PART I PRINCIPLES OF CONSTRUCTION 2003 by CRC Press LLC
PART I PRINCIPLES OF CONSTRUCTION TX846_Frame_C01 Page 1 Monday, November 18, 2002 10:34 AM © 2003 by CRC Press LLC
COMPOSITE MATERIALS, INTEREST,AND PROPERTIES 1.1 WHAT IS COMPOSITE MATERIAL? As the term indicates,composite material reveals a material that is different from common heterogeneous materials.Currently composite materials refers to materials having strong fibers-continuous or noncontinuous-surrounded by a weaker matrix material.The matrix serves to distribute the fibers and also to transmit the load to the fibers. Notes:Composite materials are not new.They have been used since antiquity. Wood and cob have been everyday composites.Composites have also been used to optimize the performance of some conventional weapons.For example: In the Mongolian arcs,the compressed parts are made of corn,and the stretched parts are made of wood and cow tendons glued together. Japanese swords or sabers have their blades made of steel and soft iron: the steel part is stratified like a sheet of paste,with orientation of defects and impurities in the long direction'(see Figure 1.1),then formed into a U shape into which the soft iron is placed.The sword then has good resistance for flexure and impact. One can see in this period the beginning of the distinction between the common composites used universally and the high performance composites. The composite material as obtained is ■Very heterogeneous. Very "anisotropic."This notion of "anisotropy"will be illustrated later in Section 3.1 and also in Chapter 9.Simply put this means that the mechanical properties of the material depend on the direction. In folding a sheet of steel over itself 15 times,one obtains 2=32.768 layers. 2003 by CRC Press LLC
1 COMPOSITE MATERIALS, INTEREST, AND PROPERTIES 1.1 WHAT IS COMPOSITE MATERIAL? As the term indicates, composite material reveals a material that is different from common heterogeneous materials. Currently composite materials refers to materials having strong fibers—continuous or noncontinuous—surrounded by a weaker matrix material. The matrix serves to distribute the fibers and also to transmit the load to the fibers. Notes: Composite materials are not new. They have been used since antiquity. Wood and cob have been everyday composites. Composites have also been used to optimize the performance of some conventional weapons. For example: In the Mongolian arcs, the compressed parts are made of corn, and the stretched parts are made of wood and cow tendons glued together. Japanese swords or sabers have their blades made of steel and soft iron: the steel part is stratified like a sheet of paste, with orientation of defects and impurities in the long direction1 (see Figure 1.1), then formed into a U shape into which the soft iron is placed. The sword then has good resistance for flexure and impact. One can see in this period the beginning of the distinction between the common composites used universally and the high performance composites. The composite material as obtained is Very heterogeneous. Very “anisotropic.” This notion of “anisotropy” will be illustrated later in Section 3.1 and also in Chapter 9. Simply put this means that the mechanical properties of the material depend on the direction. 1 In folding a sheet of steel over itself 15 times, one obtains 215 = 32,768 layers. TX846_Frame_C01 Page 3 Monday, November 18, 2002 10:34 AM © 2003 by CRC Press LLC
Stress Concentration Random Defects Oriented Defects Poor tensile resistance Good tensile resistance Figure 1.1 Effect of the Orientation of Impurities 1.2 FIBERS AND MATRIX The bonding between fibers and matrix is created during the manufacturing phase of the composite material.This has fundamental influence on the mechanical properties of the composite material. 1.2.1 Fibers Fibers consist of thousands of filaments,each filament having a diameter of bet- ween 5 and 15 micrometers,allowing them to be producible using textile machines;for example,in the case of glass fiber,one can obtain two semi- products as shown in Figure 1.2.These fibers are sold in the following forms: Short fibers,with lengths of a few centimeters or fractions of millimeters are felts,mats,and short fibers used in injection molding. Long fibers,which are cut during time of fabrication of the composite material,are used as is or woven. Principal fiber materials are ■Glass Aramid or Kevlar(very light) Carbon (high modulus or high strength) Boron (high modulus or high strength) Silicon carbide (high temperature resistant) In forming fiber reinforcement,the assembly of fibers to make fiber forms for the fabrication of composite material can take the following forms: One wants to have fibers as thin as possible because their rupture strength decreases as their diameter increases,and very small fiber diameters allow for effective radius of curvature in fiber bending to be on the order of half a millimeter.However,exception is made for boron fibers (diameter in the order of 100 microns).which are formed around a tungsten filament (diameter 12 microns).Their minimum radius of curvature is 4 mm.Then,except for particular cases,weaving is not possible. 2003 by CRC Press LLC
1.2 FIBERS AND MATRIX The bonding between fibers and matrix is created during the manufacturing phase of the composite material. This has fundamental influence on the mechanical properties of the composite material. 1.2.1 Fibers Fibers consist of thousands of filaments, each filament having a diameter of between 5 and 15 micrometers, allowing them to be producible using textile machines;2 for example, in the case of glass fiber, one can obtain two semiproducts as shown in Figure 1.2. These fibers are sold in the following forms: Short fibers, with lengths of a few centimeters or fractions of millimeters are felts, mats, and short fibers used in injection molding. Long fibers, which are cut during time of fabrication of the composite material, are used as is or woven. Principal fiber materials are Glass Aramid or Kevlar‚ (very light) Carbon (high modulus or high strength) Boron (high modulus or high strength) Silicon carbide (high temperature resistant) In forming fiber reinforcement, the assembly of fibers to make fiber forms for the fabrication of composite material can take the following forms: Figure 1.1 Effect of the Orientation of Impurities 2 One wants to have fibers as thin as possible because their rupture strength decreases as their diameter increases, and very small fiber diameters allow for effective radius of curvature in fiber bending to be on the order of half a millimeter. However, exception is made for boron fibers (diameter in the order of 100 microns), which are formed around a tungsten filament (diameter = 12 microns). Their minimum radius of curvature is 4 mm. Then, except for particular cases, weaving is not possible. TX846_Frame_C01 Page 4 Monday, November 18, 2002 10:34 AM © 2003 by CRC Press LLC
Filaments Continuous Discontinuous Fiber Fiber Glass Fibers Staple for Fiber Weaving Textile Filament Roving or Strand Figure 1.2 Different Fiber Forms Unidimensional:unidirectional tows,yarns,or tapes ■ Bidimensional:woven or nonwoven fabrics (felts or mats) Tridimensional:fabrics (sometimes called multidimensional fabrics)with fibers oriented along many directions (>2) Before the formation of the reinforcements,the fibers are subjected to a surface treatment to Decrease the abrasion action of fibers when passing through the forming machines. Improve the adhesion with the matrix material. Other types of reinforcements,full or empty spheres(microspheres)or powders (see Section 3.5.3),are also used. 1.2.1.1 Relative Importance of Different Fibers in Applications Figure 1.3 allows one to judge the relative importance in terms of the amount of fibers used in the fabrication of composites.One can immediately notice the industrial importance of fiber glass (produced in large quantities).Carbon and Kevlar fibers are reserved for high performance components. Following are a few notes on the fibers: Glass fiber:The filaments are obtained by pulling the glass(silicon+sodium carbonate and calcium carbonate:T>1000C)through the small orifices of a plate made of platinum alloy. Kevlar fiber:This is an aramid fiber,yellowish color,made by DuPont de Nemours (USA).These are aromatic polyamides obtained by synthesis at -10C,then fibrillated and drawn to obtain high modulus of elasticity. Carbon fiber:Filaments of polyacrylonitrile or pitch(obtained from residues of the petroleum products)are oxidized at high temperatures(300C).then heated further to 1500C in a nitrogen atmosphere.Then only the hexagonal 2003 by CRC Press LLC
Unidimensional: unidirectional tows, yarns, or tapes Bidimensional: woven or nonwoven fabrics (felts or mats) Tridimensional: fabrics (sometimes called multidimensional fabrics) with fibers oriented along many directions (>2) Before the formation of the reinforcements, the fibers are subjected to a surface treatment to Decrease the abrasion action of fibers when passing through the forming machines. Improve the adhesion with the matrix material. Other types of reinforcements, full or empty spheres (microspheres) or powders (see Section 3.5.3), are also used. 1.2.1.1 Relative Importance of Different Fibers in Applications Figure 1.3 allows one to judge the relative importance in terms of the amount of fibers used in the fabrication of composites. One can immediately notice the industrial importance of fiber glass (produced in large quantities). Carbon and Kevlar fibers are reserved for high performance components. Following are a few notes on the fibers: Glass fiber: The filaments are obtained by pulling the glass (silicon + sodium carbonate and calcium carbonate; T > 1000∞C) through the small orifices of a plate made of platinum alloy. Kevlar fiber: This is an aramid fiber, yellowish color, made by DuPont de Nemours (USA). These are aromatic polyamides obtained by synthesis at -10∞C, then fibrillated and drawn to obtain high modulus of elasticity. Carbon fiber: Filaments of polyacrylonitrile or pitch (obtained from residues of the petroleum products) are oxidized at high temperatures (300∞C), then heated further to 1500∞C in a nitrogen atmosphere. Then only the hexagonal Figure 1.2 Different Fiber Forms TX846_Frame_C01 Page 5 Monday, November 18, 2002 10:34 AM © 2003 by CRC Press LLC
Mass (tons) 1.800,000 Glass 1,100,000 7000 Carbon;Kevlar 2000 3500 1984 1987 1990 1993 Figure 1.3 Relative Sale Volume of Different Fibers Carbon fiber Figure 1.4 Structure of Carbon Fiber carbon chains,as shown in Figure 1.4,remain.Black and bright filaments are obtained.High modulus of elasticity is obtained by drawing at high temperature. ■ Boron fiber:Tungsten filament (diameter 12 um)serves to catalyze the reaction between boron chloride and hydrogen at 1200C.The boron fibers obtained have a diameter of about 100 um (the growth speed is about 1 micron per second). Silicon carbide:The principle of fabrication is analogous to that of boron fiber:chemical vapor deposition (1200C)of methyl trichlorosilane mixed with hydrogen. The principal physical-mechanical properties of the fibers are indicated in Table 1.3.Note the very significant disparity of the prices per unit weight. 2003 by CRC Press LLC
carbon chains, as shown in Figure 1.4, remain. Black and bright filaments are obtained. High modulus of elasticity is obtained by drawing at high temperature. Boron fiber: Tungsten filament (diameter 12 mm) serves to catalyze the reaction between boron chloride and hydrogen at 1200∞C. The boron fibers obtained have a diameter of about 100 mm (the growth speed is about 1 micron per second). Silicon carbide: The principle of fabrication is analogous to that of boron fiber: chemical vapor deposition (1200∞C) of methyl trichlorosilane mixed with hydrogen. The principal physical–mechanical properties of the fibers are indicated in Table 1.3. Note the very significant disparity of the prices per unit weight. Figure 1.3 Relative Sale Volume of Different Fibers Figure 1.4 Structure of Carbon Fiber TX846_Frame_C01 Page 6 Monday, November 18, 2002 10:34 AM © 2003 by CRC Press LLC
1.2.2 Matrix Materials The matrix materials include the following: Polymeric matrix:thermoplastic resins (polypropylene,polyphenylene sulfone,polyamide,polyetheretherketone,etc.)and thermoset resins (poly- esters,phenolics,melamines,silicones,polyurethanes,epoxies).Their prin- cipal physical properties are indicated in the Table 1.4. Mineral matrix:silicon carbide,carbon.They can be used at high tem- peratures (see Sections 2.2.4,3.6,7.1.10,7.5). Metallic matrix:aluminum alloys,titanium alloys,oriented eutectics 1.3 WHAT CAN BE MADE USING COMPOSITE MATERIALS? The range of applications is very large.A few examples are shown below. Electrical,Electronics Insulation for electrical construction Supports for circuit breakers Supports for printed circuits Armors,boxes,covers ■Antennas,radomes Tops of television towers ■Cable tracks ■Windmills ■ Buildings and Public Works ■Housing cells ■Chimneys ■Concrete molds Various covers (domes,windows,etc.) ■Swimming pools ■Facade panels ■Profiles Partitions,doors,furniture,bathrooms ■Road Transports ■Body components ■Complete body Wheels,shields,radiator grills, ■Transmission shafts ■Suspension springs ■ Bottles for compressed petroleum gas ■Chassis ■Suspension arms ■Casings ■Cabins,seats Highway tankers,isothermal trucks ■Trailers 2003 by CRC Press LLC
1.2.2 Matrix Materials The matrix materials include the following: Polymeric matrix: thermoplastic resins (polypropylene, polyphenylene sulfone, polyamide, polyetheretherketone, etc.) and thermoset resins (polyesters, phenolics, melamines, silicones, polyurethanes, epoxies). Their principal physical properties are indicated in the Table 1.4. Mineral matrix: silicon carbide, carbon. They can be used at high temperatures (see Sections 2.2.4, 3.6, 7.1.10, 7.5). Metallic matrix: aluminum alloys, titanium alloys, oriented eutectics. 1.3 WHAT CAN BE MADE USING COMPOSITE MATERIALS? The range of applications is very large. A few examples are shown below. Electrical, Electronics Insulation for electrical construction Supports for circuit breakers Supports for printed circuits Armors, boxes, covers Antennas, radomes Tops of television towers Cable tracks Windmills Buildings and Public Works Housing cells Chimneys Concrete molds Various covers (domes, windows, etc.) Swimming pools Facade panels Profiles Partitions, doors, furniture, bathrooms Road Transports Body components Complete body Wheels, shields, radiator grills, Transmission shafts Suspension springs Bottles for compressed petroleum gas Chassis Suspension arms Casings Cabins, seats Highway tankers, isothermal trucks Trailers TX846_Frame_C01 Page 7 Monday, November 18, 2002 10:34 AM © 2003 by CRC Press LLC
■Rail transports: ■Fronts of power units ■Wagons Doors,seats,interior panels Ventilation housings ■Marine Transports: ■Hovercrafts ■Rescue crafts ■Patrol boats ■Trawlers ■Landing gears ■Anti-mine ships ■Racing boats ■Pleasure boats ■Canoes ■Cable transports: ■Telepherique cabins ■Telecabins ■Air transports All composite passenger aircrafts All composite gliders Many aircraft components:radomes,leading edges,ailerons,vertical stabilizers Helicopter blades,propellers ■Transmission shafts ■Aircraft brake discs ■Space Transports ■Rocket boosters ■Reservoirs ■Nozzles Shields for atmosphere reentrance General mechanical applications ■Gears ■Bearings ■Housings,casings ■Jack body ■Robot arms ■Fly wheels ■Weaving machine rods ■Pipes Components of drawing table Compressed gas bottles Tubes for offshore platforms Pneumatics for radial frames ■ Sports and Recreation Tennis and squash rackets ■Fishing poles ■Skis 2003 by CRC Press LLC
Rail transports: Fronts of power units Wagons Doors, seats, interior panels Ventilation housings Marine Transports: Hovercrafts Rescue crafts Patrol boats Trawlers Landing gears Anti-mine ships Racing boats Pleasure boats Canoes Cable transports: Telepherique cabins Telecabins Air transports All composite passenger aircrafts All composite gliders Many aircraft components: radomes, leading edges, ailerons, vertical stabilizers Helicopter blades, propellers Transmission shafts Aircraft brake discs Space Transports Rocket boosters Reservoirs Nozzles Shields for atmosphere reentrance General mechanical applications Gears Bearings Housings, casings Jack body Robot arms Fly wheels Weaving machine rods Pipes Components of drawing table Compressed gas bottles Tubes for offshore platforms Pneumatics for radial frames Sports and Recreation Tennis and squash rackets Fishing poles Skis TX846_Frame_C01 Page 8 Monday, November 18, 2002 10:34 AM © 2003 by CRC Press LLC
■Poles used in jumping ■Sails ■Surf boards, ■Roller skates ■Bows and arrows ■Javelins ■Protection helmets ■Bicycle frames ■Golf clubs ■Oars 1.4 TYPICAL EXAMPLES OF INTEREST ON THE USE OF COMPOSITE MATERIALS In the domain of commercial aircraft,one can compare the concerns of manufac- turers with the principal characteristic properties of composite materials.The concerns of the manufacturers are performance and economy.The characteristics of composite components include the following: Weight saving leads to fuel saving.increase in payload,or increase in range which improves performances. Good fatigue resistance leads to enhanced life which involves saving in the long-term cost of the product. ■ Good corrosion resistance means fewer requirements for inspection which results in saving on maintenance cost. Moreover,taking into account the cost of the composite solution as compared with the conventional solution,one can state that composites fit the demand of aircraft manufacturers. 1.5 EXAMPLES ON REPLACING CONVENTIONAL SOLUTIONS WITH COMPOSITES Table 1.1 shows a few significant cases illustrating the improvement on price and performance that can be obtained after replacement of a conventional solution with a composite solution. 1.6 PRINCIPAL PHYSICAL PROPERTIES Tables 1.2 through 1.5 take into account the properties of only individual com- ponents,reinforcements,or matrices.The characteristics of composite materials resulting from the combination of reinforcement and matrix depend on The proportions of reinforcements and matrix(see Section 3.2) The form of the reinforcement (see Section 3.2) The fabrication process 2003 by CRC Press LLC
Poles used in jumping Sails Surf boards, Roller skates Bows and arrows Javelins Protection helmets Bicycle frames Golf clubs Oars 1.4 TYPICAL EXAMPLES OF INTEREST ON THE USE OF COMPOSITE MATERIALS In the domain of commercial aircraft, one can compare the concerns of manufacturers with the principal characteristic properties of composite materials. The concerns of the manufacturers are performance and economy. The characteristics of composite components include the following: Weight saving leads to fuel saving, increase in payload, or increase in range which improves performances. Good fatigue resistance leads to enhanced life which involves saving in the long-term cost of the product. Good corrosion resistance means fewer requirements for inspection which results in saving on maintenance cost. Moreover, taking into account the cost of the composite solution as compared with the conventional solution, one can state that composites fit the demand of aircraft manufacturers. 1.5 EXAMPLES ON REPLACING CONVENTIONAL SOLUTIONS WITH COMPOSITES Table 1.1 shows a few significant cases illustrating the improvement on price and performance that can be obtained after replacement of a conventional solution with a composite solution. 1.6 PRINCIPAL PHYSICAL PROPERTIES Tables 1.2 through 1.5 take into account the properties of only individual components, reinforcements, or matrices. The characteristics of composite materials resulting from the combination of reinforcement and matrix depend on The proportions of reinforcements and matrix (see Section 3.2) The form of the reinforcement (see Section 3.2) The fabrication process TX846_Frame_C01 Page 9 Monday, November 18, 2002 10:34 AM © 2003 by CRC Press LLC
Table 1.1 Properties of Commonly Used Resins Price of Previous Price of Composite Application Construction Construction 65 m'reservoir for Stainless steel 0.53 chemicals installation:1. Smoke stack for chemical Steel:1. 0.51 plant Nitric acid vapor washer Stainless steel:1. 0.33 Helicopter stabilizer Light alloys steel Carbon/epoxy (9 kg):0.45 (16kg:1. Helicopter winch support Welded steel(16 kg):1. Carbon/epoxy (11 kg):1.2 Helicopter motor hub (Mass:1):1. Carbon/Kevlar/epoxy (mass:0.8:0.4 X-Y table for fabrication of Cast aluminum:Rate of Carbon/epoxy honeycomb integrated circuits fabrication:30 plates/hr sandwich:55 plates/hr Drum for drawing table Speed of drawing:15 to Kevlar/epoxy:40 to 30 cm/sec 80 cm/sec Head of welding robot Aluminum:Mass =6 kg Carbon/epoxy:Mass =3 kg Weaving machine rod Aluminum:Rate =250 Carbon/epoxy:Rate =350 shots/minute shots/minute Aircraft floor (Mass=1:1. Carbon/Kevlar/epoxy (mass:0.8):1.7 These characteristics may be observed in Figure 1.5,which shows the tensile strength for different fiber fractions and different forms of reinforcement for the case of glass/resin composite,and Figure 1.6,which gives an interesting view on the specific resistance of the principal composites as a function of temperature. (The specific strength is defined as the strength divided by the density orup/p.) Other remarkable properties of these materials include the following: Composite materials do not yield (their elastic limits correspond to the rupture limit;see Section 5.4.5). Composite materials are very fatigue resistant (see Section 5.1). Composite materials age subject to humidity (epoxy resin can absorb water by diffusion up to 6%of its mass;the composite of reinforcement/resin can absorb up to 2%)and heat. Composite materials do not corrode,except in the case of contact "aluminum with carbon fibers"in which case galvanic phenomenon creates rapid cor- rosion. Composite materials are not sensitive to the common chemicals used in engines:grease,oils,hydraulic liquids,paints and solvents,petroleum. However,paint thinners attack the epoxy resins. ■ Composite materials have medium to low level impact resistance (inferior to that of metallic materials). ■ Composite materials have excellent fire resistance as compared with the light alloys with identical thicknesses.However,the smokes emitted from the combustion of certain matrices can be toxic. 2003 by CRC Press LLC
These characteristics may be observed in Figure 1.5, which shows the tensile strength for different fiber fractions and different forms of reinforcement for the case of glass/resin composite, and Figure 1.6, which gives an interesting view on the specific resistance of the principal composites as a function of temperature. (The specific strength is defined as the strength divided by the density srupt/r.) Other remarkable properties of these materials include the following: Composite materials do not yield (their elastic limits correspond to the rupture limit; see Section 5.4.5). Composite materials are very fatigue resistant (see Section 5.1). Composite materials age subject to humidity (epoxy resin can absorb water by diffusion up to 6% of its mass; the composite of reinforcement/resin can absorb up to 2%) and heat. Composite materials do not corrode, except in the case of contact “aluminum with carbon fibers” in which case galvanic phenomenon creates rapid corrosion. Composite materials are not sensitive to the common chemicals used in engines: grease, oils, hydraulic liquids, paints and solvents, petroleum. However, paint thinners attack the epoxy resins. Composite materials have medium to low level impact resistance (inferior to that of metallic materials). Composite materials have excellent fire resistance as compared with the light alloys with identical thicknesses. However, the smokes emitted from the combustion of certain matrices can be toxic. Table 1.1 Properties of Commonly Used Resins Application Price of Previous Construction Price of Composite Construction 65 m3 reservoir for chemicals Stainless steel + installation: 1. 0.53 Smoke stack for chemical plant Steel: 1. 0.51 Nitric acid vapor washer Stainless steel: 1. 0.33 Helicopter stabilizer Light alloys + steel (16 kg): 1. Carbon/epoxy (9 kg): 0.45 Helicopter winch support Welded steel (16 kg): 1. Carbon/epoxy (11 kg): 1.2 Helicopter motor hub (Mass: 1): 1. Carbon/Kevlar/epoxy (mass: 0.8): 0.4 X–Y table for fabrication of integrated circuits Cast aluminum: Rate of fabrication: 30 plates/hr Carbon/epoxy honeycomb sandwich: 55 plates/hr Drum for drawing table Speed of drawing: 15 to 30 cm/sec Kevlar/epoxy: 40 to 80 cm/sec Head of welding robot Aluminum: Mass = 6 kg Carbon/epoxy: Mass = 3 kg Weaving machine rod Aluminum: Rate = 250 shots/minute Carbon/epoxy: Rate = 350 shots/minute Aircraft floor (Mass = 1): 1. Carbon/Kevlar/epoxy (mass: 0.8): 1.7 TX846_Frame_C01 Page 10 Monday, November 18, 2002 10:34 AM © 2003 by CRC Press LLC
C2003 CRC Press Table 1.2 Properties of Commonly Used Metals and Alloys and Silicon Coefficient of Coefficient of Thermal Density Elastic Shear Tensile Thermal Conductivity Heat Useful Metals and p ModulusModulus Poisson Strength Elongation Expansion at at20°C Capacity Temperature Alloys (kg/m) E(MPa) G(MPa) Ratio v Gue:(Mpa) (%) 20℃ac-) 入(W/mC) c(l/kg'C) Limit Tmax (C) Steels 7800 205,000 79,000 0.3 400to 1.8to10 1.3×10 20to100 400to800 800 1600 Aluminum 2800 75,000 29,000 0.3 450 10 2.2×10-5 140 1000 350 Alloy 2024 Titanium 4400 105,000 40,300 0.3 1200 14 0.8×10 17 540 700 Alloy TA 6V Copper 8800 125,000 48,000 0.3 200to 1.7×109 380 390 650 500 Nickel 8900 220,000 500to 70 500 900 850 Beryllium 1840 294,000 0.05 200 1.2×105 150(20°C) 1750(20°C) 900 90(800C) 3000(800°C) Silicon 2200 95,000 5 1.4(20C) 750(20C) 1300 3(1200C) 1200(500C)
Table 1.2 Properties of Commonly Used Metals and Alloys and Silicon Metals and Alloys Density r (kg/m3) Elastic Modulus E (MPa) Shear Modulus G (MPa) Poisson Ratio n Tensile Strength sult (Mpa) Elongation (%) Coefficient of Thermal Expansion at 20∞C a (∞C-1) Coefficient of Thermal Conductivity at 20∞C l(W/m∞C) Heat Capacity c(J/kg˚C) Useful Temperature Limit Tmax (˚C) Steels 7800 205,000 79,000 0.3 400 to 1600 1.8 to 10 1.3 ¥ 10-5 20 to 100 400 to 800 800 Aluminum Alloy 2024 2800 75,000 29,000 0.3 450 10 2.2 ¥ 10-5 140 1000 350 Titanium Alloy TA 6V 4400 105,000 40,300 0.3 1200 14 0.8 ¥ 10-5 17 540 700 Copper 8800 125,000 48,000 0.3 200 to 500 1.7 ¥ 10-5 380 390 650 Nickel 8900 220,000 500 to 850 70 500 900 Beryllium 1840 294,000 0.05 200 1.2 ¥ 10-5 150 (20˚C) 90 (800˚C) 1750 (20˚C) 3000 (800˚C) 900 Silicon 2200 95,000 5 1.4 (20˚C) 3 (1200˚C) 750 (20˚C) 1200(500˚C) 1300 TX846_Frame_C01 Page 11 Monday, November 18, 2002 10:34 AM © 2003 by CRC Press LLC