1 Introduction to Composite Materials Chapter Objectives Define a composite,enumerate advantages and drawbacks of com- posites over monolithic materials,and discuss factors that influence mechanical properties of a composite. Classify composites,introduce common types of fibers and matri- ces,and manufacturing,mechanical properties,and applications of composites. Discuss recycling of composites. Introduce terminology used for studying mechanics of composites. 1.1 Introduction You are no longer to supply the people with straw for making bricks;let them go and gather their own straw. Exodus 5:7 Israelites using bricks made of clay and reinforced with straw are an early example of application of composites.The individual constituents,clay and straw,could not serve the function by themselves but did when put together. Some believe that the straw was used to keep the clay from cracking,but others suggest that it blunted the sharp cracks in the dry clay. Historical examples of composites are abundant in the literature.Signifi- cant examples include the use of reinforcing mud walls in houses with bamboo shoots,glued laminated wood by Egyptians(1500 B.c.),and lami- nated metals in forging swords(A.D.1800).In the 20th century,modern composites were used in the 1930s when glass fibers reinforced resins.Boats 1 2006 by Taylor Francis Group,LLC
1 1 Introduction to Composite Materials Chapter Objectives • Define a composite, enumerate advantages and drawbacks of composites over monolithic materials, and discuss factors that influence mechanical properties of a composite. • Classify composites, introduce common types of fibers and matrices, and manufacturing, mechanical properties, and applications of composites. • Discuss recycling of composites. • Introduce terminology used for studying mechanics of composites. 1.1 Introduction You are no longer to supply the people with straw for making bricks; let them go and gather their own straw. Exodus 5:7 Israelites using bricks made of clay and reinforced with straw are an early example of application of composites. The individual constituents, clay and straw, could not serve the function by themselves but did when put together. Some believe that the straw was used to keep the clay from cracking, but others suggest that it blunted the sharp cracks in the dry clay. Historical examples of composites are abundant in the literature. Signifi- cant examples include the use of reinforcing mud walls in houses with bamboo shoots, glued laminated wood by Egyptians (1500 B.C.), and laminated metals in forging swords (A.D. 1800). In the 20th century, modern composites were used in the 1930s when glass fibers reinforced resins. Boats 1343_book.fm Page 1 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC
2 Mechanics of Composite Materials,Second Edition and aircraft were built out of these glass composites,commonly called fiber- glass.Since the 1970s,application of composites has widely increased due to development of new fibers such as carbon,boron,and aramids,*and new composite systems with matrices made of metals and ceramics. This chapter gives an overview of composite materials.The ques- tion-answer style of the chapter is a suitable way to learn the fundamental aspects of this vast subject.In each section,the questions progressively become more specialized and technical in nature. What is a composite? A composite is a structural material that consists of two or more combined constituents that are combined at a macroscopic level and are not soluble in each other.One constituent is called the reinforcing phase and the one in which it is embedded is called the matrix.The reinforcing phase material may be in the form of fibers,particles,or flakes.The matrix phase materials are generally continuous.Examples of composite systems include concrete rein- forced with steel and epoxy reinforced with graphite fibers,etc. Give some examples of naturally found composites. Examples include wood,where the lignin matrix is reinforced with cellu- lose fibers and bones in which the bone-salt plates made of calcium and phosphate ions reinforce soft collagen. What are advanced composites? Advanced composites are composite materials that are traditionally used in the aerospace industries.These composites have high performance rein- forcements of a thin diameter in a matrix material such as epoxy and alu- minum.Examples are graphite/epoxy,Kevlart/epoxy,and boron/ aluminum composites.These materials have now found applications in com- mercial industries as well. Combining two or more materials together to make a composite is more work than just using traditional monolithic metals such as steel and alu- minum.What are the advantages of using composites over metals? Monolithic metals and their alloys cannot always meet the demands of today's advanced technologies.Only by combining several materials can one meet the performance requirements.For example,trusses and benches used in satellites need to be dimensionally stable in space during temperature changes between-256F(-160C)and 200F(93.3C).Limitations on coeffi- cient of thermal expansiont thus are low and may be of the order of +1 x Aramids are aromatic compounds of carbon,hydrogen,oxygen,and nitrogen. t Kevlaris a registered trademark of E.I.duPont deNemours and Company,Inc.,Wilimington,DE. t Coefficient of thermal expansion is the change in length per unit length of a material when heated through a unit temperature.The units are in./in./F and m/m/C.A typical value for steel is6.5×10in./in.℉(11.7×10-m/mC). 2006 by Taylor Francis Group,LLC
2 Mechanics of Composite Materials, Second Edition and aircraft were built out of these glass composites, commonly called fiberglass. Since the 1970s, application of composites has widely increased due to development of new fibers such as carbon, boron, and aramids,* and new composite systems with matrices made of metals and ceramics. This chapter gives an overview of composite materials. The question–answer style of the chapter is a suitable way to learn the fundamental aspects of this vast subject. In each section, the questions progressively become more specialized and technical in nature. What is a composite? A composite is a structural material that consists of two or more combined constituents that are combined at a macroscopic level and are not soluble in each other. One constituent is called the reinforcing phase and the one in which it is embedded is called the matrix. The reinforcing phase material may be in the form of fibers, particles, or flakes. The matrix phase materials are generally continuous. Examples of composite systems include concrete reinforced with steel and epoxy reinforced with graphite fibers, etc. Give some examples of naturally found composites. Examples include wood, where the lignin matrix is reinforced with cellulose fibers and bones in which the bone-salt plates made of calcium and phosphate ions reinforce soft collagen. What are advanced composites? Advanced composites are composite materials that are traditionally used in the aerospace industries. These composites have high performance reinforcements of a thin diameter in a matrix material such as epoxy and aluminum. Examples are graphite/epoxy, Kevlar®†/epoxy, and boron/ aluminum composites. These materials have now found applications in commercial industries as well. Combining two or more materials together to make a composite is more work than just using traditional monolithic metals such as steel and aluminum. What are the advantages of using composites over metals? Monolithic metals and their alloys cannot always meet the demands of today’s advanced technologies. Only by combining several materials can one meet the performance requirements. For example, trusses and benches used in satellites need to be dimensionally stable in space during temperature changes between –256°F (–160°C) and 200°F (93.3°C). Limitations on coeffi- cient of thermal expansion‡ thus are low and may be of the order of ±1 × * Aramids are aromatic compounds of carbon, hydrogen, oxygen, and nitrogen. † Kevlar® is a registered trademark of E.I. duPont deNemours and Company, Inc., Wilimington, DE. ‡ Coefficient of thermal expansion is the change in length per unit length of a material when heated through a unit temperature. The units are in./in./°F and m/m/°C. A typical value for steel is 6.5 × 10–6 in./in.°F (11.7 × 10–6 m/m°C). 1343_book.fm Page 2 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC
Introduction to Composite Materials 3 10-7in./in./F(+1.8 x 107m/m/C).Monolithic materials cannot meet these requirements;this leaves composites,such as graphite/epoxy,as the only materials to satisfy them. In many cases,using composites is more efficient.For example,in the highly competitive airline market,one is continuously looking for ways to lower the overall mass of the aircraft without decreasing the stiffness*and strengtht of its components.This is possible by replacing conventional metal alloys with composite materials.Even if the composite material costs may be higher,the reduction in the number of parts in an assembly and the savings in fuel costs make them more profitable.Reducing one lbm(0.453 kg)of mass in a commercial aircraft can save up to 360 gal (1360 1)of fuel per year;fuel expenses are 25%of the total operating costs of a commercial airline.? Composites offer several other advantages over conventional materials. These may include improved strength,stiffness,fatiguet and impact resis- tance,*thermal conductivity,tt corrosion resistance,etc. How is the mechanical advantage of composite measured? For example,the axial deflection,u,of a prismatic rod under an axial load, P,is given by PL 1= (1.1) AE where L=length of the rod E=Young's modulus of elasticity of the material of the rod Because the mass,M,of the rod is given by M=pAL, (1.2) where p =density of the material of the rod,we have *Stiffness is defined as the resistance of a material to deflection. t Strength is defined as the stress at which a material fails. t Fatigue resistance is the resistance to the lowering of mechanical properties such as strength and stiffness due to cyclic loading,such as due to take-off and landing of a plane,vibrating a plate,etc. ++Impact resistance is the resistance to damage and to reduction in residual strength to impact loads,such as a bird hitting an airplane or a hammer falling on a car body. Thermal conductivity is the rate of heat flow across a unit area of a material in a unit time, when the temperature gradient is unity in the direction perpendicular to the area. Corrosion resistance is the resistance to corrosion,such as pitting,erosion,galvanic,etc. 2006 by Taylor Francis Group,LLC
Introduction to Composite Materials 3 10–7 in./in./°F (±1.8 × 10–7 m/m/°C). Monolithic materials cannot meet these requirements; this leaves composites, such as graphite/epoxy, as the only materials to satisfy them. In many cases, using composites is more efficient. For example, in the highly competitive airline market, one is continuously looking for ways to lower the overall mass of the aircraft without decreasing the stiffness* and strength† of its components. This is possible by replacing conventional metal alloys with composite materials. Even if the composite material costs may be higher, the reduction in the number of parts in an assembly and the savings in fuel costs make them more profitable. Reducing one lbm (0.453 kg) of mass in a commercial aircraft can save up to 360 gal (1360 l) of fuel per year;1 fuel expenses are 25% of the total operating costs of a commercial airline.2 Composites offer several other advantages over conventional materials. These may include improved strength, stiffness, fatigue‡ and impact resistance,** thermal conductivity,†† corrosion resistance,‡‡ etc. How is the mechanical advantage of composite measured? For example, the axial deflection, u, of a prismatic rod under an axial load, P, is given by , (1.1) where L = length of the rod E = Young’s modulus of elasticity of the material of the rod Because the mass, M, of the rod is given by , (1.2) where ρ = density of the material of the rod, we have * Stiffness is defined as the resistance of a material to deflection. † Strength is defined as the stress at which a material fails. ‡ Fatigue resistance is the resistance to the lowering of mechanical properties such as strength and stiffness due to cyclic loading, such as due to take-off and landing of a plane, vibrating a plate, etc. ** Impact resistance is the resistance to damage and to reduction in residual strength to impact loads, such as a bird hitting an airplane or a hammer falling on a car body. †† Thermal conductivity is the rate of heat flow across a unit area of a material in a unit time, when the temperature gradient is unity in the direction perpendicular to the area. ‡‡ Corrosion resistance is the resistance to corrosion, such as pitting, erosion, galvanic, etc. u PL AE = M A = ρ L 1343_book.fm Page 3 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC
4 Mechanics of Composite Materials,Second Edition PL2 1 M=4E/P (1.3) This implies that the lightest beam for specified deflection under a specified load is one with the highest(E/p)value. Thus,to measure the mechanical advantage,the (E/p)ratio is calculated and is called the specific modulus(ratio between the Young's modulus*(E) and the densityt (p)of the material).The other parameter is called the specific strength and is defined as the ratio between the strength(o.)and the density of the material (p),that is, E Specific modulus= 0 Specific strength= The two ratios are high in composite materials.For example,the strength of a graphite/epoxy unidirectional compositet could be the same as steel, but the specific strength is three times that of steel.What does this mean to a designer?Take the simple case of a rod designed to take a fixed axial load The rod cross section of graphite/epoxy would be same as that of the steel, but the mass of graphite/epoxy rod would be one third of the steel rod.This reduction in mass translates to reduced material and energy costs.Figure 1.1 shows how composites and fibers rate with other traditional materials in terms of specific strength.3 Note that the unit of specific strength is inches in Figure 1.1 because specific strength and specific modulus are also defined in some texts as E Specific modulus=- PS Specific strength=gw。 P8 where g is the acceleration due to gravity(32.2 ft/s2 or 9.81 m/s2). Young's modulus of an elastic material is the initial slope of the stress-strain curve. t Density is the mass of a substance per unit volume. A unidirectional composite is a composite lamina or rod in which the fibers reinforcing the matrix are oriented in the same direction. 2006 by Taylor Francis Group,LLC
4 Mechanics of Composite Materials, Second Edition . (1.3) This implies that the lightest beam for specified deflection under a specified load is one with the highest (E/ρ) value. Thus, to measure the mechanical advantage, the (E/ρ) ratio is calculated and is called the specific modulus (ratio between the Young’s modulus* (E) and the density† (ρ) of the material). The other parameter is called the specific strength and is defined as the ratio between the strength (σult) and the density of the material (ρ), that is, The two ratios are high in composite materials. For example, the strength of a graphite/epoxy unidirectional composite‡ could be the same as steel, but the specific strength is three times that of steel. What does this mean to a designer? Take the simple case of a rod designed to take a fixed axial load. The rod cross section of graphite/epoxy would be same as that of the steel, but the mass of graphite/epoxy rod would be one third of the steel rod. This reduction in mass translates to reduced material and energy costs. Figure 1.1 shows how composites and fibers rate with other traditional materials in terms of specific strength.3 Note that the unit of specific strength is inches in Figure 1.1 because specific strength and specific modulus are also defined in some texts as where g is the acceleration due to gravity (32.2 ft/s2 or 9.81 m/s2). * Young’s modulus of an elastic material is the initial slope of the stress–strain curve. † Density is the mass of a substance per unit volume. ‡ A unidirectional composite is a composite lamina or rod in which the fibers reinforcing the matrix are oriented in the same direction. M PL E = 2 4 1 /ρ Specific modulus Specific strength = E , = ρ ult . σ ρ Specific modulus Specific strength = E g , = ρ g σult ρ . 1343_book.fm Page 4 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC
Introduction to Composite Materials 5 10 Aramid fibers, carbon fibers 8 Composites 4 Wood, stone Bronze Cast iron Steel Aluminum 0 1400 1500 1600 1700 1800 1900 2000 Year FIGURE 1.1 Specific strength as a function of time of use of materials.(Source:Eager,T.W.,Whither advanced materials?Adu.Mater.Processes,ASM International,June 1991,25-29.) Values of specific modulus and strength are given in Table 1.1 for typical composite fibers,unidirectional composites,cross-plyt and quasi-isotropict laminated composites,and monolithic metals. On a first look,fibers such as graphite,aramid,and glass have a specific modulus several times that of metals,such as steel and aluminum.This gives a false impression about the mechanical advantages of composites because they are made not only of fibers,but also of fibers and matrix combined; matrices generally have lower modulus and strength than fibers.Is the comparison of the specific modulus and specific strength parameters of unidirectional composites to metals now fair?The answer is no for two reasons.First,unidirectional composite structures are acceptable only for carrying simple loads such as uniaxial tension or pure bending.In structures with complex requirements of loading and stiffness,composite structures including angle plies will be necessary.Second,the strengths and elastic moduli of unidirectional composites given in Table 1.1 are those in the direction of the fiber.The strength and elastic moduli perpendicular to the fibers are far less. A unidirectional laminate is a laminate in which all fibers are oriented in the same direction. t A cross-ply laminate is a laminate in which the layers of unidirectional lamina are oriented at right angles to each other. Quasi-isotropic laminate behaves similarly to an isotropic material;that is,the elastic proper- ties are the same in all directions. 2006 by Taylor Francis Group,LLC
Introduction to Composite Materials 5 Values of specific modulus and strength are given in Table 1.1 for typical composite fibers, unidirectional composites,* cross-ply† and quasi-isotropic‡ laminated composites, and monolithic metals. On a first look, fibers such as graphite, aramid, and glass have a specific modulus several times that of metals, such as steel and aluminum. This gives a false impression about the mechanical advantages of composites because they are made not only of fibers, but also of fibers and matrix combined; matrices generally have lower modulus and strength than fibers. Is the comparison of the specific modulus and specific strength parameters of unidirectional composites to metals now fair? The answer is no for two reasons. First, unidirectional composite structures are acceptable only for carrying simple loads such as uniaxial tension or pure bending. In structures with complex requirements of loading and stiffness, composite structures including angle plies will be necessary. Second, the strengths and elastic moduli of unidirectional composites given in Table 1.1 are those in the direction of the fiber. The strength and elastic moduli perpendicular to the fibers are far less. FIGURE 1.1 Specific strength as a function of time of use of materials. (Source: Eager, T.W., Whither advanced materials? Adv. Mater. Processes, ASM International, June 1991, 25–29.) * A unidirectional laminate is a laminate in which all fibers are oriented in the same direction. † A cross-ply laminate is a laminate in which the layers of unidirectional lamina are oriented at right angles to each other. ‡ Quasi-isotropic laminate behaves similarly to an isotropic material; that is, the elastic properties are the same in all directions. 10 8 6 4 2 0 1400 1500 Wood, stone Bronze Cast iron Steel Aluminum Composites Aramid fibers, carbon fibers 1600 1700 1800 Year Specific strength, (106) in 1900 2000 1343_book.fm Page 5 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC
6 Mechanics of Composite Materials,Second Edition TABLE 1.1 Specific Modulus and Specific Strength of Typical Fibers,Composites,and Bulk Metals Young's Specific Specific Material Specific modulus strength modulus strength Units gravity (Msi) (ksi) (Msi-in.3/Ib) (ksi-in.3/1b) System of Units:USCS Graphite fiber 1.8 33.35 299.8 512.9 4610 Aramid fiber 1.4 17.98 200.0 355.5 3959 Glass fiber 2.5 12.33 224.8 136.5 2489 Unidirectional graphite/epoxy 1.6 26.25 217.6 454.1 3764 Unidirectional glass/epoxy 1.8 5.598 154.0 86.09 2368 Cross-ply graphite/epoxy 1.6 13.92 54.10 240.8 935.9 Cross-ply glass/epoxy 1.8 3.420 12.80 52.59 196.8 Quasi-isotropic graphite/epoxy 1.6 10.10 40.10 174.7 693.7 Quasi-isotropic glass/epoxy 1.8 2.750 10.60 42.29 163.0 Steel 7.8 30.00 94.00 106.5 333.6 Aluminum 2.6 10.00 40.00 106.5 425.8 Young's Ultimate Specific Specific Material Specific modulus strength modulus strength Units gravity (GPa) (MPa) (GPa-m2/kg) (MPa-m2/kg) System of LInits:SI Graphite fiber 1.8 230.00 2067 0.1278 1.148 Aramid fiber 1.4 124.00 1379 0.08857 0.9850 Glass fiber 2.5 85.00 1550 0.0340 0.6200 Unidirectional graphite/epoxy 1.6 181.00 1500 0.1131 0.9377 Unidirectional glass/epoxy 1.8 38.60 1062 0.02144 0.5900 Cross-ply graphite/epoxy 1.6 95.98 373.0 0.06000 0.2331 Cross-ply glass/epoxy 1.8 23.58 8825 0.01310 0.0490 Quasi-isotropic graphite/epoxy 1.6 69.64 276.48 0.04353 0.1728 Quasi-isotropic glass/epoxy 1.8 18.96 73.08 0.01053 0.0406 Steel 7.8 206.84 648.1 0.02652 0.08309 Aluminum 2.6 68.95 275.8 0.02652 0.1061 Specific gravity of a material is the ratio between its density and the density of water. A comparison is now made between popular types of laminates such as cross-ply and quasi-isotropic laminates.Figure 1.2 shows the specific strength plotted as a function of specific modulus for various fibers,metals, and composites. Are specific modulus and specific strength the only mechanical parameters used for measuring the relative advantage of composites over metals? No,it depends on the application.+Consider compression of a column, where it may fail due to buckling.The Euler buckling formula gives the critical load at which a long column buckles ass 2006 by Taylor Francis Group,LLC
6 Mechanics of Composite Materials, Second Edition A comparison is now made between popular types of laminates such as cross-ply and quasi-isotropic laminates. Figure 1.2 shows the specific strength plotted as a function of specific modulus for various fibers, metals, and composites. Are specific modulus and specific strength the only mechanical parameters used for measuring the relative advantage of composites over metals? No, it depends on the application.4 Consider compression of a column, where it may fail due to buckling. The Euler buckling formula gives the critical load at which a long column buckles as5 TABLE 1.1 Specific Modulus and Specific Strength of Typical Fibers, Composites, and Bulk Metals Material Units Specific gravitya Young’s modulus (Msi) Ultimate strength (ksi) Specific modulus (Msi-in.3/lb) Specific strength (ksi-in.3/lb) System of Units: USCS Graphite fiber Aramid fiber Glass fiber Unidirectional graphite/epoxy Unidirectional glass/epoxy Cross-ply graphite/epoxy Cross-ply glass/epoxy Quasi-isotropic graphite/epoxy Quasi-isotropic glass/epoxy Steel Aluminum 1.8 1.4 2.5 1.6 1.8 1.6 1.8 1.6 1.8 7.8 2.6 33.35 17.98 12.33 26.25 5.598 13.92 3.420 10.10 2.750 30.00 10.00 299.8 200.0 224.8 217.6 154.0 54.10 12.80 40.10 10.60 94.00 40.00 512.9 355.5 136.5 454.1 86.09 240.8 52.59 174.7 42.29 106.5 106.5 4610 3959 2489 3764 2368 935.9 196.8 693.7 163.0 333.6 425.8 Material Units Specific gravity Young’s modulus (GPa) Ultimate strength (MPa) Specific modulus (GPa-m3/kg) Specific strength (MPa-m3/kg) System of Units: SI Graphite fiber Aramid fiber Glass fiber Unidirectional graphite/epoxy Unidirectional glass/epoxy Cross-ply graphite/epoxy Cross-ply glass/epoxy Quasi-isotropic graphite/epoxy Quasi-isotropic glass/epoxy Steel Aluminum 1.8 1.4 2.5 1.6 1.8 1.6 1.8 1.6 1.8 7.8 2.6 230.00 124.00 85.00 181.00 38.60 95.98 23.58 69.64 18.96 206.84 68.95 2067 1379 1550 1500 1062 373.0 88.25 276.48 73.08 648.1 275.8 0.1278 0.08857 0.0340 0.1131 0.02144 0.06000 0.01310 0.04353 0.01053 0.02652 0.02652 1.148 0.9850 0.6200 0.9377 0.5900 0.2331 0.0490 0.1728 0.0406 0.08309 0.1061 a Specific gravity of a material is the ratio between its density and the density of water. 1343_book.fm Page 6 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC
Introduction to Composite Materials 7 5000 0 Graphite fiber 4000 O Unidirectional graphite/epoxy 3000 2000 1000 Quasi-isotropic graphite/epoxy 0 OCross-ply graphite/epoxy Aluminum Steel 0 0 100 200 300 400 500 600 Specific modulus (Msi-in3/lb) FIGURE 1.2 Specific strength as a function of specific modulus for metals,fibers,and composites. π2E1 Pa= 2, (1.4) where P=critical buckling load (Ib or N) E=Young's modulus of column (lb/in.2 or N/m2) I second moment of area (in.or m) L=length of beam (in.or m) If the column has a circular cross section,the second moment of area is I= d (1.5) 64 and the mass of the rod is πdL M=P (1.6) 2006 by Taylor Francis Group,LLC
Introduction to Composite Materials 7 , (1.4) where Pcr = critical buckling load (lb or N) E = Young’s modulus of column (lb/in.2 or N/m2) I = second moment of area (in.4 or m4) L = length of beam (in. or m) If the column has a circular cross section, the second moment of area is (1.5) and the mass of the rod is , (1.6) FIGURE 1.2 Specific strength as a function of specific modulus for metals, fibers, and composites. 5000 4000 3000 2000 1000 0 0 100 200 Quasi-isotropic graphite/epoxy Aluminum Specific modulus (Msi-in3/lb) Cross-ply graphite/epoxy Unidirectional graphite/epoxy Graphite fiber Steel Specific strength (Ksi-in3/lb) 300 400 500 600 Pcr EI L = π2 2 I d = π 4 64 M = d L 4 ρ π 2 1343_book.fm Page 7 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC
8 Mechanics of Composite Materials,Second Edition where M=mass of the beam (lb or kg) p density of beam (Ib/in.3 or kg/m3) d diameter of beam (in.or m) Because the length,L,and the load,p are constant,we find the mass of the beam by substituting Equation (1.5)and Equation (1.6)in Equation (1.4)as M 21Pa 1 (1.7) √元E2/p This means that the lightest beam for specified stiffness is one with the highest value of E12/p. Similarly,we can prove that,for achieving the minimum deflection in a beam under a load along its length,the lightest beam is one with the highest value of E1/3/p.Typical values of these two parameters,E12/p and E1/3/p for typical fibers,unidirectional composites,cross-ply and quasi-isotropic laminates,steel,and aluminum are given in Table 1.2.Comparing these numbers with metals shows composites drawing a better advantage for these two parameters.Other mechanical parameters for comparing the perfor- mance of composites to metals include resistance to fracture,fatigue,impact, and creep. Yes,composites have distinct advantages over metals.Are there any draw- backs or limitations in using them? Yes,drawbacks and limitations in use of composites include: High cost of fabrication of composites is a critical issue.For example, a part made of graphite/epoxy composite may cost up to 10 to 15 times the material costs.A finished graphite/epoxy composite part may cost as much as $300 to $400 per pound ($650 to $900 per kilogram).Improvements in processing and manufacturing tech- niques will lower these costs in the future.Already,manufacturing techniques such as SMC (sheet molding compound)and SRIM (structural reinforcement injection molding)are lowering the cost and production time in manufacturing automobile parts. Mechanical characterization of a composite structure is more com- plex than that of a metal structure.Unlike metals,composite mate- rials are not isotropic,that is,their properties are not the same in all directions.Therefore,they require more material parameters.For example,a single layer of a graphite/epoxy composite requires nine 2006 by Taylor Francis Group,LLC
8 Mechanics of Composite Materials, Second Edition where M = mass of the beam (lb or kg) ρ = density of beam (lb/in.3 or kg/m3) d = diameter of beam (in. or m) Because the length, L, and the load, P, are constant, we find the mass of the beam by substituting Equation (1.5) and Equation (1.6) in Equation (1.4) as . (1.7) This means that the lightest beam for specified stiffness is one with the highest value of E1/2/ρ. Similarly, we can prove that, for achieving the minimum deflection in a beam under a load along its length, the lightest beam is one with the highest value of E1/3/ρ. Typical values of these two parameters, E1/2/ρ and E1/3/ρ for typical fibers, unidirectional composites, cross-ply and quasi-isotropic laminates, steel, and aluminum are given in Table 1.2. Comparing these numbers with metals shows composites drawing a better advantage for these two parameters. Other mechanical parameters for comparing the performance of composites to metals include resistance to fracture, fatigue, impact, and creep. Yes, composites have distinct advantages over metals. Are there any drawbacks or limitations in using them? Yes, drawbacks and limitations in use of composites include: • High cost of fabrication of composites is a critical issue. For example, a part made of graphite/epoxy composite may cost up to 10 to 15 times the material costs. A finished graphite/epoxy composite part may cost as much as $300 to $400 per pound ($650 to $900 per kilogram). Improvements in processing and manufacturing techniques will lower these costs in the future. Already, manufacturing techniques such as SMC (sheet molding compound) and SRIM (structural reinforcement injection molding) are lowering the cost and production time in manufacturing automobile parts. • Mechanical characterization of a composite structure is more complex than that of a metal structure. Unlike metals, composite materials are not isotropic, that is, their properties are not the same in all directions. Therefore, they require more material parameters. For example, a single layer of a graphite/epoxy composite requires nine M L P E cr = 2 1 2 1 2 π ρ / / 1343_book.fm Page 8 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC
Introduction to Composite Materials 9 TABLE 1.2 Specific Modulus Parameters E/p,E12/p,and E//p for Typical Materials Young's Material Specific modulus Elp ER/p E/p Units gravity (Msi)(Msi-in.3/Ib)(psi-in.3/b)(psit-in./Ib) System of UInits:UISCS Graphite fiber 1.8 33.35 512.8 88,806 4,950 Kevlar fiber 1.4 17.98 355.5 83836 5,180 Glass fiber 2.5 12.33 136.5 38,878 2,558 Unidirectional graphite/epoxy 1.6 26.25 454.1 88,636 5,141 Unidirectional glass/epoxy 1.8 5.60 86.09 36384 2,730 Cross-ply graphite/epoxy 1.6 13.92 240.8 64545 4,162 Cross-ply glass/epoxy 1.8 3.42 52.59 28,438 2317 Quasi-isotropic graphite/epoxy 1.6 10.10 174.7 54,980 3,740 Quasi-isotropic glass/epoxy 1.8 2.75 42.29 25,501 2,154 Steel 7.8 30.00 106.5 19,437 1,103 Aluminum 2.6 10.00 106.5 33,666 2294 Young's Material Specific modulus Elp E/p Elp Units gravity (GPa) (GPa-m3/kg) (Pa-m3/kg) (Pais-m3/kg System of UInits:SI Graphite fiber 1.8 230.00 0.1278 266.4 3.404 Kevlar fiber 1.4 124.00 0.08857 251.5 3.562 Glass fiber 2.5 85.00 0.034 116.6 1.759 Unidirectional graphite/epoxy 1.6 181.00 0.1131 265.9 3.535 Unidirectional glass/epoxy 1.8 38.60 0.02144 109.1 1.878 Cross-ply graphite/epoxy 1.6 95.98 0.060 193.6 2.862 Cross-ply glass/epoxy 1.8 23.58 0.0131 8531 1.593 Quasi-isotropic graphite/epoxy 1.6 69.64 0.04353 164.9 2.571 Quasi-isotropic glass/epoxy 1.8 18.96 0.01053 76.50 1.481 Steel 7.8 206.84 0.02652 58.3 0.7582 Aluminum 2.6 68.95 0.02662 101.0 1.577 stiffness and strength constants for conducting mechanical analysis. In the case of a monolithic material such as steel,one requires only four stiffness and strength constants.Such complexity makes struc- tural analysis computationally and experimentally more compli- cated and intensive.In addition,evaluation and measurement techniques of some composite properties,such as compressive strengths,are still being debated. Repair of composites is not a simple process compared to that for metals.Sometimes critical flaws and cracks in composite structures may go undetected. 2006 by Taylor Francis Group,LLC
Introduction to Composite Materials 9 stiffness and strength constants for conducting mechanical analysis. In the case of a monolithic material such as steel, one requires only four stiffness and strength constants. Such complexity makes structural analysis computationally and experimentally more complicated and intensive. In addition, evaluation and measurement techniques of some composite properties, such as compressive strengths, are still being debated. • Repair of composites is not a simple process compared to that for metals. Sometimes critical flaws and cracks in composite structures may go undetected. TABLE 1.2 Specific Modulus Parameters E/ρ, E1/2/ρ, and E1/3/ρ for Typical Materials Material Units Specific gravity Young’s modulus (Msi) E/ρ (Msi-in.3/lb) E1/2/ρ (psi1/2-in.3/lb) E1/3/ρ (psi1/3-in.3/lb) System of Units: USCS Graphite fiber Kevlar fiber Glass fiber Unidirectional graphite/epoxy Unidirectional glass/epoxy Cross-ply graphite/epoxy Cross-ply glass/epoxy Quasi-isotropic graphite/epoxy Quasi-isotropic glass/epoxy Steel Aluminum 1.8 1.4 2.5 1.6 1.8 1.6 1.8 1.6 1.8 7.8 2.6 33.35 17.98 12.33 26.25 5.60 13.92 3.42 10.10 2.75 30.00 10.00 512.8 355.5 136.5 454.1 86.09 240.8 52.59 174.7 42.29 106.5 106.5 88,806 83,836 38,878 88,636 36,384 64,545 28,438 54,980 25,501 19,437 33,666 4,950 5,180 2,558 5,141 2,730 4,162 2,317 3,740 2,154 1,103 2,294 Material Units Specific gravity Young’s modulus (GPa) E/ρ (GPa-m3/kg) E1/2/ρ (Pa-m3/kg) E1/3/ρ (Pa1/3-m3/kg ) System of Units: SI Graphite fiber Kevlar fiber Glass fiber Unidirectional graphite/epoxy Unidirectional glass/epoxy Cross-ply graphite/epoxy Cross-ply glass/epoxy Quasi-isotropic graphite/epoxy Quasi-isotropic glass/epoxy Steel Aluminum 1.8 1.4 2.5 1.6 1.8 1.6 1.8 1.6 1.8 7.8 2.6 230.00 124.00 85.00 181.00 38.60 95.98 23.58 69.64 18.96 206.84 68.95 0.1278 0.08857 0.034 0.1131 0.02144 0.060 0.0131 0.04353 0.01053 0.02652 0.02662 266.4 251.5 116.6 265.9 109.1 193.6 85.31 164.9 76.50 58.3 101.0 3.404 3.562 1.759 3.535 1.878 2.862 1.593 2.571 1.481 0.7582 1.577 1343_book.fm Page 9 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC
10 Mechanics of Composite Materials,Second Edition 一2a ↓↓↓↓↓↓↓ FIGURE 1.3 A uniformly loaded plate with a crack. Composites do not have a high combination of strength and fracture toughness*compared to metals.In Figure 1.4,a plot is shown for fracture toughness vs.yield strength for a 1-in.(25-mm)thick mate- rial.3 Metals show an excellent combination of strength and fracture toughness compared to composites.(Note:The transition areas in Figure 1.4 will change with change in the thickness of the specimen.) Composites do not necessarily give higher performance in all the properties used for material selection.In Figure 1.5,six primary material selection parameters-strength,toughness,formability, In a material with a crack,the value of the stress intensity factor gives the measure of stresses in the crack tip region.For example,for an infinite plate with a crack of length 2a under a uniaxial load o (Figure 1.3),the stress intensity factor is K=6yia. If the stress intensity factor at the crack tip is greater than the critical stress intensity factor of the material,the crack will grow.The greater the value of the critical stress intensity factor is,the tougher the material is.The critical stress intensity factor is called the fracture toughness of the material.Typical values of fracture toughness are 23.66 ksivin.(26 MPavm)for aluminum and 25.48 ksivin.(28 MPavm)for steel. 2006 by Taylor Francis Group,LLC
10 Mechanics of Composite Materials, Second Edition • Composites do not have a high combination of strength and fracture toughness* compared to metals. In Figure 1.4, a plot is shown for fracture toughness vs. yield strength for a 1-in. (25-mm) thick material.3 Metals show an excellent combination of strength and fracture toughness compared to composites. (Note: The transition areas in Figure 1.4 will change with change in the thickness of the specimen.) • Composites do not necessarily give higher performance in all the properties used for material selection. In Figure 1.5, six primary material selection parameters — strength, toughness, formability, FIGURE 1.3 A uniformly loaded plate with a crack. * In a material with a crack, the value of the stress intensity factor gives the measure of stresses in the crack tip region. For example, for an infinite plate with a crack of length 2a under a uniaxial load σ (Figure 1.3), the stress intensity factor is . If the stress intensity factor at the crack tip is greater than the critical stress intensity factor of the material, the crack will grow. The greater the value of the critical stress intensity factor is, the tougher the material is. The critical stress intensity factor is called the fracture toughness of the material. Typical values of fracture toughness are for aluminum and for steel. σ σ 2a K a =σ π 23.66 ksi in. (26 MPa m ) 25.48 ksi in. (28 MPa m ) 1343_book.fm Page 10 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC