© 2003, P. Joyce

© 2003, P. Joyce

Composite Composite –– Materials, Materials, Manufacturing, and MechanicsManufacturing, and Mechanics

(An Introduction)(An Introduction)

OverviewDefinition and descriptionAdvantages over traditional materialsHistoryChallenges and problemsRecent developments

© 2003, P. Joyce

About the InstructorAbout the InstructorPeter J. Joyce• Asst. Professor, Mechanical Engineering Dept., U.S. Naval Academy (1999-present)

• Teaching: Composites, Materials Science, Mechanics of Materials, Statics, Dynamics

• Research: Resin transfer molding, Filament winding, Experimental mechanics of composite materials,Visco-elastic materials characterization of filled polymers. . .

• Ph.D. Materials Science & Engineering, UT-Austin• Effects of defects in FRP laminate composites

• M.S. Materials Science & Engineering, UT-Austin• Development of a technique for characterizing fiber waviness

• Teaching Assistant, Dept. of Mechanical Engineering, UT-Austin• Materials Processing lab

• Research Assistant, Dept. of Mechanical Engineering, UT-Austin• B.S. Engineering Mechanics, Univ. of Illinois

• Elevated temperature fracture toughness of MMCs• Valeo Systemes D’Essuyage (1991)• DTRC, Annapolis, Fatigue & Fracture branch (1987-1990)

© 2003, P. Joyce

General DefinitionGeneral Definition

Materials system created by combining two or more individual base materials which provides a specific set of mechanical and physical characteristics.

© 2003, P. Joyce

A Few ExamplesA Few Examples

Fiberglass (glass fibers/polymer matrix)Carbon fiber composites (carbon fibers/polymer matrix)Laminated plywood (wood/adhesive)Corrugated cardboard (paper/adhesive)Steel reinforced concrete (steel rebar/concrete)

© 2003, P. Joyce

What about metal alloys, ceramics?What about metal alloys, ceramics?

Materials Science

A composite is a multiphase material that is artificially made, as opposed to one that occurs or forms naturally. In addition, the constituent phases must be chemically dissimilar and separated by a distinct interface. Thus most metallic alloys and many ceramics do not fit this description because their multiple phases are formed as a consequence of natural phenomena.

© 2003, P. Joyce

Say that againSay that again

METALS

Metals and alloys, two-phased

PLASTICS

Plastics,Polyblends,

Rubber-toughenedpolymers

CERAMICS

Ceramics andGlasses, two-phased

structures (e.g. concrete)

GFRP

CFRP

cermets,MMCs

metal-filledpolymers

CMCs

© 2003, P. Joyce

Advantages of Composite MaterialsAdvantages of Composite Materialsover Traditional Materialsover Traditional Materials

Composites have inherent properties that provide performance benefits over metals. A wide range of fibers and resins are available to select the optimal material combination to meet the structural requirements.

Light Weight Resistance to CorrosionResistance to Fatigue DamageGood Damping CharacteristicsLow Coefficient of Thermal ExpansionCan Tailor the Fiber/Resin Mix to Meet Stiffness/Strength/Manufacturing Requirements Reduced Machining Part Consolidation Allows Reduced Number of Assemblies and Reduced Fastener CountTapered Sections and Compound Contours Easily (?) Accomplished

© 2003, P. Joyce

Weight SavingsWeight Savings

Weight savings of 25 to 50% are attainable over traditional materials. Some applications may require thicker composite sections to meetstrength/stiffness requirements, however, a weight savings will still result.The strength-to-weight and stiffness-to-weight ratios are the primary reasons composites are used.

Material Density (lb/in.3)

Steel 0.29Aluminum 0.10Composites 0.045-0.072

© 2003, P. Joyce

Improved Fatigue ResistanceImproved Fatigue Resistance

The fiber reinforcements provide high resistance to fatigue.The fracture toughness of composites is better than that of aluminum castings. By their nature, castings basically have built-in notches that can catastrophically fracture under impact. The fiber reinforcement of composites alters this failure sequence; resulting in an increased resistance to impact. The impact toughness of composites can be maximized by fiber selection, length of fiber and use of tougher resin such as thermoplastics.

© 2003, P. Joyce

Parts ConsolidationParts Consolidation

Consolidating many parts in an assembly into one part is a major benefit gained by using composite materials. It enables the designer to go beyond mere material substitution and produce true composite structures. The attachment areas of parts are where the majority of failures occur; due to high point loads and stress concentrations.

Complex shapes can be produced with composite materials. Fiber reinforcement across the former interfaces ensures adequate strength.Elimination of these interfaces improves the reliability of the structure.

Part consolidation reduces part count, fasteners and assembly time. This reduces weight due to fewer fasteners and thinner parts.

© 2003, P. Joyce

What about Cost?What about Cost?

Low cost, high volume manufacturing methods are used to make composites cost competitive with metals. Tooling costs for high volume production of metals and composites parts are similar. The production labor time is similar. The higher cost of composite parts is mostly due to high raw material costs.

Selection of the optimal material for the part, not the best material, will control these costs. Judicious selection of suppliers can minimize the cost penalty.

© 2003, P. Joyce

HistoryHistoryWWII –

Sandwich construction used on MosquitoFirst fiberglass boat molded, no parting agent used (1942)Laminates of cloth-filed phenolic used in bomb tubes and bazooka barrels (1943)

Post War developmentsEpoxy introduced commercially in the U.S. as an adhesive (1947)Honeycomb fuel cell support panels used in B-36 bomber (1949)First metal-to-metal adhesives used in aircraft primary structures (UK)Experimental Spitfire fuselage fabricated of flax fiber and phenolic resin (UK)Full scale wing spar constructed of flax fiber and phenolic resin for a Bristol "Blenheim" bomber (UK) (High-strength and high modulus, S-glass and boron fibers developed (1960)Graphite fibers become available for research (1964)First application of FRP in high temperature aircraft structure, F-111 (1965)First advanced composite part designed and produced, F-14 (1969)

© 2003, P. Joyce

HistoryHistoryCommercial introduction of prepreg materials (1970)Carbon fibers first incorporated by golf club manufacturers (early 1970s)Composite materials widely used in recreational marine craft (1970s)Introduction of first all-composite sandwich panels

First sold to Boeing for use in 747 (1974)Carbon fibers first introduced in rocket motor industry (late 1970s)

First used for the space shuttle solid rocket motor and Trident II (D5) missile PMCsbased on epoxy resin used in space applications (1970s and 80s).Int. modulus carbon fibers standard on Delta II, III, IV, Pegasus and Titan IV (late 1980s)

Thermoplastics evaluated for composites applications (early 1980s)Cyanate ester resin introduced in 1990s.For higher temperature applications Bismaleimide (BMI) resin systems are increasingly being used (1990s).Mercedes-Benz do Brasil introduces headrest reinforced with coconut fibers.DaimlerChrysler adding flax, sisal, coconut, cotton, and hemp to upholstery, door paneling, and rear panel shelf of Mercedes-Benz C-Class.

© 2003, P. Joyce

Horten Horten NurflugelNurflugel, 1936, 1936((Nothing But WingNothing But Wing))

Experimental two-seater fighterWings constructed entirely from synthetic materials

(“Mipolan” and “Astralon” developed by Dynamit AG), consisted mainly of phenol resins with paper filler.

Plagued by • problems with CTE mismatch, • glue would dissolve varnish,• insufficient stiffness of molded parts.

Ultimately synthetic materials abandoned b/c manufacture too time intensive

© 2003, P. Joyce

Horten Horten NurflugelNurflugel, 1936, 1936((Nothing But WingNothing But Wing))

Ho V a Photo from Nurflügel, by P. F. Selinger and Dr. R. Horten

Experimental two-seater fighterWings constructed entirely from synthetic materials

(“Mipolan” and “Astralon” developed by Dynamit AG), consisted mainly of phenol resins with paper filler.

Plagued by • problems with CTE mismatch, • glue would dissolve varnish,• insufficient stiffness of molded parts.

Ultimately synthetic materials abandoned b/c manufacture too time intensive

© 2003, P. Joyce

Horten Horten NurflugelNurflugel, 1936, 1936

Ho V b (steel and wood construction), photo from Nurflügel, by Peter F. Selinger and Dr. Reimar Horten

© 2003, P. Joyce

FF--111 111 AardvarkAardvark(the original Tactical Fighter Experimental (TFX))(the original Tactical Fighter Experimental (TFX))

F-111: multipurpose tactical bomber capable of supersonic speeds.

F-111A first flown 1964, operational aircraft first delivered, 1967, used for tactical bombing in SE Asia.

F-111B (Navy mod) canceled prior to production.

F-111C flown by Royal Australian Air Force.

F-111D, improved avionics, newer turbofan engines

F-111E, modified air intake capable of speeds up to Mach 2.2

Used by RAF in Operation Desert Storm.

F-111F, improved Turbofan engines (35% more thrust, Mach 2.5),

Also improved weapons targeting system (Pave Tack)

Flown in combat over Libya (1986).

Used for night bombing in Iraq (1991).

F-111G, converted FB-111A, used for training only.

© 2003, P. Joyce

FF--111 and the Boron/Epoxy 111 and the Boron/Epoxy BandAidBandAid

Crashes in early production aircraft, attributed to fatigue cracks in the forged-steel wing-pivot fitting.Instead of thickening the plate, Northrop Grumman used a boron/epoxy doubler (BandAid).Achieved a 21% cost savings vs. redesign (1968)First cost effective application of advanced composite materials.

Photo courtesy of Specialty Materials

© 2003, P. Joyce

Fighter AircraftFighter Aircraft

AV/8B Harrier II Plus (McDonnell Douglas)

© 2003, P. Joyce

F/AF/A--18E 18E Materials UtilizationMaterials Utilization

© 2003, P. Joyce

Eurofighter Eurofighter TyphoonTyphoon

Wings, front fuselage and tail section fabricated from Hexcel 8552 prepregBismaleimide (BMI) used for high temperature componentsFilm adhesive used to bond all composite parts.

© 2003, P. Joyce

Fighter Aircraft Fighter Aircraft -- Composites Composites UtilizationUtilization

This drawing is generic, to allow the maximum number of potential composite applications

to be identified. The drawing is not intended to represent a specific aircraft.

(http://www.hexcelcomposites.com/Markets/Markets/Aerospace/Defense.htm)

1 - Radar Transparent Radome: Epoxy or BMI prepreg or RTM resins and woven preforms (socks)2 - Foreplane Canard Wings: Epoxy carbon prepregs3 - Fuselage Panel Sections: Epoxy carbon prepregs. Non-metallic honeycomb core and Redux adhesives

4 - Leading Edge Devices: Epoxy carbon and glass prepregs5 - Fin Fairings: Epoxy glass and carbon prepregs6 - Wing Skins and Ribs: Epoxy carbon and glass prepregs7 - Fin Tip: Epoxy/quartz prepregs8 - Rudder: Epoxy carbon prepreg9 - Fin: Epoxy carbon/glass prepreg10 - Flying Control Surfaces: Epoxy carbon and glass prepregs. Honeycomb core material and Redux adhesives

© 2003, P. Joyce

Fighter Aircraft Fighter Aircraft –– Composites Composites UtilizationUtilization

1 Radar Transparent Radome: Epoxy or BMI prepreg or RTM resins and woven preforms (socks)

2 Foreplane Canard Wings: Epoxy carbon prepregs3 Fuselage Panel Sections: Epoxy carbon prepregs. Non-metallic honeycomb core

and Redux adhesives4 Leading Edge Devices: Epoxy carbon and glass prepregs5 Fin Fairings: Epoxy glass and carbon prepregs6 Wing Skins and Ribs: Epoxy carbon and glass prepregs7 Fin Tip: Epoxy/quartz prepregs8 Rudder: Epoxy carbon prepreg9 Fin: Epoxy carbon/glass prepreg10 Flying Control Surfaces: Epoxy carbon and glass prepregs. Honeycomb core

material and Redux adhesives

© 2003, P. Joyce

Experimental AircraftExperimental Aircraft

X-29 (1984-1992)— first aircraft to take advantage of aeroelastic tailoring using composite materials.

© 2003, P. Joyce

Civil AircraftCivil Aircraft

Composites accounted for about 5% of the dry weight of the original model of the Boeing 737.This figure has risen to almost 20% of the dry weight of the new Airbus A340.Virtually all that can be seen externally of a modern civil aero-engine is composite, and composite materials represent some 10% of an engine’s total weight.The newest application for composites in civil aircraft primary structures is the Airbus keel beam, made from carbon fiber prepreg.

© 2003, P. Joyce

Civil Aircraft Civil Aircraft –– Composites Composites UtilizationUtilization

This drawing is generic, to allow the maximum number of potential composite applications

to be identified. The drawing is not intended to represent a specific aircraft.

(http://www.hexcelcomposites.com/Markets/Markets/Aerospace/Civil.htm)

© 2003, P. Joyce

Civil Aircraft Civil Aircraft –– Composites Composites UtilizationUtilization

1 Radome: Specialized glass prepregs. Flexcore® honeycomb 2 Landing Gear Doors and Leg Fairings: Glass/carbon prepregs,honeycomb and Redux bonded assembly. Special process honeycomb. 3 Galley, Wardrobes, Toilets: Fabricated Fibrelam panels 4 Partitions: Fibrelam panel materials5 Wing to Body Fairing: Carbon/glass/aramid prepregs. Honeycombs. Redux adhesive. 6 Wing Assembly: (Trailing Edge Shroud Box) Carbon/glass prepregs. Nomex®

honeycomb. Redux bonded assembly7 Flying Control Surfaces - Ailerons, Spoilers, Vanes, Flaps:

Glass/carbon/aramid prepregs. Honeycomb. Redux adhesive8 Passenger Flooring: Fibrelam panels9 Engine Nacelles and Thrust Reversers: Carbon/glass prepregs. Nomex®

honeycomb. Special process parts.10 Pylon Fairings: Carbon/glass prepregs. Bonded assembly. Redux adhesives

© 2003, P. Joyce

Civil aircraft Civil aircraft –– composites composites utilizationutilization

11 Winglets: Carbon/glass prepregs 12 Keel Beam: Carbon prepregs13 Cargo Flooring: Fibrelam panels14 Flaptrack Fairings: Carbon/glass prepregs. Special process parts15 Overhead Storage Bins: prepregs/fabricated Fibrelam panels16 Ceiling and Side Wall Panels: Glass prepregs17 Airstairs: Fabricated Fibrelam panels18 Pressure Bulkhead: Carbon prepregs19 Vertical Stabilizer: Carbon/glass/aramid prepregs20 Rudder: Carbon/glass prepregs. Honeycomb bonded assembly21 Horizontal Stabilizer: Carbon/glass prepregs22 Elevator: Carbon/glass prepregs. Honeycomb bonded assembly23 Tail Cone: Carbon/glass prepregs

© 2003, P. Joyce

Airbus A380 Airbus A380 –– Composites UtilizationComposites Utilization

(More examples)

© 2003, P. Joyce

AeroAero--enginesenginesRolls-Royce RB108 was one of the first aero-engines to be manufactured using composites technology (early 1950s).

glass fiber compressor rotor blades and casingsModern engine nacelles and thrust reversers include so many major composite components (50% by volume carbon fiber epoxy prepreg)

The GE90 developed for the 777 is the first large commercial turbofan to use epoxy/carbon composite first stage compressor blades (1990s)Other components within the engine, such as guide vanes and fairings, are also converting to composites (1990s).

© 2003, P. Joyce

AeroAero--engines engines –– composites composites utilizationutilization

1- Electronic Control Unit Casing: Epoxy carbon Prepregs2 - Acoustic Lining Panels: Carbon/glass Prepregs, high temperature adhesives, aluminum honeycomb3 - Fan Blades: Epoxy carbon Prepregs or Resin Transfer

Molding (RTM) construction4 - Nose Cone: Epoxy glass prepreg, or RTM5 - Nose Cowl: Epoxy glass prepreg or RTM construction6 - Engine Access Doors: Woven and UD carbon/glass

prepregs, honeycomb and adhesives7 - Thrust Reverser Buckets: Epoxy woven carbon

prepregs or RTM materials, and adhesives8 - Compressor Fairing: BMI/epoxy carbon prepreg.

Honeycomb and adhesives9 - Bypass Duct: Epoxy carbon prepreg, non-metallic

honeycomb and adhesives10 - Guide Vanes: Epoxy carbon RFI/RTM construction

© 2003, P. Joyce

Polaris A2Polaris A2Submarine Launched Ballistic MissileSubmarine Launched Ballistic Missile

Polaris A2 (1962) achieved a 50% increase in range through

Development of an improved propellantLightweighting of components (Hercules)

2nd stage - Glass filament wound motor chamber

© 2003, P. Joyce

Polaris A3Polaris A3Submarine Launched Ballistic MissileSubmarine Launched Ballistic Missile

Third generation Polaris A3 (1964) first SLBM to achieve 2500 nm range.

All composite construction1st stage -Fiberglass motor case2nd stage – Fiber glass motor case

Improved propellant

© 2003, P. Joyce

Trident II DTrident II D--55Three-stage, solid propellant, inertially guided FBM with a range of more than 4,000 nautical miles All three stages of the Trident II are made of lighter, stronger, stiffer graphite epoxy, whose integrated structure mean considerable weight savings .First deployed in 1990.

© 2003, P. Joyce

Space ShuttleSpace ShuttleIn 1974, NASA choose ATK Thiokol to design and build the solid rocket motors that would boost the fleet of orbiters from the launch pad to the edge of space.Maiden flight of in 1981 (Columbia)Space Shuttle reusable solid rocket motor (RSRM) is the largest solid rocket motor to ever fly, also the first designed for reuse, and the only one rated for human flight.

© 2003, P. Joyce

Delta II Delta II -- Medium Launch VehicleMedium Launch Vehicle

Delta II

Intermediate modulus carbon fibers standard on rocket motor cases used on expendable launch vehicles late 1980’s.

© 2003, P. Joyce

Titan IVTitan IV

Intermediate modulus carbon fibers standard on rocket motor cases used on expendable launch vehicles late 1980’s.

© 2003, P. Joyce

RotorcraftRotorcraftNH 90 and Tiger

complete composite structures with carbon/glass hybrid prepreg engine fairings, glass prepreg blades and a structure (fuselage, cockpit and tail boom) built in 180°C curing carbon prepreg.

© 2003, P. Joyce

RotorcraftRotorcraft

Eurocopter EC 135fully shrouded fan and tail boom (fenestron) built with Hexcel’s180°C self-adhesive, self-extinguishing prepreg with a carbon/glass hybrid woven reinforcement.

Rotor blades for the EH 101, Lynx and Sea King helicopters contain a specially machined honeycomb core for low weight and superior stiffness. Super Lynx Firing Sea Skua

© 2003, P. Joyce

PERCENT OF STRUCTURAL WEIGHT

ALUMINUM 33.9%

STEEL 22.8%

TITANIUM 1.6%

CARBON/EPOXY 0.8%

GLASS/EPOXY 13.9%

OTHER 27.0%

TOTAL 100%

UH1UH1--Y Twin Huey (4BN) Materials Y Twin Huey (4BN) Materials BreakdownBreakdown

((PRELIMINARY)PRELIMINARY)

S2 Glass/8552 Toughened EpoxyUsed in Rotor Blades and Yokes

S2 Glass/IM-7 Carbon/8552 Toughened Epoxy Used in Rotor Blades and Yokes

AS-4 Carbon/3501-6 EpoxyUsed in Fuselage Panels

Prepared by BHTI Materials & ProcessesDept. 81, Group 25 - 10/24/97

© 2003, P. Joyce

AHAH--1Z 1Z

PERCENT OF STRUCTURAL WEIGHT

ALUMINUM 32.9%

STEEL 25.5%

TITANIUM 3.0%

CARBON/EPOXY 1.9%

GLASS/EPOXY 16.3%

OTHER 20.4%

TOTAL 100%

Cobra (4BW) Materials Cobra (4BW) Materials BreakdownBreakdown

((PRELIMINARY)PRELIMINARY)

S2 Glass/8552 Toughened EpoxyUsed in Rotor Blades and Yokes

AS-4 Carbon/3501-6 EpoxyUsed in Fuselage Panels

Prepared by BHTI Materials & ProcessesDept. 81, Group 25 - 10/24/97

S2 Glass/IM-7 Carbon/8552 Toughened Epoxy Hybrid

Used in Rotor Blades and Yokes

© 2003, P. Joyce

VV--2222

© 2003, P. Joyce

VV--22 EMD/LRIP Materials 22 EMD/LRIP Materials BreakdownBreakdown

AS4/3501-6 PW Fabric LaminateIM6/3501-6 Tape & AS4/3501-6 CSW Fabric Hybrid LaminateS-2/8552 Tape & Towpreg and IM7/8552 TapeIM7/8552 Slit Tape Grip w/ S-2 & IM7/8552 Tape & Towpreg Hybrid of IM6/3501-6 Tape & AS4/3501-6 PW Fabric Laminate

Fiber-Placed IM7/8552 Towpreg SandwichFiber-Placed IM6/3501-6 Towpreg LaminateHand Placed AS4/3501-6 CSW Fabric Laminate

OtherAluminumIM7/8552 Towpreg

© 2003, P. Joyce

Unmanned AircraftUnmanned Aircraft

X-45A UCAV (Boeing Phantom Works)

Global Hawk UAV (Northrop Grumman)

© 2003, P. Joyce

Unmanned AircraftUnmanned Aircraft

Helios UAV (NASA Dryden)

© 2003, P. Joyce

Unmanned AircraftUnmanned Aircraft

X-50 Canard Rotor Wing UAV (Boeing)

© 2003, P. Joyce

Satellite hardware Satellite hardware –– composite composite utilizationutilization

1- Solar Panels : Epoxy carbon prepregs, aluminum honeycomb, film adhesive2 - Reflectors Antennae : Epoxy/aramid prepreg, cyanate carbon prepreg,aramid/aluminum honeycomb3 - Satellite Structures : Carbon prepreg, aluminum honeycomb, film adhesive

© 2003, P. Joyce

Performance sailboats Performance sailboats –– composite composite utilizationutilization

1 - Sails: Carbon fiber tow for stiffening.2 - Rudders: Carbon Glass, Woven/UD. Nomex* honeycomb.3 - Sail Battens: Glass/carbon prepregs.4 - Hardware: Carbon fiber composites.5 - Hull & Deck: Carbon/glass prepreg. Nomex* honeycomb, film adhesive.6 - Keel: Carbon/glass Prepregs (monolithic).7 - Mast and Spars: UD carbon tape, Woven carbon, Prepreg.8 - Interior fittings and bulkheads: Hexlite® Panels.

© 2003, P. Joyce

© 2003, P. Joyce

Naval Applications (Marine)Naval Applications (Marine)

© 2003, P. Joyce

Wind energy industryWind energy industry

Wind power is the world’s fastest growing energy source. The latest wind turbines are designed with rotors up to 110m in diameter and are capable of generating up to 5MW of power.

Operating at this level of efficiency requires materials that combine light weight with great stiffness, strength and durability. These requirements are met with sandwichcomposite materials, increasingly carbon fiber composites.

© 2003, P. Joyce

Automotive ApplicationsAutomotive Applications

© 2003, P. Joyce

Trek bicycle frames Trek bicycle frames –– composites composites utilizationutilization

1 - Honeycomb made with Aramid® Paper: The strong, shapablematerial that makes the Y frame possible.2 - Carbon Prepreg

© 2003, P. Joyce

Trek bicycle frames Trek bicycle frames –– composites composites utilizationutilization

Unique direction-specific strength

Allows spot-tuning for extra rigidity in some parts - shock-dampening flex in others.

Maximum strength-to weight ratio

Frames made with carbon prepreg weigh just 2.44 lbs. (1.11 kg), but are incredibly strong..

© 2003, P. Joyce

Consumer Products Consumer Products ––Composites Composites UtilizationUtilization

© 2003, P. Joyce

Where Do We Go From Here?Where Do We Go From Here?

OpportunitiesJSFUAV, UCAVMarine Apps

DisastersNASA X-34 Reusable Launch VehicleAmerican Airlines A300, Jamaica Bay, NYNASA SST TPS

© 2003, P. Joyce

Further ReadingFurther ReadingHexcel website, www.hexcelcomposites.comReinforced Plastics website, www.reinforcedplastics.com“Wright Brothers legacy flying high,” Reinforced Plastics, April, 2003, pp. 18-24.“The Evolving Nature of Aerospace Composites,” Griffith, J.M., in Proceeding of the 34th International SAMPE Technical Conference –2002 M&P - Ideas to Reality, Vol. 34, 2002, pp. 1-11.“A Brief History of Composites in the U.S. – The Dream and the Success,” Scala, E.P., Journal of Materials, February, 1996, pp. 45-48.“Innovation in Aircraft Structures – Fifty Years Ago and Today,” Hoff, N.J., AIAA Paper No. 84-0840, 1984.“Composite Materials in Aircraft Structures,” Hoff, N.J. in Progress in Science and Engineering of Composites, Proceeding of ICCM-IV, Tokyo, 1982, pp. 49-61.Mechanics of Composite Materials, Jones, R.M., 1999, pp. 37-52.