The stress rupture strength of silicon carbide fiber-reinforced silicon carbide (SiCSiC) composites with a boron nitride (BN) fiber coating decreases with time within the intermediate temperature range of 700-950 C. Various theories have been proposed to explain the cause of the time dependent stress rupture strength. Some previous authors have suggested that the observed composite strength behavior is due to the inherent time dependent strength of the fibers, which is caused by the slow growth of flaws within the fibers. Flaw growth is supposedly enabled by oxidation of free carbon at the grain boundaries. The objective of this paper is to investigate the relative significance of the various theories for the time-dependent strength of SiCSiC composites. This is achieved through the development of a numerically-based progressive failure analysis routine and through the application of the routine to simulate the composite stress rupture tests. The progressive failure routine is a time marching routine with an iterative loop between a probability of fiber survival equation and a force equilibrium equation within each time step. Failure of the composite is assumed to initiate near a matrix crack and the progression of fiber failures occurs by global load sharing. The probability of survival equation is derived from consideration of the strength of ceramic fibers with randomly occurring and slow growing flaws as well as the mechanical interaction between the fibers and matrix near a matrix crack. The force equilibrium equation follows from the global load sharing presumption. The results of progressive failure analyses of the composite tests suggest that the relationship between time and stress-rupture strength is attributed almost entirely to the slow flaw growth within the fibers. Although other mechanisms may be present, they appear to have only a minor influence on the observed time dependent behavior

Sullivan, Roy M.

NASA Technical Reports Server

National Aeronautics and Space Administration
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A Numerical Solution Routine for Investigating Oxidation-Induced 
Strength Degradation Mechanisms in SiC/SiC Composites
Roy M. Sullivan
Materials and Structures Division
NASA Glenn Research Center
Cleveland, OH
Materials Science & Technology 2015
October 4-8, 2015 
Greater Columbus Convention Center
Columbus, OH, USA 
https://ntrs.nasa.gov/search.jsp?R=20150023066 2019-08-31T05:00:38+00:00Z
National Aeronautics and Space Administration
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0
50
100
150
200
250
300
350
400
1.00E+00 1.00E+02 1.00E+04 1.00E+06
C
o
m
p
o
si
te
 S
tr
es
s 
(M
Pa
)
Time (sec)
815 C fast fracture from Brewer,
Calomino, Verilli (unpublished)
815 C rupture data from Morscher,
Hurst, Brewer 2000
880 C rupture data from Morscher,
Hurst Brewer 2000
fast fracture 
strength
2
What causes the time dependent strength degradation in SiC/SiC
composites at intermediate temperatures (700 – 900 °C)?
Hi-NicalonTM composite
8 plies thick
Tow spacing: 17 epi
500 filaments per tow
R = 7mm
f = 0.1965
Stress versus time-to-failure of Hi-NicalonTM composite specimens at intermediate 
temperatures from Morscher, Hurst and Brewer (2000). 
National Aeronautics and Space Administration
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Time Dependent Strength Degradation Mechanisms
Theory #1: Oxidation of BN fiber coating causes fusing of fibers to one another and to 
matrix resulting in embrittled composite. 
• Fusing causes local load sharing (LLS): Fibers adjacent 
to failed fibers are overloaded, causing a cascading of 
fiber failures and composite failure.
• Embrittlement is time dependent since extent of the 
cross-section that is fused increases with time.
2322
2
3
2 NOBOBN 
glassteborosilicaSiOOB  232
Heredia, et al. (1995)
Morscher (1997)
Glime and Cawley (1998)
Morscher, Hurst and Brewer (2000)
Morscher and Cawley (2002).
Micrograph of SiC/SiC composite showing oxidized BN 
fiber coating. Courtesy of Ram Bhatt (NASA/GRC).
National Aeronautics and Space Administration
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Time Dependent Strength Degradation Mechanisms
Theory #2: Oxidation of SiC fiber results in tensile stress in fiber.
• Molar volume of silica is greater than SiC causing 
compression in oxide and tension in fiber.
• Tensile stress in fiber increases with time since 
oxide thickness grows with time.
• Results in an apparent loss in fiber strength over 
time.
2222 COSiOOSiC 
Xu, Zok and McMeeking (2014)
Hay (2012).
SiC SiO2
2O
SiC fiber
Fiber with oxide scale
SiC matrix
Matrix crack 2
O
National Aeronautics and Space Administration
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Time Dependent Strength Degradation Mechanisms
Theory #3: SiC fiber strength is intrinsically time dependent due to slow crack 
growth in fibers. 
Rupture time versus stress for Hi-NicalonTM single filaments 
and tows at 800 °C. Data from Gauthier and Lamon (2009).
Forio, Lavaire and Lamon (2004)
Gauthier, Pailler, Lamon and Pailler (2009)
Gauthier and Lamon (2009).
Some evidence of slow crack growth 
on fiber fracture surfaces
At intermediate temperatures, tows and 
single fibers have a stress vs time-to-
failure relationship that follows
Atnf 
1.00E+00
1.00E+01
1.00E+02
1.00E+03
1.00E+04
1.00E+05
1.00E+06
1.00E+07
100 300 500 700 900 1100 1300 1500 1700 1900
Ti
m
e 
(s
ec
)
Stress (MPa)
Hi-NicalonTM
800 °C
National Aeronautics and Space Administration
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Objective
• Investigate the cause of the time-to-failure vs. stress relationship in SiC/SiC
composites with a BN fiber coating at intermediate temperatures.
Approach
• Develop a progressive failure analysis routine (based on Theory #3) and 
apply it to simulate the composite stress rupture tests that produced the 
results shown on the first slide. The ability to simulate the stress vs. time-to-
failure behavior will judge its validity.
Assumptions
• Composite failure initiates at a matrix crack.
• The progression of fiber failure occurs under global load sharing (GLS).
National Aeronautics and Space Administration
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






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
m
o
f
o
f
SL
L
P

exp1
2









Y
K
C
s
f
Ic
i

n
IK
dt
dC
v 1
Fiber Failure Model (Relationship between Pf –  – t)
Time-to-failure versus applied stress for Hi-NicalonTM single fibers (gold circles) 
and tows (black squares) at 800 °C from Gauthier and Lamon (2009).
1
m
n
IcK
Fitting the probability of failure curves to the 
data, one can extract values for the constants
oS
m
n
f
o
n
Ic
on
f
PL
L
K
S
nY
t
2
2
2
1
1
1
ln
)2(
2






















1.00E+00
1.00E+01
1.00E+02
1.00E+03
1.00E+04
1.00E+05
1.00E+06
1.00E+07
100 300 500 700 900 1100 1300 1500 1700 1900
Ti
m
e 
(s
ec
)
Stress (MPa)
Pf = 0.998
Pf = 0.002
Fast Fracture Strength
Flaw Growth Velocity (Davidge, et al., 1973)
Weibull FF Strength Distr.
Flaw Growth Parameters
Weibull Statistical Parameters
Fracture Toughness
National Aeronautics and Space Administration
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




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



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


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
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 

2
2
1
2 )2(
2
1
exp1 n
nm
f
m
o
ICn
m
o
f
S
K
tnY
L
L
P 
m
n
f
o
n
Ic
on
f
PL
L
K
S
nY
t
2
2
2
1
1
1
ln
)2(
2






















Rearrange the previous expression to get an expression for 
the Probability of Failure
Length effect
National Aeronautics and Space Administration
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Progressive Failure Analysis (PFA) Routine
fo
o
f
AN
F
N
N

• Add time step, 
























 

2
2
1
2 )2(
2
1
exp1 n
nm
f
m
o
ICn
m
oo
f
S
K
tnY
L
L
N
N
P 
ttt ii  1
Converge?
yes
no
• Iterate between two equations
Global Load Sharing (GLS) Model
• Numerically similar to Lara Curzio (1997)
• Based on Global Load Sharing (GLS) Model
Prob. of Survival
Force Equilibrium
N number of fibers that are not failed
Flowchart
oN number of fibers initially
F
N
f
Cross-sectional area of fibersfA
National Aeronautics and Space Administration
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0
200
400
600
800
1000
1200
1400
1 100 10000 1000000
A
p
p
lie
d
 T
o
w
 S
tr
es
s 
(M
Pa
)
Time (sec)
10
PFA Simulation of Tow Tensile Tests from Gauthier and Lamon (2009)
F
500oN
F
f
f
NA
F

Model results
200
250
300
350
400
450
500
550
1 10 100 1000 10000 100000 1000000
N
u
m
b
er
 o
f 
Fi
b
er
s 
R
em
ai
n
in
g
Time (sec)
1100 MPa
800 600 
400 
0
200
400
600
800
1000
1200
1400
1600
1800
1 10 100 1000 10000 100000 1000000
Fi
b
er
 S
tr
es
s 
(M
p
a)
Time (sec)
mmLo 25
National Aeronautics and Space Administration
www.nasa.gov 11


f
z
E
Ef
f
R
l m
)1(
2


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
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
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


E
E f

f
T


the fiber radius
the fiber volume fraction in loading 
direction
the sliding resistance shear stress
m E
Em
l
Analysis of Composite Systems
Matrix crack
Assumption: Composite failure initiates at a 
matrix crack.
Aveston, Cooper and Kelly (1971)
Curtin (1991)
Curtin (1994)
Curtin, Ahn and Takeda (1998)
Thouless and Evans (1988)
Matrix 
stress
Fiber 
stress

Slip length
R

f
R
2
National Aeronautics and Space Administration
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

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1
2
)2(
2
12
exp1
22
1
2
n
mn
T
S
K
tnY
L
l
P
n
mn
m
o
ICn
m
o
f 
Length of fiber loading is now 2l and probability of failure now 
involves fiber stress at crack plane T
Analysis of Composite Systems
E
Ef
f
R
l m
)1(
2










National Aeronautics and Space Administration
www.nasa.gov 13
h

fpoftot ANNTNAAF   )(
 h
R
p


2
For a single matrix crack, force equilibrium 
at crack plane requires




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
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
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
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 p
ofo
o
N
N
AN
F
N
N
T 1
Analysis of Composite Systems
totA
Average Pull-out stress
Average Pull-out length*h
* Expression for average pull-out length 
obtained from Thouless and Evans (1988)
Rearranging
f
T

h
R
2
unbroken
broken
R/2
f
E
E f

l
Force carried by 
unbroken fibers
Force carried by 
broken fibers via 
pullout stress
National Aeronautics and Space Administration
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0
1
2
3
4
5
6
7
8
9
10
100 120 140 160 180 200 220 240
C
ra
ck
 S
p
ac
in
g 
(m
m
)
Composite Stress (Mpa)
Crack Spacing and Shear Stress Calculations
Shear stress can be estimated from crack density 
measurements when cracks are saturated.
mc
x
Crack density versus composite stress for Hi-NicalonTM
composite from Morscher and Cawley (2002)
Aveston, et al. (1971)
Kimber and Keer (1982)
Curtin (1991)
x
Matrix crack
E
Ef
f
R
x mmc
)1(
2
337.1



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
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MPa5
mR m7
1965.0f
mmx 4.0
MPamc 130
E
Ef
f
R
x mmc
)1(
2
337.1










National Aeronautics and Space Administration
www.nasa.gov 15
0
0.5
1
1.5
2
2.5
3
0
1
2
3
4
5
6
7
8
9
10
100 150 200 250 300 350
R
at
io
 o
f 
sl
ip
 le
n
gt
h
 t
o
 c
ra
ck
 s
p
ac
in
g
C
ra
ck
 S
p
ac
in
g 
(m
m
)
Composite Stress (Mpa)
crack spacing
l/x ratio
f
z
l2
Multiple Matrix Cracks within the Slip Length of One Another


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
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

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



x
l
N
N
AN
F
T
o
fo 111
Force Equilibrium at Central Crack 
Plane (Curtin, et al. (1998))
Crack spacing and the ratio l/x versus composite stress. Crack 
spacing from crack density data from Morscher and Cawley (2002).
Matrix crack
AB
E
Ef
f
R
l m
)1(
2










x
f
T









x
l2
1
Number of matrix cracks within the 
slip length of any one matrix crack
Central crack
If matrix cracks are close enough, fiber failures in 
nearby matrix cracks affect the force equilibrium 
equation in a central matrix crack plane
National Aeronautics and Space Administration
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











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


 p
ofo
o
N
N
AN
F
N
N
T 1
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
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
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
1
2
)2(
2
12
exp1
22
1
2
n
mn
T
S
K
tnY
L
l
N
N
P
n
mn
m
o
ICn
m
oo
f 
Progressive Failure Analysis routine now involves:
Analysis of Composite Systems




















x
l
N
N
AN
F
T
o
fo 111
Multiple Matrix CracksSingle Matrix Cracks
Iteration Iteration
Prob. of survival
Force equilibrium
National Aeronautics and Space Administration
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Analysis of Composite Systems
towspliesepi
mm
5.67)8)(17(
4.25
6.12






750,33)500(5.67 oN
12.6 mm
8 plies
0
50
100
150
200
250
300
350
400
1.00E+00 1.00E+02 1.00E+04 1.00E+06
C
o
m
p
o
si
te
 S
tr
es
s 
(M
Pa
)
Time (sec)
Multiple 
Matrix Cracks
Single 
Matrix Crack
500 fibers per tow
tow spacing 17 epi
R = 7 mm
Lo = 25 mm
matrix cracking stress
0
50
100
150
200
250
300
350
400
1.00E+00 1.00E+02 1.00E+04 1.00E+06
C
o
m
p
o
si
te
 S
tr
es
s 
(M
Pa
)
Time (sec)
9% fiber 
damage
Multiple Matrix Cracks
500 fibers per tow
tow spacing 17 epi
R = 7 mm
Lo = 25 mm
Tau = 5 MPa
matrix cracking stress
Results: Each line represents a series 
of PFA solutions
Note: Marshall and Evans (1985) measured a shear 
stress value in other SiC fiber-reinforced ceramic 
matrix composites in the range of 2 - 2.5 MPa.
National Aeronautics and Space Administration
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Discussion and Conclusions
• The time dependent strength of Hi-NicalonTM fiber reinforced composites 
has been shown to be largely due to the intrinsic time dependent strength 
of the fibers. Other mechanisms (e.g. fusing and embrittlement) may have 
a small effect at later times.
• Best agreement with the measured time-to-failure versus composite 
stress was obtained with progressive failure analyses solutions using 
multiple matrix crack formulation and with a combination of shear stress 
values between 3.5 – 5 MPa and fiber damage values of < 9%.
• If slow crack growth in fibers requires oxidation of inter-granular interface, 
what is the source of oxygen? Does it flow from the surrounding 
atmosphere down a matrix crack or is there enough present in the 
constituents? SiC fibers? BN fiber coating?
National Aeronautics and Space Administration
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Aveston J., Cooper G.A. and Kelly A., “Single and Multiple Fracture,” pp. 15-26 in the Properties of Fiber Composites, Conference Proceedings of the 
National Physical Laboratory. IPC Science and Technology Press Ltd. Surrey, England, 1971.
Curtin W.A., “Theory of Mechanical Properties of Ceramic Matrix Composites,” J. Am. Ceram. Soc., 74 [11] 2837-45 (1991).
Curtin W.A., “In-situ Fiber Strengths in Ceramic Matrix Composites from Fracture Mirrors,” J. Am. Ceram. Soc. 77 [4] 1075-78 (1994).
Curtin W.A., Ahn B.K. and Takeda N., “Modeling Brittle and Tough Stress-Strain Behavior in Unidirectional Ceramic Matrix Composites,” Acta mater. 
46 [10] 3409-3420 (1998).
Davidge R.W., McLaren J.R. and Tappin G., ”Strength-probability-time (SPT) relationships in ceramics,” Journal of Materials Science 8 1699-1705 
(1973).
Forio P., Lavaire F. and Lamon J., “Delayed Failure at Intermediate Temperatures (600 – 700 °C) in Air in Silicon Carbide Multifilament Tows,” J. Am. 
Ceram. Soc. 87 [5] 888-893 (2004).
Gauthier W., Pailler F., Lamon J. and Pailler R., “Oxidation of Silicon Carbide Fibers During Static Fatigue in Air at Intermediate Temperatures,” J. Am. 
Ceram. Soc. 92 [9] 2067-2073 (2009).
Gauthier W. and Lamon J., “Delayed Failure of Hi-Nicalon and Hi-Nicalon S Multifilament Tows and Single Filaments at Intermediate Temperatures 
(500 °C – 800 °C),” J. Am. Ceram. Soc. 92 [3] 702-709 (2009).
Glime W.H. and Cawley J.D., “Stress Concentration Due to Fiber-Matrix Fusion in Ceramic-Matrix Composites,” J. Am. Ceram. Soc. 81 [10] 2597-604 
(1998).
Hay R.S., “Growth Stress in SiO2 During Oxidation of SiC Fibers,” J. Appl. Phys. 111 (2012).
List of References
National Aeronautics and Space Administration
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Heredia F.E., McNulty J.C., Zok F.W. and Evans A.G., “Oxidation Embrittlement Probe for Ceramic Matrix Composites,” J. Am. Ceram. Soc. 78 [8] 
2097-2100 (1995).
Kimber A.C. and Keer J.G., “On the Theoretical Average Crack Spacing in Brittle Matrix Composites Containing Continuous Aligned Fibers,” Journal of 
Materials Science Letters, 1 353-354 (1982).
Lara-Curzio E., “Stress-Rupture of Nicalon/SiC Continuous Fiber Ceramic Composites in Air at 950 C,” J. Am. Ceram. Soc., 80 [12] 3268-72 (1997).
Marshall D.B. and Evans A.G., “Failure Mechanisms in Ceramic Fiber/Ceramic Matrix Composites,” J. Amer. Ceram. Soc., 68 [5] 225-31 (1985).
Morscher G.N., “Tensile Stress Rupture of SiCf/SiCm Minicomposites with Carbon and Boron Nitride Interphases at Elevated Temperatures in Air,” J. 
Am. Ceram. Soc. 80 [8] 2029-42 (1997).
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National Aeronautics and Space Administration
www.nasa.gov 21
Acknowledgements
This work was funded by the Transformational Tools and Technologies 
Project and the Transformative Aeronautics Concepts Program under 
NASA’s Aeronautics Research Mission Directorate. 


A Numerical Solution Routine for Investigating Oxidation-Induced Strength Degradation Mechanisms in SiC/SiC Composites

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