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MIXED-MODE INTERFACIAL FRACTURE TOUGHNESS OF SANDWICH
COMPOSITES AT CRYOGENIC TEMPERATURES
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
This document is dedicated to the graduate students of the University of Florida.
It is appropriate at this point to acknowledge the people that have made this
research possible. Without the support and guidance of Dr. B.V. Sankar, this research
would not have been possible. He has been my adviser and sponsor during my entire
academic and research experience at the University of Florida. He is a generous and
intelligent person who can lead and advise many people academically. Also I want to say
thanks to Dr. C.C. Hsu for his advice and help at the beginning of my graduate school.
Doing my research work, I received a lot of help and advice from my colleagues at
the Center for Advanced Composites. They are very friendly and open-minded people, so
I had a good relationship with them. In addition to academic work, they have also made
me have a lot of fun and unforgettable memories in the U.S. So I would like to thank all
of them, too.
Like other research, without funding it would not have been possible to do this
research. The people at NASA Glenn Research Center supported this proj ect from the
beginning to the end. Glenn Research Center supported the grant (NAG3-2750) and
cooperated with the Center for Advanced Composites and the University of Florida.
Finally I appreciate my parents, Soo-Kyoung Noh and Keum-Sik Min, and my
sisters, Sun-Ju and Sun-Hee. They give me valuable mental and material support during
my school life and U.S. life.
TABLE OF CONTENTS
ACKNOWLEDGMENT S .........__.. ..... .__. .............._ iv...
LIST OF TABLES ........._.___..... .__. ..............vii....
LI ST OF FIGURE S ........._.___..... .__. .............._ viii..
AB S TRAC T ......_ ................. ............_........x
1 INTRODUCTION ................. ...............1.......... ......
Background Information............... ...............
Literature Review .............. ...............2.....
Scope of the Thesis............... ...............4.
2 SPECIMEN AND TEST SETUP .............. ...............6.....
Experimental Setup............... ...............6..
Specimen Preparation ............... ... ...............6.......... ......
Cryogenic Environmental Chamber ................. ...............10........... ....
Experimental Procedure .............. ...............12....
Specimen Property Test ................. ...............15........... ....
Carbon Fiber Face Sheet .............. .. .......... ............1
Four-Point Bending Test at Room Temperature ................. .......................15
Four-Point Bending Test at Cryogenic Temperature .............. .....................1
Honeycomb Core Material .............. ...............20....
Summary and Conclusion............... ...............2
3 FRACTURE TOUGHNESS TEST .............. ...............22....
Double Cantilever Beam (DCB) Tests .............. ...............22....
DCB Tests at Room Temperature .............. ...............23....
DCB Tests at Cryogenic Temperature .............. ...............27....
Four-Point Bending Tests ........._._ ...... .... ...............28...
Summary and Conclusion............... ...............3
4 FINITE ELEMENT ANALYSIS .............. ...............33....
M odeling ................. ...............34.................
A analysis .............. ... ...............37..
Summary and Conclusion............... ...............4
5 CONCLUSIONS .............. ...............43....
Conclusion ................ .............. ...............43.......
Suggestion for Future Work .............. ...............45....
A CRACKS IN DIS SIMILAR ANISOTROPIC MEDIA ................. ......................46
B EXPERIMENTAL RESULTS AT ROOM TEMPERATURE ................. ...............50
C EXPERIMENTAL RESULTS AT CRYOGENIC TEMPERATURES ....................52
D MATERIAL INFORMATION OF SANDWICH COMPOSITES AND CURE
CY CLE .............. ...............54....
E MATERIAL TESTS RESULTS................ ...............56
LIST OF REFERENCES ................. ...............58................
BIOGRAPHICAL SKETCH .............. ...............59....
LIST OF TABLES
2.1 Mechanical properties of composite prepreg provide by company. ........................ 15
2.2 Investigated material properties of tested composite laminates at room
temperature ................. ...............17.................
2.3 Investigated material properties of tested composite laminates at cryogenic
temperature ................. ...............18.................
2.4 Honeycomb properties of 2D model in ABAQUS ................. ........................20
3.1 Average Go for different core thickness with and without the initial crack data. The
Coefficient of Variation is given in parenthesis. ....._._._ ... ....... ..............24
3.2 Experimental investigated fracture toughness at room temperature and at cryogenic
temperature ................. ...............28.................
4.1 Comparison of fracture toughness between from experimental and from FEM
according to core thickness and temperature. ............. ...............38.....
4.2 Calculated parameters for bimaterial media by MATLAB coding. .........................39
4.3 Fracture toughness and phase angle. .............. ...............40....
B.1 Experimental data from sandwich composites with 0.25 inch core............._.._.. ......50
B.2 Experimental data from sandwich composites with 0.5 inch core ................... ........51
B.3 Experimental data from sandwich composites with 1.0 inch core ................... ........51
C.1 Experimental data from sandwich composites with 0.25 inch core ................... ......52
C.2 Experimental data from sandwich composites with 0.5 inch core ................... ........53
C.3 Experimental data from sandwich composites with 1.0 inch core ................... ........53
LIST OF FIGURES
2.1 Preparation of vacuum bag ................. ...............8......._._ ...
2.2 Preparation of vacuum bag before and after the vacuum bag is sealed. ................... .8
2.3 Autoclave before a cure cycle runs. ............. ...............9.....
2.4 Specimen preparation: (a) Specimen bonding with loading taps, (b) The painted
interface. .............. ...............9.....
2.5 Cross section view of cryogenic chamber. ....._._._ .... ... .__ ......._._.........1
2.6 Entire cryogenic test setup during dispensing of LN2. -------------- ....._.... ----------1 1
2.7 Double cantilever beam test (DCB) loading. ............. ...............12.....
2.8 Observation specimens with a microscope. ............. ...............13.....
2.9 Typical example of loading graph during mixed-mode DCB test at cryogenic
temperature. ....___................. ........___.........14
2.10 Specimen in liquid Nitrogen and whole facility during cryogenic tests. ........._......14
2.11 Specimen geometry and test setup of four point bending tests. ............. ..... ........._.17
2.12 In-situ cryogenic point bending test in liquid Nitrogen. ............. ....................19
2.13 2D model of test setup and specimen. ................. .....___... ........... ....1
3.1 Distribution of fracture toughness and average values with variation of core
thickness. .............. ...............25....
3.2 Distribution of fracture toughness and average values with variation of core
thickness excluding 1st crack propagation data of each specimen. ..........................25
3.3 Trend lines and all data of fracture toughness vs. crack length. ............. ................26
3.4 Slope of fracture toughness according to core thickness. ............. ....................27
3.5 Comparison of experimentally investigated fracture toughness at room
temperature and at cryogenic temperature. ............. ...............29.....
3.6 Notched four-point bending specimen with asymmetrical interfacial cracks..........30
3.7 Transverse crack made during 4-point bending tests. ............... ...................3
3.8 Example diagram of 4-point bending flexural test with center-cracked sandwich
specimen ................. ...............31......__ _.....
4.1 Crack displacement modes. .............. ...............34....
4.2 Schematic view illustrating the model loading and boundary conditions ........36
4.3 FE models of the sandwich specimen; (a) Plane (two-dimensional) solid model,
(b) Radial FE mesh in the vicinity of the crack tip. ................ .......................36
4.4 FE models of the sandwich specimen; (a) Three-dimensional model, (b) Plane
(two-dimensional) solid model............... ...............37.
4.5 Plot of fracture toughness between from experimental and from FEM according
to core thickness and temperature. ............. ...............39.....
4.6 Fracture toughness at room temperature and at cryogenic temperature according
to core thickness. ............. ...............41.....
4.7 Phase angle for mixed mode at room temperature and cryogenic temperature. ......41
D.1 Toray Composites cure cycle for composite laminates ................. ........_.._.. .....55
E. 1 Load-deflection graph for material property based on temperature and orientation56
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
MIXED-MODE INTERFACIAL FRACTURE TOUGHNESS OF SANDWICH
COMPOSITES AT CRYOGENIC TEMPERATURES
Chair: Bhavani V. Sankar
Major Department: Mechanical and Aerospace Engineering
The aim of this study is to understand the failure phenomena of sandwich
composites constructed from carbon fiber/epoxy composite face-sheets and Nomex
honeycomb core under cryogenic conditions. Both experimental testing and finite
element analysis are performed to understand the conditions under which face sheet
debonding occurs and propagates. One of the maj or obj ectives of this study is to measure
the critical energy release rate or fracture toughness of the face sheet/core interface,
which will be a strong function of mode-mixity and temperature. Furthermore, mode-
mixity itself will depend on geometric factors such as crack length, face sheet and core
thickness and material stiffness parameters.
Fracture tests similar to double cantilever beam tests are performed on sandwich
panels containing initial delaminations. The fracture toughness is measured for various
crack lengths. The loads at which crack propagation occurs are applied in the finite
element model of the panel to obtain the detailed stress field in the vicinity of the crack
tip. From the results of the fracture tests and finite element analyses, it is found that the
interfacial fracture toughness of the sandwich composites decreases significantly at
Honeycomb sandwich composites are found in a wide range of structural
applications due to their high strength and stiffness-to-weight ratio compared to other
systems. Current use of sandwich composites ranges from secondary structures in
commercial aircraft to primary structures in military aircraft, helicopters, and reusable
launch vehicles (RLV), e.g., Space Shuttle. One of applications of sandwich construction
is the liquid hydrogen tank of future RLV. Because of its low density and high stiffness,
sandwich construction is attractive for LH2 tanks. However, past tests have shown that
leakage of hydrogen through the composite face-sheets and subsequent debonding of the
face-sheets is one of the maj or concerns in using sandwich construction. This problem
can be eliminated by thorough understanding of the fracture mechanics of face sheets
under cryogenic conditions.
Delamination is a particularly serious damage mode for high-performance
laminated sandwich composites. The double cantilever test (DCB) has been used
frequently to characterize the delamination resistance of laminates, and the energy area
method has been used to perform experimental analyses. Finite element analyses (FE) are
performed complementarily to investigate the stress intensity factor (SIF), the energy
release rate (G) and the phase angle (TI) for mode-mixity in the vicinity of the crack-tip
The fracture mechanics analysis of a delamination between the core and the face
sheet is complicated by the fact that the crack-tip stress fields have the complex
oscillatory characteristics and bi-material fracture mechanics concepts have to be used.
Ducept et al. performed global, local and numerical methods to describe the failure
phenomena around the crack-tip and found that the local and numerical method values
were close to each other, while global method values were quite different.
Research has been conducted to predict the thermal effect on the stress intensity
factor, the energy release rate and the mode mixity at room temperature and also at
cryogenic temperature using several approaches. Grau  modeled sandwich composites
with pre-crack at the core/face-sheet interface at the edge of panels. Sandwich panels
with honeycomb cores were modeled as a double cantilever beam (DCB) wherein
orthotropic properties were used for the core of the commercial FE software ABAQUS
was used to build 2D and 3D models for various crack lengths of the sandwich
Cryogenic chamber and testing methods, created by Johnson, Melcher, and Pavlick
in the Mechanical Properties Research Lab at Georgia Institute of Technology, were used
to investigate tensile properties and fracture toughness.
Schutz  has provided a compilation of test data for several material systems. In
general, he showed that static properties such as tensile modulus, tensile strength and
compressive strength all increased as the test temperature was decreased from 300 K to
77 K. It was also found that thermal stresses had a large influence on failure behavior and
that the temperature dependent properties of the material system could be used to help to
explain the stress-strain response of laminated composites. For compression loading,
Gates et al. discovered that cryogenic temperatures produced an increase in both the
modulus and the strength of all the laminates. The greatest increase in compressive
strength occurred in the laminates with a 90-degree orientation. The greatest increase in
modulus occurred in the laminates with a 45-degree orientation.
Bitter  explained that normally provided honeycomb properties are the
compressive strength modulus in the T direction and the shear strengths and moduli in the
LT and WT directions. The properties not provided by company are seldom tested as they
are extremely minimal. In some finite element programs, the Poisson's ratio of the
material must be entered or the program will not run. Usually the honeycomb core
moduli are so much smaller than the facings that it does not matter what honeycomb
Poisson's ratio value is assumed. He advised to use a honeycomb Poisson's ratio of 0. 1 in
the FE program, then use 0.5 and see if there was any difference in the results. This
procedure would show the program sensitivity to the honeycomb Poisson's ratio.
The fracture toughness of the bond line was measured through the double
cantilever beam test by Ural et al. at room and low temperatures. In order to
investigate the effect of mode-mixity on Go values, they performed numerical
simulations. Those analyses showed that not only the mode-mixity was low, but also it
did not change significantly with crack length. For each crack growth step, the
corresponding energy release rate was calculated and these values were averaged to
obtain a single Go value. The experiment was complementary to the numerical work.
Thus tensile strength and fracture toughness of the face-sheets/core bond, measured by
the experiments, were used as parameters for simulation of the delamination and
propagation tests. As expected, low temperature tests resulted in decreased values of G,.
This shows that a decrease in temperature leads to a more critical state for the material
and the error involved in the calculation of Go depends on the measurement of the load,
P, and the crack length, a. They referred that possible error included in the measurement
of P is 0.5% of the load range.
Suo  derived the necessary equations and developed the fracture mechanics
concepts necessary for interfacial fracture mechanics of anisotropic solids. For bonded
orthotropic materials, a complex-variable representation is presented for a class of
degenerated orthotropic materials. The work came from both historical and recent
experiments and theoretical investigations of several research groups on fracture
behaviors of woods, composites, bicrystals and oriented polymers. To gain more insight,
Suo derived the necessary equations relating to orthotropic materials. This is shown in
Scope of the Thesis
The next-generation RLV will have an internal liquid-hydrogen fuel tank that not
only functions as a container for the fuel but must also perform as a load-carrying
structure during launch and flight operations. Presently, it appears that the replacement of
traditional metallic cryogenic fuel tanks with composite tanks may lead to significant
weight reduction and hence increased load-carrying capabilities.
The scope of the present research is to assess the thermal/mechanical phenomena of
sandwich composites at cryogenic temperatures, document the test methods, and provide
insight into the effects of temperature on mechanical performance. The selected test
methods include a range of crack lengths, core thicknesses, loads and temperatures which
could be experienced during the usage of cryogenic hydrogen tanks. It is expected that
the results of this study will be important in the development of future material
qualification methods and design verification.
SPECIMEN AND TEST SETUP
Sandwich specimens used in this study consist of Toray Composites unidirectional
carbon fiber prepreg as face-sheets and Euro Composites aramid fiber ECA type
honeycomb as the core material. Sandwich panels of size 10 in. x 10 in. were constructed
and specimens were machined from the panel for various tests. In order to obtain and test
specimens from the sandwich panels, several tasks have to be completed in the following
order: fabricating sandwich composites; machining out beams; attaching tabs to the
beams; and painting the interface region for the purpose of crack detection.
Typically, an adhesive layer is placed between the core and face-sheets during a co-
curing cycle to promote better adhesion. However, due to the properties of the prepreg
material (typically prepreg contains 40 % resin/adhesive) it is decided that a direct lay-up
of the prepreg onto the top of the honeycomb core will provide sufficient bonding
strength. This method has also been verified by Grau .
The next sequence includes laying the unidirectional fiber tapes within the face-
sheets. Several previous tests were performed to find the optimum specimen. It is
necessary to note that the lay-up should be symmetric when layering the unidirectional
prepreg. If the layering for face-sheets is not symmetric, residual stresses that will likely
result in warping of the sandwich panel will develop after curing . Teflon sheet
(PTFE) laid between the core and the face sheet will produce a delamination, as shown in
Vacuum bagging is used as the system for applying vacuum to the sandwich lay-up
during the cure cycle. The lay-up sequence is as follows: A 0.5 in, sheet of aluminum is
used as a base tool; a Non-porous Teflon film (PTFE) is placed above the tool to release
the sandwich after the cure cycle; an 8 ply [0/90]2S faCe Sheet is laid as the bottom side of
the sandwich; then a Nomex honeycomb core with a designated thickness of either 1 in.,
0.5 in. or 0.25 in. is placed on top of the bottom face-sheets; a strip of PTFE is used to
create the artificial crack between the core and the top face-sheets; then another 8 ply
face-sheet is used on top of the core/PTFE strip; a PTFE sheet is placed over top of the
sandwich; finally, a breather material is laid on top of the other components to allow for
adequate air evacuation during the vacuum process. A vacuum port is installed in the bag
material near the edge of the tool to ensure it does not affect the sandwich. Figure 2. 1
shows the schematic lay-up design without the vacuum port. Figure 2.2, shows an actual
lay-up before and after the vacuum bag is sealed. All of the material and its suppliers are
documented in Appendix D. It is necessary to note that the release film used is not porous
and therefore will not allow any excess epoxy to flow from the prepreg to the breather.
This lay-up design requires all of the epoxy to remain in the sandwich to ensure adequate
However, when this method is used to create the sandwich panels described in
Appendix D the pressure crushes the cores in the in-plane directions (L or W direction).
After further testing, the Toray cure cycle was modified with no pressure and with a
nominal vacuum of 23 psig. Using only a vacuum, a sandwich composite with sufficient
adhesion between the face-sheets and the core was created. It should be noted that further
experimentation was conducted to evaluate the newly tested material properties.
However, for all of the experimentation documented in this thesis, the cure cycle is used
with no autoclave pressure. Figure 2.3 shows the autoclave with a lay-up inserted before
the cure cycle has begun.
Figure 2. 1 Preparation of vacuum bag.
Figure 2.2 Preparation of vacuum bag before and after the vacuum bag is sealed.
Eight specimens were machined from each of the sandwich panels. The specimens
were cut from the panels using a water-cooled tile saw with a diamond-coated blade.
Honeycomb core sandwich materials are difficult to machine because of the heat and
debris generated by traditional machining. Slow cutting with the water-cooled tile saw
negated those problems. While parallel cutting can be made, the width varies from
specimen to specimen. Even though the width varies on each specimen, the overall width
did not vary in relation to the overall length. The average width of all specimens is
regarded as one inch.
Figure 2.3 Autoclave before a cure cycle runs.
After machining the specimen to its final dimensions (6.5 in. x 1.0 in.), aluminum
piano hinges are adhesively bonded to both sides of the sandwich composites as shown in
Figure 2.4. Piano hinges function as load introduction points for the specimen. One side
of the hinge is connected with a load-cell. Another part of the hinge is gripped by testing
Figure 2.4 Specimen preparation: (a) Specimen bonding with loading taps, (b) The
White paint (typing correction fluid) has been applied to the interfacial surface of
the specimen over the region where the crack is expected to grow. Using a fine tip pen,
points have been made at 1.0 inch along the interface region.
Cryogenic Environmental Chamber
For several types of in-situ cryogenic tests, four-point bending tests, and fracture
toughness tests, a facility for exposing the specimens to LN2 had not previously existed at
the Center for Advanced Composites (CAC) of University of Florida. The CAC has only
a cryogenic chamber, EC-12, which is not suitable for in-situ cryogenic tests. With the
courtesy of Dr. W. S. Johnson in MPRL at the Georgia Institute of Technology, and Dr.
Ihas, Professor of Physics at the University of Florida, a cryogenic environmental
chamber, consisting of a double-walled structure, was fabricated. The chamber consists
of two different-sized buckets and the expanding foam of DOW which functions as an
insulation material between the two buckets. The base has a hole to allow a pull-rod to
pass through for both 4-point bending and fracture toughness tests. A silicon-stopper was
installed into a hole to prevent LN2 fTOm leaking out from it. Upon testing with LN2 and
consulting with the lab technician in the UF Physics department's Cryogenic Lab, plastic
bags were used as an additional sealing precaution, because of their high tear resistance
and high puncture resistance. The perfectly insulated LN2 Storage in the CAC is not
equipped for recycling, therefore the used LN2 Should be vaporized after every test has
been completed. The cryogenic chamber at the CAC is shown in Figures 2.5 and 2.6.
Figure 2.6 depicts the entire test setup for in-situ cryogenic test environment. The
liquid nitrogen tank has a steel hose to dispense it into chamber. For safety purposes
personal equipment, such as leather gloves, face shields, and aprons, should be used
carefully once the in-situ cryogenic tests are being performed.
Cross-section view of Cryogenic chambers
Pl ~stic bag
Load cell o
O O- adihba
Otelo O tDe
Figure 2.5 Cross section view of cryogenic chamber.
Figure 2.6 Entire cryogenic test setup during dispensing of LN2.
In order to calculate the fracture toughness of the interface, an accurate
experimental technique must be used. Various experimental configurations have been
reviewed that include tests for a double cantilever beam (DCB) and for four point
bending. After some consideration, the DCB test was chosen for determining the
interfacial fracture toughness of the sandwich composite, due to the ease of the test and
its relative high accuracy. Experimental procedures presented in this thesis utilize a
double cantilever beam comprised of layered carbon fiber composite face sheets bonded
to a Nomex" honeycomb core.
In principle the DCB test is quite simple. A specimen is prepared with an initial
crack of length a within the interface, where the fracture toughness is of interest. The
specimen is then placed in a loading test fixture created specifically for the DCB test.
Loading of the specimen occurs such that the surfaces lying on the interface are separated
as shown in Figure 2.7.
Fiur 27 oulecatievr ea tst(DB)lodig
Th rcur et er aredoti 1,0-b MIts mcieuin 00
lb odcl.Tw in igs r tahdt the pl-ro ftecosed let
were conducted in displacement control with a crosshead loading rate of 0.05 in./min.
Force and displacement were recorded using a data-acquisition card installed in the
computer throughout the loading and unloading of each test. By an optical microscope
(see Figure 2.8), the whole sequence and the phenomena of crack propagation was
observed and controlled manually.
Figure 2.8 Observation specimens with a microscope.
First, the initial crack was recorded at the beginning of testing. The movement of
the MTI crosshead was controlled and monitored along the crack propagation. The
specimen was loaded with a specific loading rate until the crack reached the 1.0 inch
mark or the force dropped suddenly, as shown in Figure 2.9.
Once the new crack-tip length was checked and recorded, the direction of the
crosshead was reversed and the related data was recorded. Next, to investigate the effect
of cryogenic temperatures on the fracture toughness of sandwich composites, the DCB
test was performed in liquid nitrogen at 77K. Because the specimen is submerged in a
plastic insulated vessel at an extremely low temperature (as shown in Figure 2. 10) it is
impossible to monitor crack propagation.
RMMD 0.25 3
- cycle 1 -cycle 2 cycle 3 -cycle 4
1 1.5 2
2.5 3 3.5 4
Figure 2.9 Typical example of loading graph during mixed-mode DCB test at cryogenic
Figure 2.10 Specimen in liquid Nitrogen and whole facility during cryogenic tests.
The deflection of the specimen was used as a guide to determine the point of
unloading. After the deflection reached a certain value, the specimen was unloaded, as it
was in room temperature tests. Then, the crack propagation length was measured by the
same microscope after it was taken out of liquid Nitrogen.
Specimen Property Test
Carbon Fiber Face Sheet
As previously described, the curing method used for specimen preparation differs
from the methods provided by Toray composites, (as provided in Appendix D.) Hence it
is expected that the material properties would have been altered. The mechanical
properties of the composite prepreg as reported by its manufacturer, Toray composites,
Inc., are shown in Table 2.1. The material properties used in the present study are
calculated by the methods that follow.
Table 2. 1 Mechanical properties of composite prepreg provide by company
Elastic modulus at laminar direction (El) 23.5 Msi
Elastic modulus at transverse direction (E2) 1.1 Msi
Shear modulus (G12) 0.64 Msi
Poisson's ratio (v12) 0.34
Four-Point Bending Test at Room Temperature
There are several methods available for measuring the material properties of
composite laminate. Three-point bending, four-point bending, tension, and compression
tests are suitable for composite materials. In the present study, we chose the 4-Point
Bending Test for measuring the elastic properties of composite laminates. It was thought
that the four-point bending test would yield more accurate and repeatable results than the
three-point bending test. Additionally, there would be no shear transverse shear force at
the deflection of the mid-point. A small offset of the loading point, with respect to the
whole setup, would not significantly affect the results.
The specimen dimensions are depicted in Figure 2. 12. The stacking sequence of the
specimen was [0/90]2S. The thickness of the laminate is 0.048 inch; and the width is about
1.0 inch, which has very small tolerance. Four different elastic properties (El, E2, G12,
v12) must be calculated to be used in FE analysis, therefore three-orientation specimens
have been performed in the same test setup. The specimen with 0-degree orientation is
for El, 90-degree is for E2, and 45-degree is for G12. Poisson's ratio is assumed to be
unchanged with respect to temperatures. The tests are conducted under displacement
control in a material testing machine at the rate of 0.05 in. /min. Load-deflection
diagrams and test results are shown in Appendix E.
The elastic properties were calculated from the transformed lamina stiffness using
the following formula :
Ex = (2, 1)
c1 _, 2v, 1 :22+1
E1 E, G2E2
where Ex is the transformed lamina stiffness with x degree determined by following the
beam deflection theory:
3max = (3L2 4a2) (2,2)
where P, 3max, respectively, is the load and the maximum deflection of the center, L is the
total span, and loading point, a, is the distance from support. The inertia of moment (1 is
calculated from geometry. To get specific deflections, all tests have been stopped when
the mid-point of the specimen reached 0.45 inches from the initial position.
Fiue21 peie emty n etstp ffu on bnigtss
Table 4 2. netgtdmaeilpoete o etdcmoie aiae tro
Elasti mdlsala i rdireto E)2. s
Elastic mouu t rnvrs ietin (2 11 s
ForPintBndn es tCroeiTmertr
CTguE Th saeme goer n test setup asro tmeaur et wasr oindut end to otai h mtra
prpetesatcyoenctem perature s;te a ple nF aayisoni hpe
4.si ouu tlmnr ieto E)2. s
Also an in-situ cryogenic 4-point bending test was performed with the same test
setup in a cryogenic chamber as described earlier in this chapter. The isothermal
cryogenic test conditions at 77K were achieved by immersing the test specimen and
loading the introduction apparatus into liquid nitrogen. In order to reach thermal
equilibrium, the specimen stayed immersed in a constant level of the liquid Nitrogen for
at least 30 minutes prior to mechanical loading.
The effects of cryogenic temperature on the modulus were found by examining the
results from a specimen subj ected to thermal condition. The s laminate (El)
experienced a slight (12%) increment in modulus at cryogenic temperatures. Similarly,
the 8 laminate for calculation of the shear modulus increased as the temperature
decreased. In particular, the shear modulus increased by as much as 140% when tested at
77K. The transverse modulus (E2) Showed a slight incline at cryogenic temperatures,
while the transverse modulus went up by approximately 65%, when the temperature was
reduced to 77K. Lastly, Poisson's ratio was assumed to be unaffected with respect to
thermal conditions. Load-deflection graphs related to cryogenic temperatures are
presented with room-temperature test results in Appendix E.
Table 2.3 Investigated material properties of tested composite laminates at cryogenic
Elastic modulus at laminar direction (El) 23.4 Msi
Elastic modulus at transverse direction (E2) 1.92 Msi
Shear modulus (G12) 2.71 Msi
Poisson's ratio (v12) 0.34
Figure 2.12 In-situ cryogenic point bending test in liquid Nitrogen.
Loading rate = 0.05 in / min
Increment r: Step Tunae = 1.ODO
Deformed Var: U Deformation Scale Factor: +1.481e+0DI
Figure 2.13 2D model of test setup and specimen.
At the same time, material properties from experimental analysis were verified
through FE analysis. The commercial FE program, ABAQUS is used to make a 2D solid
model of the test setup and specimen. After running a program with material properties in
Table 2.2 and 2.3, the mid-point deflection of the specimen showed very good agreement
with the experimental results.
Honeycomb Core Material
For honeycomb material property, mechanical properties are generally determined
the following: peak and crush compressive strength, crush compressive modulus, L and
W plate shear strengths and moduli. For energy absorption applications the crush strength
is needed, which is approximately 50% of the bare compressive strength. All of the
honeycomb manufacturers provide brochures containing their core product's properties.
It is assumed that the material properties of honeycomb could be the same at both room
and cryogenic temperatures.
The Poisson' s ratio of a material is the ratio of the lateral strain to the axial strain
where the strains are caused by uni-axial stress only. Generally it is in the range of 0. 15
to 0.35. In extreme cases, values as low as 0.1 (concrete) and as high as 0.5 (rubber)
occur. The latter value is the largest possible.
Table 2.4 Honeycomb properties of 2D model in ABAQUS
Elastic modulus at L direction 1000 psi
at T direction 30000 psi
Shear modulus at LT direction 10000 psi
at LW direction 100 psi
at WT direction 5000psi
Poisson's ratio 0.1
For normal materials a tension or compression test is conducted measuring the
lateral and axial deformations. In addition the Poisson's ratio is calculated. This does not
work for honeycomb. If the honeycomb core is compressed, the cell walls can buckle
inward or outward. Also, one side can go in and the other out. In some FE programs the
Poisson' s ratio of material must be entered or the program will not run. Usually the
honeycomb core moduli are so much smaller than the facings that it does not matter what
honeycomb Poisson's ratio value is assumed. The core just moves with the facings,
offering almost no resistance. The in-plane honeycomb properties are almost zero and
would offer little resistance. Perhaps the best method is to use a honeycomb Poisson's
ratio of 0. 1 in the FE program, then use 0.5 and see if there is any difference in the
results. This will show the program sensitivity to the honeycomb Poisson's ratio.
Summary and Conclusion
With three different orientations at room temperatures and cryogenic temperatures,
six composite laminate specimens have been examined to evaluate elastic modulus. The
cryogenic chamber is created for tests at 77K. The research related to the thermal
dependent properties is not available from the manufacturers so the specimens must be
tested to determine property variations with respect to temperature. In a four-point
bending test, as temperature is reduced, the modulus of all the laminates increased. The
notable increase in elastic property occurs in the G12-
FRACTURE TOUGHNESS TEST
Double Cantilever Beam (DCB) Tests
Most of the important interface fracture problems involve combinations of normal
and shear forces along the crack, such that "Mixed Mode" conditions prevail. Now for
clarification and completeness it is necessary to understand the differences in loading
modes and how they are defined. There are three loading modes in fracture mechanics;
Mode I, Mode II and Mode III. Mode I is dominated by opening load, Mode II is
dominated by in-plane shearing load, and Mode III is done by out-of-plane load.
Mixed mode conditions are possible when two or more loading conditions are
present. Generally, in any bulk material, a crack will propagate in the direction that
minimizes the mode component of loading. However, in constrained or interfacial
loading, the crack can propagate such that the mode I and mode II components are both
significant. Mixed mode conditions are quantified by a mode mixity phase angle yr,
which is 00 for pure mode I and 900 for pure mode II. Understanding the mode mixity of
a loading condition is important because of its effects on crack propagation.
r=- ta K, (3.1)
Fracture at interfaces between dissimilar materials is a critical phenomenon in
many systems, ranging from composites to microelectronic devices. However, both the
fundamental mechanics of this process and experimental techniques capable of
systemically characterizing such fracture are incompletely developed. The principal
intent of the present paper concerns the development of a test procedure for purpose of
systematic measurement of the interface fracture resistance.
It should be noted that the DCB test is usually performed in mode I fracture studies
but experiments on asymmetric DCB specimens should provide the same data as other
mixed mode tests. This study is performed by using asymmetric DCB loading, with
three-core thicknesses at room and cryogenic temperatures. The recorded data and
calculated values are listed in Appendix B and C. However, it is not possible to calculate
the phase angle for mixed mode conditions with this data, because the experimental data
represents the global behavior. A detailed FE analysis is required in order to understand
the local crack tip stress behavior and hence to determine the mode mixity.
DCB Tests at Room Temperature
The energy release rate was calculated from the experimental data. The load and
displacement values were obtained during the fracture test. The energy released for a
given extension is the area under the load-displacement curve. Examples of the areas
used for unsteady and steady crack growth are shown in Figure 2.9. The area is calculated
under each loading-unloading cycle.
The area of the graph, AE, corresponds to the energy-released as the crack grows.
The critical energy release rate or fracture toughness (G,), was obtained using
G _=- (3 .2)
In this expression, AE is the area calculated from the trapezoid rule, Aa is the crack
extension noted during the test, and b is the width of the specimen. The value calculated
is the average energy released for the crack extension, Aa. The procedure was repeated
for each loading/unloading cycle or between indicated critical load values. Hence, several
values were obtained from a single test specimen. The method was repeated for
specimens of various thicknesses.
Average Go values were calculated using Equation 3.2, disregarding the first few
cells of crack propagation where the non-porous Teflon is put in the sandwich composites
to make pre-existing cracks. When fabricating the test specimens the initial crack tip will
likely look and behave differently compared to subsequent cracks created by the natural
crack propagation. It should be noted that, when making an artificial crack, the radius of
the crack tip will be finite depending on the thickness of the material used to prohibit
bonding of the crack surfaces. Therefore, how the crack was formed affects the state of
stress and the fracture toughness. We anticipated disagreement in the results from the first
crack propagation when compared to those of subsequent crack propagation. Due to the
effect of cells on the first crack of the specimen, Figure 3.1 and Figure 3.2 show the
difference of average G,. The average of Go is given in Table 3.1.
Table 3.1 Average Go for different core thickness with and without the initial crack data.
The Coefficient of Variation is given in parenthesis.
Core Thickness (inch) 0.25 0.5 1.0
Average (lb./in.) w/ 1st crack data 2.93 (22.3%) 2.04 (38.7%) 1.64 (39.9%)
Average (lb./in.) w/o 1st crack data 3.27 (11.8 %) 2.3 (21.1 %) 1.49 (44.3 %)
The effect of including and excluding the data from initial crack propagation is
shown in Fig. 3.1.
Distibution of Gc
* 0.25 inch 0.5 inch a
1.0 inch -*-avg 0.25 inch -m-avg 0.5 inch -a-avg 1.0 inch
Figure 3.1 Distribution of fracture toughness and average values with variation of core
Distibution of Gc (except 1st crack)
* 0.25 inch m 0.5 inch a
1.0 inch -*avg 0.25 inch -m-avg 0.5 inch -aavg 1.0 inch
Figure 3.2 Distribution of fracture toughness and average values with variation of core
thickness excluding 1st crack propagation data of each specimen.
The experimental data were analyzed to understand the effects of core thickness
and crack length (R-Curve effect) on the fracture toughness. Figure 3.3 shows that the
variation of fracture toughness as a function of crack length for different core thicknesses.
A linear fit was used to curve-fit the data.
Frac Toughness vs. crack length
0.25 in n 0.5 in r 1.0 in
-Linear (0.25 in) Linear (0.5 in) Linear (1.0 in)
y =0.027x + 3.1764 +
** y = Of896x +1.3356
8 y = 0.0186x + 1.5898
1 .5 2.5 3.5 4.5 5.5
Figure 3.3 Trend lines and all data of fracture toughness vs. crack length.
A statistical analysis was conducted on the experimental data to calculate the
average G,. Initially all data of the specimens were plotted separately and compared to
consider a general trend of core thickness affecting fracture toughness. Figure 3.4
illustrates the trend of fracture toughness vs. core thickness from experimental data,
excluding the first crack data of the specimen. Good consistency is shown in a decreasing
fracture toughness Go vs. an increasing core thickness, when reviewing the data having
core thickness 0.25 in, 0.5 in and 1.0 in.
Therefore, it is logical to say that, even though there is a slight discrepancy within
data, core thickness for honeycomb sandwich composites indeed affects the critical
fracture toughness at an inversely proportional rate.
DCB Tests at Cryogenic Temperature
The aim of this study is to understand the failure phenomena of the sandwich
composites under cryogenic conditions.
Fractu re Toug henss vs. core Thickness
-owl 1st -a-w/o 1st
0 0.2 0.4 0.6 0.8 1 1 .2
Core thickness (in.)
Figure 3.4 Slope of fracture toughness according to core thickness.
To investigate the effect of cryogenic temperatures on the fracture toughness of
sandwich composites, the DCB tests described in Chapter 2 were performed in liquid
Nitrogen at 77K. It is not possible to see the crack propagation in cryogenic tests because
the specimen is immersed in liquid nitrogen in an insulated vessel. Hence, the deflection
of the specimen is used as a guide to determine the point of unloading. After the opening
displacement reaches a certain value, the specimen is unloaded as in room temperature
tests. In manufacturing the specimen, a cryogenic adhesive is used to bond the loading
tabs to the face-sheets. During tests, M/S Epoxy 907 was first used to bond the face
sheets and tabs, but proved that general adhesive is not useful at cryogenic temperatures.
Therefore a special cryogenic adhesive was applied to tests at cryogenic temperatures.
Except bonding, most test setups and procedures were the same as at room
temperature. The same equation was applied to get the energy release rate at cryogenic
temperatures with test data excluding the first crack data. Cryogenic test data is listed in
Appendix C, and the calculated fracture toughness G,, based on three-different
thicknesses, are shown in Figure 3.4, with those at room temperature. Figure 3.5 shows
the degree to which fracture toughness dropped at cryogenic temperatures, compared to
Table 3.2 Experimental investigated fracture toughness at room temperature and at
Temperature Room Cryogenic
Thickness 0.25 0.5 1.0 0.25 0.5 1.0
Experimental Go 3.27 2.3 1.49 1.69 1.19 0.91
As shown in Figure 3.5, the fracture toughness drops by approximately 40 % at
cryogenic temperature and the fracture toughness decreases with increasing core
thickness as in the case of room temperature tests.
Four-Point Bending Tests
Most of the important interface fracture problems involve combinations of normal
and shear forces along the crack, such that "Mixed Mode" conditions prevail. As will be
seen later the DCB tests yield conditions where in the mode mixity ranges from 10 deg.
to 25 deg. In order to obtain fracture toughness at larger angles, e.g., 50-60 deg. range, a
different specimen is needed. An appropriate specimen is depicted in Figure 3.6,
consisting of a notched, bimaterial flexural beam. It will be demonstrated that this
specimen provides fracture results for conditions of approximately equal normal and
shear forces in the interface crack far from the tip.
Comparison of Fracture Toughness
-o-Room Temp. -m-Cryogenic Temp.
0 0.25 0.5 0.75 1 1.25
Figure 3.5 Comparison of experimentally investigated fracture toughness at room
temperature and at cryogenic temperature.
Consequently, when used in conjunction with other specimens, fracture resistance
data can be obtained for a range of mixed mode conditions.
Charalambides et al.  evaluated the utility of the flexural specimen in Figure
3.6 for determining the interfacial fracture toughness of aluminum/PMMA bi-material
specimens. Specifically, laminates of these materials have been bonded with an initial
interface crack created by placing a small piece of non-porous Teflon along the interface,
at the center of specimen prior to bonding. The interfacial crack propagations from the
initial crack on loading are averted by causing controlled extension of the crack prior to
testing. Crack lengths monitored from the displacement movement of MTI are
independently checked by means of direct optical observations of the front crack.
Figure 3.6 Notched four-point bending specimen with asymmetrical interfacial cracks.
In this research, the same method was tried to estimate the interfacial fracture
toughness of honeycomb core sandwich specimens. Four-point bending tests for fracture
toughness have generated a greater phase angle than in asymmetric DCB tests . By
considering this bending test and DCB test at the same time, the fracture toughness of
asymmetric bimaterial sandwich systems can be investigated for a wide range of mode-
However, the shear strength of the honeycomb material is much less than the
interfacial bond strength. Hence before the crack could propagate the core fails as shown
in Figure 3.7. In Figure 3.8, it is very difficult to check which point is the critical load at
the beginning of the crack-tip because there is no sudden load drop in the diagram. Hence
it is concluded that the aforementioned specimen is not suitable for sandwich specimens
with a highly flexible and weak core material.
0 0.1 0.2 0.3 0.4 0.5 0.6
Figure 3.8 Example diagram of 4-point bending flexural test with center-cracked
Figure 3.7 Transverse crack made during 4-point bending tests.
Load -Deflection diagram
Summary and Conclusion
Sandwich composites of carbon/face-sheets and honeycomb cores were tested to
estimate their fracture toughness at room temperature and at 77K in liquid Nitrogen
(cryogenic temperature). A specialized fixture and test procedure were developed for
testing at cryogenic conditions. The resulting load-deflection diagrams were used to
estimate the interfacial fracture toughness using the area method. First, an asymmetric
specimen was tested at two different temperatures: room temperature and cryogenic
temperature with three different core thicknesses. It is shown that fracture toughness
drops significantly at cryogenic temperatures. This should be a factor in using the
sandwich composite system in liquid Hydrogen tanks.
Moreover, as a core thickness gets thinner, fracture toughness increases. So, in
sandwich systems, core thickness could be considered as one significant factor
dominating fracture toughness.
On the other hand, even though four-point bending tests were performed with the
same sandwich composites, this did not produce any valid results. Due to the low
stiffness and strength of the honeycomb core, the transverse crack occurred in the
specimen. Therefore the four-point test method is not suitable for such specimens.
However, it was anticipated that the four-point bending test would yield a higher range of
fracture toughness and mode-mixity.
In the next chapter the FE model used to estimate the mode-mixity in the test
specimens are described. The purpose of the FE analysis is that the fracture toughness
can be correlated with mode-mixity rather than core thickness.
FINITE ELEMENT ANALYSIS
In structures, damages may be detected by using a number of sophisticated
techniques or by viewing visible deformation. Damage in composite structures is rarely
visible, and non-destructive evaluation often does not detect certain forms of damage.
These undetected cracks can result in the failure of the component, incurring loss of
human life, damage to machinery, or reduced equipment life. The study of the initiation
and growth of cracks is termed "fracture mechanics".
Laminated composites are susceptible to flaws that develop in the interface region
between laminated plies . Such flaws are referred to as delaminationn" and can
develop from a host of root causes that range from manufacturing defects to low-energy
impact. Delaminations of this type lead to degradation in the load carrying ability of the
structure and under certain conditions can lead to catastrophic failure of a structural
component. Composite sandwich structures can fail in much the same way. It is common
for flaws to develop at the interface of the face-sheet and the core. In sandwich materials
with an open-celled core, such as a honeycomb core, this happens in the adhesive layer,
and the skins can peel away from the core. This is termed interfaciall failure" and stems
from the interfacial crack.
When a crack is present in a load bearing structure, there are three-modes of
fracture that may occur simultaneously. They are: opening mode (Mode-I), sliding or in-
plane shearing mode (Mode-II), and tearing or out-of-plane shearing mode (Mode-III),
(shown in Figure 4. 1). In general, all three modes exist for a flaw in a structure subj ected
to complex loading. However, in some instances, Mode-I, Mode-II or Mode-III,
combinations of two modes may exist. In this study time-dependent behavior (fatigue)
and Mode-III are not considered.
Monde IE Aode II MIode III
Openling Sliding Tearinlg
Figure 4.1 Crack displacement modes.
In the preceding discussion , analytical expressions are shown that can be used
to evaluate fracture toughness in sandwich composites. These analytical expressions are
useful because they show a methodology that can be used to evaluate the fracture of more
complex configurations. Unfortunately, exact analytical expressions do not exist for all
crack configurations. Numerical techniques must be used to evaluate the fracture
parameters for these configurations. The most common numerical method used to
evaluate structures is FE modeling. Several techniques to evaluate the crack tip stress
fields in cracked solids have been developed based on FE analysis. Methods exist for the
evaluation of fracture parameters using forces and displacements obtained from a FE
analysis. As noted previously, to predict fracture toughness, a critical value of the stress
intensity factor (SIF) must be known. This is compared to the local state of stress in a
cracked solid. Fracture occurs when the local value reaches the critical value. Critical
values of fracture toughness or the stress intensity factor are developed from fracture
testing. Hence, in order to evaluate fracture toughness in the sandwich material, a
computational model must be developed for the cracked material. Both the stress
intensity factor (SIF) and the phase angle (qi) can be determined from these models.
Typical elastic moduli of face-sheets and core material are investigated as
described in Chapter 2, and assumed for the transversely isotropic layer. For the present
analysis, FE models are constructed with the commercial code ABAQUS using 2D 4-
node bilinear, reduced integration with hourglass control. The FE models are designed
using the experimental setup as a base. The face-sheets are separated into individual
layers of 0 and 90 degrees with the properties given in Chapter 2. Three core-thickness
models, 0.25, 0.5 and 1.0 inch, are created for determining the mode mixity. Figure 4.1
represents schematically the 3D model loading and boundary conditions: lower edge
displacements in the x and z directions are restricted, z-direction displacement is applied
to the upper edge, i.e. u=0 [l l]. Figure 4.2 shows a typical FE mesh including a zoom-in
view of the vicinity of the crack tip zone. For high accuracy, the area of 0.012 inch x
0.012 inch around the crack tip is represented by 1600 elements with radial mesh. Away
from the crack tip, bigger elements have been made to avoid excessive computational
cost. Crack length and applied load can be determined from experimental data for use in
(u= C, w= 0~)
Figure 4.2 Schematic view illustrating the model loading and boundary conditions [l l].
Figure 4.3 FE models of the sandwich specimen; (a) Plane (two-dimensional) solid
model, (b) Radial FE mesh in the vicinity of the crack tip.
Therefore, it is decided that the experimental critical load can be used in the model
and the crack length should be checked to match deflections from experimental tests and
FE modeling. The critical load as related to deflection value, the experimental fracture
toughness (G,) and the average of the Go value for given core thicknesses of the modeled
specimens are given in Appendices B and C.
Moreover, to verify the validation of this two-dimensional model, three-
dimensional analysis has been executed simultaneously. The same critical load was
applied in both models and then the deflection in the out-of plane direction at the end of
the specimen is compared. Both deflections were found to be nearly the same; therefore
the 2D model in this paper is proven to be valid, and will be used in subsequent analyses.
Figue 44 FEmodls o th sanwic speime; (a Thee-dmeniona moel, b) lan
Figue 4.(tw odl t snwc pcm; a he-dimensional) oi model. b ln
The FEM (finite element modeling) in this paper is performed by applying loads
as measured experimentally and then comparing resulting crack lengths and fracture
toughnesses. Numerical results are listed in Appendix B and C. Material properties are
shown Tables in Chapter 2.
ABAQUS has the specific command for fracture toughness, "CONTOUR
INTEGRAL", which can yield the J-Integral value in the data, which is equal to the
energy release rate in a linear elastic body. In this analysis, J-Integral from FEM can be
considered as fracture toughness (G,) when the experimental fracture load is applied. The
comparison of values is given in Table 4. 1, and shown in Figure 4.3.
Table 4. 1 Comparison of fracture toughness between from experimental and from FEM
according to core thickness and temperature.
Thickness Experimental Go FEM J-Integral
0.25 3.27 3.3
0.5 2.3 2.13
1.0 1.49 1.45
0.25 1.69 1.81
0.5 1.19 1.2
1.0 0.91 0.98
As provided in Table 4.1, the difference between FE analysis and experimental
results is less than 10 % for both room temperatures and cryogenic temperatures. J-
Integral also dropped significantly, by about 50%, at cryogenic temperature, as much as
fracture toughness did at the same thermal condition.
Next, investigation of phase angle for mixed mode and fracture toughness of
sandwich composites, which is considered as a bimaterial system, was performed. For
this analysis, the stress intensity factor for mode I and mode II is calculated from the
results of the FE solution.
F ractu re To ugIh ness vs. Co re Th ic kness
SExp Gc_Room -cFEM J_Room t-Exp Gc_Cryo ~t FEM J_Cryo
0 0.25 0.5 0.75 1 1.25
Core Thickness (in.)
Figure 4.5 Plot of fracture toughness between from experimental and from FEM
according to core thickness and temperature.
Calculations of fracture toughness and the stress intensity factor in dissimilar
anisotropic media were discussed by Suo , and the results are provided in the
Appendix. First, the bimaterial parameters, e, 3 and a are calculated at room and
cryogenic temperatures, using MATLAB. The values are shown in Table 4.2. Equation
(A. 13) is used to obtain Hy; and Hzz and values of normal stress and shear stress in the
vicinity of the crack tip can be obtained from the output data of the 2D FE model
solution. Thus fracture toughness of sandwich composites can be obtained from Equation
(A. 14) which is rearranging Equation (A. 11), (A. 12) and (A. 13).
Table 4.2 Calculated parameters for bimaterial media by MATLAB coding.
Temperature Hy; Hzz B E
Room 0.0011 1.98e-4 0.1781 -0.0573
Cryogenic 0.0011 1.9765e-4 0.1784 -0.0574
With parameters in Table 4.2 and local stresses from ABAQUS, the energy release
rate and stress intensity factors are calculated using Equation (A. 13) and (A. 14).
Consequently, the phase angle for mode-mixity can be known from Equation (A. 15). The
calculated results are listed in Table 4.3.
Table 4.3 Fracture toughness and phase angle.
Temp. Thickness Exp. Go FEM J Integral Gaby Suo Phase Angle
0.25 3.27 3.3 3.6 14
0.5 2.3 2.13 2.11 18.7
1.0 1.49 1.45 1.46 18.1
0.25 1.69 1.81 1.9 13.9
0.5 1.19 1.2 1.17 19.1
1.0 0.91 0.98 0.95 19.2
Figure 4.4 shows the consistency of fracture toughness reduction as the core
thickness increases and also at cryogenic temperatures. For each case, in both in
experimental results and the FE results, the Go values decrease by the same portion. Good
agreement is shown among three methods to calculate fracture toughnesses: the
experimental area method, the J-Integral by ABAQUS and Suo's equation considering
Fracture toughnesses at cryogenic and room temperatures have been investigated
using three methods. Those values at cryogenic temperature are smaller than those at
room temperature by approximately 40 %. When core thickness increases, fracture
F ractu re Toug hness vs. Core Th ickness
~-A-Exp Gc_Room -- --- FE M J_R oom -- -*- -- Gc by Suo_ Room
SExp Gc _C ryo -- --- FEM J_C ryo -~-*-- Gc by Suo_C ryo
0 0.25 0.5 0.75 1 1.25
Core Thickness (in.)
Figure 4.6 Fracture toughness at room temperature and at cryogenic temperature
according to core thickness.
The mode-mixity values summarized in Table 4.3 also vary according to core
thickness and temperature decline. Assuming that the phase angle of a sandwich
composite with a 0-inch core thickness is close to zero, and then all phase angles for
mode-mixity are shown in Figure 4.7.
Phase angle vs. Core Thickness
-*-Phase angle_Room -m-Phase angle_Cryo
O 0.2 0.4 0.6 0.8 1 1.2
Core Thickness (in.)
Figure 4.7 Phase angle for mixed mode at room temperature and cryogenic temperature.
Consequently the values of the phase angle are within the range, O < yr < 20. As core
thickness increases, the phase angle also increases. Since the test setup is a modification
of DCB (an usual test method for Mode I), the range of the phase angle is in the lower
degree values, less than 20 degrees.
Summary and Conclusion
ABAQUS has been used to obtain the J-integral values directly from the data file.
The stress intensity factor was calculated in order to be able to evaluate the fracture
toughness and mode-mixity. FEM analysis has very good agreement with the
experimental data, within less than 10 percent difference. The equations for a bimaterial
system are used to do this analysis.
However, even though temperature has been assumed to affect the mode-mixity of
sandwich composites, which seemed to be a factor of fracture toughness, it did not
produce significant difference. More investigation should be executed to prove the
relationship between mode-mixity and fracture toughness.
Fracture toughness tests, similar to DCB tests, are performed on sandwich panels
containing initial delaminations. The fracture toughness is measured for various crack
lengths. The loads at which crack propagation occurs are applied in the FE model of the
panel to obtain the detailed stress Hield in the vicinity of the crack-tip.
With three different thicknesses both room temperatures and cryogenic
temperatures, six composite laminate specimens have been examined to evaluate elastic
modulus. The cryogenic chamber was created for tests at 77K. Since the company
manufacturing prepreg does not supply temperature dependent property data, the
specimens must be examined to discover the change in material properties with respect to
a significant drop in temperature. In a four-point bending test, as cryogenic temperatures
reduced, modulus increased in all the laminates. The greatest increase in elastic property
occurred in the G12-
Sandwich composites of carbon/face-sheets and honeycomb core, were tested in
critical loads and fracture toughnesses, at room temperature and at 77K in liquid Nitrogen
(cryogenic temperature). A specialized alignment Eixture and test procedure was
developed for the cryogenic condition testing. First of all, an asymmetric specimen was
tested at two different temperatures (room and cryogenic temperatures), with three
different core thicknesses. Experimental test results were converted to fracture toughness
using the energy-area method. It showed that fracture toughness drops significantly at
cryogenic temperatures. This should be a factor in using the sandwich composite system
in liquid Hydrogen tanks.
Moreover, as a core thickness gets thinner, fracture toughness increases. So, in
sandwich systems, core thickness can be considered as one important factor dominating
Four-point bending tests were performed using the same sandwich composites in
order to determine the fracture toughness at large mode-mixity angles. However, no valid
results were produced. Due to the low stiffness and strength of the honeycomb core,
transverse crack occurs in the specimen. So Equation 3.2 would not be valid for this test..
As expected, low temperature tests resulted in decreased values of Gc. This shows
that the decrease in temperature leads to a more critical state for the material. Specimens
showed sudden jumps during crack growth more frequently at cryogenic temperature
than at room temperature.
In the FE model, the experimental critical loads were applied and the stress field in
the vicinity of the crack tip was investigated. The FE analysis showed the degradation of
fracture toughness resulting from cryogenic conditions.
ABAQUS was used to obtain J-integral values directly from the data. It also
yielded the stress intensity factors that can be used to calculate the fracture toughness and
mode-mixity. Fracture toughness of FEM analysis concurs closely with the experimental
results within less than 10 percent difference. The equations by Suo for a bimaterial
system were used to perform the analysis. It is expected that the results of this study will
be important in the development of future material qualification methods and design of
sandwich structures for cryogenic applications.
Suggestion for Future Work
1. One of the assumptions made was to consider a honeycomb core as a material in
FEM analysis. However, honeycomb is not a material, but a structure from the micro-
structural point of view. Future research should be carried out in consideration of
honeycomb material as a structure, which consists of a wall structure and bonding
material. This research could reduce the error of analysis in investigation of fracture
mechanics with sandwich composites.
2. Another suggestion is to make a sandwich specimen using more layers of face-
sheets. In this thesis, eight-layer laminates were used as face-sheets; so the difference in
the variation of core thickness and temperature is changed slightly more than what is
expected. If more lay-ups are used to make sandwich composites, it will be easier to
check and compare analyses.
3. In order to determine the effect of larger values of mode-mixity on fracture
toughness new test methods have to be developed such that the core does not tear before
crack propagation. On the other hand tough core materials such as foam and balsa wood
can be used in four-point bimaterial fracture tests in order to understand the effects of
CRACKS INT DISSIMILAR ANISOTROPIC IVEDIA
For a homogeneous material with xy-plane as a symmetry plane, the characteristic
equation for in-plane deformation is 
1(pu) = s,, p4 2sl6 3' + (2slZ + s66 2~U S26 p + SZ = 0 (A.1)
where pu are distinct complex numbers with positive imaginary part and s,, are elastic
constants in given orthotropic solids.
It has been shown by Lekhnitskii (1963) that the roots of an equation can never be
real, and thus they occur in two conjugate pairs. Assuming they are distinct, one can
choose two different roots, pul and pu2, with positive imaginary parts, to each of which a
complex variable z,=x+pu~y is associated. The matrix A, L, B and H are 2 x 2, and the
elements for A and L can be specialized from A.3 and A.4 with rll= rl2=0,
s11 Im(pu, + pu ) -i(pzp us,, + s)
B- 1iAL- r- _z I(u, u,' (A.2)
The elements of the matrices A and L are given by
L= 1 1 r, (A.3)
Al, = sll p, + s,, sl6~U a a (S15 a, S14),(A4a
Az, = s21 p, + szz / pU, s, + r, (s s,4 a~U ), (A.4.b)
A3a = S41 Ua + S42 lIa S46 + a (S45 S44 lIa), (A.4.c)
for a = 1,2, and
A13 = 3 S11U32 + S12 S16 U3) + S15 U3 S14,(A4d
A23 = 3 S21 U3 + S22 I3 S26) + S25 S24 lI3, (A.4.e)
A33 = 3 (S41 I3 + S42 I3 S46) + S45 S44 lI3, (A.4.f)
In deriving A.2 the standard relationship between roots and coefficients has been
used. These algebraic results provide, basically, all that is needed to specialize various
To gain more insight, orthotropic materials are considered below. The principal
axes of each material are considered to be parallel to the x and y axes, since other
orientations may be treated by in-plane rotations and associated tensor rules. Given an
orthotropic solid, since S16=S26= 0, only four elastic constants, sol, s22, S12, and s66 enter
the plane problem formulation. Following the notation introduced earlier (Suo 1990), two
non-dimensional parameters are defined as
ii = s,, / s22, p = (2sl2 + S66 )(S11S22 2 (A.5)
the characteristic equation A. 1 is then
Ap41 + 2pl p2 +1 = 0. (A.6)
The roots with positive imaginary parts are
#1 ) 2 4 i,-a, ,> rlp,
Pr2 4 ) -~n 1?2 4 for-1 MI 12 4 ;tifor p= 1
nI = (1 + p)] m = 1(1 p) 2
The matrix B for an orthotropic material, reduced from A.2 is
B= 2nF<(s,,, ) s22) 2 /~ (S11S22)2 SI ) (A.8)
-i(~s2 2 +S112) 2nA4(S11S?22 +E2
It is interesting to note that B is still well-behaved even if p=1 (A and L are singular
for this case). The matrix H for the two orthotropic materials with aligned principal axes
H = H, ,
Sip(H,, H22 2
(H,,H22) B= [S11S22) +S12] 2 S11S22): +S12 1, (A.10c)
Here a is a generalization of one of the Dundurs (1969) parameters. The non-oscillatory
fields can be obtained by the corresponding results ifH is real, or B = 0. The case ff 0
will be focused below.
The oscillatory index e, solved from the eigenvalue problem is
E = (27r) In((1 p) /(1+ P)).
H,,= nA szs2 ]1 + 2ni/(szzs22 2, ]
H22 = 2nf t(szs21 ill+ 2n/ 4(S112 ,sZI
With the complex stress intensity factor K, the traction in the interface is given by
(H22 / Hll)2 22 12~l = (2r) 2Kr (A.12)
K, + iK,
= cr2 CO(61HT) +712 in(6H T + I/ T12 ~o, CO(1)- &2Sin(ElH T)]
The energy release rate is thereby
G = H,,IK 2 /(4 cosh2 nE) (A.14)
and the phase angle for mode-mixity is
r= tani K, (A.15)
The stress intensity factors for this case, however defined, may not reduce to the classical
definition as the bimaterial degenerates to have e = 0, because H22/H11 / 1 if3l / 1. For
the case e = 0 one may rescale Re(K) by (H22/H11)1/2 to recover the classical stress
Table B.1 Experimental data from sandwich comp osites wit 2 0.25 inc 3 core
Front a Back a Avg a Distance r Work Pc dc Gc
1 0.512 0.383 0.4475 2 0.961 5.615 0.312 2.166989
1.044 1.062 1.053 2.4475 3.316 6.578 0.618 3.177697
1.03 1.154 1.092 3.5005 3.919 6.16 1.351 3.621421
0.942 1 0.971 4.5925 3.397 4.92 2.242 3.530227
2 0.378 0.391 0.3845 2 0.735 5.8 0.32 1.892647
0.918 0.856 0.887 2.3845 2.453 5.65 0.495 2.73812
1.286 1.258 1.272 3.2715 4.954 5.858 1.216 3.856093
0.98 1.119 1.0495 4.5435 3.711 4.918 2.085 3.50096
3 0.53 0.541 0.5355 2 1.206 5.393 0.337 2.252101
1.22 1.174 1.197 2.5355 3.646 6.988 0.769 3.045948
1.072 1.032 1.052 3.7325 3.45 5.975 1.602 3.279468
1.678 1.753 1.7155 4.7845 4.116 4.582 2.369 2.3993
4 0.883 0.74 0.8115 2 1.716 6.9 0.412 2.101991
1.009 1.069 1.039 2.8115 3.677 6.816 1.033 3.517873
E E 3.8505 6.01 1.782 E
5 0.598 0.505 0.5515 2 1.014 6.126 0.353 1.847861
1.056 1.142 1.099 2.5515 3.501 5.712 0.623 3.201 631
1.159 1.198 1.1785 3.6505 3.781 5.433 1.55 3.224438
0.816 0.865 0.8405 4.829 2.869 4.099 2.425 3.430597
*E: The point that could not get crack propagation due to sudden jump of crack
EXPERIMENTAL RESULTS AT ROOM TEMPERATURE
Table B.2 Experimental data from sandwich composites with 0.5 inch core
Front a Back a Avg a Distance r Work Pc dc Gc
1 0.314 0.23 0.272 2 0.435 6.425 0.314 1.645334
1.004 0.874 0.939 2.272 1.517 4.836 0.354 1.662087
1 1.19 1.095 3.211 1.994 4.877 0.866 1.873461
1.01 0.92 0.965 4.306 2.12 4.03 1.53 2.260176
2 0.391 0.357 0.374 2 0.603 5.54 0.291 1.662164
1.336 1.116 1.226 2.374 2.171 4.71 0.396 1.825566
1.697 2.047 1.872 3.6 4.613 5.437 1.152 2.540422
3 0.605 0.641 0.623 2 0.688 5.275 0.289 1.162457
1.013 2.307 1.66 2.623 3.348 4.06 0.593 2.123018
1.806 0.903 4.283 E
4 0.459 0.587 0.523 2 0.68 6.617 0.374 1.306725
1.118 1.036 1.077 2.523 1.849 6.48 0.632 1.725433
1.019 1.211 1.115 3.6 3.164 3.857 0.953 2.851 928
1.021 0.885 0.953 4.715 2.717 4.81 2.279 2.865323
5 0.379 0.519 0.449 2 0.674 5.048 0.309 1.56366
2.493 2.549 2.521 2.449 7.029 5.494 0.663 2.904353
0.934 0.655 0.7945 4.97 2.038 3.259 2.131 2.672016
Table B.3 Experimental data from sandwich composites wit 2 1.0 inch core
Front a Back a Avg a Distance r Work Pc dc Gc
1 1.12 0.286 0.703 2 0.771 4.254 0.259 1.128321
1.566 2.107 1.8365 2.703 1.269 4.3 0.58 0.710893
1.163 1.015 1.089 4.5395 0.708 1.6 1.055 0.668866
2 0.553 0.503 0.528 2 0.943 7.379 0.298 1.77181
0.931 1.08 1.0055 2.528 1.74 6.7 0.45 1.716748
1.221 1.26 1.2405 3.5335 2.514 5.465 1.02 2.010518
0.915 0.724 0.8195 4.774 1.97 3.94 0.82 2.384826
3 0.624 0.735 0.6795 2 1.539 8.01 0.327 2.283166
1.253 1.597 1.425 2.6795 3.947 7.8 0.616 2.792162
1.274 1.262 1.268 4.1045 2.574 4.73 1.32 2.046339
4 0.968 1.041 1.0045 2 1.258 7.29 0.299 1.249865
0.904 0.71 0.807 3.0045 0.913 3.77 0.48 1.129092
1.61 1.241 1.4255 3.8115 2.052 4.92 1.067 1.436622
Table C.1 Experimental data from sandwich comp osites wit a 0.25 inc 3 core
Front a Back a Avg a Distance r Work Pc dc Gc
1 0.551 0.623 0.587 2 0.789 4.181 0.233 1.344123
1.067 1.203 1.135 2.587 1.992 4.796 0.492 1.755066
1.274 0.912 1.093 3.722 2.484 4.38 1.156 2.272644
2 0.347 0.389 0.368 2 0.699 5.93 0.283 1.899457
0.863 0.907 0.885 2.368 1.144 4.51 0.586 1.292655
1.482 1.59 1.536 3.253 3.251 5.23 1.089 2.116536
3 0.6 0.5 0.55 2 0.932 7.4 0.345 1.694545
1.147 1.027 1.087 2.55 1.85 4.81 0.428 1.701932
1.59 1.386 1.488 3.637 2.84 4.364 1.059 1.908602
4 0.545 0.417 0.481 2 0.481 6.857 0.302 1
1 1.328 1.164 2.481 1.279 4.154 0.385 1.098797
1.716 1.616 1.666 3.645 2.786 3.43 0.893 1.672269
5 0.494 0.382 0.438 2 0.7 5.18 0.246 1.598174
1.009 1.15 1.0795 2.438 1.244 4.88 0.385 1.152385
1.43 1.304 1.367 3.5175 2.611 3.74 0.963 1.910022
EXPERIMENTAL RESULTS AT CRYOGENIC TEMPERATURES
Table C.2 Experimental data from sandwich composites with 0.5 inch core
Front a Back a Avg a Distance r Work Pc dc Gc
1 0.783 0.624 0.7035 2 0.415 4.42 0.236 0.589908
1.536 1.81 1.673 2.7035 1.651 3.52 0.384 0.98685
0.952 0.7 0.826 4.3765 1.17 2.6 1 1.416465
2 0.43 0.394 0.412 2 0.645 6.13 0.372 1.565534
1.378 1.67 1.524 2.412 1.863 4.99 0.463 1.222441
1.38 1.015 1.1975 3.936 1.661 2.iB2 1.045 1.387056
3 0.642 0.557 0.5995 2 0.654 5.8 0.26 1.090909
1.468 1.766 1.617 2.5995 1.182 3.63 0.319 0.730983
1.025 1.08 1.0525 4.2165 1.314 3.96 1.273 1.248456
4 0.515 0.435 0.475 2 0.396 4.488 0.215 0.833684
2.015 2.164 2.0895 2.475 1.57 3.157 0.278 0.751 376
0.762 0.867 0.8145 4.5645 1.676 3.02 1.82 2.057704
5 0.46 0.46 0.46 2 0.205 5.18 0.184 0.445652
1.763 1.636 1.6995 2.46 1.394 4.35 0.238 0.820241
1.154 0.937 1.0455 4.1595 1.358 3.27 1.025 1.2989
Table C.3 Experimental data from sandwich composites with 1.0 inch core
Front a Back a Avg a Distance r Work Pc dc Gc
1 1.02 0.82 0.92 2 0.74 5.26 0.194 0.804348
1.762 1.542 1.652 2.92 1.325 3.34 0.366 0.802058
1.928 4.572 1.6 3.47 1.107 0.829876
2 0.771 0.726 0.7485 2 0.561 5.25 0.185 0.749499
2.46 2.43 2.445 2.7485 1.386 4.86 0.353 0.566871
1.546 1.41 1.478 5.1935 1.85 1.096 2.99 1.251691
3 0.513 0.352 0.4325 2 0.407 5.91 0.2 0.941 04
1.683 1.872 1.7775 2.4325 1.565 4.1 0.208 0.88045
1.143 1.029 1.086 4.21 0.83 3.32 0.927 0.764273
4 0.552 0.738 0.645 2 0.583 4.61 0.182 0.903876
0.83 1.375 1.1025 2.645 1.031 3.68 0.353 0.935147
1.58 1.343 1.4615 3.7475 1.816 3.35 0.794 1.242559
MATERIAL INFORMATION OF SANDWICH COMPOSITES AND CURE CYCLE
ECA, 1/8 inch cell, 4.0 pcf (lb/ft3)
Unidirectional Carbon Fiber Prepreg
Designation: T800HB-12K-40B/3 63 1, Roll Number B 1-210-100-8-1
Manufacturer: Toray Composites (America) Inc.
Vacuum Bag Material
Designation: Econolon Nylon Film
Manufacturer: Airtech International
Designation: Air weave@~ N-10 100z/yd2
Manufacturer: Airtech International
Designation: NA100-3/3 8 Non-Porous Teflon Coated fiberglass cloth
Distributor: National Aerospace Supply
Adhesive for Room Temperature
Designation: Epoxy 907 Adhesive System
Manufacturer: Miller-Stephenson chemical co., Inc.
Adhesive for Cryogenic Temperature
Manufacturer: PRC-DeSoto International
-Pressure, psig -Temperature, Fahrenheit
Figure D. 1 Toray Composites cure cycle for composite laminates.
1. Apply at least 560 mm (22 inches) Hg vacuum to the bag.
2. Pressurize the autoclave to 6.0 Kgf/cm2 (85 psig). Vent the vacuum bag to the
atmosphere when the pressure reaches 1.4 +0.7/-0.0 kgf/cm2 (20 +10/-0 psig).
Keep the bag vented until the end of the cure. The pressure under the vacuum
bag shall be 0 [+0.35/-0.0] kgf/cm2 (0 [+5/-0] psig) throughout the remainder
of the cure cycle.
3. Start the temperature ramp after the autoclave has been fully pressurized.
4. The heat up ramp shall be 1.1 to 2.2 OC/minute (2 to 4 OF/minute). The
nominal heat-up rate shall be 1.7 OC/minute (3 OF/minute)
5. Hold for 120 + 60/-0 minutes at 179.5 +/- 5.50C (355 +/- 10 OF) and 6.0 +1.0/-
0.0 kgf/cm2 (85 +15/-0 psig). The temperature is based on an atmosphere
thermocouple. The hold part of the cycle begins when the last thermocouple
reaches the minimum cure temperature.
6. Cool down under pressure until the part temperature reaches 60 oC (140 OF) or
below The natural pressure drop (1.3 kgf/cm2 (19 psig) maximum) in the
autoclave due to the cool down is allowed. The cool down rate shall be 2.7
oC/minute (5 OF/minute) maximum.
7. When the part temperature reaches below 600C (140 OF), release the pressure
and remove the part.
To prevent from crushing honeycomb core due to pressure, No.3 and No.7
procedures are not applied in this thesis.
MATERIAL TESTS RESULTS
Graph for material verification
-o Room 00 -m Room 45 Room 90
-a Cryo 00 -* Cryo 45 Cryo 99|
0 0.05 0. 1 0.15 0.2 0.25 0.3 0.35
Figure E. 1 Load-deflection graph for material property based on temperature and
Table E. 1 Experimental results and calculated material properties
Room ( unit = psi)
theta 0 45 90
P 20.9135 1.6515 0.9584
delta 0.20035 0.20212 0.20169
(0.316,51.3) (0.296,5.75) ((0.306,2.86)
Ex at 0 Ex at -45 Ex at 90
2.09E+07 2.27E+06 1.16E+06
El G12 E2
Property 2.09E+07 1.13E+06 1.16E+06
Cryo ( unit = psi)
theta 0 45 90
P 23.8391 2.2279 1.4662
delta 0.20039 0.20114 0.20048
(0.316,57.6) (0.296,10.9) (0.306,4.73)
Ex at 0 Ex at -45 Ex at 90
2.34E+07 4.43E+06 1.92E+06
El G12 E2
Property 2.34E+07 2.71E+06 1.92E+06
b=1.0 in h=0.048 in L=5.0 in
LIST OF REFERENCES
1. Ducept, F., Gamby, D. and Davies, P., "A Mixed-Mode Failure Criterion Derived
from Tests on Symmetric and Asymmetric Specimens" Composites Science and
Technology 1998; 59: 609-619
2. Grau, D., "Relating Interfacial Fracture Toughness to Core Thickness in
Honeycomb-Core Sandwich Composites" Master's Degree Thesis, Department of
Mechanical and Aerospace Engineering, University of Florida, Gainesville, 2003
3. Schutz, J.B., "Properties of Composite Materials for Cryogenic Applications"
Cryogenics 1998; 38(1): 3-12
4. Gates, T.S., Whitley, R.W., Grenoble, R.W. and Bandorawalla, G.T.,
"Thermal/Mechanical Durability of Polymer-Matrix Composites in Cryogenic
Environments" AIAA Journal 2003
5. Bitter, T., Honeycomb Technology, Chapman and Hill, London, 1997
6. Ural, A., Zehnder, A.T. and Ingraffea, A.R., "Fracture Mechanics Approach to
Facesheet Delamination in Honeycomb: Measurement of Energy Release Rate of
the Adhesive Bond" Engineering Fracture Mechanics 2002; 70: 93-103
7. Suo, Z., "Singularities, Interfaces and Cracks in Dissimilar Anisotropic Media"
Proceedings of the Royal Society of London. Series A, Mathematical and Physical
Science 1990; 427: 331-358
8. Gibson, R.F., Principles of Composite Material M~echanics, McGraw-Hill, New
9. Anderson, T.L., Fracture M~echanics (2nd Edition) CRC Press LLC, Boca Raton,
10. Charalambides, P.G., Lund, J., Evans, A.G. and McMeeking, R.M., "A Test
Specimen for Determining the Fracture Resistance of Bimaterial Interfaces"
Journal of Applied Mechanics 1989; 56: 77-82
11. de Morais, A.B., "Double Cantilever Beam Testing of Multidirectional Laminates"
Composites Part A: Applied Science and Manufacturing 2003; 34: 1135-1142
12. Hutchinson, J.W. and Suo, Z., "Mixed Mode Cracking in Layered Materials."
Advances in Applied Mechanics 1992; 29: 64-163
13. Avery III, J.A. and Sankar, B.V., "Compressive Failure of Sandwich Beams with
Debonded Face-Sheets" Journal of Composite Materials 1999; 34: 1 176-1 199
14. Sun, C.T. and Qian, W. "A Frictional Interfacial Crack under Combined Shear and
Compression" Composites Science and Technology 1998; 58: 1753-1761
Won-Jong Noh was born in Seoul, Korea, on April 3, 1975 and raised with his
generous parents and two adorable sisters. They have supported him physically and
mentally throughout his whole life. He has lived his life in a friendly environment
surrounded by great people such as his relatives and friends.
He attended schools in Seoul throughout his pre-college career, and then entered
the Department of Aerospace and Mechanical Engineering at Hankuk Aviation
University in 1994. After taking engineering classes for four years, he established good
relationships with his professors and classmates, and also took ROTC training courses
during his junior and senior years. After graduating with a Bachelor of Science degree, he
served the Republic of Korea Air Force as an engineering officer for three years. In 2002,
he wished to pursue deeper study in his maj or, so he j oined Dr. Bhavani V. Sankar' s lab,
the Center for Advanced Composites at the University of Florida, to study sandwich
structures and composites and has studied to get a Master of Science degree.
As the time comes to face the next step of his life, he hopes that it will be filled
with great success and plenty of happiness. He will endeavor to do his best to succeed in
this new phase of his life.