within the limits set by the FE modeling of deflection of a
Permeability and Gas Selection
The final analysis performed on the fiberglass specimens was on the relationship of
permeability and gas selection. Two gases were used in these tests: helium and nitrogen. Prior
to conducting the tests, the assumption was that permeability values should be lower for nitrogen
because it is a larger molecule than helium.
Helium values converged at a logarithmic permeability of -17.6429 from Table 3-1. From
Table 3 -2, it can be seen that nitrogen values converge to -17.83 50. Only permeability values
based on the permeability versus time analysis were used in averaging. The higher the
magnitude (absolute value) of the logarithmic permeability, the lower the permeability, or the
less gas that leaks through the specimen. This proves the initial theory that nitrogen permeates at
a slower rate than helium. Helium gas was used for the duration of testing.
Due to the multiple readings that are made during these tests, an uncertainty analysis was
performed to investigate how each measurement affects the final calculation. The first step in
determining the uncertainty in each calculation was to first set up a general equation for
calculating the permeability of the material. Next, the derivative of the general equation was
taken with respect to each variable present in the equation. Once the derivatives were expressed
in terms of the measured variables, the error in each measurement was determined. Error was
associated with ruler readings, eye sight, and pressure sensors. In all cases, reasonable error (u)
was determined, as shown in Table 3-4.
The next step of the uncertainty analysis involves substituting the experimental values
obtained during the test into each derivative equation. This value of the derivative is noted as dk,
where k is the respective variable from Table 3-4 for each case. Finally, Equation 3-1 illustrates
how the uncertainty (U) is obtained for the overall test.
U= dk2 k2 dl2 12 dm2 m2 +... (3-1)
Once the uncertainty value is calculated, it is added and subtracted to the initial
permeability value obtained from the test. Once this has been completed, the logarithm is taken.
The MATLAB code used in this method is shown in Appendix A. By analyzing each
dk2 k2 COmponent of Equation 3 -1, the affect of each measurement can be compared with each
other to determine the largest sources of error. The largest sources of error were observed to be
any readings made with a ruler. These included the distance the slug moves, the radius of the
capillary tube, the thickness of the specimen, and the radius of the testing area. Of particular
note is that the distance the slug moves contributes to a large source of error.
This supports the conclusion that the permeability does not depend on upstream pressure.
Differences in those measurements were less than one millimeter, which is difficult to observe
with the naked eye. However, even those small differences can contribute to large error in the
final results. Error bars were plotted according to this uncertainty method, as shown in Figure 3-
Table 3-1. Permeability versus time. Helium gas, 30 psi, fiberglass.
Slug Movement (cm)
Time Interval (minutes) Run 1 Run 2 Run 3
0-5 minutes 1 0.35 0.21 0.25
5-10 minutes 2 0.20 0.09 0.09
10-15 minutes 3 0.24 0.10 0.03
15-20 minutes 4 0.21 0.11 0.10
20-25 minutes 5 0.05 0.09 0.09
25-30 minutes 6 0.10 0.09 0.08
Slug Movement in Final 15
Table 3-2. Permeability versus time.
Nitrogen gas, 30 psi, fiberglass.
Slug Movement (cm)
Run 2 Run 3
Time Interval (minutes)
0-5 minutes 1
5-10 minutes 2
10-15 minutes 3
15-20 minutes 4
20-25 minutes 5
25-30 minutes 6
30-45 minutes 7
45-60 minutes 8
in Intervals 4 6
in Intervals 4 8
in Intervals 7 8
-17.4810 -17.5337 -17.6337
Table 3-3. Permeability versus time. Helium gas, multiple upstream pressures, [0/0/90/90]s.
Slug Movement (cm)
Time Interval (minutes) 10 psi 50 psi 60 psi
0-5 minutes 1 0.27 0.65 0.51
5-10 minutes 2 0.18 0.33 0.28
10-15 minutes 3 0.22 0.27 0.21
15-20 minutes 4 0.19 0.15 0.20
20-25 minutes 5 0.13 0.15 0.10
25-30 minutes 6 0.18 0.16 0.15
in Final 15 minutes
Table 3-4. Error used in uncertainty analysis.
Variable Quantity Measured
Po Ambient Pressure
dslug Distance Slug Move
rc Capillary Tube Rad
P Upstream Pressure
Rt Testing Area Radiu
R Universal Gas Cons
time Time of Test
0 5 10 15 20 25 30 3i
Figure 3-1. Slug position versus time. Helium gas, 30 psi, fiberglass.
Figure 3-2. Permeability versus time. Helium gas, 30 psi, fiberglass.
0 10 20 30 40 50 60 70
Figure 3-3. Slug position versus time. Nitrogen gas, 30 psi, fiberglass of thickness 0.5 mm.
Time Interval #
0 2 4 6 8 1
Time Interval #
Figure 3-4. Permeability versus time. Nitrogen gas, 30 psi, fiberglass.
- 10 psi
0 1 2 3 4 5 6 7
Time Interval #
Figure 3-5. Slug movement versus time interval. Helium gas, multiple pressures, [0/0/90/90]s.
1)1 2 3
Time Interval #
Figure 3-6. Permeability versus time interval. Helium gas, multiple pressures, [0/0/90/90]s.
Figure 3-7. Error bars associated with helium gas, 30 psi, and fiberglass.
Grouping the Specimens
Strength testing was performed with the rectangular specimens. These specimens were
broken down into two groups. The first group contained six-ply laminates and followed a layup
of [+6/-6/+6/-6/+6/-6]. The other group consisted of four-ply laminates with a [90/+6/-6/90]
layup. Failure tests were performed on the six-ply laminates as well as the inverse dog bone
shaped specimens before permeability testing was to take place. The failure strain was
established for the six-ply laminates so that the specimens would not break while the
permeability apparatus was connected. Once this ceiling was established, various permeability
tests were conducted at lower strain levels.
Another facet of the analysis was to pull the four-ply laminates to a strain level higher than
that of the six-ply laminates. This was to ensure that the internal plies would fail, but the 900
layers would keep the specimen intact due to the elastic modulus values. Permeability testing
was conducted at these higher strain levels to see if the 900 layers would prevent gas from
permeating through even if the internal plies failed.
All failure tests were performed on the MTI material testing machine. A LabVIEW
program was used to set the load level at very high values. Once failure occurred, the program
was terminated and the data was analyzed. Plexi-glass panels were used for protection for
Inverse Dog Bone Failure
Initial failure tests on these specimens were used to obtain some material properties to
compare with some accepted values to confirm the strain and load readings were correct. A
[0/90/0/90]s specimen was used for the failure test. Once failure occurred, shown in Figures 4-1
and 4-2, the data was tabulated from the LabVIEW program. This program outputs load versus
strain. Knowing the cross-sectional area of the specimen allowed for a stress versus strain plot.
The slope of this line, the modulus of elasticity, was compared to accepted values. These plots
are shown in Figures 4-3 and 4-4.
A modulus of elasticity value from the stress versus strain curve was calculated to be 7.99
Msi. Accepted values for similar materials are El = 19.0 M~si and E2 = 1.5 M~si . Due to a
layup of [0/90/0/90]s, the specimen was expected to have a modulus somewhere in between
those values. This procedure confirmed that the load cell and strain gage were working as
Rectangular Strip Failure
Failure tests on these specimens were conducted on the six-ply laminates. Due to the
layup consisting of [+6/-6/+6/-6/+6/-6], it was expected that these specimens would fail quite
early on in the loading process. There were six of these six-ply specimens to be tested. Of the
six, two had inherent flaws in them that prevented them from being tested. Of the remaining
four, two failed simply when the grips were attached to the specimen. With two specimens
remaining, one was taken to failure to learn the strain ceiling that could be placed on such a
laminate. This specimen failed at 0.37% strain. Figures 4-5 and 4-6 illustrate the type of failure
that occurred along the ply angle. It was assumed then that taking the last laminate to a strain
level of 0.33% would be ok. This worked fine until an upstream pressure of helium gas was
applied to the specimen. When this happened, the specimen failed across the testing area due to
the deflection caused by the upstream pressure.
No permeability tests were able to be completed on these six-ply laminates for the reasons
stated above. However, the useful information taken out of them was two fold: the internal ply
failure strain of the four-ply laminates, and the idea that the specimen undergoes a strain increase
over the testing area that cannot be detected by the strain gage. An analysis of this strain level
had to be conducted.
Strain Through the Thickness
In a four-ply laminate, when the specimen is pulled to 1000 pounds and an upstream
pressure of 100 psi is applied, the strain gage reads 0.2537% strain. With an upstream pressure
of 100 psi, there must be a large deformation across the testing area and an associated strain with
it. Using Abaqus FE software, the strain in each layer was able to be extracted across the testing
area by picking a node within this area to analyze. The model in Figure 2-7 was used for this
analysis. A node close to where the strain gage was placed was also analyzed. This would
confirm that the FE model was in fact giving results comparable to the experimental results. For
the 100 psi case, Figure 4-7 shows the strain in each layer with the coordinate along the fiber
The strain gage readings were confirmed with the FE model; both were close to 0.25%
strain. However, the strain reading through the testing area was larger. Thus, the strain gage
readings only tell part of the story. However, if we only use 50 psi upstream pressure, the
difference between the two readings is much smaller as shown in Figure 4-8. This is another
reason why 50 psi was selected for the upstream pressure during the permeability tests.
A further investigation was completed using a Failure Analysis of Laminated Composites
(FALCO). The MATLAB code for FALCO is included in Appendix B. In Figure 4-9, the
strains through the thickness were analyzed. As with the FE model, the experimental strain
reading of 0.2537% strain matches up very closely with computer-generated results. With
FALCO though, the upstream pressure cannot be taken into consideration.
Permeability and Strain
The goal of these tests is to Eind at which strain level the permeability increases by an order
of magnitude. Strips of [90/+6/-6/90] laminates were subj ected to strain levels beyond the failure
strain of the internal [+6/-6] plies. First, a test was completed without any external strain. Then,
the LabVIEW program would be configured to pull the specimen to a desired load and hold it
there for 200 minutes. This would give plenty of time to configure the permeability apparatus
around the specimen and conduct a 100 minute test. Then the specimen would be unloaded and
loaded to a load 500 pounds greater and the test would be repeated.
When this thesis was written, the strain level had reached roughly 0.6%. The
corresponding permeability values are shown graphically in Figure 4-10. A general rule to note
is that the error associated with these results was about 0.25 towards the more permeable end and
0.63 towards the less permeable end. For each of these tests, the slug was monitored every 20
minutes and the permeability calculated over each of these intervals. Again, the first 20 minutes
of testing were disregarded. An average of permeability was then taken over the remaining data
set. A good example of how this works is shown in Figure 4-11 for a strain reading of 0.33 89%.
The average permeability value taken from this data was -18.4.
No significant permeability increase was noted up to 0.6% strain. This is well beyond the
0.37% internal ply failure strain. So, the conclusion can be made that the 900 outer plies resist
gas from leaking through up to 0.6% strain even when the internal plies have failed. Pictures of
this testing are included in Figures 4-12 and 4-13.
Figure 4-1. Inverse dog bone specimen failure.
Figure 4-2. Failed inverse dog bone specimen.
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Specimen failed at 0.905195 % strain and 6,751.058 lbs.
Figure 4-3. Load versus strain curve for inverse dog bone specimen [0/90/0/90]s.
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Specimen failed at 0.905195 % strain and 71,854.93 psi
Modulus of Elasticity from failure = 7.99 Msi
Figure 4-4. Stress versus strain curve for inverse dog bone specimen [0/90/0/90]s.
Figure 4-5. Failure on the front side of the specimen.
'"' ;"..L. 'L-~i- .. *
'r f' ~*r**, r .'F~~u
~ I-, ~ ~"~~~jiLlr:",~;E;~;d~'~;LiP
Figure 4-6. Failure on the back side of specimen.
50 -1.00 -0.50 0.00 ~0. O 1.00 1.
Through the Thickness
Figure 4-7. six strain through the thickness from the FE analysis at 100 psi upstream pressure.
w +ln Testing Area
-- 00 +S train Gage Location
50 -1.00 -0.50 0.00 O0 1.00 1.
Through the Thickness
Figure 4-8. six strain through the thickness from the FE analysis at 50 psi upstream pressure.
+ln Testing Area
-H Strain Gage Locationtri a Lcio
.5 -7 5 1
Normalized Through the Thickness
Figure 4-9. six, 822, and yl2 through the thickness from the laminate analysis program FALCO.
Only axial load is assumed to act on the specimen. No upstream pressure is used.
0.)0 0.10 0.20 0.30 0.40 0.50 0.60 0.0
Figure 4-10. Logarithmic permeability versus strain for [90/+6/-6/90] laminate.
1 2 3 4 5
Figure 4-12. Grip assembly for permeability versus strain measurements.
Figure 4-11. Logarithmic permeability versus time. 0.3389% strain, [90/+6/-6/90], 50 psi
upstream pressure for specimen #144.
Figure 4-13. Side view of assembly for permeability versus strain measurements.
CONCLUSIONS AND FUTURE WORK
Due to the micro-cracking associated with various strain levels during launch and landing,
the permeability of gas through graphite/epoxy laminates is a maj or area of concern for reusable
launch vehicles and future space vehicles. An effective method for testing the permeability of
graphite/epoxy composite laminates under load was developed. This testing method allows for
permeability values to be determined at various strain levels.
Finite element modeling was instrumental in exploring other specimen geometries and in
establishing criteria for testing standards. Permeability was found to level out after 20 minutes
of testing. Prior to any micro-cracking developments, permeability did not depend on upstream
pressure. In addition, permeability was lower for nitrogen compared to helium. Thus, testing
with helium takes shorter time than nitrogen tests. A standard test evolved which included
testing with helium gas at an upstream pressure of 50 psi. An uncertainty analysis was
performed to investigate the contributions of the testing devices to the overall error in the system.
Finally, permeability was found to remain relatively constant up to 0.6% strain for the
four-layer laminates. This is past the point where the internal plies of the laminate fail. Up to
this strain level, the 900 layers prevent gas from leaking through. Future work from here would
involve combining the cryogenic environment with the strain level. An insulated casing of some
type could be placed around the already developed testing apparatus to conduct the permeability
tests at cryogemic temperatures.
MATLAB CODE FOR PERMEABILITY
%%%%% Program for computing the permeability of composite laminates %%%%%
%%%%% Created by Jim VanPelt %%%%%
%%% USER INPUTS %%%
Amb_press_Hg = 30.223; %%% Ambient pressure read by PASPORT sensor in inches Mercury
Upstream_press_psi = 50; %%% Upstream pressure measured by Labview software "single.vi"
time_min = 20; %%% Time permeability test is allowed to run in minutes
distance_mm = 5.0; %%% Distance slug moved in millimeters
thickness_in = .026; %%% Thickness of specimen in inches
%%% CONVERSION %%%
radius_cap_m = 0.000525; %%% Radius of Capillary Tube in meters
radius test m = 0.0159; %%% Radius of testing area in meters
Amb_press_Pa = 3386.388666667 Amb_press_Hg; %%% Converts pressure from inches
mercury to Pascals
time sec = 60 time min; %%% Converts time from minutes to seconds
distance m = distance mm / 1000; %%% Converts distance slug moved from millimeters to
Upstream_press_Pa = 6894.75728 Upstream_press_psi; %%% Converts upstream pressure from psi
thickness m = 0.0254 thickness in; %%% Converts thickness from inches to meters
%%% PROPERTIES OF TESTING APPARATUS %%%
Area_cap = pi*radius_cap_m^2; %%% Cross sectional area of capillary tube in m^\2
Area_test = pi*radius test m^2; %%% Cross sectional testing area in m^\2
To = 300; %%% Ambient temperature in Kelvin
R = 8.3143e3; %%% Universal gas constant in (L*Pa)/(mol*K)
%%% VOLUMETRIC FLOW RATE %%%
slope = distance_m / time_sec; %%% Rate at which slug moves in m/s
Vr = slope Area_cap; %%% Volumetric flow rate in m^\3/s
%%% GAS TRANSMISSION RATE %%%
GTR = (Amb_press_Pa Vr) / (Area_test R To); %%% Gas transmission rate calculation
%%% PERMEANCE %%%
P = GTR / (Upstream_pressPa Amb_press_Pa); %%% Calculates permeance of specimen
%%% PERMEABILITY %%%
Perm = P thickness_m; %%% Calculates permeability of specimen
%%% LOG OF PERMEABILITY %%%
P_bar = log10(Perm); %%% Calculates log of permeability for easier quantification
%%%%% Uncertainty Analysis %%%%%
%%% Displacements %%%
u_Amb_press_Pa = 16.932;
%%% Uncertainty in Ambient Pressure measurements
u distance m = 0.0005; %%% Uncertainty in Slug measurements
u_radius_cap_m = 0.0000127; %%% Uncertainty in Capillary Tube Radius measurement
u_Upstream_press_Pa = 9.191; %%% Uncertainty in Upstream pressure measurements
u thickness m = 0.0005; %%% Uncertainty in thickness of specimen measurement
u radius test m = 0.000794; %%% Uncertainty in testing area radius
u time s = 1; %%% Uncertainty in time measurements
%%% Derivatives %%%
dP bar dAmb_press = (distance_m radius_cap_m^2 Upstream_press_Pa thickness_m) /
((Amb_press_Pa Upstream_press_Pa)^\2 *radius_test_m^2 R* To *time_sec);
dP bar ddslug = (-Amb_press_Pa radius_cap_m^2 thickness_m) / ((Amb_press_Pa -
Upstream_press_Pa) radius~test_m^2 *R To *time_sec);
dP bar dradius_cap = (-2 radius_cap_m Amb_press_Pa distance_m thickness_m) /
((Amb_press_Pa Upstream_press_Pa) radius~test_m^2 *R To *time_sec);
d P bard dupstrea m_press = (-Amb_press_Pa d istance_m rad ius_cap_m^2 th ickness_m) /
((Upstream_press_Pa Amb_press_Pa)^2 radius_test_m^2 *R To *time_sec);
dP bar dthickness = (-Amb_press_Pa distance_m radius_cap_m^2) / ((Amb_press_Pa -
Upstream_press_Pa) radius~test_m^2 *R To *time_sec);
dP bar dradius test = (2 Amb_press_Pa distance_m radius_cap_m^2 thickness_m) /
(radius_test_m^3 (Amb_press_Pa Upstream_press_Pa) R *To *time_sec);
dP bar time = (Amb_press_Pa distance_m radius_cap_m^2 thickness_m) / (time_sec^2 *
(Amb_press_Pa Upstream_pressPa) radius_test_m^2 *R To);
%%% Calculating the overall uncertainty %%%
U = ((dP_bar_dAmb_press^\2 umb_press_Pa^2) + (dP_bar_ddslug^2 u_distance~m^2) +
(dP_bar_d radius_cap^2 u_radius_cap_m^2) + (d P_bar_dupstream_press^\2 *
u_U pstream_press_Pa^2) + (dP_bar_dthickness^\2 u_th ickness_m^2) + (d P_bar dradius test^\2 *
u_radius_test_m^2) + (dP_bar dtime^2 u time_s^2))^0.5;
Perm_Upper = Perm + U;
Perm_Lower = Perm U;
P bar_ Upper = log 10(Perm_U pper);
P bar Lower = log10O(Perm_Lower);
Difference_Upper = P_bar_Upper P_bar;
Difference Lower = P bar P bar Lower;
P bar Upper
P bar Lower
% Contribution_Ambient_Pressure = (dP_bar_dAmb_press^\2 umb_press_Pa^2)
% Contribution_Slug_Movement = (dP_bar_ddslug^2 u_distance~m^2)
% Contribution_Capillary_Radius = (dP_bar_drad ius_cap^2 u_radius_cap_m^2)
% Contribution_U pstream_Pressu re = (d P_ba r_d upstream_press^2 u_U pstream_press_Pa^2)
% Contribution_Speci men_Th ickn ess = (d P_bar_dth ickness^\2 u_th ickness_m^2)
% Contribution_Test_Radius = (dP_bar dradius test^\2 u radius test m^2)
% Contribution_Time = (dP_bar dtime^2 u time_s^2)
% Total =
Contribution Ambient Pressure+ContributiolgMvmn+ ntiuoCplayRdsCnrbt
ion_Upstream_ Pressure+Contribution_SpecimnTikesCtrbiosRdu+ nrbtoi
% Square Root = Total^0O.5
MATLAB CODE FOR FALCO
%FALCO FAILURE ANALYSIS OF LAMINATED COMPOSITES
E1=20e6;E2=1 .3e6;nul2=0.3;G12=1 e6;
alphal =-0.3e-6;alpha2=28.1 e-6;
%Number of plies NL >or= 2, ply thickness h(k)and fiber angle thetad(k)
%Force and Moment Resultants, N & M, and Temperature differential
N= [0; 571 .429; 0]; M= [0; 0; 0];
%Calculate [S] and [Q]
S= [1/E1,-nul2/E1 ,0;-nul2/E1,1 /E2,0;0,0,1/G12];
Q= inv(S) ;
%Calculate laminate thickness
%Calculate the z-coordinate of the midplane of each ply (zbar)
zba r(1 )=-t/2+ h(1 )/2 ;
z ba r(k)= zba r(k-1 )+h (k-1)/2+h (k)/2;
%Calculate the A, B and D matrices and the thermal forces and moments NT and MT
A= zeros(3,3); B= zeros(3,3);D= zeros(3,3);NT zeo(,); MT= zeros(3,1);
c=cos(thetad(k)*pill 80);s=sin(thetad(k)*pill 80);
T_eps= [c*c,s*s,c*s;s*s,c*c,-c*s;-2*c*s,2 *scc-s]
D= D+(h(k)^\3/1 2+h(k)*zbar(k)^\2)*Qbar;
%Augment the ABD Matrix and the Force Resultants including thermal forces
F= [N+NT; M+ MT];
%Compute the laminate deformations,
%midplane strains eps0 and curvatures kappa
eps0= [def(1 );def(2);def(3)];kappa= [def(4);def(5);def6]
%determine the strains and stresses in each ply
%Strains and Stresses are calculated at the top and bottom surfaces of each ply
%strains and stresses are in respective principal material coordinates
epsl 2=zeros(3,1 ,NL,2);sigl 2=zeros(3,1,NL,2);
c=cos(thetad(k)*pill 80);s=sin(thetad(k)*pill 80);
T_eps= [c*c,s*s,c*s;s*s,c*c,-c*s;-2*c*s,2 *scc-s]
epsxy= eps0+(zba r(k)+h (k)/2)*kappa;
sig xy= T_eps'*Q*T_eps*epsxy;
%Calculate the strains and stresses at the top of the ply
e psl1 2(: :, k, 1)= T_e ps*e psxy;
sigl2(:,:,k,1 )= Q*(epsl2(:,:,k,1 )-DeltaT*[alphal ;alpha2;0]);
%Calculate the strains and stresses at the bottom of the ply
e psl1 2(: :, k,2)= T_e ps*e psxy;
sig 12(:, :, k,2)= Q*e psl2(:, :,k,2);
%Factor of Safety (FS) is determined for each ply at bottom and top surfaces
%Factor of Safety according to Max Stress Theory is FS1
%Factor of safety According to Max strain theory is FS2
%Factor of Safety according to Tsai-Hill is FS3
%Factor of safety according to Tsai-Wu is FS4
%Similarly failure mode FModel, FMode2 etc are calculated
%FMode=1 means fiber failure, 2 indicates transverse failure and 3 Shear failure
FS1 =zeros(NL,2);FS2=zeros(NL,2);FS3=zeros(N L,)F4zrsN,)
%Maximum Stress Theory, find Factor of Safety FS1 and failure mode FModel
% for each ply, both at top and bottom
for j=1 :2
Str(1 )= SLplus;
if sig(1) <0
Str(1 )=-S Lmi nus;
if sig(2) <0
elseif sig (2)==0
if FSS(i)== FS1(k,j)
%Maximum Strain Theory, find Factor of Safety FS2 and failure mode FMode2
% for each ply, both at top and bottom
%Calculate allowable strains
eLplus=SLplus/E1 ;eLminus=SLminus/E1 ;eTplus=STplus/E2;eTminus=STminus/E2;eLT=STG2;
for j=1 :2
eps=epsl 2(:,:, k,j);
if eps(1) <0
if eps(2) <0
if FSS(i)== FS2(k,j)
%Tsai-Hill Theory FS3, Note that Failure Mode is determined based on Max. Stress Theory
% i.e., FMode3=FModel
for j=1 :2
Str(1 )= SLplus;
if sig(1) <0
Str(1 )=-S Lmi nus;
if sig(2) <0
FS3(k,j)=1 /sqrt((sig(1)/Str(1 ))^\2-sig(1 )*sig(2)/Str(1 )^2+(sig(2)/Str(2))^\2+(sig(3)/Str(3))^2)
FMode3(k,j)= FModel (k,j);
%Tsai-Wu Theory FS4, Note that Failure Mode is determined based on Max. Stress Theory
% i.e., FMode4=FModel
%Compute Tsai_Wu coefficients F11, Fl, F22 etc.
F11=1 /(SLplus*SLminus);F1 =1/SLplus-1 /SLminus;F22=1 /(STplus*STminus);F2=1 /STplus-1/STminus;
for j=1 :2
FS4(k,j)=1/(F11 *sig(1 )^2+F22*sig(2)^\2+F66*sig(3)^\2+F1 *sig(1 )+F2*sig(2)+2*F1 2*sig(1)*sig(2));
LIST OF REFERENCES
1. Gibson, Ronald F. (1994). Principles of Composite Ma'~terial M~echanics.. New York:
McGraw-Hill Companies, Inc.
2. Grimsley, B., Cano, R., Johnston, N., Loos, A. and McMahon, W., "Hybrid Composites for
LH2 Fuel Tank structure," Proceedings of the 33rd International SAMPE Technical Conference,
NASA Langley Research Center, November 4-8, 2001.
3. NASA, Final Report of the X-33 Liquid Hydrogen Tank Test Investigation Team, George C.
Marshall Space Flight Center, Huntsville, 2000, May.
4. Choi, Sukjoo. "Micromechanics, Fracture Mechanics and Gas Permeability of Composite
Laminates for Cryogenic Storage Systems." University of Florida, 2006.
5. Herring, H. M., "Characterization of Thin Film Polymers Through Dynamic Mechanical
Analysis and Permeation," NASA CR 212422, June 2003.
6. Glass, D. E., Raman, V.V., Venkat, V. S., and Sankaran, S. N., "Honeycomb Core
Permeability Under Mechanical Loads," NASA CR 206263, December 1997.
7. Stokes, E. H., "Hydrogen Permeability of Polymer Based Composite Tank Material Under
Tetra-Axial Strain," Proceedings of the 5h COnfCTCHCO On Aerospace Materials, Processes, and
Environmental Technology (AMPET), Huntsville, AL, September 16-18, 2002.
8. Nettles, A.T., "Permeability Testing of Impacted Composite Laminates for Use on Reusable
Launch Vehicles," NASA/TM-2001-21 0799, 2001.
9. Yokozeki, T., Aoki, T., and Ishikawa, T., "Gas Permeability of Microcracked Laminates
Under Cryogenic Conditions," Proceedings of the 44th AIAA/ASME/ASCE/AHS Structures,
Structural Dynamics, and Materials Conference, Norfolk, VA, April 7-10, 2003.
10. ASTM D1434-82 (Reapproved 1992), "Standard Test Method for Determining Gas
permeability Characteristics of Plastic Film and Sheeting," ASTM, 203-213, 1992.
James VanPelt III (Jim) was born on August 17, 1982 in Bloomfield, NJ. He spent much
of his young childhood moving from New Jersey to Pennsylvania to Virginia before finally
settling back in West Chester, PA prior to the second grade. Jim later graduated in May of 2000
from West Chester East High School about 30 minutes west of Philadelphia. Some of his
activities included playing the viola in district and regional state orchestras, golfing on the high
school team, playing travel soccer, becoming proficient in horseback riding, and achieving Star
in Boy Scouts.
In the summer of 2000, Jim began undergraduate studies at the University of Florida in
Aerospace Engineering. He j oined the social fraternity Beta Theta Pi which would be the source
of many fond memories in his undergraduate life. Some of his other activities included helping
to found the Small Satellite Design Club and being an active member of the American Institute
of Aeronautics and Astronautics. After graduating from the University of Florida in April 2005,
Jim began graduate school under the tutelage of Dr. Bhavani V. Sankar in the Department of
Mechanical and Aerospace Engineering. It was here that his interest in composites began to
grow as he conducted permeability experiments on graphite/epoxy laminates. He graduated with
a Master of Science in aerospace engineering from the University of Florida in December 2006.
Jim is the son of James VanPelt II and Daphne Faye Hager. He has a younger brother,
Quinn Hager, and a younger sister, Holly Hager, whom he loves very much. After graduating,
Jim will work on space systems for Lockheed Martin in New Orleans, LA.