MFGT 104
Materials and Quality
Composites
Professor Joe Greene
CSU, CHICO
MFGT 104
1
Chap 9: Polymers Composites
• Objectives
– Define the components and difference types of composites.
– Explain the different types of composite construction and the
reasons behind them.
– Describe the various manufacturing methods used to produce
composites.
– List the different reinforcing materials used in composites.
– List the various matrix materials used in composites.
• Excellent Web sites
– Michigan State http://islnotes.cps.msu.edu/trp/
– U of Delaware http://www.ccm.udel.edu/publications/CU/99/
– Cornell University
http://www.engr.siu.edu/staff2/abrate/NSFATE/links.htm
2
Composites
• Composite definition
– A composite is a material comprised of two or more physically distinct
materials with at least one material providing reinforcing properties on
strength and modulus.
• Natural Composites
– Bone
– Wood
– Bamboo: Natures fiber glass due to pronounced fibrillar structure which is
very apparent when fractured.
– Muscle and other tissue
• Engineering Composites
– Reinforced concrete beams
– Thermoset composites: Thermoset resins (polyurethanes, polesters, epoxies)
• Glass fibers, Carbon fibers, Synthetic fibers, metalfibers, or ceramic fibers
– Thermoplastic composites (polypropylene, nylon, polyester,TPU,polyimide)
• Glass fibers, Carbon fibers, Synthetic fibers, metalfibers, or ceramic fibers
3
SMC
Sheet Molding
Compound
Automotive Applications of
Plastics and Composites
n
Composite Intensive Vehicles
RTM
Resin Transfer Molding
8-25 -98
M41_au 25
4
Automotive Plastics and Composites Use
• Exterior Composite Panels
– doors
• Sheet Molded Compound (SMC): Camaro, Firebird and Corvette
• Resin Transfer Molding (RTM): Viper
– hoods
• Sheet Molded Compound (SMC): Camaro, Firebird, Corvette, Ford trucks
• Resin Transfer Molding (RTM): Viper, Heavy duty trucks)
– bumper beams
• Glass Mat Thermoplastic (GMT): Camaro, Firebird, Venture, Transport,
• Interior
– floor pan
• Resin Transfer Molding (RTM): Corvette
• Engine
– valve covers, intake manifolds, fluid containers, etc.
5
Automotive Plastics and Composites Use
SMC
Sheet Molding
Compound
SMC
Sheet Molding
Compound
6
Recreational Plastics and Composites Use
• Snow Equipment
– skis, snow boards, snow mobiles, etc.
• Water Sports Equipment
– water skis, water crafts, snorkel equipment, fishing gear
– diving equipment
• Land Sports Equipment
– shoes, roller blades, skate boards, tennis, golf
• Air Sports Equipment
– plane kits
7
• Epoxy
Applications for Thermosets
– Protective coatings: maintenance coatings for industrial and marine,
tank linings, industrial floorings, beer and beverage can coatings,
food cans, appliance primers, hospital and laboratory furniture.
– Bonding and adhesives: Automotive and aircraft industries adhesive
to metals and composites.
– Molding, casting and tooling: Molding compounds in electrical and
electronic industries, casting resins, potting resins. Prototype and
master model tools.
– Laminating and composites: Binders in fiber reinforced laminates and
composites. Laminates are used in printed wiring boards. Composite
applications include filament winding (high performance pipes in oil
fields, pressure vessels, tank and rocket motor housings), pultrusion,
casting, and molding (graphite composites for aerospace applications)
– Building and construction: Flooring (seamless, self-leveling, or epoxy
terrazzo floors), repair of bridges and roads with glass and carbon
fiber wraps, concrete crack repair, coat reinforcing bars, binders for
8
patios, swimming pool decks, and soil around oil-well drills.
Applications for Thermosets
• Polyester
–
–
–
–
–
Boat hulls, shower stalls, electrical components, appliances
Recreation vehicles, automotive body panels, floor pans; SMC
Soft tooling, patterns
Cultured marble, buttons, corrosion resistant tanks and parts,
Corrugated and flat paneling, simulated wood furniture, bowling balls,
polymer concrete, and coatings
• Polyurethane
– Rigid foams: (MDI) Laminated board stock, Moldings, Bun, Foam in place
insulation, sprayed foam, packaging
– Semi-flexible foam: (MDI and TDI) Moldings, Integral-skin moldings
– Flexible foam:(TDI) Moldings, integral skin molding, carpet underlay
– Packaging: (TDI) Furniture cushioning
– Microcellular foam: (MDI) RIM parts, shoe soles
– Non-foam cast elastomers
9
– Coatings, binders, thermoplastic elastomers, sealants, paints
Composite Classifications
• Reinforcement Type
– Discontinuous (fibers are chopped and dispersed in matrix resin)
• Short fibers: fiber lengths 3mm or less (most injection molded materials)
• Long fibers: fiber lengths greater than 6 mm. (Some injection molded materials
with 6mm fibers, Sheet Molding Compound (SMC) with 1” fibers, DFP
Directed Fiber Preforms for RTM and SRIM)
• Particulates: fibers is forms as spheres, plates, ellipsoids (some injection
molded materials reinforced with mineral fibers)
– Continuous (fibers are throughout structure with no break points)
• Glass roving: glass bundles are wound up in a packet similar to yarn.
• Roving is woven into several weaves using a loom machine like in apparel.
– Mat products: random swirl glass pattern.
– Woven product: roving is woven into machine direction (warp) and
cross direction (weft)
– Uni product: roving is woven in one direction with a cross thread given
to hold mat together.
10
Composites Have a Fiber Preform
• Fiber type
– Roving form that can be sprayed into a 3-D preform
– Roving form that is woven into a glass sheet and then formed to
shape (preform)
11
Processing of Composites
• Open Mold processes
– Hand lay-up and Spray-up
– Filament winding
12
Composite Classifications
• Resin (or matrix) type
– Thermoset resins- those that undergo a chemical cross-linking reaction
• Epoxy: reaction of bisphenol A and epichlorohydrin
• Polyester: reaction of difunctional acid (or anhydride) and a difunctional
alcohol (glycol)
• Polyurethane: reaction of alcohol and isocyanate
• Phenolic
• Silicone
• Melamine
– Thermoplastic resins- those that are formed under heat
•
•
•
•
Polyamines (nylon) (short and long fibers)
Polyesters (short and long fibers)
Polypropylene (short, long fibers and continuous fibers)
Other thermoplastic resins (short and long fibers)
13
Properties of Materials
• Tensile modulus
–
–
–
–
–
Low alloy steel
Aluminum
Carbon fiber
Glass fiber
Aramid fiber
(Kevlar)
207GPa(30Mpsi)
72GPa (10Mpsi)
300GPa(40Mpsi)
76GPa (10Mpsi)
125GPa (20Mpsi)
• Tensile strength
–
–
–
–
–
Low alloy steel
Aluminum
Carbon fiber
Glass fiber
Aramid fiber
(Kevlar)
1500MPa(220Kpsi)
500MPa(75Kpsi)
2400MPa(360Kpsi)
2000MPa(300Kpsi)
3000MPa (450Kpsi)
Density
Spec Mod
7.85 g/cc
2.8 g/cc
1.8 g/cc
2.56g/cc
1.4g/cc
26spGPa
26spGPa
167spGPa
30spGPa
89spGPa
Density
Spec Str
7.85 g/cc
2.8 g/cc
1.8 g/cc
2.56g/cc
1.4g/cc
191spMPa
178spGPa
4320spGPa
781spGPa
2140spGPa
14
Thermoset Definition
• Thermoset materials are polymers that under go a
chemical reaction to build molecular weight and viscosity.
• Thermosets are set or crosslinked with heat and can not be
reheated for forming repeated forming.
15
Thermosets History
• Thermosets are polymers that undergo a chemical reaction
during the polymerization.
• Thermosetting reaction is not reversible under heat.
• Epoxy
– Standard epoxy is based on bisphenol A and epichlorohydrin.
– Others based on phenols and formaldehyde or aromatic amines and
aminophenols
– Curing can occur at room temperature with the use of 2 component
systems. Curing at elevated temperature with use of onecomponent.
– Properties include good adhesion to many substrates, low
shrinkage, high electrical resistivity, good corrosion resistance, and
thermal.
– Processing is achieved without generation of volatiles.
16
Epoxy Chemistry
• Epoxy: O
C C
H H
epoxide group
H
H
H + H2N (C) N (C) NH2
H
H
+
amines (DETA)
epoxy
• Other epoxy resins
–
–
–
–
diglycidyl ether of bisphenol A (DGEBRA)
tetraglycidyl methylene dianiline (TGMDA
epoxy phenol cresol novolac
cycloaliphatic epoxies (CA)
• Curing agents (hardeners, catalysts, cross-linking agents)
– aliphatic or aromatic amines (DETA, TETA, hexamethylene tetramine,etc.)
– acid anhydrides (phthalic anhydride, pyromellitic dianhydride, etc.)
17
• Active hydrogen react with epoxide groups. 15% hardener is needed
Epoxy Chemistry
18
Polyester Chemistry
• Unsaturated Polyesters
– Thermoset reaction between a difunctional acid (or anhydride) and
a difunctional alcohol (glycol)
– At least some of the acid (or anhydride) features double bonds
between adjacent carbon atoms for unsaturation.
– Characteristic ester linkages are formed, hence the name Polyester
O
O
C6H4(COOH)2 + (CH2)2(OH)2
O]-
-[(CH2)2 -O- C
terephthalic acid
Polyethylene terephthalate (PET)
+ ethylene glycol
- C-
– Acids include: maleic, fumaric, isophthalic, terphthalic, adipic, etc.
– Anhydrides include: maleic, phthalic
– Glycols include ethylene glycol, diethylene glycol, propylene
glycol
19
Polyester Chemistry
• Heat or radiation can trigger the cross linking reaction
• Catalyst (or initiator) is used. Methyl ethyl ketone (MEK)
peroxide, benzoyl peroxide, and cumene hydroperoxide
• Accelerators (or promoters) speed up the reaction.
• Inhibitors extend shelf life (hydroquinone, tertiary butyl
catechol)
• Condensation Reaction results in CO2 and H2O
• Monomer required to polymerize, e.g., Styrene, to react
with the unsaturations in the polyester molecules to form
3-D network.
– Styrene at 30% to 50% in commercial polyester systems
– vinyl toluene for vinyl ester
– methyl methacrylate for methyl methacrylate ester
20
Polyester Chemistry
21
•
Polyester
and
Polyurethane
Polyester
– Thermoset reaction between a difunctional acid (or anhydride) and
a difunctional alcohol (glycol)
– Heat or radiation can trigger the cross linking reaction
– Accelerators (or promoters) speed up the reaction.
– Condensation Reaction results in CO2 and H2O.
– Monomer required to polymerize, e.g., Styrene at 30% to 50% in
commercial polyester systems
• Polurethane
– Reaction between isocyanate and alcohol (polyol). Condensation
Reaction results in CO2 and H2O.
– Crosslinking occurs between isocyanate groups (-NCO) and the
polyol’s hydroxyl end-groups (-OH)
– Thermoplastic PU (TPU) have some crosslinking, but purely by
physical means. These bonds can be broken reversibly by raising
the material’s temperature, as in molding or extrusion.
22
Polyurethane Chemistry
• Reaction between isocyanate and alcohol (polyol).
• Crosslinking occurs between isocyanate groups (-NCO)
and the polyol’s hydroxyl end-groups (-OH)
• Thermoplastic PU (TPU) have some crosslinking, but
purely by physical means. These bonds can be broken
reversibly by raising the material’s temperature, as in
molding or extrusion.
• Ratio between the two give a range of properties between
a flexible foam (some crosslinking) to a rigid urethane
(high degree of crosslinking).
• In PUR foams density can range from 1 lb/ft3 to 70 lb/ft3.
• Foams are produced by chemical blowing agents.
23
• Catalyst are used to initiate reaction.
Polyurethane Chemistry
24
Processing of Composites
• Open Mold processes
–
–
–
–
–
Hand lay-up
Spray-up
Vacuum bag, pressure bag, autoclave
Filament winding
Centrifugal casting
• Closed Mold Processes
– Compression molding
– Injection Molding [high pressure]
– Resin Transfer Molding (RTM), Structural Reaction Injection
Molding (SRIM) [low pressure]
– Pultrusion
25
Processing of Composites
• Closed Mold Processes
– Compression molding [moderate pressure]
– Injection Molding [high pressure]
– Resin Transfer Molding (RTM), Structural Reaction Injection
Molding (SRIM) [low pressure]
– Pultrusion [low pressure]
Injection
Molding
Annual Part 30K – 200K
Production
Volume
Part Size
Small
< 2 lbs
Compression
Molding
30K – 200K
Structural
RIM
5K – 200 K
Medium
2 lbs – 20 lbs
Fixed
Assets
Tooling
Cost
Cycle Time
$500K-$2M
Medium
Medium to large 5 lbs
2 lbs – 20
– 50 lbs
lbs
$300K-$1M $10K - $150K
Materials
$300K -$2M
$50K -$500K
$150K-$500K $50K$300K
1 sec –
30 sec –
30 sec –
30 sec
90 sec
120 sec
Thermoplastic Thermoplastic Thermoset
Thermoset
Resin Transfer
Molding
0.5K –5 K
$20K - $300K
5 min – 30 min
Thermoset
26
Polyurethane Processing
• Polyurethane can be processed by
– Casting, painting, foaming
– Reaction Injection Molding (RIM)
27
Structural RIM
• Fiber preform is placed into mold.
• Polyol and Isocyanate liquids are injected into a closed
mold and reacted to form a urethane.
28
Processing of Composites
• Open Mold processes
– Vacuum bag, pressure bag, SCRIMP
– autoclave: Apply Vacuum Pressure and Heat in an oven which can
be 5 feet to 300 feet long
29
Thermoset Reacting Polymers
• Process Window
– Temperature and pressure must be set to produce chemical reaction
without excess flash (too low a viscosity), short shot (too high a
viscosity), degradation (too much heat)
30
Sheet Molding Compound (SMC)
• SMC is the paste that is compression molded
– 33% polyester resin and stryrene, which polymerizes and
crosslinks
– 33% glass fibers (1” fibers)
– 33% Calcium Carbonate
31
Compression Molding
• Compression molding was specifically developed for replacement of metal
components with composite parts. The molding process can be carried out with
either thermosets or thermoplastics. However, most applications today use
thermoset polymers. In fact,compression molding is the most common method
of processing thermosets.
32
Resin Transfer Molding
• In the RTM process, dry (i.e.,unimpregnated )
reinforcement is pre-shaped and oriented into skeleton of
the actual part known as the preform which is inserted into
a matched die mold.
• The heated mold is closed and the liquid resin is injected
• The part is cured in mold.
• The mold is opened and part is removed from mold.
33
Injection Molding
Glass Reinforced Composites
• Plastic pellets with glass fibers are melted in screw,
injected into a cold mold, and then ejected.
Glass filled resin pellets
34
Composites Have Directional Properties
• Fiber type and Fiber %
– Different fibers have different strength, modulus, and strain at failure
• Generally, the stiffer the fiber, the smaller the strain at failure.
– The higher the fiber %, the higher the properties
• Fiber % for automotive is 35% by volume
• Fiber % for aerospace is 60% by volume
• Fiber Orientation
– Carbon fiber is Amoco high modulus pitch based fiber
– Effect of orientation on carbon fiber properties
• Unidirectional had double the strength and triple the modulus as a quasi-isotropic
material
• Unidirectional material had 10% of the strength and 3% of the modulus in the
transverse direction as the quasi-isotropic laminate
– Mechanical Properties of Carbon-Fiber Composites with Epoxy and PEEK
• Epoxy resin had 25% higher tensile strength and 60% higher tensile modulus than
the peek composite in the 0° direction
• Peek resin had 40% higher strength and 330% higher Fracture strain in the 45°
direction than epoxy.
35
Carbon/Graphite Fibers
• Need for reinforcement fibers with strength and modulii
higher than those of glass fibers has led to development of
carbon
• Thomas Edison used carbon fibers as a filament for
electric light bulb
• High modulus carbon fibers first used in the 1950s
• Carbon and graphite are based on layered structures of
hexagonal rings of carbon
• Graphite fibers are carbon fibers that
– Have been heat treated to above 3000°F that causes 3 dimensional
ordering of the atoms and
– Have carbon contents GREATER than 99%
– Have tensile modulus of 344 Gpa (50Mpsi)
36
Carbon/Graphite Fibers
• Manufacturing Process
– Current preferred methods of producing carbon fibers are from
polyacrylonitrile (PAN), rayon (regenerated cellulose), and pitch.
• PAN
– Have good properties with a low cost for the standard modulus
carbon
– High modulus carbon is higher in cost because high temperatures
required
• PITCH
– Lower in cost than PAN fibers but can not reach properties of PAN
– Some Pitch based fibers have ultra high modulus (725 GPa versus
350GPa) but low strength and high cost (Table 3-2)
37
Carbon/Graphite Fibers
• PAN Manufacturing Process Figures 3-3 and 3-4
– Polyacrylonitrile (PAN) is commercially available textile fiber and is a ready
made starting material for PAN-based carbon fibers
– Stabilized by thermosetting (crosslinking) so that the polymers do not melt in
subsequent processing steps. PAN fibers are stretched as well
– Carbonize: Fibers are pyrolyzed until transformed into all-carbon
• Heated fibers 1800°F yields PAN fibers at 94% carbon and 6% nitrogen
• Heated to 2300°F to remove nitrogen yields carbon at 99.7% Carbon
– Graphitize: Carried out at temperatures greater than 3200° F to
• Improve tensile modulus by improving crystalline structure and three dimensional
nature of the structure.
– Fibers are surface treated
• Sizing agent is applied
• Finish is applied
• Coupling agent is applied
– Fibers are wound up for shipment
38
Carbon/Graphite Fibers
• PITCH Manufacturing Process Figure 3-3
– Pitch must be converted into a suitable fiber from petroleum tar
• Pitch is converted to a fiber by going through a meso-phase where the polymer
chains are somewhat oriented though is a liquid state (liquid crystal phase)
• Orientation is responsible for the ease of consolidation of pitch into carbon
– Stabilized by thermosetting (crosslinking) so that the polymers do not melt in
subsequent processing steps
– Carbonize: Fibers are pyrolyzed until transformed into all-carbon
• Heated fibers 1800°F
• Heated to 2300°F
– Graphitize: Carried out at temperatures greater than 3200° F to
• Improve tensile modulus by improving crystalline structure and three dimensional
nature of the structure.
– Fibers are surface treated
• Sizing agent is applied
• Finish is applied
• Coupling agent is applied
– Fibers are wound up for shipment
39
Carbon Fiber Mechanical Properties
• Table 3-2
Carbon Fiber Mechanical Properties
PAN Based
Tensile Modulus (Mpsi)
33 - 56
Tensile Strength (Msi)
0.48 - 0.35
Elongation (%)
1.4 - 0.6
Density (g/cc)
1.8 - 1.9
Carbon Assay (%)
92 - 100
PITCH Based Rayon Based
23 -55
5.9
0.2 - 0.25
0.15
0.9 - 0.4
25
1.9 - 2.0
1.6
97 - 99
99
40
Mechanical Properties Pitch versus PAN
• Carbon Fiber Properties for 62% volume carbon fiber
– PITCH fiber has higher density
– PAN Fiber intermediate modulus has tensile strength and shear
strength but a lower tensile modulus and lower thermal
conductivity than PITCH intermediate modulus fiber.
– PITCH High modulus fiber has higher tensile modulus and higher
thermal conductivity but lower tensile strength and compressive
strength than PAN Intermediate fiber.
Property
PAN Int Mod PITCH Int Mod PITCH High Mod
Density, g/cc
1.6
1.7
1.8
Tensile Strength (MPa)
2585
896
1206
Tensile Modulus (GPa)
172
220
517
Compressive Strength (MPa)
1723
510
268
Shear Strength (Mpa)
124
55
27
Thermal Conductivity (W/m-K)
8.65
74
398
41
Directional Properties Carbon Fiber
• Different types of carbon fiber composites
• Epoxy resin with 60% volume carbon fiber, PITCH or
PAN
• Results
– High strength PAN fibers have lower modulus that high modulus
PAN
– High strength PITCH fibers have lower modulus that high modulus
PITCH
Fiber
T300
Tensile (Brittle Resin)
PAN
Strength (MPa)
Modulus (GPa)
Tensile (Ductile Resin)
Strength (MPa)
Modulus (GPa)
Compresion
Strength (MPa)
Modulus (GPa)
T50
PAN
T650
PAN
1862
138
1311
241
T1000
P55
P100
PAN
PITCH
PITCH
2413
3447
723
1138
170
159
234
483
2790
138
1414
241
3070
170
3795
234
890
483
1206
1725
124
965
234
1650
151
1690
199
483
505
276
42
Directional Properties Carbon Fiber PEKK Laminates
• Fiber Volume Fraction is 60% Aerospace Quality
– Continuous fiber has higher strength and modulus for tensile,
compression, and shear in the 0° than long fiber composite.
– Long Fiber PEKK composites has higher Tensile strength and
modulus and Poisson ratio in the 90° direction than continuous
Long Fiber
Long Fiber
fiber.
Property
(56mm)
Continuous
%Increase (56mm)
Continuous
Tensile (MPa)
Strength, 0°
Modulus, 0°
Poisson ratio
Strength, 90°
Modulus, 90°
Compressive (MPa)
Strength, 0°
Modulus, 0°
Flexural (MPa)
Strength, 0°
Modulus, 0°
Shear (MPa)
Strength, 0°
Modulus, 0°
Short Beam strength
1610
123.5
0.35
91
10.3
1676
129.7
0.33
73.1
8
Continuous Fraction Transverse (90°) versus In-plane (0°)
4.09937888
1
1
5.02024291
1
1
-5.7142857
-19.67033 0.056521739 0.043616
-22.330097
0.08340081 0.061681
1262
111
1393 10.3803487
121.4 9.36936937
1655
120
1931 16.6767372
127.6 6.33333333
146
5.5
110
142 -2.739726
5.8 5.45454545
117 6.36363636
43
Directional Properties Carbon Fiber
• Unidirectional (0°/ 90°) versus Quasi-isotropic laminate
(0°/30°/60°/90°/120°/150°)
• Fiber Volume Fraction is 60% Aerospace Quality
– Polymer is Epoxy and Carbon Fiber is PITCH High Modulus fiber
• Results
– Uni-directional laminate is 40 times stronger and 92 times stiffer in
the 0° direction versus the transverse 90° direction in tensile.
– The quasi isotropic laminate is stronger and stiffer in tension in the
0° direction than the 90° direction. The opposite is true for
compression
Unidirectional Laminate
Quasi-isotropic Laminate
Testing Angle
0°
90°
0°/90° Ratio 0°
90° 0°/90° Ratio
Tensile Strength (MPa)
793
20
39.65
379
241
1.57
Tensile Modulus (GPa)
303
3.3
91.82
104
97
1.07
Tensile Ultimate Strain, %
0.25
0.5
0.50
0.27
0.23
1.17
Compressive Strength (MPa)
400
158
2.53
172
200
0.86
Compressive Modulus (GPa)
255
6.7
38.06
76
88
0.86
Compressive Ultimate Strain, % ------0.55
0.86
0.64
44
Directional Properties Carbon Fiber
• Unidirectional (0°) versus Quasi-isotropic laminate (45°)
• Results
– Uni-directional laminate is stronger and stiffer in the 0° direction
versus the transverse 45° direction in tensile for Epoxy and PEEK
– The quasi isotropic laminate is has higher fracture strain% in the
45° direction than the 0° direction for epoxy and for PEEK.
Fiber
Tensile Strength Tensile
Fracture
Polymer Matrix Orientation (MPa)
Modulus(GPa) Strain %
Epoxy
0°
932
83
1.1
Epoxy
45°
126
1.3
PEEK
0°
740
51
1.1
PEEK
45°
194
14
4.3
45
Directional Properties Thermoplastic Composites
• Results
– PEEK APC2 and AS-4 Carbon fiber had the highest tensile strength
– Kevlar 49 had high strength but the lower tensile modulus than
carbon
Resin
PEEK (APC2)
APC aromatic
ketone
PEKK
PPS Ryton
Torlon-C
Polyamidlimide
ULTEM 1000
polyetherimide
AVIMID
Polyimide
UDEL
Polysulfone
J-2 Poly
arylamide
Fiber
AS-4
Carbon
Fiber
Tensile Strength
(MPa)
Tensile
Compresive
Modulus (GPa) Strength (M Pa)
2242
138
1069
138
AS-4
AS-4
AS-4
1656
138
1138
1390
655
C-6000
1390
140
1390
AS-4
138
IM-6
AS
1345
131
1035
Kevlar
1310
76
276
46
Rule of Mixtures
• Mechanical properties of a composite material made from
two materials can be estimated based upon the volume
fraction of each material times the material property of
each.
• Modulus, strength, CLTE, shrinkage, density, and others
• formula: Ec = Ef*Vf + EmVm = Ef*Vf + Em(1-Vf), where E is Tensile
modulus, f is fiber, m is matrix, and c is composite
• Example,
vol frac fib
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Composite: Epoxy and Glass
modulus, Gpastrength, Mpa
5
50
12
165
19
280
26
395
33
510
40
625
47
740
54
855
61
970
68
1085
75
1200
given
Ef
Em
ten str glas
ten str epox
75
5
1200
50
Gpa
Gpa
MPa
MPa
formula: Ec = Ef*Vf + EmVm = Ef*Vf + Em(1-Vf)
Rule of Mixtures for
1
47
Rule of Mixtures
dens glass
dens epoxy
• Example, Density
2.56 g/cc
1.2 g/cc
– Epoxy and Glass,
– formula: c = f*Vf + mVm = f*f + m(1-Vf), where  is
density, f is fiber, m is matrix, and c is composite
vilume fraction
fibers
Rule of Mixtures for Density
1
0.8
0.6
0.4
0.2
0
Series1
0
0.5
1
Weight fraction fibers
48
Rule of Mixtures
• Example, Epoxy and Glass
– Formula: Ec = Ef*Vf + EmVm = Ef*Vf + Em(1-Vf), where E is
Tensile modulus, f is fiber, m is matrix, and c is composite
– Formula: TSc = TSf*Vf + TSmVm = TSf*Vf + TSm(1-Vf), where
TS is Tensile strength, f is fiber, m is matrix, and c is composite
Tensile Strength of Polyester
Composite
Tensile Modulus of Polyester
Composite
80
1200
60
Strength (MPa)
Tensile Modulus, GPa
1400
40
20
0
0
0.5
Volume Fraction fiber
1
1000
800
600
400
200
0
0
0.5
Volume Fraction fiber
1
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Rule of Mixtures
• Comparison with published data
• Example,
– Polyester with 33% glass fibers 0/90 Ply
– Experimental
• Tensile strength = 360 MPa
• Tensile modulus = 17 GPa
– Rule Mixture (Theoretical)
• Tensile strength = 395 MPa
• Tensile modulus = 26 GPa
– % Experimental with Theoretical
• Tensile strength = - 8.86%
• Tensile modulus = - 34.6%
50
Rule of Mixtures
• Comparison with published data
• Example,
– Epoxy with 60% carbon fibers 0/90 Ply
– Experimental
• Tensile strength = 2040 MPa
• Tensile modulus = 134 GPa
– Rule Mixture (Theoretical)
• Tensile strength = 2283 MPa
• Tensile modulus = 197 GPa
– % Experimental with Theoretical
• Tensile strength = - 10.6%
• Tensile modulus = - 31.4%
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