Material B: BFG C/SiC. .... Otherfactorsthat influenceoxidationof the carbonfibers in a matrix were ... Test couponsare cut from the panelanda SiC externalseal-.
ARL-TR-2296
NASA/TM--2001-210520 U.S.
RESEARCH
ARMY
LABORATORY
The Oxidation Fibers Michael
Space
Glenn
June
in a Cracked
of Continuous
Ceramic
Matrix
Research
Laboratory,
Aeronautics Administration
Research
2001
Center
and
Glenn
Research
Center,
Cleveland,
Carbon Composite
C. Halbig
U.S. Army
National
Kinetics
Ohio
Acknowledgment
The author
would
like to acknowledge
James
D. Cawley
Available NASA Center 7121 Standard Hanover,
for Aerospace Drive
Information
and Andrew
J. Eckel or their guidance.
from National
Technical
Information
Service
5285 Port Royal Road Springfield, VA 22100
MD 21076
Available
electronically
at http://gltrs.grc.nasa.gov/GLTRS
TABLE 1.
OF CONTENTS
Introduction
1 3 4
1.1 Objectives 1.2 Materials 2.
Description
2.I
Materials 2.1.1
and Experimental TGA of T-300 Carbon
2.1.2
2.2
19
TGA of C/SiC Coupons
19
Stressed
20
2.1.4
Creep of C/SiC Coupons Stressed Oxidation of Four Different
2.1.5 Results
Oxidation
of C/SiC
Coupons C/SiC
Materials
TGA
of T-300
Carbon
099
TGA
of C/SiC
Coupons
2.2.3
Stressed
2.2.4
Creep of C/SiC Coupons Stressed Oxidation of Four Different
Oxidation
Fiber
25
of C/SiC
TGA
of T-300
Carbon
2.3.2
TGA
of C/SiC
Coupons
2.3.3
Stressed
2.3.4 2.3.5
Creep of C/SiC Coupons Oxidation Patterns and Trends
2.3.6
Stressed
Experimental
Oxidation
27 34
Coupons C/SiC
Materials
Fiber
38 44
Coupons
of Four Different
45 47 C/SiC
Materials
71
Summary
73
Development
3.1.1 3.1.2
Oxygen Carbon
3.1.3
Model Geometry Solutions
Concentration Consumption
73 81
at Steady-State
Study
and Comparison
to Analytical 86
Results
95
3.2.1
Oxygen Carbon
3.2.2 3.2.3
Concentration Consumption
Model Geometry Solutions
95 98
at Steady-State
Study
and Comparison
to Analytical 105
3.3 Discussion
5. 6.
55 73
3.1 Model
,
35 38 43
of C/SiC
Oxidation
24
Modeling
3.2
21 21 24
2.2.1
2.3 Discussion 2.3.1
2.4
18 Fiber
2.1.3
2.2.5
,
5 18
1.3 Theory Experimental Studies of C/SiC
3.3.1
Oxygen
3.3.2
Carbon
3.3.3
Model Geometry Solutions
3.4 Modeling Conclusions Appendix
Concentration
at Steady-State
112
Consumption Study
to Analytical
122 the Effect
125
of Flaws
133
Bibliography
NASA/TM--2000-210520
and Comparison
117 120
Summary
- Studying
111 111
iii
LIST
OF TABLES
Table
I. Calculated
constant
values
and the resulting
Table
II. Objectives
C/SiC
composite
Table
Times
Table
and the reaction
rate
number.
14
tests conducted
on carbon
fiber
and 18
and processing
properties
of four different
C/SiC 23
to failure
coupons
V. Times
of C/SiC
coefficient
material.
Constituents
of C/SiC
Sherwood
of experimental
Table III. materials. IV.
for the diffusion
and strains
in air at a stress to failure
coupons
NASA/TM--2000-210520
for the stressed
oxidation
of 69 MPa ( 10 ksi).
and strains
in air at a stress
to failure
to failure
for the stressed
of 172 MPa (25 ksi).
iv
29 oxidation 30
LIST OF FIGURES Figure
1. Oxidation
Figure
2. Polished
through
of crack
bridging
cross-section
fibers
of C/SiC
at an elevated
material
temperature
showing
cracks
in air.
traversing
the material.
Figure 3. Generalized a matrix crack.
representation
of continuous
carbon
fiber
tows bridging 8
Figure
4.
Temperature
effect
on the diffusion
coefficient.
15
Figure
5. Temperature
effect
on the reaction
rate constant.
16
Figure 6. controlled Figure
7. Percent
of T300 Figure
11.
versus of 350°C
Strain
of 750°C
Strain
at temperatures
versus
versus
of 750°C
Figure 12. Creep environments.
25
time for the thermogravimetric
analysis 26
time for the stressed and 550°C
oxidation
and stresses
time for the stressed to 1500°C
and a stress
time for the stressed to 1500°C
coupons
test coupons 172 MPa.
of C/SiC
32
of C/SiC
test coupons 33
of 172 MPa.
at 750°C
31
test coupons
of 69 MPa.
oxidation
and a stress
of C/SiC
of 69 MPa and
oxidation
in air and inert 34
C/SiC
Figure 14. Times to failure for 4 different of 1454°C and a stress of 172 MPa.
C/SiC
Figure
15. Determination
energy
Figure
16. Polished
NASA/TM--2000-210520
analysis
environment.
tests of C/SiC
preferentially
17
time for the thermogravimetric
Figure 13. Times to failure for 4 different of 1454°C and a stress of 69 MPa.
occurring
of fiber tows for reaction
environment.
loss versus
in an oxygen
9. Strain
10.
loss versus
in an oxygen
weight
coupons
at temperatures Figure
fiber
8. Percent
at temperatures Figure
weight
carbon
of C/SiC Figure
Illustrations of the oxidation of an array and diffusion controlled kinetics.
of the activation
cross-section along
showing
materials
at a temperature 36
materials
at a temperature 37
oxidation
of T300
carbon
of carbon
fiber.
42
fibers 49
microcracks.
v
Figure 17. Fracture surface showing oxidation of the pyro-carbon interphase and narrowing of the fiber cross-section.
50
Figure 18. Fracture surface showing right away from a matrix crack.
51
fibers
receding
to the left and
Figures
19a-c.
Cross-sections
of a sample
tested
at 750°C/69
Figures
20a-c.
Cross-sections
of a sample
tested
at 1400°C/69
Figure
21a-c.
Material
A: DuPont-Lanxide
Figure
22a-c.
Material
B: BFG
surface MPa.
of a sample
Figure 24. Fracture tested at 1454°C/69
surface MPa.
of a sample
which Figures
25a-b. shows 26a-b.
which
shows
Figure
27a-d.
Polished boron
that was stressed
that was stressed
oxidation 59
of the interior
61
of the interior
of material
particulates.
C: DuPont-Lanxide
enhanced
C/SiC.
of a DLC tested at
Figure 31a-c. with CBS.
Material
Figure 32a-b. Incomplete carbide into fiber tows. Figure 33a-b. Oxidation gradient region.
NASA/TM--2000-210520
failure
63
64
65
locations.
D: DuPont-Lanxide
D 62
Figure 29. SEM micrograph of the fracture surface enhanced C/SiC sample that was stressed oxidation 1454°C/172 MPa. Test coupon
C
particulates.
cross-section
containing
of material
of a DLC tested at
30a-b.
56
oxidation
Figure 28. SEM micrograph of the fracture surface enhanced C/SiC sample that was stressed oxidation 1454°C/172 MPa.
Figure
54
58
containing
Material
C/SiC.
53
57
cross-section
Polished boron
MPa.
C/SiC.
Figure 23. Fracture tested at 1454°C/69
Figures
standard
MPa.
66 enhanced
C/SiC 68
chemical
vapor
infiltration
of silicon 69
in a cross-section
taken
from
the thermal 70
vi
Figure
34.
Illustration
Figure shown
35a-b.
Figure
36. Detail
Figure
37.
Figure
38a-e.
Figure
39. Geometry
of a 12x 12 array of crack
One-quarter
in the sectioned
diffuses
represented
carbon
by square
cells.
bounded
concentration
86 89
material
where
oxygen 91
by carbon.
at steady-state
for Sh=0.1
and 96
Figure 41. Oxygen concentrations for several Sherwood values.
across
Figure
42.
Shrinking
core without
geometry
Figure
43.
Shrinking
core with geometry
Figure
44.
Radius
geometry
8O
in the models.
of cracked column
75
as
near fiber tow.
considered
an open
Figure 40. Oxygen Sh= 0.0001.
orientated
tows.
76
core of carbon
Cases
pattern
fiber
square.
of cell pattern
Circular
down
plot of the matrix
bridging
reduction
the center
of the surface 97
for reacting
99
correction.
100
correction. core with and without
101
correction.
Figure
45.
Model
results
for cross-section
at a temperature
of 1400°C.
103
Figure
46. Model
results
for cross-section
at a temperature
of 700°C.
104
Figure 47. Oxygen concentration along the midline for the analysis of the case of diffusion down a column bounded by continuous walls of carbon.
106
Figure 48. the column
Oxygen concentrations one-eighth of the distance down length for the CW model and the 2-D analytical solution
for the five line positions Figure
49.
Oxygen
of width
concentrations
parallel across
107
to the midline. the midline
for different 109
geometries. Figure 50. Oxygen concentration 12 x 36 F-I'A model.
NASA/TM--2000-210520
across
the long dimension
of the 110
vii
Figure
5 la-b.
at 95% carbon geometry Figure
Close-up reacted
of carbon without
core originally
a geometry
of 59 cells in radius
correction
and with a 115
correction. 52.
Modeling
Figure 53. Correcting wall model.
NASA/TM--2000-210520
a realistic
C/SiC
the continuous
116
geometry. wall models
to fit the bumped 119
viii
1. INTRODUCTION Carbon matrix
fiber
composite
applications. turbines This
Applications
material
fiber
major
nozzle
1997;
strength
high
use of conventional
use of high temperature
materials
flexible
designs
savings.
Despite
the benefits
which
particularly
and component The oxidation
forms
of carbon
(Ismail,
fibers
to
Higher
in these
applications
oxidizing
types
increased
cooling
are thrust
is important and since
schemes.
The
for simpler
designs
and weight
vehicle
of applications,
which
in
can allow
is the degradation
environments,
capability
than 3000°C)
little or no cooling overall
that are
are primarily
capability
the use of complex
C/SiC
of
The use
failures
for C/SiC
temperature
lead to smaller
of using
weight.
the brittle
benefits
1993B). capability,
and high temperature
lead
that requires
Eckel,
and
one
of the
of the carbon can
lead
to
fiber
strength
failure. of carbon
1991)
in complex
NASA./TM--2000-210520
can
and
temperature
used is very high (greater
would
in
applications
structural
turbopumps,
and thus lighter
to reduce
weight,
requires
to its use in high-temperature
reduction
light
of the fuels
and more
reinforcement
proposed
strength,
superalloys
ratio
offers
Herbell
as higher
are a ceramic
temperature
thrusters,
1993A;
such
in ceramics
payload.
temperature
Eckel,
(C/SiC)
high
nozzles,
to density
The
composites
several
ramps,
superalloys
increased
since
fabric
over
matrix for
and
weight
and/or
barriers
Herbell
Lighter
(performance)
the
include
ceramics.
requirements.
the flame
is proposed
reinforcement
where
carbide
that
higher
in monolithic applications
silicon
benefits
resistance,
of continuous inherent
et al.,
offers
shock
space
material
(Effinger
thermal
reinforced
in its bulk
has been composite
(Pickup
well investigated. systems
1
are
et al., 1986; However, less known.
Wood
et al.,
1980)
and
the oxidation
kinetics
Many
involve
studies
thermo_avimetric analysis(TGA) in which weight loss of the compositeis monitored over time (Goujard et
al.,
Filipuzzi
et al., 1994).
oxidation
of the composites
unstressed cracks
state,
near
composite Vix-Guterl can prevent
types
of studies
in unstressed
formation
1993).
cracks
from
of silica
sealing
provide
near seals
environment However
et al.,
1994;
states
1200°C the
real
due to wide
information,
the
and
1993;
however
closing
protects
et al., 1994;
application
crack
et al.,
the
can be very different.
and
cracks
(Lamouroux
in many
Lamouroux
valuable
and stressed
temperature
the outside
et al.,
of pre-existing
the interior
Filipuzzi
conditions,
openings
In an
of the
et al.,
stresses
and the relatively
1994; present
slow rate
growth. While
silicon not
Lamouroux
These
the processing from
of silica
the
1994:
TGA
carbide
be
tests
matrix
monitored
were
as
composites
provide
microscopy
of polished
amount
of
a model
conducted,
also
in TGA
a gage
studied
the
of the amount
The to gain
and
the
kinetics
conditions. times
fracture
were
understanding
strains
Optical
and
also
give
surfaces
results
of carbon Although,
and
of oxidation.
experimental a better
oxidation
in stressed
experiments,
cross-sections
oxidation.
developing
were
used
of diffusion
to
to
in a
weight failure
scanning
could of
the
electron
indications
provide
and
fibers
of the
a basis
for
reaction-controlled
kinetics. A finite into a matrix individual visual,
difference crack
bridged
continuous
qualitative,
NASA/TM--2000-210520
model
carbon and
was developed
by an array fibers,
quantitative
of carbon
often basis
which
simulates
fiber
in bundles
tows of
for understanding
2
the diffusion
where
1000.
of oxygen
a tow is a bundle
The
model
the oxidation
of
provides
kinetics.
a The
influenceof importantvariables,T (temperature),D (diffusion coefficient), K (reaction rateconstant),geometry,andenvironment,wereall studiedusingthe model. 1.1Objectives There were severalobjectives to the work in this thesis. The first two were to investigatethroughexperimentationthe susceptibilityof carbonfiber to oxidationandto studythe oxidationkinetics. The activationenergyof carbonfiber wasdetermined.The two primary regimesof oxidation kinetics, diffusion-controlledand reaction-controlled, were identified. Oxidation patterns and trends relating to each regime were also investigated.Otherfactorsthat influenceoxidationof the carbonfibers in a matrix were analyzedandincludedmatrix oxidation,crackclosure,stress,environment,andoxidation inhibitors. Objectives relating to the developmentand use of the model included identifying the kinetic regimes,simulatingexperimentalresults, studying the effect of sample geometry,and comparingthe model to analytical solutions. Analysis of the model by using different Sherwoodnumbersgaveoxygen concentrationsthat relatedto the two regimesand showedthe effect of specific variablesin relation to oneanother such as temperature,diffusion coefficient, characteristiclength, oxygenpartial pressure and,reactionrateconstantwhich for the systemunderconsiderationis the effectivemass transfer coefficient. The Sherwoodnumber,which will be describedin greaterdetail later in this thesis,is a dimensionlessparameterthat describesthe gradientin oxygen concentrationat the surface. Oxidation patternsfor reactedcross-sectionsthatcorrelated with experimentalresultswereobtainedusingthe model. Comparingthemodelresultsto analyticalsolutionshelpedvalidatethe modelanddeterminecaseswhenit is preferredto conductanalysiswith the simplerto useanalyticalsolutions.
NASA/TM---2000-210520
3
1.2Material Description Processingand propertiesof the constituentsin C/SiC compositeswill now be discussedwith the focus being on one common form of the composite.The C/SiC composite materials to be discussedin this work were made by DuPont-Lanxide Composites Inc. (now known as Honeywell Advanced Composites,Inc.) and B.F. Goodrich. The compositesconsistedof PAN-basedT300 carbonfibers that are in tows of 1000fibers (bundles). The fibers are madefrom polymer precursorsin the form of textile fibers that leavea residueof carbonanddo not melt during pyrolysis in an inert atmosphere. The fibers havea diameterof 8 micronsand are groupedinto bundlesof 1000continuousfibers called lk fiber tows. The carbonpreformconsistsof 0° and90° fiber tows woven into what is called a plain weave configuration. Fibers in the 0° direction are woven with fibers in the 90° direction to form a two layer weavecalled a ply. The plies are stackeduntil the desiredthicknessis achieved. A pyrolytic-carbon interphase,typically 0.5-1.0 microns in thickness,is then depositedonto the carbon preformusing chemicalvapordeposition. The SiC matrix is depositedthroughchemical vaporinfiltration. The compositepanelsarecommonly20.3cm x 25.4and0.32 cm thick (8" x 10" and 1/8" thick). Test couponsare cut from the panelanda SiC externalsealcoatingis appliedusingchemicalvapordeposition. C]SiC materialshavea pre-crackedas-receivedconditiondue to the SiC matrix crackingwhencooleddown from the processingtemperature.The microcracksarisedue the coefficient of thermalexpansionmismatchbetweenthe carbonfiber and the silicon carbide matrix and the large change in temperaturewhen cooling down from the processingtemperature.Lamourouxsummarizedthe coefficientsof thermalexpansions
NASA/TM----2000-210520
4
(CTE)
from
other
et al., 1993). expansion
researchers
The T300
carbon
in the longitudinal
x 10 .6 to -1.1 x 10 .6/°C thermal was
expansion
reported
fiber
(Lowden,
1989).
direction,
the matrix
develops
microcracks
coefficient
the coefficient
is put under
during
a larger
a tensile
stress
of the carbon
using The
is reported
by the woven to the
fiber
a TEM
technique, of thermal
in its longitudinal during
axis.
cooling
Also,
and
since
in the radial
direction
is larger
decohesion
between
the
for the matrix,
of
to be 4.8 x 10 .6 [C
fibers
fiber
of -0.1
The coefficient
coefficient
CTE than the fiber
perpendicular
expansion
1993).
of thermal
in the range
et al., 1993).
determined
et al.,
(Lamouroux
the coefficient
and has low values
to be isotropic
having
in directions
of thermal
occurs
is assumed
expansion
material;
direction,
(Villeneuve
Due to the matrix
of thermal
with one another
et al., 1989; Yasada
in the radial
SiC which
relation
is negative
(Mensessier
to be 7 x 10 -6/°C for CVI
their
is an anisotropic
direction
for T300
expansion
matrix
and discussed
the than
fiber
and
matrix
was
cooling.
1.3 Theory The related used
in the
oxidation
Portions
edge
fibers
1.
Cracks
as the
Based
will
of a finite
bridge that
An example these
NASA/TM--2000-210520
traverse
bridge
difference,
matrix
These
traced
in a non-reactive matrix
that has
cracks
allow
will be susceptible
from
the
fiber
cracked
composite
a crack
through
of a polished types
of a carbon
the crack.
can be readily
cracks
on
in the oxidation
In a ceramic
of the fibers
material. 2.
development
kinetics.
continuous
Figure
theory
one edge
fibers
cross-section
of microstructural
tows
5
as-fabricated for the
of the matrix and
used
matrix
ingress
cracks
an idealization
of oxygen. as shown
across
of the
to study
microcracks,
to oxidation
of traversing analyses,
model
in
to the other
interior
is shown of the
of the
in Figure relevant
geometry
is assumed
microcracks dioxide).
as illustrated
and react The oxide
with carbon
then diffuses
in Figure to form
3.
Oxygen
an oxide
(either
out of the microcrack
is able carbon
to diffuse monoxide
to the atmosphere.
Fiber Regions
Fiber R,
Figure
1.
temperature
NASA/TM--2000-210520
Oxidation
of
crack
bridging
in air.
6
fibers
at an
elevated
into
the
or carbon
Figure through
2. the
Polished
cross-section
of
C/SiC
material
material.
NASA/TM--2000-210520
7
showing
cracks
traversing
_.. Oxide Oxygen Oxide Oxygen
Figure bridging
3. Generalized a matrix
NASA/TM--2000-210520
representation
of continuous
crack.
8
carbon
fiber tows
The oxidation parabolic
rate law [Eckel 2
X kp
of carbon
can be described
by the linear-
et al., 1995]:
=t,
(1)
k t
x (m)
(m:/sec),
for the recession
X
+ --
where
kinetics
is the
recession
k_ is the linear
the case of planar
distance
of the
rate constant
recession
such
(m/sec)
carbon,
kp is the
and t is time (sec).
as for the case of a single
fiber
parabolic
rate
Equation
constant
(1) is used
that is end-on
for
in a crack
free matrix. The
parabolic
specifically equations papers
the
and
linear
diffusion
coefficient
will be discussed. by Eckel
rate constants
More
et al. (Eckel
and
the
thorough
et al.,
1995)
can be related reaction discussions
and Glime
rate
to more
familiar
constant.
Only
and derivations and
Cawley
constants, the
relevant
can be found
(Glime
in
and Cawley,
1995). When
the linear
is the evolving
oxide,
term
in equation
the equation
(1) drops
for the recession
out (or for small x) and carbon distance
is expressed
dioxide
as (Eckel
et al.,
1995)
1/2 X = t 1/2
kp
1/2
=
2DAB Cox
(2)
t
9c such that
(2DAB kp
where
=,
C P--c
DAB (m 2 / sec)
stationary
or stagnant
atmosphere
(mol
ox
)
(3)
is the
diffusion
atmosphere
/ m 3 ) and
coefficient
of gas B (oxide),
Pc is the
molar
of gas
A (oxygen)
Co× is the oxygen
density
of carbon
diffusing
in the
concentration
of the
(mol
/ m3).
In some
experimental situations,carbon monoxide is the reaction product, but the form of Equation(2) will be the sameandtherewill bea modest30%differencein its magnitude (Eckel et
al., 1995).
The collisions factor
discussion are
until
material
more
Also, the model The parabolic
limiting
drops
consider
Knudsen
inter-molecular
as small
cracks
considers
can be expressed
than
becomes
typical
second
term
not
frequent
the pore
studied,
does
a stressed case
lam (Eckel
and
state where occurs
out and the linear
et al.,
limits.
molecular-wall effects
1995).
larger
In this case,
even than
are not a
In the
are on the order
are open
is much
kp
which
Knudsen
seal coating
the cracks
when term
in
collisions.
as 0.1
in the matrix
effects
C/SiC
of 1 lam.
further. k_, i.e. when
the recession
the
distance
as
x = t k 1= t
K Cox
(4)
PC
such
that K Cox k_ -
(5) 9c
where
K is the reaction The
substituted molecules using
above by
the
rate constant
equation oxygen
in the atmosphere,
(m/s).
takes
an alternate
partial
pressure,
Ca- (mol/m3).
the ideal gas law so that Equation
k, =(
_--c )(X CT)K
NASA/TM--2000-210520
form
when
_,
times
The
total
the
the
oxygen
total
concentration
concentration
concentration can
(6)
10
gas
be substituted
(5) becomes
= / _c )(-_--_)K
of
is
where
P is pressure
temperature
(Pa),
R is the
gas
(J/mol
K),
and
T is the
absolute
(K).
Substituting ") X _
values
for kp and kj, Equation
X-
X
+
kP
kl
diffusion
(2DAB
coefficient,
(Geankoplis,
(1) becomes
9 X
t =--+--=
The
constant
(7)
C°x
DAB, can
RT )K
9c
be obtained
from
Chapman-Enskog
kinetic
theory
1978) 1/2
T 3/2 DAB
=(5.9543X10
-24)
1 (1MA+MB),
(8)
P (YXB AB and the reaction
rate constant,
K (m/s),
can be expressed
in an Arrhenius
form:
exp( 1 where
DAB (m 2 / sec) again
stationary
or stagnant
the molecular
weights
GAB (m) and _ and
calculating 1978).
atmosphere of gases
integral energy
A and
are Leonard
the collision
integral
Q is the activation
can
energy
for
between be found (J/tool).
potentials the
the
in tables The
term
(Bird
(Pa).
in the
The symbols
for the collision
collision
molecules
diffusing
(K), MA and MB are
and P is pressure
Jones
Values
interaction
of gas A (oxygen) T is temperature
B (kg/mol),
respectively. of
coefficient
of gas B (oxide),
(dimensionless)
collision
characteristic
is the diffusion
diameter which
et al.,
is 1963,
k0 is a pre-exponential
diameter and
the
needed
for
Geankoplis, constant
(m/s). From constant
(9),
the
above
it is seen
NASA/TM--2000-210520
equations that
one
for the diffusion of the
two
11
coefficient
arguments
(8) and the reaction
in Equation
rate
(7) will dominate
dependingon temperatureandif x is smallor large. The diffusion coefficientdependson T3/2,with the effect being even less when the decreasingmolar density of the gas is consideredwith increasingtemperature.The reactionrate constantvariesexponentially with inversetemperaturewhenlargeactivationenergiesareconsidered. It can be seenthat Equation(7) describesa two stepprocessoccurring in series. Eachstephasthe potentialto limit the overall process.Although Equation(7) is usedto describeplanar recession,qualitativetrendscan be predictedfor an alternategeometry suchas for crack bridging fiber tows. For the caseof bridging fiber tows, which will be further discussedin the experimentalportion of this thesis,recessionis first in the radial direction of the fiber tow andthenalongfiber tow axis. Equation (7) is usedto illustrate the two stepprocessfrom which the dominatingkineticsdevelop. For the caseof crack bridging fiber tows,predictionandanalysisof oxygen concentrationswas usedto study kinetics andthe Sherwoodnumberwasusedto further conveytheconceptof the two step process. From reactant
using
and product
al., 1995)
reaction
were
in Figure
coefficient which
rate
has a much
Examples
calculated
4 and 5 and
will change greater
temperature cases
(assuming
energy
values
versus
of 3.
range
this
In marked
dependence, are illustrated
12
from Eckel
are shown
temperature
contrast, will change
and
range
CO
as the
et al. (Eckel
et
rate constant
at
the diffusion
of 600-1500°C
temperature
across
02
the reaction
of 100 kJ/mol),
temperature
that
data
(to determine
the
show
by a factor
of the two limiting
NASA/TM---2000-210520
rate at 800°C
across
theory
and from using
an activation
constants The
Kinetic
respectively)
recession
assuming
determined.
plotted
gasses
for the linear
this temperature and
Chapman-Enskog
coefficients (873-1773K)
in Table the
I and
diffusion
the reaction
rate constant,
by 3 orders
of magnitude.
in Figure 6 and correspond
to the cross-
sectionsof an open region where fibers bridge a crack such as the case illustrated Figure the
3.
When
process
temperature
the reaction
will
be
and/or
material
faster
illustrated
small
than
the
compared
consumed. included
reaction
react
reaction
so that
the high
over
fibers.
A shrinking in the modeling
NASA/TM--2000-210520
of
core effect
time,
is controlled
temperature
oxygen
pore
carbon/oxygen
process
and
i.e.
becomes there
will
reactions by the
inward
will be obtained.
part of this thesis.
13
as These
occur
As
into the As
oxidation is small
as soon as oxygen diffusion
illustrated kinetics,
the
low
in oxygen.
coefficient
slower
x).
(for
be a general
if the diffusion
/or large
is large,
and therefore
saturated
of diffusion-controlled
traveling
coefficient
reaction-controlled
into the cracks
However,
over time for the case front
the
and the diffusion
rate,
will diffuse
rate constant,
case
is small
of oxidation
of bridging
(for
the
Oxygen
stages
In this
of oxidation
moving
it can
array
diffusion-controlled
by
x).
to the reaction
is supplied.
stages
limited
in the two
throughout
rate constant
in
step,
i.e.
in the
two
there
will be a
carbon
continues
to be
two types
of kinetics
will be
T (K)
Table
D
Sh !
K
(cmA2/sec)
(cm/s)
773 873 973
1.08 1.25 1.54
0.179 1.17 4.84
1073 1173 1273 1373 1473 1573 1673 1773
1.79 2.06 2.32 2.68 3.01 3.36 3.73 4.12
15.3 39.8 89.1 177 321 540 853
8.29E-04 4.68E-03 1.57E-02 4.25E-02 9.66E-02 0.192 0.330 0.533 0.804 1.14
1270
1.55
I. Calculated
values
for the diffusion
constant and the resulting Sherwood to determine the Sherwood number
NASA/TM---2000-210520
coefficient
and the reaction
number. The geometry was 5.0 x 10 .5 cm.
14
based
rate
Ax value
used
....
4 09 _ O4
, )
" X
2.0E-06
0
1.0E-06
1 47
O.OE+OO-
93
',r"-iiiiiiUi!Uii!i
09 O0 ,,(/3 9.0E-068.0E-06 tO
8 t-
7.0E-06 6.0E-065.0E-06 4.0E-O63.0E-06-
0
1
2.0E-06 1.0E-O6-
47
O.OE+O0-
93
O3
Figure (left)
45.
Model
and oxygen
% of the carbon
NASA/TM--2000-210520
results
for the cross-section
concentration consumed
for one-quarter
(top to bottom).
103
at I400°C. section
Overall (right)
oxidation
pattern
for 25 %, 75 %, and 95
1.4E-05 tO
1.2E-05 1.0E-05
t-"
8.0E-06 tO
0
6.0E-06
t-
4.0E-06 ×
1
2.01::-06
0
47 O.OE+O0-
93 CO CO
,-
1.4E-05 tO
°m
1.2E-05 1.0E-05-
to tO
8.0E-O6-
(0
6.0E-06-
t-
4.0E-06 x
0
1
2.0E-06 47 O.OE+O0-
93 CO
1.4E-05 t-
1.2E-05
_
1.0E-05
o
t-
o c o
8.0E-066.0E-06
e--
4.0E-O6x
0
1
2.0E-0647 O.OE+O0 _
93 CO
Figure
46.
Mode]
results
for the cross-section
at a temperature
oxidation pattern (left) and oxygen concentration for one-quarter %, ?5 %, and 95 % of the carbon consumed (top to bottom).
NASA/TM--2000-210520
104
of 700°C. section
,,03
Overall (fight)
for 25
3.2.3
Model The
Geometry
oxygen
analytical
analysis 47.
1-D analytical midlines The
oxygen
numbers.
2-D
analytical
column
length.
one another numbers,
predicted
the
effect
of five
_adient
in oxygen
concentrtion
gradient
in oxygen
concentration
The
one curve
Figure
predicted
by the
48 as the tick marked
NASA/TM--2000-210520
CW
in oxygen
model
the
the
is for
1-D solution
width)
can
midline
the line
solution
of
in Figure for low the
for the
The
to the line parallel
to and
of the distance
into the
while
There
compared
number,
curve
directly
adjacent
for each local
Sherwood
line.
105
was
well
with
Sherwood more
of a
to the midline.
the curve the
very
At high local
be seen. wall
concentration
to be determined.
compared
and in trends.
Sherwood
is along
types
than
oxygen
48 for one-eighth
width
the
the
the midline
to the carbon local
were
i.e. Sh_>0.1,
concentration
allowed
from
concentrations
for each
three
concentration
numbers,
1-D
solution
38e, are shown
in oxygen
and the 2-D analytical
adjacent
the
solution.
in Figure
along
transfer for these
Sherwood
gradient
lines going
oxygen
directly curves
local
CW model,
mass
in Figure
of a (one-half
are shown
of position
for the curve packet
positions
CW model
in both specific
the
difference
the midline
prediction
and 2-D analytical
Solution
analytical
illustrated
a higher
and
finite
along
for higher
for the five
The
2-D
similar
However,
wall,
the
as was
a very
line for the 5 cell
to the carbon
by the
concentrations
solution
concentrations
adjacent
each
gave
solution
and
wall case,
of the CW model
any
gradient
oxygen
methods
to Analytical
determined
solution,
for the reactive
local Sherwood
along
transfer
Resulting
All three
and Comparison
concentrations
mass
compared.
Study
with with
the lowest the
to the carbon number
In
largest wall.
appears
in
--
Finite Difference
......
1-D Analytic Sol.
....... 2-D Analytic Sol.
Sh=0.0001
j
O tO .m
iii E:
"_
Sh=0.001 ¢-. O
rot-
X
o Sh=0.01 0 0
50
100
150
200
Position Across Matrix (Grid Spacing)
Figure
47.
Oxygen
concentration
diffusion
of down
analyzed
using the finite
2-D analytical
NASA/TM--2000-210520
a column
solution.
along
bounded
the midline
by continuous
difference
CW model,
Sherwood
numbers
106
for the analysis wall of carbon.
the 1-D analytical
are local
Sherwood
250
Sh=1.0
of the case of The case was solution,
numbers.
and the
2-D
and
.......
CW have 5 lines per Sh,
ticked
line 1-D has 1 line per Sh
Sh=0.0001
o t-
00.8 o
Sh=0.001 O.6
.£ o
dO.4
\
tO
Sh=0.01
0 Sh=O. 1
_0.2 x
0
Sh=1.0
Position
Figure
48.
column
Oxygen
length
line positions Sherwood predicted numbers•
NASA/TM--2000-210520
1/8 of the distance
concentrations
one-eighth
for the CW model of width parallel
into 250 Grid Column
of the distance
and the 2-D analytical
to the midline.
(grid spacing)
down
solution
Concentrations
the
for the five
for each
number are shown. Also the one line of oxygen concentration by the 1-D model is shown. Sherwood numbers are local Sherwood
107
The
finite
Specifically, overall
how
oxygen
oxygen
difference diffusion
model down
concentration
concentrations
were determined
by the finite
midlines
FTA
for the
models
38d.
The
Sherwood
numbers
are
shown
fiber
tow
concentrations results
matched
referred gave
along
very
similar
For midline
models
the
midline.
BW
with
the
case
of the
in the
long
direction
concentration
At high
FI'A
is shown
concentration model,
in Figure numbers.
108
the 50.
was
wide
the
BW
along
model and the
model
for several numbers
gave larger,
array
numbers,
oxygen
the BW
Sherwood
models)
to the
The steady-state
the midline
the array
Sherwood
geometry.
contributed
and
and
local
FTA
of
of the geometries
38a-c
low
12x24 when
local
for the oxygen 12x36
At
width
models,
across
for an infinitely
is seen for all local Sherwood
NASA/TM--2000-210520
49.
However case
PTA
Illustrations
concentrations
effect
of thickness.
in Figure
and
the
of the
12x36
method.
(12x12
the
model).
predictions
12x24,
in Figure
study
dimension
illustrated
oxygen
array
closely
to as the
12x12,
to
dimension
the shorter
were
in Figure
used
longer
difference
illustrated
narrower
the
across
for the
was
(12
higher ie.,
was local the
oxygen
12x36,
x infinity
the also
all of the geometries
the midline. concentration
A wide
trough
across of low
the
oxygen
1 is 12x12,2 is 12x24, 3 is 12x36,4 is BW Sh=0.0001 top line is 1 middle line is 2
O
o 0.75
bottom
,w,,_
line is 3 and 4
Sh=0.001
o
.w,,_
05
2 0
3 and4
0.25
1
_D e_0
2, 3 and 4 Sh=0.01
©
,2,3 and
and 4
0 0
Figure
50 Position 49. Oxygen
100 Arcoss Matrix
concentrations
across
150 200 (grid spacing)
the midline
for different
geometries. Midlines were shown in Figure 38a-d for the 12x12, 12x36 FTA models and the BW model. The Sherwood numbers Sherwood
NASA/TM--2000-210520
numbers
109
250
12x24, and are local
Sh:O.O001
0.75 "O 0_
"6 v tO
0.5 ¢.-
Sh=O.O01
0 tO
_D
J
0.25 Sh=0.1
0
Sh=l.0
150
300 Position
450
600
Across Marnx(cellspacing)
Figure 50. Oxygen concentration across the long dimension of the 12 x 36 FFA model. The Sherwood numbers are local Sherwood numbers.
NASA/TM--2000-210520
110
750
3.3
DISCUSSION
3.3.1
Oxygen
Concentration
In the initial in a 250x250 b
showed
mesh the
number
Sherwood
number,
saturated
in oxygen
able to bypass of a shallow that
perimeter
concentration
there
The
carbon
pattern
and realistic
further
These
would at
local Sherwood
that
upon
became
for several
at steady-state different
local
111
low
a low
became
for a high
for reaction-
local
the oxygen's
and
are
Sherwood from
initial
to bypass
of oxygen.
the
contact the outer
This is the
Diffusion-controlled
for the two main section
was
and an interior
concentration
kinetics.
highly
This pattern
temperatures
is able
local
that oxygen
be expected
devoid
Consumption
numbers
pattern
in oxygen
and no oxygen
in the Carbon
plot for
to the interior
However
patterns
local
the interior.
gradient
occurs
at a high
and enter
occur
so reactive
40a-
reactive
for diffusion-controlled
concentration
was compared
a sharp
Figure
so slowly
that
dependence.
was
mesh
from the edge
so that the interior
be expected
will be discussed
was
at steady-state
section
In the
of the
kinetics
reaction
fiber tows
regimes
NASA/TM----2000-210520
is the
was
at high temperatures.
oxygen
interior
carbon
of the
number.
tows at the perimeter
that
occur
The
The
temperature
a carbon/oxygen
would
the
concentration
tows was considered.
quarter
Sherwood
that
in oxygen
kinetics
tow array
fiber
one
Reaction-controlled
interior.
that
away
seen
in oxygen
seen
of carbon
local
the oxygen
array of fiber for
concentration.
saturated
it was
with carbon,
reacted
at a low
by a strong
to the
pattern
with a 12x12
it was
kinetics.
number,
of the model,
concentration
and
gradient
characterized
edge
pattern
the carbon
is highly
controlled
development
oxygen
Sherwood
at Steady-State
oxidation
kinetics
where
the carbon
of the
12 x12
is
are used. across
the midline
Sherwood
numbers.
The results
fiber were
shown
in Figure
concentration oxygen
41.
is able
to bypass
of analysis
Sherwood
determine
number
if two of the three the effect 3.3.2
Carbon The
the rough
that
The
shape surface
faster
cells
and then
and
is quickly
the edge
numbers,
is there
realistic
Sherwood
number
so that This type
values
the plot can be referenced in oxygen
in high
consumed
to the interior.
can allow
and the gradients
for the local
that
to be more
closely
oxidized
of the
in order to
concentration.
are known
Also,
(K, D, and
Ax),
can be determined.
The
shared
surface.
Figure
form horizontal
rate.
have
reacting
caused
surface
51 a-b show
how the diameters
for the cores
when
NAS A/TM--2000-210520
reacted
the smooth
they were
112
the smooth rate.
reacted.
to react
the geometry
more
compared 95%
surface
slowly
surfaces
rate due to the
cell
surface.
reacted
at a
at a faster
rate
correction
was
but also
the smooth
at 0 ° from horizontal When
and at
In the circle
and the rough
the shared
When
to react
why both
at a faster
allowed
surface
correction.
surface
rate and therefore
at a faster
not only the rough
it was unclear
may have
circle
at the smooth
that had no geometry
both
at a faster
of the reactive
The radius
However,
radii
between
cell may
due to its two outer cells this caused
both
was reacting
in the analysis
maintained.
for the circle
correction,
shared
added,
was used
at the same
rate than
that were
surface
rate.
numbers
in the third variable
had no geometry
rough
Sherwood
regime
correction
at a slower
"comer"
from
Sherwood
the interior
oxygen
oxygen
Consumption
geometry
the circular
reacted
variables
of variation
numbers
on the resulting
At low local
concentration
of local
kinetics
number
so that it saturates
to be calculated
the predicted
Sherwood of values.
Sherwood
in oxygen
of a wide range
local
range
carbon
local
gradient
of the
for a wide the
At high
is a large
local
effect
can be seen
concentrations. there
The
the diameter
and 45 ° at 45 ° is
compared
to the diameter
seen that the diameter
at 0 ° for the core
at 45 ° was only about
for the core that had a geometry as for the diameter
An example oxygen
correction,
as the diameter
the diameter
the
trends
for
75%,
both
conditions.
within
it is
at 0 °. However
at 45 ° was about
the fiber
area
95%
the
plots
99.5%
as long
and the corresponding
diffusion-controlled
that
reduction
carbon
were
kinetics
reacted.
suggested
in carbon
of the fiber and
tow array
of the
regimes
of oxidation fraction
and
and
kinetic
However,
and the progression in the carbon
pattern
reaction-controlled
of 25%,
analyzed stages
for
stages
steady-state
correction,
of the oxidation
at the
confirmed
81% as large
a geometry
at 0 °.
concentration
shown
that did not have
These
by the
area
was
tow array could
in the corresponding
results
analysis
also
able
be seen
oxygen
were
for to be
at various
concentration
plots. The
extension
mesh
pattern
cross
sections
give
of the
allowed
having
C/SiC
comparable
a length
included
an array
tows
an array
of 16x16
dimension
and
50 cells
numbers
that were
activation
energy
sections
for
samples. to the
A mesh
both
in the
calculated used
NASA/TM--2000-210520
and
that more
closely
of C/SiC
of 0.97x
realistically
sized
and shaped
other.
to correlate
at 25%
The This
elliptical geometry
studied
of the
113
carbon
Figure
reacted.
laid out to With
tows.
were
The
10 cells
at local
of 700°C
to the
a cell
cm (0.38"x0.13").
fiber
was
kJ/mol.
bars.
0.33
tows
with temperatures was 64.1
cells was
fiber
of the
corresponded
tensile
section
tows.
a modification
of 970x330
a cross
in the calculations
temperatures
reactivity
pattern
cross-sections
of more fiber
carbon
of a geometry
of lxl0 3 cm, this gave
The mesh were
to include
for the analysis
of tested
a geometry
model
and
Computer
in one
Sherwood
1400°C.
52 shows
fiber
The
the crossdifficulties
preventedthe programsfrom running to a higher percentageof carbon consumed. However, in the cross-sectioncorrelatingto 700°C a generalminimal oxidation can be seen throughout the cross-section. For the cross-sectioncorrelating to 1400°C, a shrinkingcoreandmoving reactionfront canbe seen.Thesetrendsagreewith thoseseen in Figures19and20 for actualexperimentalcross-sections. Thereweretwo observationsin this analysiswhich helpedlead to thegeometrystudy to be discussedin the next section. First, a typical run of the model required1.7 million array iterations,136billion programiterations,and 1 weekto calculateon a PC to reach the point where95% of the carbonhadbeenreactedaway. The calculationswerequite intensive even though calculations for only one quarter of the mesh pattern were calculatedandthe otherthreequartersweremirrored from the first quarter. Therefore,a simplified geometrycould possibly cut down on the number of calculations and the amountof time requiredfor the analysis. Second,in the cross-sectionsfor both the oxidized C/SiC couponfrom experimentationandthe oxidizedfiber tow arrayfrom the model, it was seenthat oxidation along the edge of the long dimension was uniform throughoutthe middlesectionof the sample.Oxidationalongthis middle sectionseemed to be primarily dueto oxidation into andout (downward andupward directions)of the horizontalplaneatboth long edgesandthereappearedto beno contributionfrom left and right.
Therefore a simplified geometrycould possibly be found that matched the
oxidation patternalong this uniformly oxidized region so that resultsfrom a simplified casecould beusedto approximatetheoxidationof a muchlargerregion.
NASA/'I'M2000-210520
114
-$33 S29 S25 S21 S17 S13 S9 S5 $1 cO cO
$28 $25 $22 $19 $16 $13 $10 $7 S4 $1 _--
1.0
Ob
cO _.-
I_ _--
_" 04
1.0 04
Ob 04
Figure 5 ! a-b. Close-up view of carbon core originally 59 cells in radius at 95% reacted without a geometry correction
(above)
and with a geometry
(below).
NASA/TM--2000-210520
115
correction
of
Figure52. Modelinga realisticC/SiCgeometry.Cross-sections at 25%of the carbonoxidizedfor conditionscorrelatingto 700°C(above)and 1400°C (below).
NASA/TM--2000-210520
116
3.3.3
Model
Geometry
In the analysis carbon
walls,
the analytical the
finite
difference
method
solutions
for mass
transport.
However
reactivity
of carbon
CW model it was
At high local more
a significant
also
across
gradient
its width.
given
width
along
the column
along
the line directly
The
finite
concentration found the
are the
obtained
for the
The column
the thickness Sherwood
was used
was three was
much
which had very
correlates little
the length same
for all lines
to the carbon
like that represents
or no effect
117
finite
for the case
there
oxygen from
difference
is
was
not but
along
a
contrations
the midline
to
in the oxygen models,
it was
thickness
(i.e.
12x36),
of a column
with
no flux
the case for an infinitely It is unclear
on the midline
of the
of the column,
of geometry
than the overall
to 12 x infinity).
the high
wall.
the effect FI'A
with
and the oxygen
for all positions
the column
to
Sherwood
the width
reactivity,
the predicted
numbers.
NASA/TM--2000-210520
the
well
where
along
wall),
greater
agreed
is very reactive
along
to study
was compared
numbers
carbon
by reactive
at low local
concentration
were
For the
times
Sherwood
of the high
to carbon
bounded
solution
solution
the carbon
to and parallel
with no flux walls
times
in oxygen
for the midline.
midline
(i.e. BW model
local
throughout
method
the width
array
local
adjacent
at high
solutions
width
same
1-D analytical
concentration
I-D
of colum
difference
that when
solution
walls.
(midpoint
the
column
the CW model)
analytical
Because
Solutions
a single
2-D
numbers,
in oxygen
Since
The
gradients
depleted.
down
(specifically
the
not accurate
Sherwood
quickly
only
and
also causes
to Analytical
of oxygen
the finite
difference
therefore
and Comparison
for the diffusion
numbers.
column.
Study
across
wide
why a width the thickness
fiber
tow
of three for all
The
relation
is very
between
important
calculations carbon
in analysis.
that
are
loss over
kinetics
for much
Further analysis that
the
solution
quite
composites
simpler
and quicker
has found
may
be used.
The
model
solution,
by continuous
and
which
reactive
Also
since
the BW model
from
one
volume 0.75
for the different
K in the 1-D analytical
the BW model across
which
the middle
difference
1-D
and
thickness,
of the oxidation
kinetics.
BW
analytical
had
fiber
of 10 cells
to be included
of analysis.
had a reaction length
rate constant is shown
118
CW
model
down
in diameter
and
a column
I-D
bounded
10 cells
the difference
The
the
into the column.
spaced
gave
finite
at the tip to match
that a reaction
in Figure 53.
so
to the
tow at ten cells
of 1.0 K.
model
can be simplified
included
model
oxidation
the BW
compared
to consider
and the CW Wall
and
actual
was The
It was found
iterative
an analytical
region
fiber
of
at all. Instead,
for diffusion
insulation
the first
tows
model
solution.
the case
a 10 cell
solution
of the column
NASA/TM--2000-210520
not have
column
includes
diffusion
to be used
had
methods
analysis
studying
width
simpler
thousands
does
which
a correction
require when
When
analysis
and the much
the case for the BW model
had
had
can
especially
steps.
both considered
in the BW model
arrays
of sufficient
finite
walls,
models
that even
the
the pattern
another,
time
matrix
model
analytical
large
consuming
of small
difference
CW
tow array
The
finite
difference
fiber
time
hundreds
in ceramic
can allow
the large
good oxygen
apart
in carbon
rate constant agreement
of with
concentrations
.....
Cor.
ID Analytic
Sol.
--
Fin. Dif. Bumoed
Wall
.....
Cor. Fin. Dif. Cont.
Wall
1
Sh=0.0001
Q
"3
0.75
0.5 Sh=0.001
g 0.25 ©
Sh=0.01 Sh=0.1
0
Sh=l.0
50
100 Position
Arcoss
Figure 53. Correcting the Continuous Sherwood numbers are local Sherwood
NASA/TM--2000-210520
150 Matrix
250
(grid spacing)
wall models numbers.
119
200
to fit the bumped
wall
model.
3.4
Modeling
Summary
An existing bridging state.
fiber
local
showed
Sherwood
concentration
and characteristic
as a function
of oxygen
concentration
of local
concentration.
are very steep
When
were obtained
microstructural
analysis
tested.
the model
predicted
of polished
a shrinking
tows in the center
consumed
before
of the 2-D plane
120
such
be determined
The plots
of the oxygen
that would
correlate
on the gradients gradients
and
in oxygen
of the 2-D surface.
concentration
of carbon,
of samples
from the edge
oxidation patterns
patterns
observed
to
where
the outer
would
unreacted
for the
from the
that were stressed
in the diffusion-controlled
oxidation
remained
variables
of oxygen.
number
core type of effect
diffusion
of other
the interior
with the oxidation
cross-sections
be used to
could
based
in oxygen
the removal
that correlated
energy
numbers,
saturate
is deprived
For a high local Sherwood
be completely
NASA/TM--2000-210520
the gradients
also considered
two regimes
Sherwood
the midline
rate constant,
show regimes
kinetics
of oxygen
and the interior
the model
oxidation
number
At low local
numbers,
in turn could
rate constant.
Sherwood
along
Also the effect
at steady-
for several
concentration
and activation
and the reaction
are low and high levels
the interior
Fiber
pressure,
of crack
was first investigated
i.e., reaction
length.
oxidation
was determined
which
and reaction-controlled
At high local Sherwood
tows would
gases,
coefficient
with diffusion-controlled levels
number,
to consider
model
Plots of the oxygen
from other variables,
and reactant
from the diffusion
The
the 2-D plane
of the local Sherwood
temperature,
as the product
was adapted
plane.
across
numbers.
the contributions
coefficient,
method
bridging
concentration
the effect
determine
difference
tows in a crack
The oxygen
different
finite
perimeter
progress
further
until the reaction
regime, of fiber inward. front had
reached model
them.
For a low local Sherwood
predicted
outer
perimeter
Even
when
a generalized showed
most
times
greater
used to predict The oxygen
the rectangular
a much
simpler
the 2-D plane.
as well as for the fiber
had been reacted,
showed
than the thickness)
the oxygen
remnants
along
across
this midline
regime,
Fiber
the
tows at the
tows in the very center.
of carbon
tows remained
This would solution
cross-sections
wall finite
difference
wall finite allow
to be used
difference
a slightly
121
across
could
models
model)
could
finite
be
of the section. for much
of the width
column
simpler
in the analysis
model
approximation
two-thirds
that the single
(i.e., a width
in the center
give a good
the central
and kinetics.
NASA/TM---2000-210520
enough
the thickness
would
It was shown
and the continuous
analytical
the bumped
(approximately
cross-section).
wall model.
that for wide
concentration
cross-section
solution
fit the bumped
throughout
of oxidation
analysis
concentration
of the overall
analytical
signs
in the reaction-controlled
of the 2-D plane.
The geometry three
oxidation
95% of the carbon
throughout
number
of
( 1-D be corrected
difference
of a cross-section's
to
model oxidation
or
4. CONCLUSIONS 1.
As seen from environmental modeling,
the oxidation
controlled
regime
regime
diffusion-controlled
material
component was under
that the interior occurred
front
in two primary regime.
and theoretical
regimes,
i.e, the diffusion-
The temperature
The temperature
range
range
for the
for the
there
lives were longer tension
and strains
and weight
was saturated
was a strong
loss rates
in oxygen
temperature
to failure
were lower
were lower.
and relatively
dependence. when
Calculations
In this the indicate
slow oxygen/carbon
reactions
throughout.
this regime,
that there
analysis,
was 800°C - 1500°C.
regime,
In the diffusion-controlled
material
occurs
was 500°C-800°C.
regime
In the reaction-controlled regime,
.
of carbon
microstructural
and the reaction-controlled
reaction-controlled
.
studies,
component
was under
regime, lives were
tension
NASA/TM--2000-210520
was a less of a temperature
shorter
and weight
was a sharp gradient
and a shrinking
there
in oxygen
core of the carbon
and strains
loss rates
to failure
were higher.
concentration fiber
122
tow arrays
were
dependence. higher
Calculations
up to the moving was seen.
when indicate
reaction
In the
Thermogravimetric
4,
energy
of 64.1 kJ/mol
activation
,
analysis
energy
The carbon
fiber
composite
of 7.6 kJ/mol
within
was under
stress
from
and the closing
of matrix
(550°C
from
10 to 25 ksi caused
prolonging
oxidized
or not.
- 1500°C).
of boron
was susceptible
a 67-82%
life and retaining
,
The
finite
difference
and oxidation
kinetics
concentrations, directly
diffusion
to the kinetics.
the influence coefficient,
NASA/TM---2000-210520
fibers
in oxygen
when
i.e., the formation
across
the reaction
of silica
was under
the whole
stresses
method
in cracked
concentration,
other
temperature
an increase
were effective
in stress
in significantly
the composite
was under
for studying
the oxidation
composites.
rate constant
123
The local
and the local Sherwood
variables
of
to failure.
The use of the local Sherwood
of several
self-protected
stresses
of 1454°C.
is an effective
of carbon
gradients
relate
also allows
model
in times
inhibitors
even
high as 10 and 25 ksi at a temperature
effects,
on if the
became
from 750°C-1500°C,
oxidation
strength
depending
when the composite
reduction
containing
and an apparent
the material
to oxidation
At temperatures
an activation
from 600°C - 1400°C.
stress,
However,
gave
of 500°C-600°C
due to matrix
cracks.
oxygen
very differently
Without
900°C-1400°C
range
range
for temperatures
a matrix
at temperatures
The addition
fiber in flowing
in the temperature
10 and 25 ksi, the carbon
.
of carbon
number
to be determined,
and temperature.
trends
oxygen number
as a variable i.e., the
as
.
Simplified to predict
finite
difference
the oxygen
models,
concentration
and 1-D and 2-D analytical and kinetics
cases,
depending
on the accuracy
required,
types
of analysis.
For thorough
investigations,
the whole depending
crack
on the geometry)
long dimension)
NASA/TM
bridging
plane
(or mirrored
will be required
to be determined.
2000-210520
124
the
solutions
can be used
for much
of a cross-section.
1-D model
can be sufficient
for most
a complete
finite
model
one-quarter for comer
difference
or one-eight and end effects
In most
sections, (ends
of the
for
5. APPENDIX
- STUDYING
The effects analysis
was conducted
crack bridging
diffusion
regime
of a 24x24
and for the reaction containing
that varied randomly
rest of the carbon
their effect
containing
model.
on the oxidation
was studied
controlled cells.
Flaws
As in the previous
analyses
for the
were randomly
cells were assigned
from 7.5 to 10 times the reaction
cells.
fiber tows.
for conditions
regime.
These
The
pattern of a
array of crack bridging
tow array in the 2-D plane
into 25% of the carbon
rate constant
model,
consisting
OF FLAWS
using the finite difference
in order to determine
of the fiber
controlled
introduced
were analyzed
cross-section
The oxidation
a reaction
rate constant
using
for the
the finite difference
the fiber tows are ten cells in diameter. Oxidation
both kinetic oxidation 25%,
of flaws
THE EFFECT
patterns
regimes patterns
at 25%,
for one-quarter
is located
very dependent Oxidation perimeter
presence
right-hand
primarily
was consumed,
the reaction
of flaws
tows was observed
as oxidation
NASA/TM--2000-210520
A generalized progressed.
by less reacted
125
A1-A3
to move
minimal
for
which
is
had little effect.
of carbon.
reacted.
Pockets
regions
in Figures
A1 -A6, the center of the cross-
of flaws
for the reaction
75%, and 95% carbon
had little effect.
the interior surrounded
the presence
for
of the
It is seen that in this regime
front continued
patterns
are shown
Examples
are shown
along the outer perimeters
of the oxidation for 25%,
regime
corner.
reacted
cross-section.
In all of the figures,
on the supply of oxygen,
occurred
A4-A6
controlled
reacted.
at the lower,
Examples Figures
of the overall
for the diffusion
75%, and 95% carbon
section
75%, and 95% of the carbon
Once
the outer
inward.
controlled Again,
were not observed.
are shown
it was seen that the
oxidation
of consumed
regime
of most of the fiber carbon
fiber tows in
in
In conclusion,for the flaws andflaw distributioninvestigated,the presenceof flaws hadlittle effectin theoxidationpatterns.In the reactioncontrolledregime,the flaws only hada localizedeffect. In the diffusion controlledregime,the effectwasalso localizedbut the supplyof oxygenwasthe primaryfactorin determiningthe overall oxidationpattern.
NASA/TM--2000-210520
126
iiiiiiii!iiii_!ii!i
iii!iii ii!iiiii iii
_. k-. T
Figure
A1.
controlled
NASA/TM--2000-210520
Example regime.
of a 25% One-quarter
carbon
reacted
plot of a 24x24
127
cross-section
for the diffusion
fiber tow array.
Figure
A2.
controlled
Example regime.
NASA/TM--2000-210520
of a 75% carbon One-quarter
reacted
plot of a 24x24
128
cross-section
for the diffusion
fiber tow array.
i!iiiiiiiiii!iiii
!_iiiiiiiiiiiii:i
Figure
A3.
controlled
Example regime.
NASA/TM--2000-210520
of a 95% carbon One-quarter
reacted
plot of a 24x24
129
cross-section fiber
for the diffusion
tow array.
FigureA4. Exampleof controlled
regime.
NASA/TM--2000-210520
a 25% carbon
One-quarter
reacted
plot of a 24x24
130
cross-section fiber
for the reaction
tow array.
iii!_iiiiiiiiiiii_ i,!i_i
tiiiii_iiiii
Figure A5. Example of a 75% carbon reacted cross-section for the reaction controlled regime. One-quarter plot of a 24x24 fiber tow array.
NASA/TM--2000-210520
131
Figure
A6.
controlled
NASA/TM--2000-210520
Example regime.
of a 95% carbon One-quarter
reacted
plot of a 24x24
132
cross-section fiber
for the reaction
tow array.
6. BIBLIOGRAPHY Bird, R. B.; Stewart, W. E.; Lightfoot, Inc., New York, 1963. Camus,
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at
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Abstract Park,
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REPORT Public reporting burden gathering and maintaining
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SUBTITLE
5.
Oxidation
Cracked
Kinetics
Ceramic
of Continuous
Matrix
Carbon
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data sources, aspect of this 1215 Jeffersoo 20503.
3. REPORT TYPE AND DATES COVERED
DATE
June 2001 4.
this
information Operations and Reports. Prelect (0704-0188), Washington, DC
Fibers
Memorandum
FUNDING
NUMBERS
in a
Composite
WU-242-82-77-00 IL161102AH45
6. AUTHOR(S) Michael
C. Halbig 8. PERFORMING ORGANIZATION
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) National ,aeronautics and Space Administration John H. Glenn Research Center Cleveland, Ohio 44135-3191 and
REPORT NUMBER
E-12487
U.S. Am_y Research Laboratory Cle_eland, Ohio 44135-3191 9. SPONSORING/MONITORING
AGENCY NAME(S) AND ADDRESS(ES)
10. SPONSORING/MONITORING
National Aeronautics and Space Administration
AGENCY REPORT NUMBER
Washington. DC 20546-43001 and
NASA
U.S. Army Research Laboratory Adelphi, Maryland 20783-1145
TM--2000-210520
ARL-TR-2296
11. SUPPLEMENTARY NOTES This
report
to the Case tion
code
was
submitted
Western
as a dissertation
Reserve
University,
5130,216--433-265
Subject
fulfillment Ohio,
person,
12b.
24
Available electronically
Experimental
Distribution:
observations
in the temperature °C. When fibers.
C/SiC
of Science
C. Halbig,
organiza-
DISTRIBUTION
CODE
reduction a finite
Nonstandard
suggest analysis
under
material
stress,
in times
was
to failure was
fibers.
model
allows
atically,
i.e., temperature,
The
reaction
unstressed, was
developed,
as a function
activation
from which
diffusion
301-621-0390.
in flowing
matrix
the influence
rate constant,
regimes fiber
effects
of 7.6 kJ/mol
Increasing
the
°C. Based
the diffusion
of important
variables
coefficient,
environment,
stress
NSN 7540-01-280-5500
and reaction of 64.1
from
from
900 to 1400
from
10 to 25 ksi caused
on experimental
on oxidation and sample
into
results, a matrix
kinetics
kJ/mol
600
to
°C protected
the
a 67 to
observation, crack
that is
to be studied
system-
geometry.
15. NUMBER OF PAGES composite;
17. SECURITY CLASSIFICATION OF REPORT Unclassified
energy
for temperatures
o_" oxygen
14. SUBJECT TERMS matrix
i.e., diffusion
gave an activation
at temperatures
750 to 1500 simulates
of temperature,
oxygen
energy
not observed.
at temperatures
model
by carbon
primary
of carbon
self-protection
difference
bridged
two
Information,
of 500 to 600 °C and an apparent composite
When
and theory,
and results
Thermogravimetric range
82 percent
Ceramic
of Master
Michael
at ht_;p://gltrs.grc.nasa.gov/GLTRS
kinetics.
internal
for the degree
Responsible
STATEMENT
This publication is available from the NASA Center for AeroSpace 13, ABSTRACT (Maximum 200 words)
1400
2000.
- Unlimited
Category:
controlled
of the requirements
May
l.
12a. DISTRIBUTION/AVAILABILITY Unclassified
in partial Cleveland,
Oxidation
kinetics;
Carbon
14"7 16. PRICE CODE
fiber
18. SECURITY CLASSIFICATION OF THIS PAGE
19. SECURITY CLASSIRCATION OF ABSTRACT
Unclassified
Unclassified
20. LIMITATION OF ABSTRACT
Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z39-18 298-102
