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TitleFundamentals of Metal-Matrix Composites
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LanguageEnglish
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Table of Contents
                            Contents
Preface
PART I PROCESSING
	Chapter 1 : Liquid-State Processing
	Chapter 2 Solid-state Processing
	Chapter 3: Capillary Phenomena, Interfacial Bonding, and Reactivity
PART II MICROSTRUCTURE CHARACTERIZATION
	Chapter 4: Characterization of Residual Stresses in Composites
	Chapter 5: Structure and Chemistry of Metauceramic Interfaces
	Chapter 6: Microstructural Evolution in Whisker- and Particle-Containing Materials
	Chapter 7 Aging Characteristics of Reinforced Metals
PART III MICROMECHANICS AND MECHANICS OF DEFORMATION
	Chapter 8 Crystal Plasticity Models
	Chapter 9 Continuum Models for Deformation: Discontinuous Reinforcements
	Chapter 10: Continuum Models for Deformation: Metals Reinforced with Continuous
	Chapter 11 Creep and Thermal Cycling
PART IV DAMAGE MICROMECHANISMS AND MECHANICS OF FAILURE
	Chapter 12: Models for Metal/ceramic Interface Fracture
	Chapter 13 Matrix, Reinforcement, and Interfacial Failure
	Chapter 14 Fracture Behavior
	Chapter 15 Fatigue Behavior of Discontinuously Reinforced Metal-Matrix Composites
PART V APPLICATIONS
	Chapter 16 Metal-Matrix Composites for Ground Vehicle, Aerospace, and Industrial Applications
Index
                        
Document Text Contents
Page 2

Fundamentals of Metal-Matrix Composites

Page 175

Figure 9.8. Tensile stress-strain
curves for composites reinforced
by aligned disc-shaped cylindrical
particles (ulb = 5 and f= 0.2).The
matrix material has the
Ramberg-Osgood stress-strain
curves shown. The solid line
curves for the composite were
computed using a cell model,
while the dashed line curves were
obtained using the estimation
scheme described in the text.

Figure 9.9. Comparison of experimental
data for composites of an AVMg matrix
material reinforced by Sic particles with
stress-strain curves predicted by the
estimation scheme described in the text.
(From Yang et al. 1991.) (a) Uniaxial tensile
curves for matrices reinforced by equiaxed
particles. (b) Uniaxial compression curves for
matrices reinforced by randomly oriented
platelets.

Page 176

168 MICROMECHANICS AND MECHANICS OF DEFORh4ATION

matrix as well as for composites reinforced by three
volume fractions of equiaxed particles whose average
size was 9 microns. The estimation scheme described
above was applied by fitting the Ramberg-Osgood curve
(Equation 9.4) to the matrix curve to obtain II and uo (a
was taken to be 3/7). The value of E in (Equation 9.5)
was taken from the experimental curve (which in turn
was shown to agree well with self-consistent predic-
tions), and ON was determined from Equation 9.8, using
the results for Eo from Figure 9.3 for the unit cylindrical
particles. The dashed-line curves in Figure 9.9(a) are the
result of the estimation procedure. The same procedure
was applied to the uniaxial compression data in Figure
9.9(b) for composites reinforced by randomly oriented
platelets whose average maximum diameter was 25
microns. In this case, the platelets are taken to have a
10: 1 aspect ratio and the results for 50 for the randomly
oriented ellipsoidal platelets in Figure 9.5 were em-
ployed to estimate ON.

9.3 The Influence of Residual Stress
on Composite Yielding

The results presented so far in this chapter are for
materials initially free of residual stress in the matrix
and in the reinforcements. Most metal-matrix compos-
ites are processed at high temperatures and, upon cool-
ing, develop residual stresses as a result of thermal
expansion mismatch between the matrix and the rein-
forcements. Although the residual stresses have no effect
on the purely elastic response of the composite, it is of
interest to determine the effect on the yielding of rein-
forced materials. Such effects can occur because the
residual stress can have a deviatoric component and can
thus influence the process of yielding in the matrix. The
effect has been considered by several investigators in-
cluding Povirk et a]. (1991). However, Zahl and Mc-
Meeking (1991), have provided a series of results for
strongly bonded elastic reinforcements in perfectly plas-
tic matrices showing the influence of the thermal strain
mismatch relative to the volume fraction of reinforce-
ments and the yield strain of the matrix.

The results of Zahl and McMeeking (1991) were
obtained by the unit cell method with finite elements
used for the analysis. The residual stresses were first
generated by cooling the material while the matrix was
permitted to respond elastoplastically. Thereafter, loads
were applied to cause macroscopic deformation. The
magnitude of the residual stresses generated were con-
trolled by the parameter A~ATIEo, where A a is the
thermal expansion coefficient of the reinforcement mi-
nus the thermal expansion coefficient of the matrix, and
AT is the current temperature minus the temperature at

which the composite material is free of residual stress in
both the matrix and the reinforcement. The parameter
EO is, as before, the yield strain in tension of the matrix
material. The calculations were carried out with an
elastic modulus for the reinforcement that is 6.62 times
the elastic modulus of the matrix.

Figure 9.10 shows the stress-strain curves for spher-
ical reinforcements in a perfectly plastic matrix with
A ~ T / E o = 1. This case corresponds to Sic particles in
an Al alloy matrix 256C below the stress-free temper-
ature. A softening of the composite response results at
strains comparable to the matrix yield strain for both
tension and compression with the effect much more
pronounced in the compressive cases. The compressive
stress-strain curve is up to 30% below the tensile curve
in terms of strength at the same strain magnitude.
However, as the strain increases beyond EO = AaAT,
the compressive and the tensile stress-strain curves con-
verge toward the curve for the material without initial
residual stress. The limit strength is thus the same
whether or not there are initial residual stresses. Because
the compressive stress-strain curve also represents ten-
sion applied to a material with ACXATIEO = - 1 (the sign
of the residual stresses reversed), the limit strength is
unaffected by whether the residual stresses in the matrix
are tensile or compressive. Because the limit strength of
reinforced materials is independent of the initial resid-
ual stresses, the behavior of the composite material
when the strain greatly exceeds EO = AaAT is corre-
spondingly independent of them too. However, the
limited ductility of particulate composites means that
such large strains are rarely achieved in tension and are
unusual in compression unless accompanied by internal
damage. As a consequence, tension-compression asym-
metries in the yielding of particulate composites are to
be expected, and will generally persist until fracture of
the material occurs.

The degree of yielding caused by thermal expansion
mismatch between the matrix and the reinforcements
depends on the magnitude of A~ATIEo. When this
parameter equals 1, as in the case discussed above,
approximately 50% of the matrix around spherical
particles is yielded. When AaA7'/~0 = 2, 60% of the
matrix has yielded. When A~AT/Eo = 5, the entire
matrix has deformed plastically upon cooling. The ef-
fect of these different degrees of yielding on a material
with 20% of elastic spheres on the compression and
tension stress-strain curves is shown in Figures 9.1 1 and
9.12. It can be seen that in both tension and compres-
sion the greater thermal expansion misfit causes a softer
response. Because the matrix is fully yielded when
A ~ T / E o = 5, any magnitude of AaAT/&o larger than 5
will give rise to the same tension and compression
stress-strain curves as occur for haAT/~o = 5. It is of

Page 349

Index 341

characteristics of, variation in, effects of, 206,208
of continuously reinforced composites, 204-206
of discontinuous reinforcements, 204,206-210
microstructural damage during, 205
in presence of applied strcss, 207-208, 208f-209f
and residual stresses, 69
summary of, 210-211

Thermal expansion coefficient. See Coefficient of thermal
expansion

Thermal expansion tensor, 74
Thermal management composites, 317,319f
Thermal mismatch strains, 40,209
Thermal ratcheting, prediction of, 204-205
Thermal residual stresses, 68-69, 69f, 120

calculation of, 74-75
in continuous fiber-reinforced composites, 184-187
plastic relaxation of, 124-125, 130
yielding caused by, 168-169, 169f-171f

Thermomechanical processing, 3 1-34,32f-34f
microstructure after, 33f, 33-34, 36, 36f
in polycrystalline composite model, 153

Thermomechanical variables, in aging response, 127-13 1
Thin-film cracking, 220, 220f
Thixomolding, 11
Thixotropic nature, of composite slurries, 12
Three-dimensional network, for preform fabrication, 17, 18f
Three-phase damage model, of elastic deformation in

particle fracture, 241-242, 242f
Threshold. See also Near-threshold behavior

intrinsic, 290
Tire studs, 3 14
Titanium alloys

aerospace applications of, 307, 309-310, 310t, 312
applications of, 320
properties of, 3 10t

Tool guide, for hole drilling, 66-67, 67f
Toughness measurements

of fiber-reinforced composites and unreinforced matrix

of particle- and whisker-reinforced composites, 252t
alloys, 252t

Toyota Motor Corporation, 3, 298
Transition bands, 11 1-1 12
Translation state, 104-106, 106f
Transmission electron microscopy

of aging response, 121, 122t-l23t, 126, 129, 131-132,

of chemical processes at metaVceramic interfaces, 100
conventional, 83-84, 84f
of crack propagation, 263, 263f-264f
of dislocation density, 124f, 124-126
of matrix failure, 234
objective lens of, geometric beam path through, 84, 85f
subgrain size measurement with, 116
of thermal cycle strain, 210,210f

132f

Transmission function, 84
Transport phenomena

in infiltration processes, 5-8
in spray processes, 14

after deposition, 14-15
Transverse creep, 193
Transverse loading, matrix stresses and composite creep rate

Transverse shear modulus, 177, 181, 182t
Transverse strengthening, of continuous fiber-reinforced

composites, 159, 161-163, 162f

under, prediction of, 193-194

Transverse Young’s modulus, 176, 180-181, 182t
Tresca-type yield criterion, 199
Triangle packing model, 179f, 183
Tungsten

applications of, 136f, 309t, 315-316
characteristics of, 299t

Turbine blades, hollow, fabrication of, with monotapq 24-25,27f
Tyranno, 300

Ultrasonics, measurement of residual stresses with, 62
Uniaxial creep, 191-193
Uniform strain

in elastic deformation, 175
rate of, 164

Unit cell model
of continuous fiber composites, 178-179, 179f-l81f,

of interfacial decohesion, 247-248, 248f
of particle fracture, 242-243
of polycrystalline particulate composites, 144-145, 145f
of residual stress, 168
of single crystal composites, 143-144, 144f

182t, 183

Unit density, strength and stiffness per, 23
United States, research and development programs in, 325
Unloading solution, elastic, 73
Unreinforced matrix alloys, fracture properties of, 251,252t
UTS, 252-253

Vacuum-driven infiltration, 5

V-blender, 26
Vertical clustering, of reinforcement, and stress-strain curve

Vibrational damping composite steels, 3 19
Vickers diamond pyramid indentor microhardness, aging

wetting during, promotion of, 5 1

and ductility, 236f, 236-239

response represented by, 121, 122t-l23t, 127
as function of aging time, 127-129, 128f-129f

Viscosity, of liquid metals, 11-12, 12f
Void nucleation, growth, and coalescence, 239-240, 244f,

244-245
in long fiber reinforced composites, 258-262, 259f-262f
and plastic constraint, 239, 239f

Void volume fraction, 236, 237f-238f
Voigt-type approximation, 176
Volume fraction

and crack closure levels, 286, 286f
and fatigue crack growth, 264
and fatigue life behavior, 280-282, 281f-282f
and near-threshold behavior, 288-289, 288f-289f

Vortex method, 10

Wagner’s first-order interaction parameter, 48-49
W-based alloys, 300
Weak-beam imaging, of misfit dislocations, 92-93
Wear-resistant composites, 23, 298, 314f, 314-316, 316f
Weibull distribution, 202, 202f
Wetting

enhancement of, 51-52
nonreactive, 45-48
reactive, 48-50

Whisker(s), 299t, 300. See also specific type
cracked, 244-245, 245f
deformation zones around, 112, 112f
macroscopic effect of, 112
textural weakening caused by, 114

Page 350

342 INDEX

Whisker-reinforced composites
fatigue life behavior of, 281-282
microstructural evolution in, 109-118
strengthening in, and plastic constraint, 184
stress-strain behavior of, 114-116, 115f-116f
toughness measurements of 252t

Williams’s singularity, 221-224
Work-hardened interface, strengthening effect of, 201
Work hardening, cyclic, 272
Work of adhesion, 43, 8 1

determination of, 82
experimental values of, for nonreactive metals, 45-46,

45t-47t
influence of alloying additions on, 46, 47f

Work of immersion, 43

XD synthesis, 15, 17, 310, 313
X-ray(& penetration depth of, for difference materials, 64t
X-ray diffraction, 62, 64-65
X-ray reflectivity curves, 99,99f

Yield criterion
Mises, 72, 74, 159, 182

Tresca-type, 199
Yielding, composite, influence of residual stress on, 168,

Yield strength
169f-171f

effect of CTE mismatch on, 204
in elastic cell, 230, 230f
steady-state shielding ratio as function of 228, 228f
step-function decay in, model system with, 230, 230f

Yield zone, development of, in matrix punched by glass
sphere, 125, 125f

Young-Dupr6 equation, 43,82,82f
Young’s modulus, 72,165,230,240-242

axial, 176, 181, 182t, 182
transverse, 176, 180-181, 182t

Z-axis surface scattering spectrometer, 95
Zener’s pinning effect theory, 33
Zero clearance piston, 305
Zero-degree square packing, 179

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