Transcript Chapter 16

Chapter 16: Composite Materials
ISSUES TO ADDRESS...
• What are the classes and types of composites?
• Why are composites used instead of metals,
ceramics, or polymers?
• How do we estimate composite stiffness & strength?
• What are some typical applications?
Composites
• Combine materials with the objective of getting a
more desirable combination of properties
– Ex: get flexibility & weight of a polymer plus the
strength of a ceramic
• Principle of combined action
– Mixture gives “averaged” properties
Terminology/Classification
• Composites:
-- Multiphase material with significant
proportions of each phase.
woven
fibers
• Matrix:
-- The continuous phase
-- Purpose is to:
0.5 mm
- transfer stress to other phases
- protect phases from environment
-- Classification:
metal
MMC, CMC, PMC
ceramic
cross
section
view
polymer
• Dispersed phase:
-- Purpose: enhance matrix properties.
MMC: increase sy, TS, creep resist.
CMC: increase Kc
PMC: increase E, sy, TS, creep resist.
-- Classification: Particle, fiber, structural
0.5 mm
Matrix and Disperse phase of composites
Composite Survey
Composites
Particlereinforced
Fiberreinforced
Structural
Large-
Dispersion-
Continuous
Discontinuous
particle
strengthened
(aligned)
(short)
Aligned
Laminates
Randomly
oriented
Sandwich
panels
Composite Survey: Particle-I
Particle-reinforced
Fiber-reinforced
• Examples:
- Spheroidite matrix:
ferrite (a)
steel
(ductile)
60 mm
- WC/Co
cemented
carbide
matrix:
cobalt
(ductile)
Vm :
10-15 vol%!
Structural
particles:
cementite
(Fe3 C)
(brittle)
particles:
WC
(brittle,
hard)
600 mm
- Automobile matrix:
rubber
tires
particles:
C
(stiffer)
(compliant)
0.75 mm
Composite Survey: Particle-II
Particle-reinforced
Fiber-reinforced
Structural
Concrete – gravel + sand + cement
- Why sand and gravel?
Sand packs into gravel voids
Reinforced concrete - Reinforce with steel rerod or remesh
- increases strength - even if cement matrix is cracked
Prestressed concrete - remesh under tension during setting of
concrete. Tension release puts concrete under compressive force
- Concrete much stronger under compression.
- Applied tension must exceed compressive force
Post tensioning – tighten nuts to put under tension
nut
threaded
rod
Composite Survey: Particle-III
Particle-reinforced
Fiber-reinforced
Structural
• Elastic modulus, Ec, of composites:
-- two approaches.
E(GPa)
350
Data:
Cu matrix 30 0
w/tungsten 250
particles
20 0
150
upper limit: “rule of mixtures”
Ec = VmEm + VpEp
0
lower limit:
1 Vm Vp
=
+
Ec Em Ep
20 40 60 80
(Cu)
• Application to other properties:
10 0 vol% tungsten
(W)
-- Electrical conductivity, se: Replace E in equations with se.
-- Thermal conductivity, k: Replace E in equations with k.
Composite Survey: Fiber-I
Particle-reinforced
Fiber-reinforced
Structural
• Fibers very strong
– Provide significant strength improvement to
material
– Ex: fiber-glass
• Continuous glass filaments in a polymer matrix
• Strength due to fibers
• Polymer simply holds them in place
Composite Survey: Fiber-II
Particle-reinforced
Fiber-reinforced
Structural
• Fiber Materials
– Whiskers - Thin single crystals - large length to diameter ratio
• graphite, SiN, SiC
• high crystal perfection – extremely strong, strongest known
• very expensive
– Fibers
• polycrystalline or amorphous
• generally polymers or ceramics
• Ex: Al2O3 , Aramid, E-glass, Boron, UHMWPE
– Wires
• Metal – steel, Mo, W
Fiber Alignment
aligned
continuous
aligned
random
discontinuous
Composite Survey: Fiber-III
Particle-reinforced
Fiber-reinforced
• Aligned Continuous fibers
• Examples:
-- Metal: g'(Ni3Al)-a(Mo)
-- Ceramic: Glass w/SiC fibers
by eutectic solidification.
matrix:
formed by glass slurry
Eglass = 76 GPa; ESiC = 400 GPa.
a (Mo) (ductile)
(a)
2 mm
fibers:
Structural
g ’ (Ni3Al) (brittle)
(b)
fracture
surface
Composite Survey: Fiber-IV
Particle-reinforced
Fiber-reinforced
• Discontinuous, random 2D fibers
• Example: Carbon-Carbon
-- process: fiber/pitch, then
burn out at up to 2500ºC.
-- uses: disk brakes, gas
turbine exhaust flaps, nose
cones.
(b)
(a)
• Other variations:
-- Discontinuous, random 3D
-- Discontinuous, 1D
Structural
C fibers:
very stiff
very strong
C matrix:
less stiff
view onto plane less strong
fibers lie
in plane
Composite Survey: Fiber-V
Particle-reinforced
Fiber-reinforced
Structural
• Critical fiber length for effective stiffening & strengthening:
fiber strength in tension
sf d
fiber length  15
c
fiber diameter
shear strength of
fiber-matrix interface
• Ex: For fiberglass, fiber length > 15 mm needed
• Why? Longer fibers carry stress more efficiently!
Shorter, thicker fiber:
sd
fiber length  15 f
c
Longer, thinner fiber:
fiber length  15
sf d
c
s(x)
s(x)
Poorer fiber efficiency
Better fiber efficiency
Composite Strength:
Longitudinal Loading
Continuous fibers - Estimate fiber-reinforced composite
strength for long continuous fibers in a matrix
• Longitudinal deformation
sc = smVm + sfVf
volume fraction

Ece = Em Vm + EfVf
but
c = m = f
isostrain
longitudinal (extensional)
modulus
f = fiber
m = matrix
Composite Strength:
Transverse Loading
• In transverse loading the fibers carry less of the load
- isostress
sc = sm = s f = s
c= mVm + fVf

1
Vm Vf


Ect Em Ef
transverse modulus
Composite Strength
Particle-reinforced
Fiber-reinforced
Structural
• Estimate of Ec and TS for discontinuous fibers:
sf d
-- valid when fiber length  15
c
-- Elastic modulus in fiber direction:
Ec = EmVm + KEfVf
efficiency factor:
-- aligned 1D: K = 1 (aligned )
-- aligned 1D: K = 0 (aligned )
-- random 2D: K = 3/8 (2D isotropy)
-- random 3D: K = 1/5 (3D isotropy)
-- TS in fiber direction:
(TS)c = (TS)mVm + (TS)fVf
(aligned 1D)
Composite Production Methods-I
• Pultrusion
– Continuous fibers pulled through resin tank, then
preforming die & oven to cure
Composite Production Methods-II
• Filament Winding
– Ex: pressure tanks
– Continuous filaments wound onto mandrel
Composite Survey: Structural
Particle-reinforced
Fiber-reinforced
• Stacked and bonded fiber-reinforced sheets
-- stacking sequence: e.g., 0º/90º
-- benefit: balanced, in-plane stiffness
• Sandwich panels
-- low density, honeycomb core
-- benefit: small weight, large bending stiffness
face sheet
adhesive layer
honeycomb
Structural
Composite Benefits
• CMCs: Increased toughness
Force
103
particle-reinf
ceramics
E(GPa)
PMCs
2
10
10
fiber-reinf
1
un-reinf
10 -4
6061 Al
ss (s-1)
10 -6
Increased
creep
resistance
10 -8
10 -10
metal/
metal alloys
.1 G=3E/8 polymers
.01 K=E
.1 .3 1 3 10 30
Density, r [mg/m3]
Bend displacement
• MMCs:
• PMCs: Increased E/r
6061 Al
w/SiC
whiskers
20 30 50
s(MPa)
100 200
Summary
• Composites are classified according to:
-- the matrix material (CMC, MMC, PMC)
-- the reinforcement geometry (particles, fibers, layers).
• Composites enhance matrix properties:
-- MMC: enhance sy, TS, creep performance
-- CMC: enhance Kc
-- PMC: enhance E, sy, TS, creep performance
• Particulate-reinforced:
-- Elastic modulus can be estimated.
-- Properties are isotropic.
• Fiber-reinforced:
-- Elastic modulus and TS can be estimated along fiber dir.
-- Properties can be isotropic or anisotropic.
• Structural:
-- Based on build-up of sandwiches in layered form.
Material Selection
Material Classification
Materials
Metallic
Ferrous
Nonferrous
Nonmetallic
Polymer
Ceramic
Composite
The Materials Selection Process
Composition
Mechanical
Electrical
Thermal
Optical
Etc.
Environment
Load
Applications
Functions
Properties
Structure
Shape
Materials
Processes
PRICE AND AVAILABILITY
• Current Prices on the web: e.g., http://www.metalprices.com
-- Short term trends: fluctuations due to supply/demand.
-- Long term trend: prices will increase as rich deposits
are depleted.
• Materials require energy to process them:
-- Energy to produce
materials (GJ/ton)
Al
PET
Cu
steel
glass
paper
237 (17)
103 (13)
97 (20)
20
13
9
Energy using recycled
material indicated in green.
-- Cost of energy used in
processing materials ($/MBtu)
elect resistance
propane
oil
natural gas
25
17
13
11
RELATIVE COST, c, OF MATERIALS
Metals/
Alloys
100000
50000
Relative Cost (c)
20000
10000
5000
Pt
Au
20
10
5
2
1
0.5
0.1
0.05
Polymers
Composites/
fibers
c
Diamond
Si wafer
2000
1000
500
200
100
50
Graphite/
Ceramics/
Semicond
Si nitride
Ag alloys
Tungsten
Ti alloys
Si carbide
Cu alloys
Al alloys
Mg alloys
Al oxide
high alloy
CFRE prepreg
Glass-soda
Steel
pl. carbon
Concrete
AFRE prepreg
Carbon fibers
Aramid fibers
GFRE prepreg
Nylon 6,6
PC
Epoxy
PVC PET
LDPE,HDPE
PP
PS
$ / kg
($ / kg)ref material
• Reference material:
-- Rolled A36 plain
carbon steel.
• Relative cost, c ,
fluctuates less
over time than
actual cost.
E-glass fibers
Based on data in Appendix
C, Callister, 7e.
Wood
AFRE, GFRE, & CFRE = Aramid,
Glass, & Carbon fiber reinforced
epoxy composites.
STIFF & LIGHT TENSION MEMBERS
F, d • Bar must not lengthen by more than d
under force F; must have initial length L.
-- Stiffness relation:
L
F
c2
c c
E
d
L
-- Mass of bar:
M  rLc 2
(s = E)
• Eliminate the "free" design parameter, c:
FL2 r
M
d E
minimize for small M
specified by application
• Maximize the Performance Index:
(stiff, light tension members)
E
P
r
STRONG & LIGHT TENSION MEMBERS
F, d • Bar must carry a force F without failing;
must have initial length L.
-- Strength relation:
sf
F

N c2
L
c c
-- Mass of bar:
M  rLc 2
• Eliminate the "free" design parameter, c:
r
M  FLN
sf
minimize for small M
specified by application
• Maximize the Performance Index:
(strong, light tension members)
s
P f
r
STRONG & LIGHT TORSION MEMBERS
Mt
• Bar must carry a moment, Mt ;
must have a length L.

L
-- Strength relation:

2R
-- Mass of bar:
2Mt
f

N R 3
M  rR 2L
• Eliminate the "free" design parameter, R:
2/3
M  (2 NMt )
specified by application
L
f2 / 3
minimize for small M
• Maximize the Performance Index:
(strong, light torsion members)
r
P
f2 / 3
r
DETAILED STUDY I: STRONG, LIGHT
TORSION MEMBERS
• Maximize the Performance Index:
• Other factors:
P
f2 / 3
r
--require sf > 300 MPa.
--Rule out ceramics and glasses: KIc too small.
• Numerical Data:
material
CFRE (vf = 0.65)
GFRE (vf = 0.65)
Al alloy (2024-T6)
Ti alloy (Ti-6Al-4V)
4340 steel (oil
quench & temper)
r (Mg/m3) f (MPa)
1.5
1140
2.0
1060
2.8
300
4.4
525
7.8
780
P [(MPa)2/3m3/Mg]
73
52
16
15
11
• Lightest: Carbon fiber reinforced epoxy
(CFRE) member.
DETAILED STUDY II: STRONG, LOW
COST TORSION MEMBERS
• Minimize Cost: Cost Index ~ c M ~ c /P (since M ~ 1/P)
where
M = mass of material
cost/mass of material
c = relative cost =
cost/mass of low-carbon steel
• Numerical Data:
material
CFRE (vf = 0.65)
GFRE (vf = 0.65)
Al alloy (2024-T6)
Ti alloy (Ti-6Al-4V)
4340 steel (oil
quench & temper)
P [(MPa)2/3m3/Mg]
73
52
16
15
11
c
80
40
15
110
5
( c /P)x100
112
76
93
748
46
• Lowest cost: 4340 steel (oil quench & temper)
• Need to consider machining, joining costs also.
SUMMARY
• Material costs fluctuate but rise over the long
term as:
-- rich deposits are depleted,
-- energy costs increase.
• Recycled materials reduce energy use significantly.
• Materials are selected based on:
-- performance or cost indices.
• Examples:
-- design of minimum mass, maximum strength of:
• shafts under torsion,
• bars under tension,
• plates under bending,