Chapter 16: Composites
ISSUES TO ADDRESS...
• What are the classes and types of composites?
• What are the advantages of using composite
materials?
• How do we predict the stiffness and strength of the
various types of composites?
Chapter 16 - 1
Composite
• Combination of two or more individual
materials
• Design goal: obtain a more desirable
combination of properties (principle of
combined action)
– e.g., low density and high strength
Chapter 16 - 2
Terminology/Classification
• Composite:
-- Multiphase material that is artificially
made.
• Phase types:
-- Matrix - is continuous
-- Dispersed - is discontinuous and
surrounded by matrix
Adapted from Fig. 16.1(a),
Callister & Rethwisch 8e.
Chapter 16 - 3
Terminology/Classification
• Matrix phase:
woven
fibers
-- Purposes are to:
- transfer stress to dispersed phase
- protect dispersed phase from
environment
-- Types:
0.5 mm
MMC, CMC, PMC
metal
ceramic
polymer
• Dispersed phase:
cross
section
view
-- Purpose:
MMC: increase σy, TS, creep resist.
CMC: increase KIc
PMC: increase E, σy, TS, creep resist.
-- Types: particle, fiber, structural
0.5 mm
Reprinted with permission from
D. Hull and T.W. Clyne, An
Introduction to Composite Materials,
2nd ed., Cambridge University Press,
New York, 1996, Fig. 3.6, p. 47.
Chapter 16 - 4
Classification of Composites
Adapted from Fig. 16.2,
Callister & Rethwisch 8e.
Chapter 16 - 5
Classification: Particle-Reinforced (i)
Particle-reinforced
• Examples:
- Spheroidite matrix:
ferrite (α)
steel
Fiber-reinforced
(ductile)
60 µm
- WC/Co
cemented
carbide
matrix:
cobalt
(ductile,
tough)
:
Structural
particles:
cementite
(Fe C)
3
(brittle)
Adapted from Fig.
10.19, Callister &
Rethwisch 8e. (Fig.
10.19 is copyright
United States Steel
Corporation, 1971.)
particles:
WC
(brittle,
hard)
Adapted from Fig.
16.4, Callister &
Rethwisch 8e. (Fig.
16.4 is courtesy
Carboloy Systems,
Department, General
Electric Company.)
600 µm
- Automobile matrix:
tire rubber rubber
(compliant)
0.75 µm
particles:
carbon
black
(stiff)
Adapted from Fig.
16.5, Callister &
Rethwisch 8e. (Fig.
16.5 is courtesy
Goodyear Tire and
Rubber Company.)
Chapter 16 - 6
Classification: Particle-Reinforced (ii)
Particle-reinforced
Fiber-reinforced
Structural
Concrete – gravel + sand + cement + water
- Why sand and gravel?
Sand fills voids between gravel particles
Reinforced concrete – Reinforce with steel rebar or remesh
- increases strength - even if cement matrix is cracked
Prestressed concrete
- Rebar/remesh placed under tension during setting of concrete
- Release of tension after setting places concrete in a state of compression
- To fracture concrete, applied tensile stress must exceed this
compressive stress
Posttensioning – tighten nuts to place concrete under compression
threaded
rod
nut
Chapter 16 - 7
Classification: Particle-Reinforced (iii)
Particle-reinforced
Fiber-reinforced
Structural
• Elastic modulus, Ec, of composites:
-- two “rule of mixture” extremes:
upper limit: Ec = Vm Em + Vp Ep
E(GPa)
350
Data:
Cu matrix 30 0
w/tungsten 250
particles
20 0
150
0
lower limit:
1 Vm Vp
=
+
Ec Em Ep
20 40 60 80
(Cu)
Adapted from Fig. 16.3,
Callister & Rethwisch 8e.
(Fig. 16.3 is from R.H.
Krock, ASTM Proc, Vol.
63, 1963.)
10 0 vol% tungsten
(W)
• Application to other properties:
-- Electrical conductivity, σe: Replace E’s in equations with σe’s.
-- Thermal conductivity, k: Replace E’s in equations with k’s.
Chapter 16 - 8
Classification: Fiber-Reinforced (i)
Particle-reinforced
Fiber-reinforced
Structural
• Fibers very strong in tension
– Provide significant strength improvement to the
composite
– Ex: fiber-glass - continuous glass filaments in a
polymer matrix
• Glass fibers
– strength and stiffness
• Polymer matrix
– holds fibers in place
– protects fiber surfaces
– transfers load to fibers
Chapter 16 - 9
Classification: Fiber-Reinforced (ii)
Particle-reinforced
Fiber-reinforced
Structural
• Fiber Types
– Whiskers - thin single crystals - large length to diameter ratios
• graphite, silicon nitride, silicon carbide
• high crystal perfection – extremely strong, strongest known
• very expensive and difficult to disperse
– Fibers
• polycrystalline or amorphous
• generally polymers or ceramics
• Ex: alumina, aramid, E-glass, boron, UHMWPE
– Wires
• metals – steel, molybdenum, tungsten
Chapter 16 - 10
Longitudinal
direction
Fiber Alignment
Adapted from Fig. 16.8,
Callister & Rethwisch 8e.
Transverse
direction
aligned
continuous
aligned
random
discontinuous
Chapter 16 - 11
Classification: Fiber-Reinforced (iii)
Particle-reinforced
Fiber-reinforced
• Aligned Continuous fibers
• Examples:
-- Metal: γ'(Ni3Al)-α(Mo)
-- Ceramic: Glass w/SiC fibers
by eutectic solidification.
formed by glass slurry
Eglass = 76 GPa; ESiC = 400 GPa.
matrix: α (Mo) (ductile)
(a)
2 µm
fibers: γ ’ (Ni3Al) (brittle)
From W. Funk and E. Blank, “Creep
deformation of Ni3Al-Mo in-situ composites",
Metall. Trans. A Vol. 19(4), pp. 987-998,
1988. Used with permission.
Structural
(b)
fracture
surface
From F.L. Matthews and R.L.
Rawlings, Composite Materials;
Engineering and Science, Reprint
ed., CRC Press, Boca Raton, FL,
2000. (a) Fig. 4.22, p. 145 (photo by
J. Davies); (b) Fig. 11.20, p. 349
(micrograph by H.S. Kim, P.S.
Rodgers, and R.D. Rawlings). Used
with permission of CRC
Press, Boca Raton, FL.
Chapter 16 - 12
Classification: Fiber-Reinforced (iv)
Particle-reinforced
Fiber-reinforced
• Discontinuous fibers, random in 2 dimensions
• Example: Carbon-Carbon
-- fabrication process:
- carbon fibers embedded
in polymer resin matrix,
- polymer resin pyrolyzed
at up to 2500ºC.
-- uses: disk brakes, gas
turbine exhaust flaps,
missile nose cones.
(b)
(a)
Structural
C fibers:
very stiff
very strong
C matrix:
less stiff
view onto plane less strong
500 µm
fibers lie
in plane
• Other possibilities:
-- Discontinuous, random 3D
-- Discontinuous, aligned
Adapted from F.L. Matthews and R.L. Rawlings,
Composite Materials; Engineering and Science,
Reprint ed., CRC Press, Boca Raton, FL, 2000.
(a) Fig. 4.24(a), p. 151; (b) Fig. 4.24(b) p. 151.
(Courtesy I.J. Davies) Reproduced with
permission of CRC Press, Boca Raton, FL.
Chapter 16 - 13
Classification: Fiber-Reinforced (v)
Particle-reinforced
Fiber-reinforced
Structural
• Critical fiber length for effective stiffening & strengthening:
fiber ultimate tensile strength
σf d
fiber length >
2τc
fiber diameter
shear strength of
fiber-matrix interface
• Ex: For fiberglass, common fiber length > 15 mm needed
• For longer fibers, stress transference from matrix is more efficient
Short, thick fibers:
σd
fiber length < f
2τc
Low fiber efficiency
Long, thin fibers:
σd
fiber length > f
2τc
High fiber efficiency
Chapter 16 - 14
Composite Stiffness:
Longitudinal Loading
Continuous fibers - Estimate fiber-reinforced composite
modulus of elasticity for continuous fibers
• Longitudinal deformation
σc = σmVm + σfVf
volume fraction
∴
Ecl = EmVm + Ef Vf
and
εc = εm = εf
isostrain
Ecl = longitudinal modulus
c = composite
f = fiber
m = matrix
Chapter 16 - 15
Stress along a fiber
• For L=Lc, the optimal
fiber load is achieved at
the center of the fiber
length.
• For L>Lc, the optimal
fiber load is carried by
most of the fiber. These
are considered to be
“Continuous” fibers and
are ideal.
• For L<Lc, the optimal
fiber load is never
reached, so that a
weaker, cheaper fiber or
even particles could
have been used instead.
σ f *d
Lc =
2τ c
Composite Stiffness:
Transverse Loading
• In transverse loading the fibers carry less of the load
εc= εmVm + εfVf
and
σc = σm = σf = σ
isostress
∴
1
Vm Vf
=
+
Ect E m Ef
EmEf
Ect =
VmEf + Vf Em
Ect = transverse modulus
c = composite
f = fiber
m = matrix
Chapter 16 - 17
Continuous and aligned fibers
• For longitudinal loading, assuming a ductile matrix (e.g. metal)
and a brittle fiber (ceramic with no ductility):
– Stage I includes the fiber and matrix both deforming elastically E=σ/ε
– Stage II involves plastic deformation of the matrix and elastic
deformation of the fiber. The load actually on the fiber is increased.
F
• Fibers begin to fail
at the failure strain.
• The process is not
catastrophic since:
– the fibers are
not all the
same size and
strength.
– the matrix
and
matrix/fiber
Composite Stiffness
Particle-reinforced
Fiber-reinforced
Structural
• Estimate of Ecd for discontinuous fibers:
σf d
-- valid when fiber length < 15
τc
-- Elastic modulus in fiber direction:
Ecd = EmVm + KEfVf
efficiency factor:
-- aligned:
-- aligned:
-- random 2D:
-- random 3D:
K = 1 (aligned parallel)
K = 0 (aligned perpendicular)
K = 3/8 (2D isotropy)
K = 1/5 (3D isotropy)
Values from Table 16.3, Callister &
Rethwisch 8e. (Source for Table
16.3 is H. Krenchel, Fibre
Reinforcement, Copenhagen:
Akademisk Forlag, 1964.)
Chapter 16 - 19
Longitudinal loading
F
Remember: E= modulus (GPa), sigma = stress (MPa), epsilon =
strain (ratio)
Fc = Fm + F f
• The load sustained by the composite is shared by the
matrix and the fibers.
• The stress on each component is easily calculated and
depends on the relative areas of each component (or
volume since V is proportional to A in this orientation).
• If the fiber/matrix bond is good then the strain on fiber
and matrix is the same (isostrain).
• If deformations are all elastic (stage I), Young’s
modulus is proportional to stress/strain.
• Modulus of elasticity is thus easily calculated.
• This is the upper bound of fiber composite
properties.
• The force on the fiber vs. the matrix can be determined
as well.
σ =F/A
σ c Ac = σ m Am + σ f A f
σc =
A
Am
σm + f σ f
Ac
Ac
σc =
V
Vm
σm + f σ f
Vc
Vc
εc = εm = ε f
E=
σ
ε
Ecε c =
Vf
Vm
Emε m + E f ε f
Vc
Vc
Ec =
Vf
Vm
Em + E f
Vc
Vc
Ff
σ f Af E f ε f V f E f V f
=
=
σ m Am Emε mVm EmVm
Fm
=
Transverse loading
• Now the load is applied at 90° to the fiber axis.
• No longer isostrain (same strain on matrix and
fiber)
• Instead, isostress applies (stress applied to
composite is same as that applied to each
component).
• Stain on each component sums to give the
overall strain.
• Again, if deformations are all elastic (stage I),
Young’s modulus is proportional to
stress/strain.
• This is the lower bound of particulate
composite properties.
F
σ transverse = σ c = σ m = σ f
εc =
ε=
V
Vm
εm + f ε f
Vc
Vc
σ
E
σ Vm σ V f σ
=
+
Ec Vc Em Vc E f
1 Vm 1 V f 1
=
+
Ec Vc Em Vc E f
Tensile strength review:
• Longitudinal
–
–
–
–
Maximum stress on stress/strain curve
Usually when the first fibers begin to break
Once fibers begin to break, the load is transferred to the matrix.
Longitudinal tensile strength can be calculated.
σ c*,longitudinal
• Transverse
σc
*
= σ m′
(1 − V f ) + σ * V f
,transverse
f
Vc
= Ec
σ *f
Vc
V
Vm
ε m + Ec f ε f
Vc
Vc
– The transverse tensile strength is
usually at least one order of
magnitude less than the
longitudinal strength.
– The matrix properties will
dominate, along with the
fiber/matrix bond strength.
*
σm
′
σm
Particle and Fiber variables
• Once the matrix and disperse phase materials are decided,
there are still many options that may effect properties.
Thinner and
longer is
better.
Volume
increases
Longitudin
al or
transverse
equations
apply
Composite Strength
Particle-reinforced
Fiber-reinforced
Structural
• Estimate of σ cd* for discontinuous fibers:
1. When l > lc
σ cd ′
*


l
c
= σ f Vf 1−  + σ m′ (1−Vf )
 2l 
*
2. When l < lc
σ cd ′
*
τc
l
=
Vf + σ m′ (1−Vf )
d
Chapter 16 - 24
Problem
• In an aligned and continuous glass-fiber-reinforced nylon6,6 matrix
composite, the fibers are to carry 94% of a load applied in the
longitudinal direction.
a)
determine the volume fraction of fibers necessary.
b)
What will be the tensile strength of the composite. Assume
matrix stress at fiber failure is 30 MPa.
Ff
Fm
=
EV
f f
=
E mVm
EV
f f
(
E m 1 − Vf
)
E (GPa)
σ* (MPa)
Glass fiber
72.5
3400
Nylon 6,6
3
76
F
f = 0.94 = 15.67
0.06
F
m
Ff
Fm
= 15.67 =
(72.5 GPa)Vf
σ cl = σ m ′
∗
(
(3.0 GPa) 1 − Vf
(1−V ) +σ
f
Vc
)
∗
f
And, solving for Vf yields, Vf = 0.418
Vf
Vc
And, to calculate the transverse strength:
= 1440 MPa
σc
*
,transverse
Vf
Vm
= Ec
ε m + Ec Chapter
ε f 16 Vc
Vc
Composite Production Methods (i)
Pultrusion
•
•
•
Continuous fibers pulled through resin tank to impregnate fibers with
thermosetting resin
Impregnated fibers pass through steel die that preforms to the desired shape
Preformed stock passes through a curing die that is
– precision machined to impart final shape
– heated to initiate curing of the resin matrix
Fig. 16.13, Callister & Rethwisch 8e.
Chapter 16 -
Composite Production Methods (ii)
• Filament Winding
– Continuous reinforcing fibers are accurately positioned in a predetermined
pattern to form a hollow (usually cylindrical) shape
– Fibers are fed through a resin bath to impregnate with thermosetting resin
– Impregnated fibers are continuously wound (typically automatically) onto a
mandrel
– After appropriate number of layers added, curing is carried out either in an
oven or at room temperature
– The mandrel is removed to give the final product
Adapted from Fig. 16.15, Callister & Rethwisch 8e.
[Fig. 16.15 is from N. L. Hancox, (Editor), Fibre
Composite Hybrid Materials, The Macmillan
Company, New York, 1981.]
Chapter 16 -
Classification: Structural
Particle-reinforced
Fiber-reinforced
Structural
• Laminates -- stacked and bonded fiber-reinforced sheets
- stacking sequence: e.g., 0º/90º
- benefit: balanced in-plane stiffness
Adapted from
Fig. 16.16,
Callister &
Rethwisch 8e.
• Sandwich panels
-- honeycomb core between two facing sheets
- benefits: low density, large bending stiffness
face sheet
adhesive layer
honeycomb
Adapted from Fig. 16.18,
Callister & Rethwisch 8e.
(Fig. 16.18 is from Engineered Materials
Handbook, Vol. 1, Composites, ASM International, Materials Park, OH, 1987.)
Chapter 16 - 28
Fiber composite strengthening
mechanisms
• Improvements are similar to those for
particle dispersions (hindering crack
propagation).
– Redistributing stress near a crack
tip and/or deflect cracks.
– Form bridges across crack faces.
– Absorb energy as whiskers are
pulled out of the matrix by an
advancing crack.
– Absorb energy upon fracture of
whiskers.
Chapter 16 -
Composite Benefits
• CMCs: Increased toughness
Force
• PMCs: Increased E/ρ
10
particle-reinf
E(GPa)
10
ceramics
3
2
PMCs
10
fiber-reinf
metal/
metal alloys
1
un-reinf
0.1
polymers
0.01
0.1 0.3
Bend displacement
• MMCs:
Increased
creep
resistance
3
10 30
Density, ρ [mg/m3]
10 -4
εss (s-1)
1
6061 Al
10 -6
10 -8
6061 Al
w/SiC
whiskers
10 -10
20 30 50
Adapted from T.G. Nieh, "Creep rupture of a
silicon-carbide reinforced aluminum
composite", Metall. Trans. A Vol. 15(1), pp.
139-146, 1984. Used with permission.
σ(MPa)
100 200
Chapter 16 - 30
Summary
• Composites types are designated by:
-- the matrix material (CMC, MMC, PMC)
-- the reinforcement (particles, fibers, structural)
• Composite property benefits:
-- MMC: enhanced E, σ∗, creep performance
-- CMC: enhanced KIc
-- PMC: enhanced E/ρ, σy, TS/ρ
• Particulate-reinforced:
-- Types: large-particle and dispersion-strengthened
-- Properties are isotropic
• Fiber-reinforced:
-- Types: continuous (aligned)
discontinuous (aligned or random)
-- Properties can be isotropic or anisotropic
• Structural:
-- Laminates and sandwich panels
Chapter 16 - 31
SUMMARY
• Be able to calculate the longitudinal strength for long, short, and very short
fibere composites.
• Be able to calculate the Young’s modulus for discontinuous fibers oriented in
3 dimensions, 2 dimensions, or 1 dimension.
• Know about GFRP, CFRP, and AFRP PMC’s—increased modulus/weight
ratio.
• Know the strengthening mechanisms for fibers in a composite.
• Recall transformation toughened ceramics (Yttria stabilized zirconia).
• Be familiar with carbon-carbon, hybrid, and structural composites.
• Understand fiber composite fabrication: protrusion, prepreg, and winding.