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MFGT 104Materials and Quality

Composites

Professor Joe Greene

CSU, CHICO

MFGT 104

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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

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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

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8-25-98 M41_au25 5

Automotive Applications ofPlastics and Composites

n Composite Intensive VehiclesSMCSheet Molding Compound RTM

Resin Transfer Molding

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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.

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Automotive Plastics and Composites Use

SMCSheet Molding Compound

SMCSheet Molding Compound

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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

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Applications for Thermosets• Epoxy– 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 patios, swimming pool decks, and soil around oil-well drills.

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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– Coatings, binders, thermoplastic elastomers, sealants, paints

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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.

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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)

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Processing of Composites• Open Mold processes

– Hand lay-up and Spray-up

– Filament winding

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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)

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Properties of Materials • Tensile modulus Density Spec Mod

– Low alloy steel 207GPa(30Mpsi) 7.85 g/cc 26spGPa– Aluminum 72GPa (10Mpsi) 2.8 g/cc 26spGPa– Carbon fiber 300GPa(40Mpsi) 1.8 g/cc 167spGPa– Glass fiber 76GPa (10Mpsi) 2.56g/cc 30spGPa– Aramid fiber 125GPa (20Mpsi) 1.4g/cc 89spGPa

(Kevlar)

• Tensile strength Density Spec Str– Low alloy steel 1500MPa(220Kpsi) 7.85 g/cc 191spMPa– Aluminum 500MPa(75Kpsi) 2.8 g/cc 178spGPa– Carbon fiber 2400MPa(360Kpsi) 1.8 g/cc 4320spGPa– Glass fiber 2000MPa(300Kpsi) 2.56g/cc 781spGPa– Aramid fiber 3000MPa (450Kpsi) 1.4g/cc 2140spGPa

(Kevlar)

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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.

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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 one-component.– Properties include good adhesion to many substrates, low shrinkage,

high electrical resistivity, good corrosion resistance, and thermal.– Processing is achieved without generation of volatiles.

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Epoxy Chemistry• Epoxy: O H H

C C H + H2N (C) N (C) NH2

H H H H epoxide group + 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.)

• Active hydrogen react with epoxide groups. 15% hardener is needed

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Epoxy Chemistry

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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

C6H4(COOH)2 + (CH2)2(OH)2 -[(CH2)2 -O- C - C-O]-

terephthalic acid + ethylene glycol Polyethylene terephthalate (PET)

– Acids include: maleic, fumaric, isophthalic, terphthalic, adipic, etc.

– Anhydrides include: maleic, phthalic

– Glycols include ethylene glycol, diethylene glycol, propylene glycol

O O

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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

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Polyester Chemistry

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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.

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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.• Catalyst are used to initiate reaction.• RIM process is used to produce fenders and bumper covers

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Polyurethane Chemistry

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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

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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]

InjectionMolding

CompressionMolding

StructuralRIM

Resin TransferMolding

Annual PartProductionVolume

30K – 200K 30K – 200K 5K – 200 K 0.5K –5 K

Part Size Small< 2 lbs

Medium2 lbs – 20 lbs

Medium2 lbs – 20lbs

Medium to large 5 lbs– 50 lbs

FixedAssets

$300K -$2M $500K-$2M $300K-$1M $10K - $150K

ToolingCost

$50K -$500K $150K-$500K $50K-$300K

$20K - $300K

Cycle Time 1 sec –30 sec

30 sec –90 sec

30 sec –120 sec

5 min – 30 min

Materials Thermoplastic ThermoplasticThermoset

Thermoset Thermoset

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Polyurethane Processing• Polyurethane can be processed by

– Casting, painting, foaming– Reaction Injection Molding (RIM)

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Structural RIM• Fiber preform is placed into mold.

• Polyol and Isocyanate liquids are injected into a closed mold and reacted to form a urethane.

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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

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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)

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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

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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.

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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.

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Injection MoldingGlass Reinforced Composites

• Plastic pellets with glass fibers are melted in screw, injected into a cold mold, and then ejected.

Glass filled resin pellets

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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.

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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)

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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)

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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

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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

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Carbon Fiber Mechanical Properties• Table 3-2

Carbon Fiber Mechanical PropertiesPAN Based PITCH Based Rayon Based

Tensile Modulus (Mpsi) 33 - 56 23 -55 5.9Tensile Strength (Msi) 0.48 - 0.35 0.2 - 0.25 0.15Elongation (%) 1.4 - 0.6 0.9 - 0.4 25Density (g/cc) 1.8 - 1.9 1.9 - 2.0 1.6Carbon Assay (%) 92 - 100 97 - 99 99

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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 ModDensity, g/cc 1.6 1.7 1.8Tensile Strength (MPa) 2585 896 1206 Tensile Modulus (GPa) 172 220 517Compressive Strength (MPa) 1723 510 268Shear Strength (Mpa) 124 55 27Thermal Conductivity (W/m-K) 8.65 74 398

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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

PITCHFiber T300 T50 T650 T1000 P55 P100Tensile (Brittle Resin)PAN PAN PAN PAN PITCH PITCH Strength (MPa) 1862 1311 2413 3447 723 1138 Modulus (GPa) 138 241 170 159 234 483Tensile (Ductile Resin) Strength (MPa) 2790 1414 3070 3795 890 1206 Modulus (GPa) 138 241 170 234 483Compresion Strength (MPa) 1725 965 1650 1690 483 276 Modulus (GPa) 124 234 151 199 505

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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 fiber.

PropertyLong Fiber (56mm) Continuous %Increase

Long Fiber (56mm) Continuous

Tensile (MPa) Continuous Fraction Transverse (90°) versus In-plane (0°) Strength, 0° 1610 1676 4.09937888 1 1 Modulus, 0° 123.5 129.7 5.02024291 1 1 Poisson ratio 0.35 0.33 -5.7142857 Strength, 90° 91 73.1 -19.67033 0.056521739 0.043616 Modulus, 90° 10.3 8 -22.330097 0.08340081 0.061681Compressive (MPa) Strength, 0° 1262 1393 10.3803487 Modulus, 0° 111 121.4 9.36936937Flexural (MPa) Strength, 0° 1655 1931 16.6767372 Modulus, 0° 120 127.6 6.33333333Shear (MPa) Strength, 0° 146 142 -2.739726 Modulus, 0° 5.5 5.8 5.45454545Short Beam strength 110 117 6.36363636

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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 LaminateTesting Angle 0° 90° 0°/90° Ratio 0° 90° 0°/90° RatioTensile Strength (MPa) 793 20 39.65 379 241 1.57Tensile Modulus (GPa) 303 3.3 91.82 104 97 1.07Tensile Ultimate Strain, % 0.25 0.5 0.50 0.27 0.23 1.17Compressive Strength (MPa) 400 158 2.53 172 200 0.86Compressive Modulus (GPa) 255 6.7 38.06 76 88 0.86Compressive Ultimate Strain, % ---- ---- 0.55 0.86 0.64

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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.

Polymer MatrixFiber Orientation

Tensile Strength (MPa)

Tensile Modulus(GPa)

Fracture Strain %

Epoxy 0° 932 83 1.1Epoxy 45° 126 1.3PEEK 0° 740 51 1.1PEEK 45° 194 14 4.3

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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 FiberTensile Strength (MPa)

Tensile Modulus (GPa)

Compresive Strength (M Pa)

PEEK (APC2)

AS-4 Carbon Fiber 2242 138 1069

APC aromatic ketone AS-4 138 1138PEKK AS-4 1390PPS Ryton AS-4 1656 138 655Torlon-C Polyamidlimide C-6000 1390 140 1390ULTEM 1000 polyetherimide AS-4 138AVIMID Polyimide IM-6 UDEL Polysulfone AS 1345 131 1035J-2 Poly arylamide Kevlar 1310 76 276

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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,

Composite: Epoxy and Glassvol frac fib modulus, Gpastrength, Mpa given

0 5 50 Ef 75 Gpa0.1 12 165 Em 5 Gpa0.2 19 280 ten str glas 1200 MPa0.3 26 395 ten str epox 50 MPa0.4 33 5100.5 40 625 formula: Ec = Ef*Vf + EmVm = Ef*Vf + Em(1-Vf)0.6 47 7400.7 54 8550.8 61 9700.9 68 1085

1 75 1200

Rule of Mixtures for Density

0

0.2

0.4

0.6

0.8

1

0 0.5 1

Weight fraction fibers

vil

um

e f

rac

tio

n

fib

ers

Series1

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Rule of Mixtures • Example, Density

– 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

Rule of Mixtures for Density

00.20.40.60.8

1

0 0.5 1

Weight fraction fibers

vil

um

e f

rac

tio

n

fib

ers

Series1

dens glass 2.56 g/ccdens epoxy 1.2 g/cc

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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

0

200

400

600

800

1000

1200

1400

0 0.5 1

Volume Fraction fiber

Str

eng

th (

MP

a)

Tensile Modulus of Polyester Composite

0

20

40

60

80

0 0.5 1

Volume Fraction fiber

Ten

sile

Mo

du

lus,

GP

a

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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%

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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%