Acta metall, mater. Vol. 42, No. 6, pp. 2089-2098, 1994
~
Pergamon
0956-7151(93)E0099-O
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FIBER FRACTURE D U R I N G THE CONSOLIDATION OF
METAL MATRIX COMPOSITES
J. F. GROVES, D. M. ELZEY and H. N. G. WADLEY
Department of Materials Science and Engineering, University of Virginia, Charlottesville,
VA 22903, U.S.A.
(Received 9 August 1993)
Abstract--A detailed study of conditions leading to fiber fracture during the consolidation of
Ti-14wt %A~21 wt%Nb/SiC (SCS-6) composite monotapes has been conducted. For this continuous fiber
reinforced composite system, the incidence of fracture increases with consolidation rate at higher process
temperatures. Increasing consolidation temperature at a fixed pressure reduces the number of breaks per
unit length of fiber. Examination of partially densified compacts has revealed the existence of significant
fiber bending and ultimately fracture due to monotape surface roughness (asperities) which places the
fibers in three point bending. A representative volume element has been defined for the consolidating
lay-up and its response analyzed to predict the fiber deflection (and hence probability of failure) when
the surface asperities deform either by plasticity or by steady state creep. The relationships between fiber
fracture and process conditions predicted using the volume element are similar to those observed
experimentally. The cell analysis suggests that fiber fracture is decreased by increases in fiber stiffness,
strength, and diameter and by decreases in matrix yield and creep strength and monotape surface
roughness.
Rfsum~--Une &ude d&aill6e des conditions qui mdnent ~. la fissure des fibres pendant la consolidation
des monotapes compos6s Ti-14wt%A1-21wt%Nb/SiC (SCS-6) a 6t6 effectu6e. Pour ce systdme compos6
r6inforc6 de fibres continues, l'incidence de fissure augmente avec le taux de consolidation fi des
temp6ratures de processus 61ev6es. L'augmentation de la temp6rature de consolidation ~i une pression fix6e
r6duit le nombre de fissures par unit6 de longueur dans les fibres. Une examination des compacts
partiellement densifi& a r6v616 l'existence d'une courbature importante des fibres et une 6ventuelle fissure
due aux fipretds de la surface du monotape, ce qui fait courber les fibres fi un point lorsque les bouts des
fibres restent fixes. Un 616ment de volume repr6sentatif a 6t6 d6fini pour le compos6 consolid6 et sa r6ponse
a 6t/~ analys6e pour prddire la d6flexion des fibres (et done la probabilit6 d'6chec) lors de la d6formation
des fipret6s de la surface soit par la plasticit6 soit par la d6formation non-temporelle ~i haute temp6rature
(steady state creep). Les relations pr6dites entre les fissures dans les fibres et les conditions des processus
en utilisant l'616ment de volume sont semblables ~, celles qui ont 6t6 observ6es dans les exp6riences.
L'analyse des cellules sugg6re que la fissure des fibres d6croit avec des augmentations en rigidit6, fortitude
et diam&re, et avec des d6croits en r6sistance totale de la matrice fi la d6formation et en r6sistance de
celle-ci fi la d6formation fi haute temp6rature ainsi qu'en fipret6 de la surface du monotape.
Zusammenfassung--Eine detaillierte Untersuchung der Bedingungen wurde durchgefiihrt, die bei der
Verdichtung von Ti-24AI 1Nb(gew.%)/SiC(SCS-6)-Verbundwerkstoff-Monotapes zum Faserbruch
ffihren. Bei diesem faserverst/irkten Verbundwerkstoffsystem nimmt die Fasersch/idigung bei h6heren
Temperaturen mit der Verdichtungsrate zu. Die Zahl der Briiche pro L/ingeneinheit nimmt bei konstanter
Spannung mit steigender Temperatur ab. Bei Untersuchungen von unvollstfindig verdichteten Proben
wurden h/iufig gebogene Fasern und, durch diese Verformung verursachte Briiche, beobachtet; die
Biegung ist der Oberflfichenrauhigkeit der Verbundwerkstoff-Monotapes zuzuschreiben. Mit Hilfe einer
Analyse eines verdichtenden Volumenelements, in dem der EinfluB eines viskoplastisch verformenden
Kontakts auf der elastischen Faser beschrieben wird, konnte die Faserbiegung (und dadurch die
Versagswahrscheinlichkeit) vorhergesgt werden. Das Modell zeigte eine gute ~lbereinstimmung gegeniiber
den experimentell beobachteten Verhfiltnissen zwischen Fasersch/idigung und ProzeBbedingungen. Dem
Modell zur Folge werden Verbundwerkstoffe mit minimaler Fasersch/idigung hergesteUt, in dem man
Fasern verwendet mit mfglichst hohem E-Modul, hoher Bruchfestigkeit und groBem Durchmesser. Die
Matrixmaterialien sollen eine mfglichst niedrige Streckgrenze und Kriechfestigkeit haben, die Monotapes
eine minimale Oberfl/ichenrauhigkeit.
1.
INTRODUCTION
The structural material needs o f the aerospace industry have stimulated the d e v e l o p m e n t of high-temperature materials for m a n y years. Today, materials
research for these a n d o t h e r h i g h - t e m p e r a t u r e applications is focusing u p o n c o n t i n u o u s fiber (e.g. silicon
carbide a n d a l u m i n u m oxide) reinforced metal (or
intermetallic) matrix composites because of their
attractive c o m b i n a t i o n o f specific stiffness a n d
2089
2090
GROVES et al.:
CONSOLIDATION OF METAL MATRIX COMPOSITES
strength both at ambient and high temperatures [1, 2].
Numerous processing approaches are being explored
for combining fibers and matrices into desirable end
products [3-5]. One increasingly favored approach
utilizes thin (200-550 #m) plasma-sprayed monotape
sheets consisting of uniformly spaced, continuous,
parallel fibers in an alloy matrix [6]. Lay-ups of these
monotapes can be consolidated to form near net
shape composite components by either hot isostatic
or vacuum hot pressing (HIP/VHP) [6]. The monotapes are produced by depositing plasma-melted alloy
droplets onto a unidirectional array of ceramic fibers
attached to a substrate. The tapes thus formed
(Fig. 1) typically have one smooth surface (the one in
contact with the substrate), one rough surface
(the last to solidify during deposition), and varying
degrees of internal porosity.
Several studies have reported the existence of fiber
fractures in numerous samples consolidated in this
way [5, 7-10]. However, little work has been done to
correlate fiber fracture with processing conditions, to
identify specific fiber fracture mechanisms, or to
develop predictive models of the damage process. The
one partial exception is the related work of Tszeng
et al. [11] on spherical powder-fiber compacts. They
observed that, during consolidation, individual powder particles impinged upon fibers and caused them
to bend and fracture. Based on these findings, Tszeng
et al. modeled this fiber fracture process using a
representative volume element consisting of an elastic
fixed-fixed beam (the fiber) undergoing bending as a
result of contact with a plastically deforming sphere
(the powder particle). The force exerted by the deforming particle was found to be responsible for the
fiber's fracture. Although insightful, Tszeng's study
of the interaction between powder particles and
individual fibers does not incorporate all of the
phenomena that occur in the monotape lay-ups of
interest here. For instance, it did not consider the role
of time dependent (creep) deformations which are
responsible for much of the densification during
monotape consolidation [12]. Further, the study did
not experimentally quantify the number of fiber
fractures associated with various processing conditions and did not use the calculated stress in a single
S(
sil
ca~
1.0
~
O3
._>
,~
0.8
0.6
0.4
tr
0.2
0"00
400
600
800
1000
Fracture Density cc (m-1)
Fig. 2. Predicted effect of processing-induced fiber fractures
upon the relative ambient temperature ultimate tensile
strength of a brittle matrix composite. The data are normalized by the strength for an undamaged composite [14, 15].
bent fiber to predict the number of fractures per
length of fiber for a set of processing conditions (i.e.
temperature and pressure).
In addition to limited discussion of the relationship
between consolidation induced fiber fracture and
processing conditions, the literature reports little
about the effect of consolidation damage upon mechanical properties [13]. One might expect a significant
degradation of the in-service properties of metal
matrix composite (MMC) components. The possibility can be assessed for ambient temperature
strength by a simple modification of Curtin's recent
analysis of the strength of a fiber reinforced composite [14, 15]. In the Curtin model, a Weibull
strength distribution statistically characterizes a
fiber's strength. This can be easily modified to
account for regions of the fibers which have zero
strength because of processing fractures
Equation (1) is a modified Weibull distribution that
characterizes the probability of fiber survival,
~b(L, tr), after tensile testing of a sample to an applied
stress a, where L is the total length of fiber being
stressed, L 0 is the specimen gauge length, tr0 is the
reference stress for the fiber (the stress at which the
survival probability is 1/e = 0.37), m is the experimentally determined Weibull modulus, and ct is the
number of fiber cracks per unit length of fiber after
processing (but before subsequent testing). Using (1)
for the fiber strength distribution, Curtin's analysis
leads to an expression for the composite's ultimate
tensile strength
O'ut s
Fig. 1. A cross sectional view of a typical plasma-sprayed
monotape. Note that the monotape has a smooth surface
(the one in contact with the substrate) and a rough one
(formed by solidifying droplets).
200
=f T I 1
ra° •
cttr°r •
where f is the fiber volume fraction, T is the stress
supported by the unbroken fibers, r is the fiber radius,
and z is the fiber-matrix interfacial sliding resistance.
Figure 2 shows the predicted relative strength
degradation that results from processing-induced
fiber fractures in a typical fiber reinforced
Ti-14wt%AI-21wt%Nb/SiC (SCS-6) composite.
GROVES et al.:
CONSOLIDATION OF METAL MATRIX COMPOSITES
When no fibers are broken (~t = 0), equation (2) yields
a tru~ = 1.6 GPa. The figure shows that fiber fracture
densities of around 100/(m of fiber) result in a 20%
loss of expected strength. One also anticipates that
creep resistance would be even more significantly
affected [16, 17]. To produce high quality composites
by consolidation processing, it is important to elucidate the influence of processing conditions upon, and
the mechanism responsible for, fiber damage. Then
strategies for eliminating such damage can more
confidently be pursued and more realistic models of
the damage evolution developed.
The work reported here seeks to do this. It investigates the relationships between consolidation conditions and fiber fracture, it identifies the dominant
mechanism of fiber fracture during monotape consolidation, and it proposes a unit cell micromechanical
model for the fracture process that incorporates the
competing effects of fiber and matrix deformation.
This model is used to predict the relationships between process conditions and fiber fracture and to
suggest process modifications which will reduce damage. A subsequent paper will develop a macroscopic
(stochastic) predictive model that incorporates
surface roughness and uses it to investigate the
consolidation process more fully [18].
2. MATERIALS
Plasma-sprayed monotapes composed of a
Ti-14wt%AI-21 wt%Nb matrix and continuous SCS6 silicon carbide fibers were provided by General
Electric (GE) Aircraft Engines (Lynn, Mass.). They
were produced using an inductively coupled plasma
deposition (ICPD) process. In this process, plasma
melted droplets of the metal matrix alloy are spray
deposited onto a continuous fiber array prewound
about a smooth cylindrical mandrel [19, 20]. Rotation
and translation of the mandrel during spraying ensures uniform distribution of the matrix material.
Two batches of spray-deposited monotape were used
here; they are designated LPS-485 and LPS-669. For
LPS-485 samples, the center-to-center fiber spacing
was 230 p m and the foil thickness was 0.42 mm while
the spacing for LPS-669 was 195 # m and the thickness 0.52 mm. Both batches of material had similar
surface roughness. A detailed analysis of the tapes
can be found in [21] and a complete characterization
of the matrix microstructure and its evolution during
processing in [22].
3. E X P E R I M E N T A L
The objectives of the experimental study were to (1)
establish the conditions under which fiber fracture
occurs during consolidation processing of plasma
sprayed Ti-14A1-21Nb/SCS-6 composites, (2) identify the fiber fracture mechanism, and (3) correlate the
number of fiber fractures with processing conditions
[21]. Test specimens for consolidation by either hot
2091
isostatic or vacuum hot pressing were prepared
from the monotapes by electrodischarge machining.
They were ultrasonically cleaned, first in acetone, and
then in methanol. Dissolution of the matrix showed
that fewer than 10 fiber fractures/m resulted from
sample preparation. For hot isostatic pressing, canisters were designed and constructed to accommodate
a stack of five 3 cm x 3 cm monotape layers. The
monotapes were stacked with their fibers parallel,
sealed in canisters by electron beam welding in a
5 m torr vacuum, and then consolidated in an ABB
Autoclave Systems QIH-15 HIP. Vacuum hot pressing of similar monotape lay-ups was conducted in an
ATS Model 2710 stress relaxation machine. A fixture
was designed and built to allow application of constrained uniaxial compression with stresses up
to 80MPa at temperatures as high as 1000°C in
vacuum.
Hot isostatic press conditions were varied to investigate the influence of temperature and pressure on
fiber fracture. For these experiments, LPS-485
samples were consolidated at temperatures of 825 °,
900 °, or 975°C and at pressures of 50, 100, or
200 MPa. Once attained, these conditions were maintained for half an hour. Samples were always heated
to full temperature prior to the application of the full
pressure. During heating it was necessary to maintain
a minimum "prepressure" of 2 MPa at ambient temperature, increasing to 6.5 MPa at 900°C. For all HIP
specimens, the heating rate was 20°C/min and the
pressurization rate 85 MPa/h. Cooling and depressurization to ambient conditions was performed over a
2 h period.
Two sets of vacuum hot press tests were performed.
The first set of experiments was conducted at low
pressures (2, 3.5, and 6.9 MPa) and at room temperature and was intended to investigate the effect of HIP
prepressurization upon fiber fracture. Both LPS-485
and 669 were investigated. The second set of experiments explored the influence of pressure ramp rate
upon fiber fracture. For these experiments, LPS-669
samples were used. The temperature in the evacuated
chamber was increased at 300°C/h until the specimens reached temperatures of 870 °, 955 °, or 1045°C.
Compressive loads were then applied at crosshead
displacement rates of 0.41, 0.80, or 1.67 cm/h, until
the pressure on the sample reached 50 MPa. This
pressure was held for 30 min before being rapidly
removed. The specimen was then cooled at approximately 200-300°C/h.
Because the monotape foils were thin, the HIP
specimens were found to deform significantly only in
the through-thickness direction. In-plane compressive stresses merely constrained the specimen from
lateral flow in the canister. Thus the stress state
experienced by the hot isostatically pressed specimens
approaches constrained uniaxial compression like
that of vacuum hot pressing, and it is reasonable to
presume that differences in the fiber fracture results
between hot isostatic and vacuum hot press tests are
2092
GROVES et al.:
CONSOLIDATION OF METAL MATRIX COMPOSITES
Table I. Experimentally determined Weibull parameters for SCS-6
fiber
Gauge
length
(cm)
Modulus (m)
Reference
stress (~0)
(GPa)
Unprocessed
2.54
12
4.52
Unprocessed +
acid etched
2.54
13
4.47
1.27
2.54
5.08
7.62
10.16
10
14
12
15
12
4.61
4.53
4.56
4.13
4.07
Fiber condition
f
Plasma sprayed +
acid etched
The results of these tests were used to generate a
two parameter Weibull distribution of the fibers'
strength.
4. RESULTS
Observations of fibers chemically removed from
as-received monotapes revealed that no fibers were
broken by the ICPD process. Their strengths were
measured and fit to a Weibull distribution, Table 1.
It can be seen that the fibers' strengths were not
significantly affected by the ICPD process. Thus, any
fiber damage observed after subsequent hot isostatic
or vacuum hot pressing can confidently be attributed
to either consolidation processing or sample preparation damage. The first two rows of Table 2
summarize the damage associated with sample preparation only. They show 5-7 preparation induced
fiber breaks per meter of fiber and may be expected
to contribute to the results of all tests. The remainder
of Table 2 summarizes the effect of processing on
fiber damage. It is apparent that every VHP and HIP
consolidation cycle has resulted in fiber fracture.
Sometimes, quite significant levels of fiber fracture
accompany consolidation. Table 2 shows that the
application of even small loads at room temperature
leads to fiber breaks and that LPS-669 samples
experienced significantly fewer fiber fractures than
those prepared from LPS-485 at all stress levels. This
is more clearly illustrated in Fig. 3 which plots the
fracture density versus applied load during VHP for
both materials.
only the result of using different processing conditions and/or different material batches.
The number of fiber breaks and distance between
them were determined after dissolution of the matrix
using 11.2 M H2SO 4 solution maintained at 90°C for
12-16 h. At the completion of this process, the fiber
segments were washed, dried, and their lengths
measured. Composite specimens were also sectioned
for metallographic analysis to investigate the mechanisms of fiber fracture. Metaliographic analysis involved sectioning a portion of each specimen along
all three major axes and inspecting the polished
surfaces using both optical and scanning electron
microscopy.
Finally, the strength of the SCS-6 fibers was
measured in tension. Both unprocessed fibers
and fibers extracted by acid etching from the
monotapes (prior to consolidation) were examined.
Table 2. Fiber fracture results
Test
Applied
stress
(MPa)
Temperature
(°C)
Displacement
rate
(cm/h)
Soak
time
(h)
Relative
density
Number of
fibers in
sample
Fracture
density
(m- i)
Intactd
fibers
(%)
Foil
Foil
0
0
20
20
NA
NA
NA
NA
NM
NM
109
136
6.8
5.0
95.4
95.6
VHP-01 a
VHP-02 a'c
VHP-03 b'¢
VHP-04a
VHP-05 b
2
3.5
3.5
6.9
6.9
20
20
20
20
20
NM
NM
NM
NM
NM
NA
NA
NA
NA
NA
NM
NM
NM
NM
NM
135
119
146
113
157
20.5
19.7 _+ 7.8
6.8 + 1.0
17.6
8.8
75.6
80.8 + 12.2
90.8 + 1.8
90.8
92.0
63.6
64.5
62. I
46.4
52.4
71.6
26.4
29.0
44.0
60.6
60.8
59.4
65. I
63.0
58.7
76.8
77.4
68.0
VHP-06s
VHP-07 b
VHP-08 b
VHP-09 b
VHP-10b
VHP- 11b
VHP-12b
VHP-13 b
VHP-14b
50
50
50
50
50
50
50
50
50
870
870
870
955
955
955
1045
1045
1045
0.41
0.80
1.67
0.41
0.80
1.67
0.41
0.80
1.67
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.875
0.883
0.889
0.914
0.912
0.916
0.954
0.945
0.972
350
339
363
345
370
352
352
375
352
HIP-01 a
HIP-02a
HIP-03a
HIP-04a
HIP-05a.~
HIP-06a.¢
HIP-07a
HIP-08a.e
50
50
100
7.8
50
I00
200
6.9/100
825
900
900
975
975
975
975
800/975
NA
NA
NA
NA
NA
NA
NA
NA
0.5
0.5
0.5
0.5
0.5
0.5
0.5
2.0/0.5
0.894
0.958
0.975
NM
0.979
NM
NM
NM
152
381
322
178
548
144
314
138
138.9
56.3
135.4
25.0
40.4 +_ 1.7
51.0 + 12.4
47.6
34.6
28.3
51.8
35.7
71.9
72.0 + 3.8
55.7 + 6.3
69.4
71.7
Notes: aBatch LPS-485. bBatch LPS-669. CResults shown are average for 3-4 tests, aFiber segments which are 95% of the sample length,
or longer, are considered to be intact. ~Sample subjected to a double soak. The sample was neither cooled nor depressurized between
the two soaks. NA = not applicable. NM = not measured.
GROVES et al.: CONSOLIDATION OF METAL MATRIX COMPOSITES
2093
90
Ambient Temperature
. . . . . . . . . 0 LPS- 485
3O
:
"7
I
75
24
18
...--"'"li,
~
45
........................
VHP
..*o''''''""
CI
r)
T
60
•
~
8
•
"!.........
......-°
..,...'0
ao
12
• 870
15
LL
ii
i
2
0
i
4
i
6
[ .......
VHP
0
0.0
0.5
1.0
1.5
I-I 955
2.0
Displacement Rate (cm h-1)
8
Applied Stress (MPa)
Fig. 3. Number of fiber fractures per meter of fiber after
application of stress at ambient temperature.
Fig. 5. Variation in fiber fracture density with applied
displacement rate during vacuum hot pressing to 50 MPa at
three different temperatures•
Figure 4 shows the relationship between HIP consolidation temperature and pressure and the number
of fiber fractures per meter for different pressures. It
is evident that, as the processing temperature was
increased (at a fixed pressure), the number of fiber
fractures per meter decreased. For specimens processed at a fixed temperature, higher consolidation
pressures increased the number of fiber fractures per
meter--particularly at the lower processing temperatures. Figure 5 shows the effect of loading rate during
VHP upon the number of fiber fractures per meter.
At the two highest temperatures (955 ° and 1045°C)
the number of fractures per meter increased with rate
of loading, but at the lower temperature (870°C) the
number of breaks was generally independent of the
applied displacement rate.
To investigate the cause of fiber fracture, a series
of vacuum hot press experiments was interrupted
shortly after the start of consolidation to prevent
extensive metal flow from obscuring evidence of the
failure mechanism. Examination of these partially
consolidated specimens revealed bent and broken
fibers. Figure 6(a) shows a bent and broken fiber from
a fully consolidated HIP sample. The three fibers
shown are all from the same monotape, and the
middle fiber has clearly been subjected to localized
bending. Figure 6(b) shows a side view of a typical
fiber fracture in a sample interrupted 30 s after reaching a soak temperature and pressure of 900°C and
50 MPa. The fiber has fractured, apparently in bend-
ing at an asperity. Such fibers are observed to bend,
curving about the asperity. In Fig. 6(b), the crack
appears to have started at the top of the fiber (the
tensilely loaded region) during bending and to have
arrested in the bottom part of the fiber (the compressively loaded region).
~ ] ~,,
150
12o
,
5. DISCUSSION
The experimental results from this study provide
the basis for a more quantitative, model-based investigation of fiber fracture during the hot isostatic or
vacuum hot press consolidation of plasma sprayed
monotapes. Once a model has been presented which
reasonably describes the damage mechanism, it will
SCS-6
silicon
carbide
fiber
\
lOOpm
a)
SCS-6
~ilicnn
•
Crack
/
. . . . . . . . . .L. . . . . . . . . . . . . . . . . . .
,~
~1,200•5o
Pmssuro (MPe)
b)
/
Asperity
c~
Y_
ao
l
I
O|
800
~ HIP
850
Ti-14A ~21~
latrl×
0
9;0
Temperature
9;0
1000
(°C)
Fig. 4. Effect of HIP temperature and pressure upon the
fiber fracture density.
Ti- 14A1-21Nb
matrix
Fig. 6. Bending due to rough surface contact is the dominant fiber damage mechanism during consolidation. (a) An
in-plane cross-section through a fully consolidated
Ti 14A1-21Nb/SCS-6 sample showing bent and damaged
SiC fibers. (b) A longitudinal section of a partially consolidated Ti-14-21/SCS-6 sample revealing a SiC fiber fractured at an asperity contact.
2094
GROVES et al.: CONSOLIDATION OF METAL MATRIX COMPOSITES
(a)
MacroscopicStrain Rate
Perpendicular to Fibers
¢:
(b)
Geometrically Representative
Volume Element (GRVE)
2;
U
(t)
2i
Fig. 7. (a) Embedded fibers are bent during consolidation by the irregular interfoil contact arising from
the surface roughness of plasma sprayed foils. (b) A unit cell used to explain observed fiber fracture trends
in terms of bending caused by asperity contact.
then be possible to identify material and processing
parameters most strongly influencing fiber fracture,
to reproduce experimentally observed fiber fracture
trends, and to suggest improvements in the plasma
deposition and consolidation processes. It is not our
intent here to develop a model capable of accurate
numerical prediction of cumulative fracture during
consolidation. This requires the incorporation of
stochastic features of spray-deposited surface topography and is dealt with in a separate paper [18].
Instead, we identify and analyze the behavior of a
single representative volume element.
The magnitude of the deflection of a fiber segment
spanning two adjacent asperities, and therefore the
probability of fiber fracture, will be governed by a
number of factors: the plastic and creep properties of
the matrix (which vary with temperature, pressure,
and density during consolidation), the stiffness, diameter, and strength of the fibers, and the size and
spatial distribution of the surface asperities. The role
"that these parameters play in determining the rate of
fiber fracture can be better understood by considering
the micromechanical response for the representative
volume element of Fig. 7. During consolidation,
forces can be transmitted through the monotapes
only at points where the rough surface asperities of
one foil make contact with the surface of an adjacent
foil. At the start of consolidation, contacts are widely
spaced, resulting in nonuniform loading of the fibers
and subsequent bending. Since the asperities are
comparable in diameter to a fiber, this fracture mode
may be expected to affect fibers individually [12]. For
modeling purposes it is assumed that the asperities
deform by a combination of plasticity and creep, and
it is the asperities' resistance to this deformation that
results in forces that cause fiber loading. The contact
forces due to both mechanisms of deformation have
been derived in earlier work on densification modeling [12]. The Appendix uses these results to calculate
the stresses in the fiber due to bending and thus the
probability of fiber failure (using the measured
Weibull fiber strength statistics given in Table 1).
The model considers the asperity plastic flow (timeindependent) and creep asperity deformation separately. It can first be used to examine low temperature
pressurization, e.g. HIP prepressurization, where
densification occurs only by plastic deformation. In
this case the mid-point fiber deflection associated
with plastic deformation (Vp) of a fiber segment is (see
Appendix)
2(z0 - z)
vp = (1 + 24 )
(3)
where 2z is the current volume element height (determined by the current macroscopic density), 2z0 is the
initial (undeformed) height, and ¢ is a proportionality
constant equal to ks/kp where ks is the fiber's elastic
bend stiffness and kp is a "plastic stiffness" proportional to the asperity (i.e. matrix) yield strength.
As pressure is increased and densification progresses,
the representative volume element in Fig. 7 is compacted. Thus ( z 0 - z) increases, and the fiber suffers
an increasing deflection.
Appendix equations (A4) and (A5) show ¢ (and
thus vp) to be a function of the fibers' elastic modulus
and diameter, the matrix yield strength, and the
asperity spacing. If the asperity has a low yield
strength or the fiber has a high elastic stiffness (i.e.
kp<<ks) , the proportionality constant ~ is large, the
fiber's elastic deflection small, and the probability of
fiber fracture low. The fiber's bend stiffness ks can be
raised by increasing its elastic modulus or diameter or
by decreasing its length (i.e. decreasing the asperity
spacing). This indicates that spray depositing finer
GROVES et al.:
~.o
, -. ~,
CONSOLIDATION OF METAL MATRIX COMPOSITES
i
Unit cell strain = 0.5
(;If = 142 prn
o)
0.8
~
"6
l=Sd~
0.6
;~.
.5 cm / h
. 0 0.4
J~t~
;.,
o
m=
oo =
Ef =
r=
0.2
Q..
0
900
~
1,0
".
.,..
13
4.5 GPa
425 GPa
71 pm
2.0
\',
°'-I.,
950
'
1000
Temperature
1050
11 O0
(°13)
Fig. 8. The creep model predictions of failure probability
show the relationship between temperature and displacement rate for the Ti-14AI~INb/SCS-6 composite system.
droplets (creating a more uniform surface) during
monotape manufacture should result in a composite
precursor which is more consolidation process-tolerant. Incorporation of the unit cell analysis into a
macroscopic model accounting for the statistical surface features [18] permits numerical prediction of how
much improvement results from a given refinement in
the size of spray-deposited particles. Similarly, bending in the fiber can be reduced by decreasing the
matrix yield strength (e.g. by increasing the processing temperature).
At higher temperatures (T > 0.4 Tin), asperities can
also deform by time-dependent creep mechanisms
[12]. For the case of power law creep (AI 1), the fiber's
midpoint deflection (vc) is given by
2~
. [ exp(2t x / ~ )
- 1]
(4)
where ~ is the cell compaction rate for a given applied
pressure and temperature calculated using the densification model presented in [12], t is the elapsed time
since the start of densification, and 7 is a material
constant proportional to B in the Norton power law
creep relation (A8).
Inspection of equation (4) and the expression for B
(see Appendix) reveals that as the temperature increases, 7 becomes large, causing vc to decrease
(vc--~ 0 as 7 ~ oe). Thus the probability of fracture
decreases as the temperature increases. It is also
apparent that decreasing ~ (i.e. the densification rate)
decreases vc so that the probability of fracture is
diminished with decreasing compaction rate. For this
reason one expects less fiber damage if consolidation
is allowed to proceed more slowly at first and at
higher temperatures in order to accommodate densifying strains by creep deformation of the asperities.
The extent to which the model reflects the dominant physical mechanism of fiber fracture can be
assessed from its ability to reproduce the experimentally observed trends. Combining the creep model
results for fiber deflection (4) with the measured two
parameter Weibull strength distribution allows prediction of the fiber fracture probability as a function
of loading rate and consolidation temperature (A13).
Figure 8 shows the calculated probability of fracture
(defined as the fraction of all possible fractures) using
the creep parameters for Ti-14A1-21Nb given in
Table 3. This figure shows that an increase in the
displacement rate (densification rate) at a fixed temperature raises the probability of fiber fracture, in
agreement with the experimentally observed trend at
955 ° and 1045°C (cf. Fig. 5). Another interpretation
of Fig. 8 is that as the densification rate is increased,
the consolidation temperature must be raised to
avoid fracture. These conclusions are quite similar to
those drawn by Tszeng et al. [11] on the basis of their
work with the consolidation of metal powders around
continuous fibers.
At lower processing temperature (T ~<0.4 Tm) densification is accomplished primarily by rate independent plastic yielding of asperities. Using the plasticity
model predicted fiber deflection (3) together with
Weibull strength statistics for the fiber, leads to the
result shown in Fig. 9. This figure illustrates that
increasing the fiber/matrix stiffness ratio (ks/kp) leads
to a decrease in the probability of fiber fracture for
a fixed amount of densification (indicated by the unit
cell true strain). The additional axes at the top of
Fig. 9 are intended to indicate the influence of
processing temperature on probability of fracture.
They map the process temperature to the ks/kp ratio
through the known temperature dependence of the
yield strength for the Ti-14A1-21Nb alloy [23-28].
Simply put, when the matrix has a low yield strength
(i.e. when processing is conducted at elevated temperature) the asperities deform more readily, the
fibers suffer less bending, and the probability of
failure for any amount of densification decreases.
This explains the experimental temperature trend
Table 3. Ti-14A1-21Nb material data [23-28]
Plasticity
Yield strength as f(T)
• Room temperature
• Low temp range (20 ~< T ~< 800°C
• High temp range (T > 800°C)
Creep a
Power law creep constant, B0
Stress exponent, n
Activation energy, Qc
2095
(MPa)
539.9
ay(T) = 539.9 --0.32" T
%(T) = 1019.9-0.92" T
[1/(MPa 2s. h]
(kJ/mol)
aThe steady state creep rate is described by
~: = Bo" e x p ( - R~k ) ' a ' -
10 2
2.5
285
2096
GROVES
et al.:
CONSOLIDATION OF METAL MATRIX COMPOSITES
Yield Strength (MPa)
100
i
30
,ooo
lo~s
i
15
10
6
Temperature (°C)
,o,s
1100
i
dl = 142pm
l=5df
m=13
o o = 4,5 GPa
Ef = 425 GPa
0.8
U_
0.6
I
o
0.05
0.45 = unit cell true strain
0,20
~---- 0.4
0
'
i
2 0.2
Q..
°
o
;o
',
;
°
go"
,'o
so
Stiffness Ratio P~ (ks/kp)
Fig. 9. Increasing the ratio of fiber bend stiffness to matrix
yield strength reduces the probability of fiber fracture during
densification by plastic yielding.
shown in Fig. 4. The increase in the number of
fractures with pressure (for a fixed temperature) that
is also shown in Fig. 4 is just a reflection of the larger
unit cell strain (i.e. greater densification) (see Fig. 9).
The cell analysis is also able to account for the
disappearance of a fiber fracture-displacement (densification) rate dependence at low consolidation temperatures in Fig. 5. This occurs as the contribution to
the deformation force by the plasticity mechanism
(rate independent) rises above that due to creep (rate
dependent).
One shortcoming of the creep and plasticity model
appears to be its inability to account for the experimental trend of Fig. 3. In this figure a difference in
the number of breaks for the two materials batches
is shown. This can be rationalized by noting that the
LPS-669 samples (a) had a smaller fiber spacing
(which results in a more effective load transfer to
adjacent fibers) and (b) a thicker matrix deposit
(which distributes the load more uniformly along the
fiber) [21]. The model does not consider either of
these factors. Despite this shortcoming, it is still
able to duplicate the main experimentally observed
fracture trends.
This study has several implications for the manufacture and processing of metal matrix composites.
First, precursors (e.g. monotapes and powders) need
to have as high a starting density as possible with
matrix characteristic dimensions (e.g. powder size,
asperity size and spacing, and void diameter) small
relative to the fiber diameter. This will result in
smaller overall deformations (and hence fiber distortions) and more even stress distributions along the
lengths of fibers. Second, fibers with low bend stiffness (i.e. small diameter, low modulus) cannot be
processed in combination with high strength matrices
by techniques known to result in fiber bending (e.g.
powder/fiber compacts and spray-deposited monotapes). Third, matrices of lower strength need to be
used which will deform more readily and thus keep
the fibers unbent and unbroken. Fourth, conditions
which allow densification by asperity flattening instead of fiber deflection are favored: (1) higher temperatures, since the matrix flow stress drops more
rapidly with increasing temperature than does the
fiber stiffness/strength, and (2) lower densification
rates, since the asperities' creep strength is quite
sensitive to strain rate (power law) while the fibers
remain essentially elastic throughout processing.
This study has revealed sometimes significant
amounts of fiber fracture during processing. Curtin's
strength model as presented earlier (Fig. 2) predicts
a composite strength loss of 5-20% (based on the
25-140 fractures/m observed under the range of
conditions tested). Indeed, tensile tests of consolidated specimens have indicated strengths which were
15--60% below the predicted rule-of-mixture (ROM)
strength [29]. While all of the difference between
ROM and measured strengths may not be attributable to process induced fiber fractures, they almost
certainly contribute significantly to this difference.
The experimental results and modeling insight gained
in this study should enable process and material
optimization leading to control of fiber damage
during consolidation.
6. SUMMARY
An experimental study was conducted to explore
the phenomenon of fiber fracture during the hot
isostatic and vacuum hot pressing of plasma-sprayed
Ti-14wt%Al-21wt%Nb/SCS-6 composite monotape
lay-ups. From these results we conclude that:
1. Fiber fracture during the consolidation of
plasma sprayed monotape is a significant factor
in determining material quality and final properties.
2. The number of fiber fractures during consolidation is strongly dependent upon the processing
conditions. The fiber fracture density is directly
related to consolidation pressure and inversely
related to consolidation temperature. As the
rate of pressure application increases, the number of fiber fractures increases (T < 900°C). The
application of small pressures (3-4MPa) to
unconsolidated composite specimens at room
temperature causes fiber fracture (up to 20
fractures/m).
3. The principal mechanism of fiber fracture is
bending due to stress concentrations occurring
at asperity contacts.
4. The observed dependence of damage on process
conditions can be predicted by analysis of a
volume element of porous composite in which
the interaction between fibers and deforming
matrix asperities is captured. The model predicts
that increases in fiber stiffness, strength, and
diameter, decreases in the matrix yield and creep
strength, and decreases in monotape surface
roughness will lower the fiber fracture density
associated with consolidation.
GROVES et al.:
CONSOLIDATION OF METAL MATRIX COMPOSITES
Acknowledgements--The financial support of the Defense
Advanced Research Projects Agency (Program manager,
W. Barker) and the National Aeronautics and Space
Administration through grant NAGW 16-92 is gratefully
acknowledged.
REFERENCES
1. J. Doychak, J. Metals 44(6), 46 (1992).
2. J. M. Yang and S. M. Jeng, J. Metals 44(6), 52 (1992).
3. R. Bowman and R. Noebe, Adv. Mater. Proc. 136(2), 35
(1989).
4. The New Materials Society: Challenges and Opportunities, Vol. 2. U.S. Department of the Interior, Bureau of
Mines (1990).
5. R. A. MacKay, P. K. Brindley and F. H. Froes,
J. Metals 43(5), 23 (1991).
6. D. G. Backman, E. S. Russell, D. Y. Wei and Y. Pang,
Proc. Conf. on Intelligent Processing o f Materials (edited
by H. N. G. Wadley and W. E. Eckhart Jr), p. 17. The
Metals Soc., Warrendale, Pa (1990).
7. C. A. Calow and A. Moore, J. Mater. Sci. 7, 543 (1972).
8. T. W. Chou, A. Kelly and A. Okura, Composites 16(3),
187 (1985).
9. J. W. Pickens and G. K. Watson, The 14th Conf. on
Metal Matrix, Carbon, and Ceramic Composites, NASA
CP-3097, Part 2, Hampton, Va, NASA-Langley, p. 711
(1990).
I0. C. G. McKamey et al., High-Temperature Ordered
lntermetaHic Alloys III (edited by C. T. Liu et al.),
Vol. 133, p. 609. Mater. Res. Soc., Philadelphia, Pa
(1988).
11. T. C. Tszeng, E. K. Ohriner and V. K. Sikka, A S M E
J. Engng Mater. Tech. 114, 422 (1992).
12. D. M. Elzey and H. N. G. Wadley, Acta metall, mater.
41, 2297 (1993).
13. D. R. Pank, A. M. Ritter, R. A. Amato and J. J.
Jackson, Titanium Aluminide Composite Workshop,
Orlando, Fla, p. 383 (1990).
14. W. A. Curtin, J. Am. Ceram. Soc. 74, 2837 (1991).
15. H. Deve and J. M. Duva, personal communications
(1992).
16. R. M. McMeeking, Elevated Temperature Mechanical
Behavior o f Ceramic Matrix Composites (edited by S. V.
Nair and K. Jakus). Butterworth-Heinemann, Stoneham, Mass (1993).
17. C. H. Weber, J. Y. Yang, J. P. A. Lffvander, C. G. Levi
and A. G. Evans, Acta metall, mater. 41, 2681 (1993).
18. D. M. Elzey and H. N. G. Wadley, Acta metall, mater.
Submitted.
19. Engineered Materials Handbook, Vol. 1, Composites.
ASM International, Metals Park, Ohio (1987).
20. H. P. Wang and E. M. Perry, A S M E Heat Transfer
Division Publication HTD, Vol. 132, p. 99. Am. Soc.
Min. Engng, New York (1990).
21. J. F. Groves, M. S. thesis, Univ. of Virginia (1992).
22. L. M. Hsiung, W. Cai and H. N. G. Wadley, Acta
metall, mater. 40, 3035 (1992).
23. S. J. Balsone, Proc. Conf. on Oxidation o f High Temperature Intermetallics (edited by T. Grobstein and J.
Doychak), p. 219. The Metals Soc., Warrendale, Pa
(1989).
24. P. K. Brindley et al., Proc. Conf. on Fundamental
Relationships Between Microstructure and Mechanical
Properties o f Metal Matrix Composites (edited by P. K.
Liaw and M. N. Gungor), p. 287. The Metals Soc.,
Warrendale, Pa (1990).
25. D. A. Koss et al., Proc. Conf. on High Temperature
Aluminides and Intermetallics (edited by S. H. Whang
et al.), p.175. The Metals Soc., Warrendale, Pa (1990).
26. J. M. Larsen et al., Proc. Conf. on High Temperature
Aluminides and Intermetallics (edited by S. H. Whang
et al.), p. 521. The Metals Soc., Warrendale, Pa (1990).
2097
27. D. A. Lukasak, Metall. Trans. 21A, 135 (1990).
28. M. G. Mendiratta and H. A. Lipsitt, J. Mater. Sci. 15,
2985 (1980).
29. Titanium Aluminide Composites, GE Aircraft Engines
Interim Rep. No. 4, under Contract F33657-86-C-2136,
P00008, CDRL Sequence No. 3 (1989).
30. K. L. Johnson, Contact Mechanics. Cambridge Univ.
Press (1987).
31. R. Gampala, D. M. Elzey and H. N. G. Wadley, Acta
metall, mater. In press.
32. W. Weibull, J. appl. Mech. 9, 293, (1951).
33. P. A. Siemers, R. L. Mehan and H. Moran, J. Metals
23, 1329 (1989).
APPENDIX
A micromechanical model relating the macroscopic rate
of densification to the local bending of reinforcing fibers is
developed. The macroscopic densification rate can be predicted for a laminate of spray-deposited MMC foils given
the applied pressure and temperature using a previously
developed model [12]. A unit cell assumed to typify the fiber
bend geometry (see Fig. 7) is taken to deform uniaxially with
the ceramic fiber acting as a simply-supported, cylindrical
beam undergoing purely elastic bending up to the point of
fracture. The asperities pressing against the fiber are allowed
to deform by plastic yielding and by power law creep, these
two cases being treated separately to keep the analysis as
simple as possible. The asperity contacts are treated as point
loads. The maximum tensile stress due to bending can then
be used in conjunction with a Weibull description of the
fiber strength to calculate the probability of fracture.
From the geometry of the representative unit cell problem
in Fig. 7, the total cell height (2z), which is given, must be
the sum of the heights of the deformed asperities (2y) and
the deflection (v) of the fiber
2z = 2y + v.
(A1)
[Note that v is always negative since y ~>z and that initially,
z ( = z0) = y ( = Yo).]
Considering first the case of rigid, perfect plasticity, the
asperity is assumed to undergo deformation whenever the
stress acting at the contact exceeds an effective yield stress
a c ~>C • ay
(A2)
where ay is the matrix material's yield strength in uniaxial
tension, and C is a concentration factor (C > I). This factor
accounts for the added effort needed to overcome the elastic
constraint of material surrounding the plastic zone, which
forms within the interior of spherical bodies in contact [30].
Recent work of Gampala et al. [31] has shown C to be
dependent upon the degree of deformation, but for the
present purpose it is sufficient to treat C as constant.
Accordingly, we take C = 3 corresponding to fully plastic
flow during plane strain indentation of a cylindrical punch
into a semi-infinite halfspace.
The fiber deflection can be obtained in terms of the input
cell height, z, as follows: the contact stress is just F/a¢, where
the contact area (a¢) can be approximated in terms of the
asperity displacement as a c ~ 2 n y o ( Y o - y ) [30], and the
force (F) acting on the asperity is just the force required to
bend the fiber
F = ksv
(A3)
where, from simple beam theory, the fiber bend stiffness, k s,
is
3~
df4
k~ = ~ - E r . 73.
(A4)
2098
GROVES et al.: CONSOLIDATION OF M E T A L M A T R I X COMPOSITES
Combining (A2) and (A3) and using the approximate
expression for the contact area, the deformed asperity height
can be expressed as
ksv
Y = Y0 + 6~y0a~--~ •
(A5)
Defining kp, the plastic stiffness, as 6~y0ay and substituting
(A5) into (AI) gives the fiber deflection in terms of the
imposed cell deformation
2(z - z0)
Vp- 1 + 2 ' ~
(A6)
(A7)
The time rate of change in the asperity height (9) can be
obtained from the uniaxial power law creep relation
g = B . a"
0 + 2Byo
(A8)
where B is taken to have an Arrhenius dependence on
temperature [B =Boexp(--Qo/RTk) ] and n is the stress
exponent. The strain rate, ~, is rewritten as p/y ~ Y/Yo and
the stress is again taken to be the contact stress: a c = F/ac.
Then, taking an average value for the area of contact
((~c ~ 2/3 • ny 0z) and equating the force acting on the asperity
with that required to deflect the fiber (F=k,v), (A8)
becomes'{"
v" = 2~.
(A 10)
If only constant cell displacement rates are considered and
n = 2, (A10) can be solved analytically to obtain
2~(
exp(2t x / ~ )
exp(2t x / ~ )
vc(t) =
where Y0 = x0 has been used and ~ is the dimensionless ratio
of fiber bend stiffness to plastic (asperity) stiffness. Deflections are minimized by increasing the value of ~, implying
high modulus fibers with large diameters (to resist bending)
and low matrix yield strength.
At elevated temperatures densification is achieved primarily by means o f power law creep. For this time dependent
mechanism we are interested, in analogy with (A6), in an
expression for the rate of change of fiber deflection as a
function of the overall cell deformation rate (~), the fiber
bend stiffness (ks), and the material parameters characterizing the matrix creep response. Differentiation of (A1) gives
for t~
t) = 2z" - 23~.
Solving (A9) for ~ and substituting the result into (A7)
gives a nonlinear, ordinary differential equation in the
deflection, v
- 1)
+ 1
(All)
where y-= 2Byo(ks/d¢)2. Increasing y, (i.e. decreasing the
creep resistance o f the matrix or increasing the fiber bend
stiffness), has the effect of minimizing the deflection. Given
the fiber midpoint deflection from either (A6) or (A11), the
maximum tensile stress in the fiber (af) can be calculated
from
at=
16. Fl
nd 3
(A12)
where F is determined from (A3). The cumulative probability of a fiber failing is given by a Weibull distribution [32]
af m
where a0 is a reference stress and m, the Weibull modulus,
was found to be 13.0 + 2.1 (see Table 1 for experimentally
measured values).
Since the fiber strength tests were conducted in tension as
opposed to bending, the reference stress in the Weibull
expression must be related to the stress required to cause
fracture in bending. Siemers et al. [33] have derived and
experimentally verified such a relationship
O-b= at[ ~Vt' I c
1] l/m
(AI4)
(A9)
where a b and a t are the bending and tensile stresses,
respectively, and Vb and Vt are the volumes of fiber exposed
to critical stresses in tension and bending, respectively. The
factor k depends only on the Weibull modulus and is
1.45.10 -2 for the SiC fibers considered here. Taking Vt to
be the gage length of tensile fiber samples and Vb to be the
mean asperity spacing, Vt/Vb ~ I00, gives
tThe solution of this ordinary differential equation [i.e.
y (t)] differs by only a few percent from that of equation
(16) in Ref. [121 when fl = C = 3.
For this range of values, (AI4) is quite insensitive to values
of Vb, and over the entire range of fiber segment lengths (i.e.
the distribution of asperity spacings) encountered,
oh~at = 1.9 +0.1.
~=B(k'vy.
Y0
\ a, /
a b ~ 1.9- a t.
(AI5)