Moduli determination of continuous fiber ceramic composites (CFCCs)

ELSEVIER

Journal of Nuclear Materials 219 (1995) 93-100

Moduli determination of continuous fiber ceramic composites (CFCCs) P.K. Liaw a, N. Yu b, D.K. Hsu c, N. Miriyala a W. Saini c, L.L. Snead d, C.J. McHargue a, R.A. Lowden d a Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN37996, USA b Department of Engineering Science and Mechanics, The University of Tennessee, Knoxville, TN 37996, USA c Center for NDE, Iowa State University, Ames, 1,4 50011, USA a Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA

Abstract NicalonTM/silicon carbide composites were fabricated by the Forced Chemical Vapor Infiltration (FCVI) method. Both through-thickness and in-plane (fiber fabric plane) moduli were determined using ultrasonic techniques. The through-thickness elastic constants (moduli) were found to be much less than the in-plane moduli. Increased porosity significantly decreased both in-plane and through-thickness moduli. A periodic model using a homogenization method was formulated to predict the effect of porosity on the moduli of woven fabric composites. The predicted moduli were found to be in reasonably good agreement with the experimental results.

1. Introduction Ceramic matrix composites (CMCs) are increasingly becoming recognized as candidate materials for hightemperature structural applications [1-3]. CMCs are quite advantageous because they are lightweight structural materials that exhibit a much higher resistance to high temperatures and aggressive environments than metals or other conventional engineering materials. Potential applications include gas turbines, heat exchangers, and structural components in aerospace industry. Most of these applications require engineering parts with high reliability [2]. Monolithic ceramics are highly sensitive to process and service-related flaws, making them inherently brittle. Due to their low toughness, these materials fail catastrophically. Continuous fiber reinforced ceramics (CFCCs) or whisker reinforced CMCs, however, can provide a significant amount of toughness as well as avoid catastrophic failure [1-3]. Up to the present time, relatively little work has been performed on the mechanical behavior of woven fabric reinforced CMCs, particularly with regard to the elastic moduli [3-8]. There is little theoretical model-

ing work [7] to predict the moduli of woven fabric composites in open literature. In this investigation, moduli of Nicalon T M ( S i - C - O ) fiber fabric reinforced SiC composites were measured using an ultrasonic technique and a theoretical model was formulated to predict the moduli of woven fabric composites.

2. Experimental procedure 2.1. Material

A woven Nicalon T M (Si-C-O) fiber fabric-reinforced SiC composite system was studied. The NicalonT M fibers were 10 to 15 I~m in diameter, with a chemical composition (in wt%) of 59% Si, 31% C and 10% 0 2. The fiber fabrics are typically categorized into plain and satin weaves, as shown in Fig. 1. In this work, plain weave was used to fabricate the composite. The fiber fabric was rotated in 30 increments (i.e., fiber orientations in each ply were [0/90], [30/120], and [60/150]). Approximately forty plies were present per centimeter thickness. The fiber fabrics were pyrolitically coated with 0.3 ~m carbon by a chemical vapor deposition

0022-3115/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022- 3115(94)00664-4

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P.I£ Liaw et al. /Journal of Nuclear Materials 219 (1995) 93-100

(a) Plain Weave

(b) Satin Weave

Fig. 1. Fiber fabric architecture. (a) Plain weave, (b) satin weave.

technique [3]. In this technique, the carbon coating is obtained by the decomposition of propylene gas at about ll00°C. The laminated fiber fabric preform was densified by the Forced Chemical Vapor Infiltration (FCVI) technique developed at the Oak Ridge National Laboratory [3]. A schematic of the FCVI method is shown in Fig. 2. In this process, the decomposition of methyltrichlorosilane, in the presence of hydrogen gas at around 1000°C, yields silicon carbide, which infiltrates the porous fiber fabric preform, and the by-product hydrochloric acid. The fibrous preform is retained in a

HEATING ELEMENT

graphite holder that contacts a water-cooled metal gas distributor, thus cooling the gas inlet and side surfaces of the preform. The opposite end of the fibrous preform is exposed to the hot zone of the furnace. This arrangement creates a steep temperature gradient across the preform. The reactant gases, methyltrichlorosilane and hydrogen, are forced under pressure into the cooled side of the perform where they initially do not react because of the low temperature. The gases flow from the cooled portion of the preform into the hot portion, where the silicon carbide matrix material begins to deposit on the fibers. Deposition of

HOT ZONE EXHAUSTGASES

PERFORATED LID

@

COMIK)SITE

GRAPHITE HOLDER

m@

HOT SURFACE FIBROUS PREFORM WATERCOOLED SURFACE

COLD SURFACE

REACTANT GASES Fig. 2. Schematic of the forced chemical vapor infiltration (FCVI) process to fabricate NicalonTM/SiC composites.

P.K Liaw et al. /Journal of Nuclear Materials 219 (1995) 93-100

)

95

X3

5mm

I

~X 2

1 2.Smm Fig. 3. Specimen geometry for moduli measurements.

silicon carbide within the hot region of the preform increases the density, and therefore, the thermal conductivity of the preform. As the conductivity increases, the deposition zone moves progressively from the hotter regions towards the cooler regions. The process continues until reduced permeability of the densified composite prevents a sufficient flow of reactant gases into the preform. The composites thus fabricated had a nominal fiber volume fraction of 0.4. Using the FCVI method, several disks of 7.6 cm in diameter and 1.25 cm in thickness were fabricated for the present investigation.

axis). Moduli along the through-thickness direction and the in-plane (i.e., the fiber fabric plane) direction ( X 1 or X 2 axis) were measured. Note that along the through-thickness direction, the specimen contained approximately 20 plies. Based on the acoustic wave theory [9,10], the elastic modulus ( E ) can be expressed as a function of ultrasonic velocity by Eq. (1).

E=o

V2(3V2L-4V2)

(1)

where p is the density of the material, Vs the shear velocity, and VL the longitudinal velocity. Longitudinal waves were used to carry out ultrasonic measurements. The longitudinal modulus (C) is related to the longitudinal velocity by Eq. (2).

2.2. Moduli measurement Moduli measurements were performed using an ultrasonic technique. Specimens (25 mm × 25 mm × 5 mm) were machined from the Nicalon TM reinforced SiC composite disks for modulus determinations (Fig. 3). The fiber fabric plane of the specimens was perpendicular to the thickness direction of the fabricated composite disks. A ceramic cutting machine, accurate to 0.025 mm, was used to cut the specimens. As shown in Fig. 3, the fiber fabric plane of the specimen was perpendicular to the through-thickness direction ( X 3

C =pV~

(2)

The longitudinal modulus is not to be confused with the elastic modulus; it is called the "elastic stiffness constant" or "longitudinal modulus of elasticity" [9,10]. To calculate the elastic moduli, it is necessary to make ultrasonic measurements using shear waves. However, it was difficult to make the shear velocity measurements due to the porous nature of the samples.

Transmitter

Transmitter S,~ Rubber Sheet

Fused Quartz ~eferencePiece Receiver Receiver (a) Reference test system without the presence of sample

(b) Test system with the presence of sample

Fig. 4. Ultrasonic measurement setup.

96

P.K. Liaw et al. /Journal of Nuclear Materials 219 (1995) 93-100

Porosity at the Fiber Tow Intersection

Ultrasonic measurements were performed by dry coupling to avoid contamination resulting from the couplant. A "pulse-echo overlap method" was used to measure the wave velocities. A schematic of the experimental setup is shown in Fig. 4. The reference signal was obtained by passing ultrasonic longitudinal waves through a reference test system comprised of a rubber sheet and a fused quartz piece. The test sample was then placed between the transmitting transducer and the rubber sheet in the reference test system, and ultrasonic longitudinal waves were passed through the setup. The signals were received by the receiving transducer and captured by an oscilloscope. The signal peaks from the reference test system, with and without the presence of the sample, were matched as closely as possible, and from the phase shift between the two, the time taken by the ultrasonic waves to travel through the sample was measured. The thickness of the sample divided by the time required for the ultrasonic longitudinal waves to pass through the sample was taken as the ultrasonic longitudinal velocity through the sample. Since the two signals are matched as closely as possible (i.e., overlapped), this technique is referred to as the pulse-echo overlap method. In this investigation, both in-plane and throughthickness ultrasonic longitudinal velocities were measured by the ultrasonic technique. Using Eq. (2), the in-plane moduli (Cll and C22) and through-thickness moduli (C33) were determined. Note that Cll, C22 and C33 are elastic stiffness constants, as mentioned previously.

/

(a) Planar View

Interlaminar Porosity /

3. Results

3.1. Metallography

Metallographic examination of the composite was carried out to examine the type and distribution of porosity in the samples. Planar and cross-sectional views of a composite specimen are shown in Fig. 5. It could be seen from Fig. 5 that there were two major types of porosity in the NicalonTra/SiC composite, viz. porosity at the fiber tow intersection (Fig. 5a) and interlaminar porosity (Fig. 5b). The extent of interlaminar porosity was found to be greater than the porosity present at the fiber tow intersection. The composite was highly anisotropic, and hence, it could be expected that the mechanical properties of the NicalonTM/SiC composites will vary significantly along the in-plane and through-thickness directions. The density (as measured from the specimen weight and dimensions) and percentage porosity of the speci-

(19) Cross -Sectional View Fig. 5. Fiber architecture of NicalonTM/sic composites. (a) Planar view, (b) cross-sectional view.

mens are listed in Table 1. Note that the percentage porosity in the sample is given by Eq. (3). percentage porosity = (1 - measured density/theoretical density) X 100.

(3)

The density of the samples varied from 2.06 to 2.63 g / c m 3 and the percentage porosity from 11.2 to 30.4. The theoretical density of the composite is 2.96 g / c m 3, which is based on the density of 2.6 g / c m 3 for the NicalonTM fibers and 3.21 g / c m 3 for the SiC matrix, and a fiber volume fraction of 0.4. The variation of the

97

P.IC Liaw et al. /Journal of Nuclear Materials 219 (1995) 93-100 1.2

[~

.

'

I

o a

Through-Thickness In.Plane

300 ,

250-Ooo~ ~.

0.6

o

o

•~

.=-

z~ 0.2 15

20

25

30

°° °°

,50

o

Through-Thickness In-Plane ~

•

•

Oo

1oo

o • _

•

5o

'~ 10

,

-~~"'~-,~

200

0.8

i

.

35

o

i

i

i

15

20

25

'-,,,e..~

% Porosity 10

Fig. 6. Ultrasonic velocity versus percentage porosity in Nicalon'rM/SiC composites. porosity allowed us to evaluate the effect of porosity on the moduli of the composites.

30

35

% Porosity

Fig. 7. Longitudinal moduli versus percentage porosity in NicalonTM/sic composites.

3.2. Ultrasonic measurements

The longitudinal moduli of the composites were determined in both in-plane and through-thickness orientations. The results are summarized in Table 1. The ultrasonic velocities and longitudinal moduli values are plotted against percentage porosity in Fig. 6 and 7, respectively. It could be seen that the ultrasonic velocities were greater in the in-plane direction (0.799 to 0.994 X 104 m / s ) than in the through-thickness direction (0.167 to 0.725 × 104 m / s ) . Consequently, the in-plane longitudinal moduli (130 to 248 GPa) were

greater than the through-thickness longitudinal moduli (6 to 138 GPa), as could be expected from the fabric layup. From Fig. 6, it could also be seen that porosity had a greater effect in reducing the ultrasonic velocities in the through-thickness direction than in the in-plane direction because of the greater extent of interlaminar porosity compared to the porosity at the fiber tow intersection (Fig. 5). It should be noted that the ultrasonic measurements yielded comparable C1] and C22 values along the fiber fabric plane (Fig. 3).

Table 1 In-plane and through-thickness longitudinal moduli of Nicalon/SiC composites Sample no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a

Density (g/cm 3) 2.55 2.45 2.45 2.32 2.33 2.37 2.13 2.06 2.07 2.41 2.39 2.44 2.09 2.07 2.10 2.63 2.62 2.60 2.46 2.34

Ultrasonic velocity.

% Porosity 13.85 17.23 17.23 21.62 21.28 19.93 28.04 30.41 30.07 18.58 19.26 17.57 29.39 30.07 29.05 11.15 11.49 12.16 16.89 20.95

In-plane velocity a

In-plane modulus

( X 10 4 m / s )

Through-thickness velocity a (x 10 4 m / s )

0.987 0.990 0.994 0.927 0.927 0.936 0.814 0.799 0.812 0.972 0.957 0.972 0.877 0.897 0.873 0.967 0.950 0.956 0.949 0.951

0.471 0.477 0.465 0.364 0.377 0.378 0.220 0.219 0.227 0.512 0.442 0.552 0.167 0.195 0.179 0.725 0.685 0.653 0.629 0.525

248.41 239.83 242.56 197.65 200.22 205.88 137.16 129.60 133.85 228.64 217.97 226.75 155.36 165.75 159.28 245.93 236.82 237.35 203.90 211.18

Through-thickness modulus (GPa)

(GPa)

56.57 55.68 53.08 30.47 33.12 33.58 10.02 9.74 10.46 63.44 46.50 73.13 5.63 7.83 6.70 138.24 123.12 110.74 89.57 64.36

P.K. Liaw et aL/Journal of NuclearMaterials219 (1995) 93-100

98

age periodic disturbance strains can be related to the stress-free strains by [12] +oo

X3

<:>.o=[r][c~] E (fa,glga{e*1} nDn2,n 3

x

+/a2g2ga{'*2}) Cylla~drical Fiber To

/

";ii)~i~ili~iii!i!i!~!iii!iii:.i!i:i!i,~ ~*"/~" """""'"'

for a = 1, 2,

(6)

where the term (nl, n2, n 3) = (0, 0, 0) is excluded in the summation, and the components of the fourth-order tensor, F, are given by

Void Fig. 8. A model based on periodic microstructure.

,(

F~=~

e2 - 2 ( 1 -

1+,.)

for a = 1 , 2 , 3 ,

4. Theoretical modeling

-1 A micromechanics model based on a periodic structure was developed to estimate the effect of porosity on the elastic properties of the woven fabric composites. As shown in Fig. 8, a representative unit cell, which is repeated in all directions, consists of eight woven fiber tows in the shape of elliptic cylinders and one parallelepiped that is used to model the interlaminar porosity as depicted in Fig. 5b. When the infinite composite with a periodic microstructure is subjected to a homogeneous strain field, e °, due to the existence of periodically distributed fibers and voids, the resulting stress and strain fields are tr ° + tr°(xl, x 2, x 3) and ~0 + EP(Xl, x2 ' x3), where tr ° and E° are homogeneous (average) stresses and strains, and tr p and ~P are periodic disturbance stress and strain fields, respectively. The elastic moduli of the composite are defined by Eq. (4). {~r°} = [ffl{e°}.

(4)

Based on Eshelby's [11] concept of transformation strain, one can replace the porous heterogeneous unit cell by a homogeneous cell composed of matrix material only and prescribe stress-free strains in the fibers (/21) and voids (/2z) such that the average stress and average strain fields remain the same everywhere in the unit cell before and after the homogenization. That is, the following consistency conditions (Eq. (5)) must hold:

[CD1]{" 0"1-D1}

=

[:q{,o + in

~'~2,

for ( : , / 3 ) = (1, 2), (2, 3), (3, 1),

1 ( 1 2 2

[cM]{: +

)

ro~=0 otherwise, and

ni

ai V t-~ ] + =~2 + , a 3 1 G M and v M are the shear modulus and Poisson's ratio of the matrix; 2a i (i = 1, 2, 3) are the dimensions of the unit cell; n i are integers; fa, and fa2 are fiber and void volume fractions, respectively. The shape and size of the fibers and voids are accounted for in gl and g2. For elliptic-cylindrical fiber tows,

gl

= ~t [COS~ -"~ arna '/ COSl[ '-"~ t r n 2} ' c o s ( ~ ) c o s ( x

'rrn3..~)

(gA + gB),

where 2smt--~2

(5a)

_1

for ( a , / 3 , 3') = (4, 2, 3), (5, 3, 1), (6, 1, 2),

[cM]{ e'Oq-<'P>D,--'*I}

in /21,

2G~(i _ v~) ~e ~

ro~ = r . =

gA

)Jl 1

\ a--~ + ( - -

= , .

(5b)

where the angle brackets with the subscript /21 (/22 ) represent the volume average over /21 (/22); Ca~, Caff = 0), and C M are the stiffnesses of fibers, voids, and matrix, respectively; E *1 and E *z are the stress-free homogenization strains prescribed in fibers and voids and are approximated by distinct constants. The aver-

,B= i=nlcl t ,/tn c212+ln3c,)2)

P.K~ Liaw et al. /Journal of Nuclear Materials 219 (1995) 93-100 300

'

'

'

I

o

t

•

Measured Predicted

250

200

150

=-

o %

I O0 5

I

I

I

I

I

10

15

20

25

30

35

% Porosity Fig. 9. Comparison of predicted and measured in-plane longitudinal moduli in NicalonTM/SiC composites.

with c 1 (or c 2) and c 3 being the principal radii of the elliptic cross-section and c 2 (or c I) the length of the cylinder; J1 is the Bessel function of the first kind. For a parallelepiped,

99

much less than the in-plane moduli. This trend could be related to the greater amount of interlaminar porosity than the porosity at the fiber tows intersection, as shown in Fig. 5. Increased porosity significantly decreased both in-plane and through-thickness moduli. A periodic model using a homogenization method is formulated to predict the influence of porosity on the moduli of woven-fabric composites. The theoretical prediction showed the decreased moduli with increased porosity. Moreover, the in-plane moduli are predicted to be in reasonably good agreement with the experimental results. Nevertheless, the predicted moduli are found to be slightly larger than the experimental results. In the formulation of the theoretical model, only the [0/90] plies are considered without the inclusion of the off-angle plies of [30/120] and [60/150]. The inclusion of the off-angle plies in the theoretical model could alter the differences between the predicted and measured moduli. Moreover, the calculated moduli could be considered as the upper bounds on C1~ and C33 values [12].

[ 'rrn3

= c°sl-5- ) 6. Conclusions

sin(arnlbltsin('rrn2b21sin(aVn3b_____~3 al

X

]

~

a2

]

a3

(,rrnlbl ](,rtn2b 2 / ( rrn3b3 ) al

1~

as

]

/ ,

a3

where 2b i are the dimensions of the parallelepiped. After solving the consistency conditions for suitable * ~ and E * 5, which preserve the same stress and strain fields before and after homogenization, the elastic moduli of the porous woven-fabric composites are thus determined by Eq. (7). [C]{e0} = [CM]({e0} =fo,{ e *1} nt_f.O2{E .2}).

(7)

To calculate the moduli of the composites, the following input data were used [13]: the shear modulus and Poisson's ratio of the Nicalon TM fiber were 80 GPa and 0.12, respectively, and those of the matrix were 146 GPa and 0.2. Fig. 9 presents the predicted in-plane modulus Cl1(= C22) of the NicalonTM/SiC composites versus percentage porosity. Increased porosity was found to decrease the stiffness, as observed experimentally (Fig. 7). Moreover, there is an excellent agreement between the predicted and measured moduli, as could be seen from Fig. 9.

5. Discussion In this investigation, both through-thickness and in-plane moduli are determined using ultrasonic methods. The through-thickness moduli are found to be

Nicalon TM fiber woven-fabric reinforced silicon carbide composites were fabricated by the Forced Chemical Vapor Infiltration (FCVI) technique. Both through-thickness and in-plane moduli were measured using ultrasonic methods. The in-plane moduli were found to be greater than the through-thickness moduli. Increased porosity was found to significantly decrease both through-thickness and in-plane moduli. A periodic model using a homogenization technique was developed to predict the effect of porosity on the moduli of woven fabric composites. The theoretical model predicted the decreased moduli with increased porosity. Also, the predicted moduli were found to be in reasonably good agreement with the experimental values.

Acknowledgements This work is supported by the Department of Energy under contract No. Martin Marietta llX-SL261V to the University of Tennessee. We are grateful to Dr. Arthur Rowcliffe and Dr. Everett Bloom of the Oak Ridge National laboratory (ORNL) for their encouragement and support. We would like to thank Mr. Nik Chawla of the University of Tennessee for his help in the preparation of the manuscript and Mr. Francis Rebillat of O R N L for providing the composite mechanical property data used in the present study.

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P.K~ Liaw et al. /Journal of Nuclear Materials 219 (1995) 93-100

References [1] K.K. Chawla, Ceramic Matrix Composites (Chapman & Hall, London, 1993) pp. 4-10. [2] J.A. DiCarlo, Adv. Mater. Proc. 135 (1989) 41. [3] T.M. Besmann, B.W. Sheldon, R.A. Lowden and D.P. Stinton, Science 253 (1991) 1104. [4] N. Chawla, P.K. Liaw, E. Lara-Curzio, R.A. Lowden and M.K. Ferber, Proc. Int. Symp. on High Performance Composites: Commonality of Phenomena, Rosemont, Illinois, USA, October 2-6, 1994, eds. K.K. Chawla, P.K. Liaw and S.G. Fishman (TMS, Warrendale, 1994) p. 291. [5] Y.L. Wang and S.V. Nair, paper presented at the 96th Annual Meeting of the American Ceramic Society, Indianapolis, IN, April 24-28, 1994. [6] P.K. Liaw, D.K. Hsu, N. Yu, N. Miriyala, V. Saini, H. Jeong and K.K. Chawla, Proc. Int. Symp. on High Performance Composites: Commonality of Phenomena, Rose-

[7] [8]

[9] [10] [11] [12] [13]

mont, Illinois, USA, October 2-6, 1994, eds. K.K. Chawla, P.K. Liaw and S.G. Fishman (TMS, Warrendale, 1994) p. 377. N.J. Fang and T.S. Chou, J. Am. Ceram. Soc. 76 (1993) 2539. N. Miriyala, P.K. Liaw, C.J. McHargue, L.L. Snead, D.K. Hsu and V.K. Saini, Fusion Materials Semiannual Report for the Period Ending March 31, 1994, Department of Energy (1994) p. 419. H. Jeong, D.K. Hsu, R.E. Shannon and P.K. Liaw, Metall. Trans. A 25 (1994) 799. H. Jeong, D.K. Hsu, R.E. Shannon and P.K. Liaw, Metall. Trans. A 25 (1994) 811. J.D. Eshelby, Proc. R. Soc. London A 241 (1957) 376. S. Nemat-Nasser, N. Yu and M. Hori, Mech. Mater. 15 (1993) 163. J.L. Bohet, Ph.D. Thesis, Bordeaux, France, 1993.