A unidirectional IM-9 carbon fiber/Hexply 8551-7 epoxy composite is to be designed to replace a 6061-T6 aluminum alloy rod which is to be loaded in longitudinal tension.

(a) What fiber volume fraction of the carbon fibers would be required if the composite longitudinal modulus is to be equal to that of the 6061-T6 aluminum?

(b) For the composite rod of part (a), what would be the percentage reduction in density compared with that of aluminum rod? Use the properties in Table 1.1, and neglect voids in the composite.

Table 1.1:

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Selected Properties of Bulk and Fibrous Materials Material Tensile Strength (MPa) Tensile Modulus (GPa) Specific Density (g/cm) Strength Specific Modulus (MPa/ [g/cm]) (GPa/[g/cm]) Ultimate Strain Manufacturer Bulk Metals 6061T6 Aluminum 310 69 2.71 114.4 25.5 0.17 4340 Steel 1030 200 7.83 131.5 25.5 0.19 AZ80 Magnesium 345 45 1.8 191.7 25 0.06 6AL4V Titanium 880 114 4.43 198.6 25.7 0.14 Bulk Polymers Nylon 6/6 75 2.8 1.14 65.8 Polycarbonate 65 2.4 1.2 54.2 Polyvinylchloride 40 3.1 1.44 27.8 22 2.5 0.5 1.1 2.2 0.4 Bulk Polymer Matrix Materials Hexply 8551-7 epoxy 99 Hexply 8552 epoxy CYCOM 934 epoxy 83 Hexply 954-3A cyanate 56 Derakane 411-350 vinylester 86 Ultem 2300 polyetherimide 158 Victrex 150G polyetherether-ketone 97 Fortron 0214B1 polyphenylene sulfide 86 4.1 1.27 78 3.2 0.044 Hexcel 4.7 1.3 93.1 3.6 0.017 Hexcel 4.1 1.3 63.8 3.1 0.007 Cytec 3.3 1.19 47 2.8 0.019 Hexcel 3.2 1.14 75.4 2.8 0.05 Ashland 9.3 1.51 104.6 6.2 0.03 Sabic 3.5 1.3 74.6 2.7 0.6 Victrex 4.1 1.4 61.4 2.9 0.03 Ticona Bulk Ceramics Alumina (AlO) 2600 375 3.89 668.3 96.4 Accuratus Silicon carbide (SiC) 3900 410 3.1 1258 132.2 Accuratus Silica (SiO) 1100 73 2.2 500 33.2 Accuratus Aluminum nitride (AIN) 2100 330 3.26 644.2 101.2 Accuratus Glass Fibers E-glass 3448 72 2.54 1357.5 28.3 0.048 Owens-Corning S-2 glass 4890 87 2.46 1987.8 35.8 0.057 Owens-Corning