Much work was undertaken to develop techniques of incorporating SiC whiskers into either a Si3N4 or SiC matrix. The result was the fabrication of ceramic composites with ever-increasing fracture toughness and strength. To complement this research effort, the fracture behavior of whisker-reinforced ceramics is studied so as to develop methodologies for the analysis of structural components fabricated from this toughened material. The results, outlined herein, focus on the following areas: the use of micromechanics to predict thermoelastic properties, theoretical aspects of fracture behavior, and reliability analysis

Duffy, Stephen F.

English

NASA Technical Reports Server

N88-2 410
WHISKER-REINFORCED CERAMIC COMPOSITES FOR
HEAT ENGINE COMPONENTS*
Stephen F. Duffy
Cleveland State University
Cleveland, Ohio
ABSTRACT
Much work has been undertaken to develop techniques of incorporating SiC whisk-
ers into either a Si3N 4 or SiC matrix. The result has been the fabrication of
ceramic composites with ever-increasing fracture toughness and strength. To
complement this research effort, the fracture behavior of whisker-reinforced
ceramics is studied so as to develop methodologies for the analysis of struc-
tural components fabricated from this toughened material. The results, out-
lined herein, focus on the following areas: the use of micromechanics to
predict thermoelast_c properties, theoretical aspects of fracture behavior,
and reliability analysis.
*Work performed on-site at NASA Lewis for the Structural Integrity Branch
under grant NCC3-81.
3-21
https://ntrs.nasa.gov/search.jsp?R=19880013026 2020-03-20T06:31:23+00:00Z
SCOPE
Current research activities are being focused on upgrading the performance of
heat engines by increasing operating temperatures. With this goal in mind,
whisker reinforced ceramics with improved strength and fracture toughness are
being investigated for use as structural components in engine hot sections.
Even though the fracture toughness of these composites is improved relative to
unreinforced ceramics, they remain brittle in nature. Work has been initiated
to identify and develop probabilistic methods required in the analysis of
whisker-reinforced ceramic components. In addition, approaches using micro-
mechanics to predict thermoelastic properties are under review.
• OBJECTIVES
• TOUGHENING MECHANISMS
• CRACK GROWTH MITIGATION PROCESSES IN WHISKER-REINFORCED CERAMICS
• IMPROVEMENTS IN STRENGTH AND TOUGHNESS
• MICROMECHANICS AND WHISKER ORIENTATION
• ELASTIC MATERIAL PROPERTIES
• WEIBULL DATA
• RELIABILITY ANALYSIS
• SUMMARY
CD-88-32512
3-22
OBJECTIVE
The objective of this effort includes the identification of whisker reinforced
ceramics for use in engine hot sections. Further, the technical thrust is
directed towards developing and/or refining analytical methods and computer
codes that adequately predict fast fracture and life. The effort complements
concurrent research by other organizational groups within NASA, the federal
government, academia, and industry.
• IDENTIFY WHISKER REINFORCED CERAMICS FOR USE IN
ENGINE HOT SECTIONS
• DEVELOP AND REFINE ANALYTICAL METHODS AND
COMPUTER CODES FOR PREDICTING
-- FAST FRACTURE
-- LIFE
CD-88-32513
3-23
TYPICALTOUGHENINGMECHANISMSFORCERAMICS
Historically, three approaches have been taken to improve fracture toughness.
One approach is to engineer the grain size and shape to provide a tortuous
microstructure such that the path of the crack tip is deflected from the opti-
mum orientation for crack growth. The second approach creates microstructures
containing second-phase particles resulting in transformation toughening.
Here, a zone surrounding the crack tip absorbs energy and shields the tip by
reducing the near field stress. The third approach, including whiskers in the
matrix, increases toughness by pinning, deflecting, and/or bridging the crack
tip.
• ENGINEERING GRAIN SIZE AND SHAPE
CRYSTALSHAPEOR
GRAIN BOUNDARY
PHASE DEFLECTS
l ACK ND/OR
ABSORBSENERGY
I
MICROSTRUCTURECREATESA
TORTUOUSPATH OF LEAST
RESISTANCEFORADVANCINGCRACK
• CREATING MICROSTRUCTURES WITH
SECOND-PHASE PARTICLES
I ° ,%0 o
° °]METASTABLE0 o IREGIONS
e_,) ° o 0 0 I ABSORB ENERGY,I'_ I''[" _-" o 0 0 ] CLOSINGCRACK
I_0_o o o o I
!
"ADVANCINGCRACKTIP TRANSFORMS
REGIONSAS IT PASSES
• ADDING HIGH-STRENGTH WHISKERS
t _L_l/l_ / WHISKERSABSORB
__ I(_/_ ENERGYIN DEFLECTION
AND/ORPULLOUT
_ADVANCING CRACKTIP BRANCHES,
WHISKERSBREAK,TRAILINGWHISKERS
RESISTOPENING
CD-88-32514
3-24
CRACKGROWTHMITIGATIONPROCESSES- WHISKEREINFORCEDCERAMICS
It has been demonstrated experimentally that dispersing whiskers in a brittle
matrix will mitigate crack growth. The presence of whiskers at the crack tip
modifies fracture behavior by effectively increasing the required crack driv-
ing force through several mechanisms. As noted previously, these mechanisms
include c_ack deflection, crack pinning, and whisker bridging. Faber and Evans
(1983) have studied crack deflection and provide a lucid discussion. Lange
(1971) discussed the process of crack pinning, and Wetherhold (1987) provides
a probabilistic treatment of the crack bridging phenomenon.
THREE PROCESSES INCREASE FRACTURE TOUGHNESS
• CRACK DEFLECTION
-- TILTING
-- TWISTING
• CRACK PINNING
• WHISKER BRIDGING
SEVERAL PROCESSES MAY OPERATE SIMULTANEOUSLY
CD-88-32515
3-25
IMPROVEMENTSIN STRENGTHANDTOUGHNESS
The addition of SiC whiskers in a Si3N 4 matrix offers potential for considera-
ble improvement in fracture toughness and strength. Note that the raw mate-
rials necessary for fabricating these composites are nonstrategic and are
inherently lightweight. Initial attempts to develop whisker composites with
these materials met with varying degrees of success (e.g., increased fracture
toughnes_ and decreased strength). Recently, Buljan et al. (1987) at GTE Labo-
ratories, Inc., reported improvements in both toughness and strength over the
entire range of whisker contents tested.
HOT PRESSED Si3N4"SiC WHISKER COMPOSITES
8
FRACTURE 7
TOUGHNESS,
SIC,
MPa.m _
4
0
-- 900 --I 900
/
800 8 r--" _--I 800
,oo
I I I _ 4o0 4, , , ,-J400
10 20 30 0 10 20 30
SiC CONTENT, (vol %)
1000 °C 1200 °C
MODULUS
OF
RUPTURE
MPa.m _
CD-88-32516
3-26
ANALYTICALAPPROACH
The analytical approach taken involves the development of an integrated com-
puter algorithm. The algorithm consists of (i) a micromechanics preprocessor,
(2) a fintie element code capable of incorporating material anisotropy, and
(3) a statistical failure postprocessor. Proposed use of MSC/Nastran as the
finite element code is based on its anisotropic analysis capability and wide-
spread user base. The preprocessors and postprocessors are currently under
development.
MICROMECHANICS J
DEVELOPPREPROCESSORFOR
PREDICTIONOF ELASTIC
THERMOMECHANICALPROPERTIES
I ISTRESSANALYSIS
STATISTICAL
FAILURE
ANALYSIS
USE EXISTING FINITE-ELEMENT
CODESFOR ANISOTROPIC
ELASTICANALYSIS
DEVELOPAND REFINE FAILURE
CRITERIAAND INCORPORATE
INTO A POSTPROCESSOR
CD-88-32517
3-27
MICROMECHANICSANDWHISKERORIENTATION
The thermoelastic properties of ceramic whisker composites are determined by
process-induced whisker orientation and the constituent properties. Possible
material symmetries resulting from fabrication include isotropy, transverse
isotropy, and orthotropy. To characterize the internal structure, a whisker
orientation distribution function is adopted. This approach was suggested by
Pipes et al. (1982). The function quantifies all states of orientation, from
random to perfectly aligned.
MATERIAL SYMMETRIES
*ISOTROPIC
• TRANSVERSELYISOTROPIC
• ORTHOTROPIC
DEFINEWHISKER ORIENTATIONPROBABILITYFUNCTIONn(_) SUBJECTTO
Ix__ n(_)d_=l
WHEN
n(_) = CONSTANT
n(_) = 6(_- _)
RANDOM WHISKER ORIENTATION
ALIGNEDWHISKER ORIENTATION
HERE_ IS THE DIRAC DELTAFUNCTIONAND q IS THE PRINCIPAL
MATERIALDIRECTION
CD-88-32518
3-28
MICROMECHANICSTHEORY
The micromechanics theory proposed by Wu and McCullough (1977) for short fiber
polymer composites is being considered for adaptation to whisker-reinforced
ceramics. The theory was developed using variational techniques and incorpo-
rates the degree of whisker orientation, constituent properties, and volume
fractions. The method requires the properties of a reference orientation,
usually _aken as the random orientation state. The parameters f and g
define the orientation distribution and are included in the calculation of
volume averaged properties.
EXPRESSING THE EFFECTIVE ELASTIC MATERIAL CONSTANTS AS
<Cqkl'= Ci_kl+ F(Ci_kl,CqkI)f+ G(Ci_kl,Ciikl)0
WHERE
<Cijkl! PREDICTED ELASTIC CONSTANTS OF THE COMPOSITE
ELASTIC CONSTANTS FOR RANDOM WHISKER ORIENTATION
LINEAR COMBINATION OF THE CONSTITUENT ELASTIC CONSTANTS
THE PARAMETERS f AND O ARE FUNCTIONALLY DEPENDENT UPON n(_) AND DESCRIBE
THE ORIENTATION STATE. WHEN
f=g=O RANDOM WHISKER ORIENTATION
/=g=l ALIGNED WHISKER ORIENTATION
CD-88-32519
3-29
PLANAR WHISKER ORIENTATION
The planar orientation of whiskers is often encountered in hot pressed compos-
ites. This special case was considered by Pipes et al. (1982). The orienta-
tion descriptors fp and gp along with the distribution function are defined
below. Bozarth, et-al. (1987) developed a Monte Carlo simulation that depicts
the whisker orientation for specified values fp.
APPLYING THE CONCEPT TO A PLANAR ORIENTATION OF WHISKERS
n(¢,) = K cos (X_)
fp = 2(cos 2 _i- 1
WHERE
THEN
2fp('l- 2fp)
Ixl2(COS2_)= J--_12 n(_) COS2_ d_
= 0,1 TRANSVERSE ISOTROPY
0<_<10RTHOTROPY
A MONTE CARLO SIMULATION ILLUSTRATES GRAPHICALLY VARIOUS _ VALUES
fp = 0.0 fo = 0.3 fp = 0.6 fo = 0.9
CD-88-32520
3-30
INFLUENCE OF WHISKER ORIENTATION ON MATERIAL PROPERTIES
The influence of orientation on material properties is show below (from Pipes
et al., 1982). Both the elastic modulii and the coefficients of ther,ml expan-
sion are plotted for a short glass fiber phenolic resin matrix composite. The
constants are plotted over the full range of fp. Note that for fp =: 1 and
f = 0, _he material is transversely isotropic For all other values, the ma-p
terial is orthotropic.
PREDICTIONS USING THE APPROACH FOR A SHORT FIBER POLYMER COMPOSITE
FIBER ASPECT RATIO =40-100; FIBER CONTENT BY WEIGHT = 580/0
THERMAL
EXPANSION
COEFFICIENT,
OF-1
30p
20
10
0
ORIENTATION PARAMETER, fp
5
- _ YOUNG'S
_./ MODULUS,
i I i-T- 
•2 .4 .6 .8 1.0 0 .2 .4 .6 .8 1.0
ORIENTATION PARAMETER, fp
CD-88-32521
3-31
ELASTICMATERIALPROPERTIES
The examples shown below of stress-strain curves corresponding to various
whisker contents were reported by Shalek et al. (1986). Note that the curves
exhibit a linear stress-strain response up to the point of fracture. This
indicates that crack growth involves only brittle fracture and allows for the
applicatign of linear elastic fracture mechanics (LEFM).
SiC WISKER-HOT-PRESSED Si3N4
FOUR-POINTBEND STRESS-STRAINCURVES
20 V0L % SIC-, ./
600 L (1750 oC) //_/
500_ 10 VOL % SIC--, //
/ (1850 °C) Y////Zo
s'r.Ess,.p_3ool- /// c,.oo#C
] j'//"--30 VOL % SiC
/ f,// (1750 °C)
,oo]- //_,0volvos,c
/' iF (1750oc)
100 J'--"//" \'- 0 VOL% SiC
[ / (175o.c)
_" I I I I
0 400 800 1200 1600
MICROSTRAIN
400 --
ELASTIC
MODULUS, 321]
GPa
r-i
360 --
280 -- O 1750 \
_ 1650 \
240. i_ 1100 i _
0 10 20 30 4O
SiC WHISKER CONTENT, VOL %
CD-88-32522
3-32
WEIBULL MODULUS
Greatly improved reliability has been cited by a number of authors, including
Claussen and Petzow (1985), who have reported the highest Weibull modulus (m =
24) in the open literature. Improved processing techniques have resulted in
the reduction of inhomogeneities, uniform whisker distribution, and a dense
matrix. : However, the variability of strength is still too high for the appli-
cation of deterministic fracture theories.
300/0 SiC-WHISKER-Si3N4-MATRIX COMPOSITE
WHISKER REINFORCED CERAMICS EXHIBIT A VARIABILITY IN STRENGTH; HENCE,
PROBABILISTIC METHODS OF ANALYSIS MUST BE APPLIED
PROBABILITY
OF
FAILURE
.999 --
.99 --
.9 --
•5 --
•2 --
.I --
.05--
.92
400
m=24
I I I 1
600 1000
FRACTURESTRENGTH,
MPa
CD-88-32523
3-33
TRANSVERSE ISOTROPY
As noted previously, depending on fabrication, a whisker composite may have
isotropic, transversely isotopic, or orthotropic material symmetry. It is
anticipated that the probabilistic methods used in the analysis of monolithic
ceramics will be appropriate for isotropic whisker composites. However, for
transversely isotropic whisker composites, the probability of failure Pf
must also reflect the preferred direction of the material di. This direction
is defined as the normal to the plane of isotropy. A simple but rigorous
method of including material symmetry in the functional dependence of Pf for
transverse isotropy is presented. A similar approach can be developed for
orthotropy.
TRANSVERSELY ISOTROPIC WHISKER COMPOSITES
PLANE OF ISOTROPY--,_ I x2
di _ ,t' di (UNIT VECTOR) / d;
,/;
HOT PRESSED INJECTION MOLDED
DEPENDENCE OF P! MUST REFLECT _ij, di, VOLUME AS WELL AS THE WEIBULL
PARAMETERS
P,=P,(oj djd V,....)
ASSUMING WEAKEST LINK THEORY IS APPROPRIATE, FORMULATE P! IN A WAY THAT
ACCOUNTS FOR THE ABOVE DEPENDENCE
CD-88-32524
3-34
TENSORIALINVARIANTS
As Pf is a scalar function, it must remain form invariant under arbitrary
proper orthogonal transformations. Form invariance is ensured if dependence is
taken on invariants that constitute an integrity basis or any subset thereof.
Tensorlal invariant theory (see Spencer (1971)) serves as the basic mathemati-
cal tool_in the development of the integrity basis. A subsequent geometric
argument is made in constructing a slightly different set of invariants that
corresponds to physical mechanisms related to fracture.
ADOPTTHE FOLLOWINGINTEGRITY BASIS:
11= oii I4 = di di oq
12= oij oji 15= di °ij Ojk dk
13 = oij °jk _rki
IDENTIFY DAMAGING STRESSTRACTIONVECTORS:
x2
x3''/_ xl _ ----
13, 14 MAXIMUM AND MINIMUM
NORMALSTRESSESIN
PLANEOF ISOTROPY
T1 NORMAL STRESS IN DIRECTION
OFd_
• /'2 SHEAR STRESSACTING ACROSSdi
CD-88-32525
3-35
FAILURE PROBABILITY AS A FUNCTION OF INVARIANTS
The dependence of Pf is subsequently taken on the invariants Ii, 12, 73,
and 14 . This new set of invariants corresponds to the magnitudes of the
stress traction vectors assumed to be the primary causes of fracture. These
invariants incorporate both the stress tensor aij and the direction vector
di. Adopting: the simplest of probabilistic failure theories, that is, a
noninteractive theory, results in the form of Pf shown in the figure.
FROM THE INTEGRITY BASIS CONSTRUCTINVARIANTS WITH PHYSICAL
INTERPRETATIONSCORRESPONDINGTO THE MAGNITUDESOF THE DAMAGING
STRESSTRACTIONVECTORS
x2 _ Si
.I I / 11
= COMPONENTOF Si ,""-:'_/_
PROJECTEDON
DIRECTIONdi,
/3 = V,(I1 -/4) + [('/,)12 -/5
+ 1/4(142-112)+ 1½)1114]½
= MAXIMUM NORMAL STRESSIN
PLANEOF ISOTROPY
/2 = (/5 -/42) ½
= COMPONENTOF Si
PROJECTEDON THE
PLANE OF ISOTROPY
/4 = Vz(/1 -/4) - [Fzl2 - Z5
-" MAXIMUM NORMAL STRESSIN
PLANEOF ISOTROPY
TAKING
Pf=PI QI' 12' 13' 14, V,...)
ENSURESPf IS FORM INVARIANT. ASSUMINGTHE INVARIANTSACT SEPARATELYIN
PRODUCINGFAILURE
= - + \_z/ + \_s) +v \13a/J .)
CD-88-32526
3-36
PLANE STRESS PROBABILISTIC ANALYSIS
The form of Pf is simplified for plane stress conditions considering two
planar orientations of the whiskers. In both cases it is assumed that the
whiskers are confined to the 1-3 plane due to fabrication. A random orienta-
tion of whiskers in the 1-3 plane reduces Pf to the isotropic formulation.
Alternatiyely, perfect alignment of the whiskers in the 1-3 plane reduces Pf
to a formulation proposed by Sun and Yamada (1978), Wetherhold and Pipes
(1984), and Cassenti (1984).
di- (0,1,0) / xl
1/'_ /,_ 1-3 PLANE IS
X2 4, /z _/_'I- C -_// THE PLANE OF
I/.,-_// ,so.,o.
y - :..:. t//._...._I V x3
ASSUMING PLANESTRESS
°"12 = 0"22= 023 = 0
THEN
WHERE 0.1AND 0.2ARE THE PRINCIPLE
STRESSESIN THE PLANEOF ISOTROPY
/di= (1,o,o)
X2_ //////A PLANE_,_/_._3,,_,s
,so,.,o,,,,
ASSUMING PLANE STRESS
°'13 = 0"23 = 0"33 = 0
THEN
'',
_o.,_"],,v!+ \_/ I
0D-88-32527
3-37
WHISKER BRIDGING
Attempts have been made to develop statistical models that account for the
microstructural events leading to crack propagation. Wetherhold (1987) de-
rived a model assuming that fracture behavior is dominated by whiskers bridg-
ing a critical damage zone. The damage zone is analogous to a microcrack which
is expected to grow and coalesce with other microcracks during progressive
fracture. A distribution function for composite strength is developed based
on the incorporation of random whisker strength into a bundle fracture theory,
THE FOLLOWING STATISTICAL APPROACH ACCOUNTS FOR THE
WHISKER BRIDGING MECHANISM
DEFINE
I
"---1-"
I
I
I
I
I
I
i ,-- BRIDGING/ WHISKER
I /
I
I
I
I
_ DAMAGEZONE
SPECIMEN OF
UNIT VOLUME
[A] = THE EVENT WHERE ULTIMATE COMPOSITE STRENGTH
IS GREATER THAN THE APPLIED LOAD
THEN
Ps = P[A]
N
= _ P[AJn=i]P[n=i]
i=o
WHERE
n NUMBER OF WHISKERS BRIDGING THE DAMAGE ZONE
N NUMBER OF FIBERS PER UNIT VOLUME
CD--88-32528
3-38
SUMMARY
Enoughexperimental data exist that strongly suggests whisker-reinforced
ceramics have promise, especially in the automotive industry where low-cost,
high-volume fabrication is a necessity. The Structural Integrity Branch is
identifying and refining existing design methodologies and, where necessary,
asslsting:the research community in developing new methodologies. At present,
there exists a need for analytical methods that capture the microstructural
events that lead to increased fracture toughness and strength. Finally, work
has begun on an integrated computer program capable of predicting elastic mate-
rial properties through the application of micromechanics, the state of stress
within a structural component, and the reliability of the component given the
state of stress.
EXPERIMENTAL DATA SHOW SIGNIFICANT INCREASES OF STRENGTH AND FRACTURE
TOUGHNESS DUE TO THE ADDITION OF CERAMIC WHISKERS IN A CERAMIC MATRIX
WHISKER COMPOSITES HAVE THE ATTRACTIVE FEATURE OF USING CONVENTIONAL
POWDER PROCESSING TECHNIQUES IN HIGH-VOLUME, LOW-COST FABRICATION
AN INTEGRATED STRUCTURAL ANALYSIS CODE IS BEING DEVELOPED WITH THE
FOLLOWING COMPONENTS:
-- MICROMECHANICS PREPROCESSOR
-- FINITE-ELEMENT PROGRAM
-- STATISTICAL FAILURE ANALYSIS POSTPROCESSOR
RESEARCH IS UNDERWAY TO DEVELOP AND REFINE STATISTICAL FAILURE THEORIES
TO ACCOUNT FOR MATERIAL ANISOTROPY ALONG WITH THE MICROSTRUCTURAL
EVENTS LEADING TO FAILURE (I.E., CRACK DEFLECTION AND WHISKER BRIDGING)
CD-88-32529
3-39
REFERENCES
Bozarth, M.J., Gillespie, J.W., and McCullough, R.L., 1987, "Fiber Orientation
and Its Effect Upon Thermoelastic Properties of Short Carbon Fiber Rein-
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pp. 74-81.
Buljan, S'.T., Baldoni, J.G., and Buckabee, M.L., 1987, "Si3N4-SiC Composites,"
Ceramic Bulletin, Vol. 66, pp. 347-352.
Cassenti, B.N., 1984, "Probabilistic Static Failure of Composite Material,"
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Claussen, H., and Petzow, G., 1985, "Whisker'reinforced Zirconia Toughened Cer-
amics," Tailoring Multiphase and Composite Ceramics; Proceedings of the
21st University Conference on Ceramic Science, Plenum Press, New York,
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Faber, K.T., and Evans, A.G., 1983, "Crack Deflection Processes - I. Theory,"
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3-40


Whisker-reinforced ceramic composites for heat engine components

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