1. Chapter 16 – Composites: Teamwork and Synergy in Materials
The Science and Engineering of Materials, 4th ed Donald R. Askeland – Pradeep P. Phulé
Chapter 16 – Composites: Teamwork and Synergy in Materials

2. Objectives of Chapter 16
Study different categories of composites: particulate, fiber, and laminar
Focus on composites used in structural or mechanical applications.

3. Chapter Outline 16.1 Dispersion-Strengthened Composites
16.2 Particulate Composites
16.3 Fiber-Reinforced Composites
16.4 Characteristics of Fiber-Reinforced Composites
16.5 Manufacturing Fibers and Composites
16.6 Fiber-Reinforced Systems and Applications
16.7 Laminar Composite Materials
16.8 Examples and Applications of Laminar Composites
16.9 Sandwich Structures

4. Figure 16.1 Some examples of composite materials: (a) plywood is a laminar composite of layers of wood veneer, (b) fiberglass is a fiber-reinforced composite containing stiff, strong glass fibers in a softer polymer matrix ( 175), and (c) concrete is a particulate composite containing coarse sand or gravel in a cement matrix (reduced 50%).

5. Section 16.1 Dispersion-Strengthened Composites
A special group of dispersion-strengthened nanocomposite materials containing particles 10 to 250 nm in diameter is classified as particulate composites.
Dispersoids - Tiny oxide particles formed in a metal matrix that interfere with dislocation movement and provide strengthening, even at elevated temperatures.

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Figure Comparison of the yield strength of dispersion-strengthened sintered aluminum powder (SAP) composite with that of two conventional two-phase high-strength aluminum alloys. The composite has benefits above about 300°C. A fiber-reinforced aluminum composite is shown for comparison.

8. Figure 16. 3 Electron micrograph of TD-nickel
Figure 16.3 Electron micrograph of TD-nickel. The dispersed ThO2 particles have a diameter of 300 nm or less ( 2000). (From Oxide Dispersion Strengthening, p. 714, Gordon and Breach, © AIME.)

9. Example 16.1 TD-Nickel Composite
Suppose 2 wt% ThO2 is added to nickel. Each ThO2 particle has a diameter of 1000 Å. How many particles are present in each cubic centimeter?
Example 16.1 SOLUTION
The densities of ThO2 and nickel are 9.69 and 8.9 g/cm3, respectively. The volume fraction is:

10. Example 16.1 SOLUTION (Continued)
Therefore, there is cm3 of ThO2 per cm3 of composite. The volume of each ThO2 sphere is:

11. Section 16.2 Particulate Composites
Rule of mixtures - The statement that the properties of a composite material are a function of the volume fraction of each material in the composite.
Cemented carbides - Particulate composites containing hard ceramic particles bonded with a soft metallic matrix.
Electrical Contacts - Materials used for electrical contacts in switches and relays must have a good combination of wear resistance and electrical conductivity.
Polymers - Many engineering polymers that contain fillers and extenders are particulate composites.

12. Figure 16.4 Microstructure of tungsten carbide—20% cobalt-cemented carbide (1300). (From Metals Handbook, Vol. 7, 8th Ed., American Society for Metals, 1972.)

13. Example 16.2 Cemented Carbides
A cemented carbide cutting tool used for machining contains 75 wt% WC, 15 wt% TiC, 5 wt% TaC, and 5 wt% Co. Estimate the density of the composite.
Example 16.2 SOLUTION
First, we must convert the weight percentages to volume fractions. The densities of the components of the composite are:

14. Example 16.2 SOLUTION (Continued)
From the rule of mixtures, the density of the composite is

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Figure The steps in producing a silver-tungsten electrical composite: (a) Tungsten powders are pressed, (b) a low-density compact is produced, (c) sintering joins the tungsten powders, and (d) liquid silver is infiltrated into the pores between the particles.

16. Example 16.3 Silver-Tungsten Composite
A silver-tungsten composite for an electrical contact is produced by first making a porous tungsten powder metallurgy compact, then infiltrating pure silver into the pores. The density of the tungsten compact before infiltration is 14.5 g/cm3. Calculate the volume fraction of porosity and the final weight percent of silver in the compact after infiltration.
Example 16.3 SOLUTION
From the rule of mixtures:

17. Example 16.3 SOLUTION (Continued)
After infiltration, the volume fraction of silver equals the volume fraction of pores:

18. Figure 16.6 The effect of clay on the properties of polyethylene.
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Figure 16.6 The effect of clay on the properties of polyethylene.

19. Example 16.4 Design of a Particulate Polymer Composite
Design a clay-filled polyethylene composite suitable for injection molding of inexpensive components. The final part must have a tensile strength of at least 3000 psi and a modulus of elasticity of at least 80,000 psi. Polyethylene costs approximately 50 cents per pound and clay costs approximately 5 cents per pound. The density of polyethylene is 0.95 g/cm3 and that of clay is 2.4 g/cm3.
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Figure 16.6 The effect of clay on the properties of polyethylene.

20. Example 16.4 SOLUTION
In 1000 cm3 of composite parts, there are 350 cm3 of clay and 650 cm3 of polyethylene in the composite, or:
The cost of materials is:

21. Example 16.4 SOLUTION (Continued)
Suppose that weight is critical. The composite’s density is:
If we use only 0.2 volume fraction clay, then (using the same method as above) we find that we need 1.06 lb clay and 1.67 lb polyethylene.
The cost of materials is now:
The density of the composite is:

22. Figure 16.7 Microstructure of an aluminum casting alloy reinforced with silicon carbide particles. In this case, the reinforcing particles have segregated to interdendritic regions of the casting ( 125). (Courtesy of David Kennedy, Lester B. Knight Cost Metals Inc.)

23. Section 16.3 Fiber-Reinforced Composites
The Rule of Mixtures in Fiber-Reinforced Composites
Strength of Composites - The tensile strength of a fiber-reinforced composite (TSc) depends on the bonding between the fibers and the matrix.

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Figure The stress-strain curve for a fiber-reinforced composite. At low stresses (region l), the modulus of elasticity is given by the rule of mixtures. At higher stresses (region ll), the matrix deforms and the rule of mixtures is no longer obeyed.

25. Example 16.5 Rule of Mixtures for Composites: Stress Parallel to Fibers
Derive the rule of mixtures (Equation 16.5) for the modulus of elasticity of a fiber-reinforced composite when a stress ( ) is applied along the axis of the fibers. We use the symbol ‘‘ ’’ for stress to distinguish it from the symbol used for conductivity.
Example 16.5 SOLUTION
The total force acting on the composite is the sum of the forces carried by each constituent:
Fc = Fm + Ff
Since F = σA:

26. Example 16.5 SOLUTION (Continued)
If the fibers have a uniform cross-section, the area fraction equals the volume fraction f :
From Hooke’s law, σ = εE. Therefore:
If the fibers are rigidly bonded to the matrix, both the fibers and the matrix must stretch equal amounts (iso-strain conditions):

27. Example 16.6 Modulus of Elasticity for Composites: Stress Perpendicular to Fibers
Derive the equation for the modulus of elasticity of a fiber-reinforced composite when a stress is applied perpendicular to the axis of the fiber (Equation 16-7).
Example 16.6 SOLUTION
The strains are no longer equal; instead, the weighted sum of the strains in each component equals the total strain in the composite, whereas the stresses in each component are equal (iso-stress conditions):

28. Example 16.7 Boron Aluminum Composites
Boron coated with SiC(or Borsic) reinforced aluminum containing 40 vol% fibers is an important high-temperature, lightweight composite material. Estimate the density, modulus of elasticity, and tensile strength parallel to the fiber axis. Also estimate the modulus of elasticity perpendicular to the fibers.

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Figure 16.9 The influence of volume percent boron-coated SiC (Borsic) fibers on the properties of Borsic-reinforced aluminum parallel to the fibers (for Example 16.7).

30. Example 16.7 SOLUTION
The properties of the individual components are shown below.
From the rule of mixtures:
Perpendicular to the fibers:

31. Example 16.8 Nylon-Glass Fiber Composites
Boron coated with SiC(or Borsic) reinforced aluminum containing 40 vol% fibers is an important high-temperature, lightweight composite material. Estimate the density, modulus of elasticity, and tensile strength parallel to the fiber axis. Also estimate the modulus of elasticity perpendicular to the fibers.
Example 16.8 SOLUTION
The modulus of elasticity for each component of the composite is:
Eglass = 10.5  106 psi Enylon = 0.4  106 psi

32. Example 16.8 SOLUTION (Continued)
Both the nylon and the glass fibers have equal strain if bonding is good, so:
Almost all of the load is carried by the glass fibers.

33. Section 16.4 Characteristics of Fiber-Reinforced Composites
Many factors must be considered when designing a fiber-reinforced composite, including the length, diameter, orientation, amount, and properties of the fibers; the properties of the matrix; and the bonding between the fibers and the matrix.
Aspect ratio - The length of a fiber divided by its diameter.
Delamination - Separation of individual plies of a fiber-reinforced composite.

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Figure Increasing the length of chopped E-glass fibers in an epoxy matrix increases the strength of the composite. In this example, the volume fraction of glass fibers is about 0.5.

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Figure Effect of fiber orientation on the tensile strength of E-glass fiber-reinforced epoxy composites.

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Figure (a) Tapes containing aligned fibers can be joined to produce a multi-layered different orientations to produce a quasi-isotropic composite. In this case, a 0°/+45°/90° composite is formed.

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Figure A three-dimensional weave for fiber-reinforced composites.

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Figure Comparison of the specific strength and specific modulus of fibers versus metals and polymers.

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Figure The structure of KevlarTM. The fibers are joined by secondary bonds between oxygen and hydrogen atoms on adjoining chains.

41. Example 16.9 Design of an Aerospace Composite
We are now using a 7075-T6 aluminum alloy (modulus of elasticity of 10  106 psi) to make a 500-pound panel on a commercial aircraft. Experience has shown that each pound reduction in weight on the aircraft reduces the fuel consumption by 500 gallons each year. Design a material for the panel that will reduce weight, yet maintain the same specific modulus, and will be economical over a 10-year lifetime of the aircraft.
Example 16.9 SOLUTION
let’s consider using a boron fiber-reinforced Al-Li alloy in the T6 condition. The specific modulus of the current 7075-T6 alloy is:

42. Example 16.9 SOLUTION
If we use 0.6 volume fraction boron fibers in the composite, then the density, modulus of elasticity, and specific modulus of the composite are:
If the specific modulus is the only factor influencing the design of the component, the thickness of the part might be reduced by 75%, giving a component weight of 125 pounds rather than 500 pounds. The weight savings would then be 375 pounds, or (500 gal/lb)(375 lb) = 187,500 gal per year. At about $2.00 per gallon, about $375,000 in fuel savings could be realized each year, or $3.75 million over the 10-year aircraft lifetime.

43. Figure Scanning electron micrograph of the fracture surface of a silver-copper alloy reinforced with carbon fibers. Poor bonding causes much of the fracture surface to follow the interface between the metal matrix and the carbon tows ( 3000). (From Metals Handbook, American Society for Metals, Vol. 9, 9th Ed., 1985.)

44. Section 16.5 Manufacturing Fibers and Composites
Chemical vapor deposition - Method for manufacturing materials by condensing the material from a vapor onto a solid substrate.
Carbonizing - Driving off the non-carbon atoms from a polymer fiber, leaving behind a carbon fiber of high strength. Also known as pyrolizing.
Filament winding - Process for producing fiber-reinforced composites in which continuous fibers are wrapped around a form or mandrel.
Pultrusion - A method for producing composites containing mats or continuous fibers.

45. Figure 16.17 Methods for producing (a) boron and (b) carbon fibers.
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Figure Methods for producing (a) boron and (b) carbon fibers.

46. Figure Photomicrographs of two fiber-reinforced composites: (a) In Borsic fiber-reinforced aluminum, the fibers are composed of a thick layer of boron deposited on a small-diameter tungsten filament ( 1000). (From Metals Handbook, American Society for Metals, Vol. 9, 9th Ed., 1985.) (b) In this microstructure of a ceramic-fiber–ceramic-matrix composite, silicon carbide fibers are used to reinforce a silicon nitride matrix. The SiC fiber is vapor-deposited on a small carbon precursor filament ( 125). (Courtesy of Dr. R.T. Bhatt, NASA Lewis Research Center.)

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Figure The effect of heat-treatment temperature on the strength and modulus of elasticity of carbon fibers.

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Figure A scanning electron micrograph of a carbon tow containing many individual carbon filaments (x200).

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Figure Production of fiber tapes by encasing fibers between metal cover sheets by diffusion bonding.

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Figure Producing composite shapes in dies by (a) hand lay-up, (b) pressure bag molding, and (c) matched die molding.

51. Figure 16.23 Producing composite shapes by filament winding.
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Figure Producing composite shapes by filament winding.

52. Figure 16.24 Producing composite shapes by pultrusion.
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Figure Producing composite shapes by pultrusion.

53. Section 16.6 Fiber-Reinforced Systems and Applications
Advanced Composites - The advanced composites normally are polymer–matrix composites reinforced with high-strength polymer, metal, or ceramic fibers.
Metal-Matrix Composites - These materials, strengthened by metal or ceramic fibers, provide high-temperature resistance.
Ceramic-Matrix Composites - Composites containing ceramic fibers in a ceramic matrix are also finding applications.

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Figure A comparison of the specific modulus and specific strength of several composite materials with those of metals and polymers.

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Figure The specific strength versus temperature for several composites and metals.

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Figure The manufacturer of composite super-conductor wires: (a) Niobium wire is surrounded with copper during forming. (b) Tim is plated onto Nb-Cu composite wired. (c) Tin diffuses to niobium to produce the Nb3Sn-Cu composite.

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Figure A comparison of the specific strength of various carbon-carbon composites with that of other high-temperature materials relative to temperature.

60. Figure Two failure modes in ceramic-ceramic composites: (a) Extensive pull-out of SiC fibers in a glass matrix provides good composite toughness (x20). (From Metals Handbook, American Society for Metals, Vol. 9, 9th Ed., 1985.) (b) Bridging of some fibers across a crack enhances the toughness of a ceramic-matrix composite (unknown magnification). (From Journal of Metals, May 1991.)

61. Example 16.10 Design of a Composite Strut
Design a unidirectional fiber-reinforced epoxy-matrix strut having a round cross-section. The strut is 10 ft long and, when a force of 500 pounds is applied, it should stretch no more than 0.10 in. We want to assure that the stress acting on the strut is less than the yield strength of the epoxy matrix, 12,000 psi. If the fibers should happen to break, the strut will stretch an extra amount but may not catastrophically fracture. Epoxy costs about $0.80/lb and has a modulus of elasticity of 500,000 psi.

62. Example SOLUTION
For high modulus carbon fibers, E = 77  106 psi; the density is 1.9 g/cm3 = lb/in.3, and the cost is about $30/lb. The minimum volume fraction of carbon fibers needed to give a composite modulus of 14.5  106 psi is:
The volume fraction of epoxy remaining is An area of times the total cross-sectional area of the strut must support a 500-lb load with no more than 12,000 psi if all of the fibers should fail:

63. Example 16.10 SOLUTION (Continued)
Although the carbon fibers are the most expensive, they permit the lightest weight and the lowest material cost strut. (This calculation does not, however, take into consideration the costs of manufacturing the strut.) Our design, therefore, is to use a in.-diameter strut containing volume fraction high modulus carbon fiber.

64. Section 16.7 Laminar Composite Materials
Rule of Mixtures - Some properties of the laminar composite materials parallel to the lamellae are estimated from the rule of mixtures.
Producing Laminar Composites - (a) roll bonding, (b) explosive bonding, (c) coextrusion, and (d) brazing.

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Figure Techniques for producing laminar composites: (a) roll bonding, (b) explosive bonding, and (c) coextrusion, and (d) brazing.

66. Section 16.8 Examples and Applications of Laminar Composites
Laminates - Laminates are layers of materials joined by an organic adhesive.
Cladding - A laminar composite produced when a corrosion-resistant or high-hardness layer of a laminar composite formed onto a less expensive or higher-strength backing.
Bimetallic - A laminar composite material produced by joining two strips of metal with different thermal expansion coefficients, making the material sensitive to temperature changes.

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Figure Schematic diagram of an aramid-aluminum laminate, Arall, which has potential for aerospace applications.

68. Section 16.9 Sandwich Structures
Sandwich - A composite material constructed of a lightweight, low-density material surrounded by dense, solid layers. The sandwich combines overall light weight with excellent stiffness.
Honeycomb - A lightweight but stiff assembly of aluminum strip joined and expanded to form the core of a sandwich structure.

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Figure (a) A hexagonal cell honeycomb core, (b) can be joined to two face sheets by means of adhesive sheets, (c) producing an exceptionally lightweight yet stiff, strong honeycomb sandwich structure.

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Figure In the corrugation method for producing a honeycomb core, the material (such as aluminum) is corrugated between two rolls. The corrugated sheets are joined together with adhesive and then cut to the desired thickness.