A unidirectional continuous fiber composite is to be made from T300 graphite fibers in a high-modulus (HM) epoxy matrix, and the composite is to have a longitudinal coefficient of thermal expansion of zero. Using the fiber and matrix properties in Tables 3.1 and 3.2, determine the required fiber-volume fraction. Is this a practical composite? Sketch a graph showing the longitudinal CTE of the composite versus the fiber-volume fraction, and show the range of fiber-volume fractions over which the longitudinal CTE would be negative.

Table 3.1:

Table 3.2:

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Fiber Properties for Use in Chamis Simplified Micromechanics Equations (SME) Properties Units Boron HMS AS T300 KEV S-G E-G Number of fibers per end 1 10,000 10,000 3000 580 204 204 Fiber diameter in. 0.0056 0.0003 0.0003 0.0003 0.00046 0.00036 0.00036 Density lb/in. 0.095 0.070 0.063 0.064 0.053 0.090 0.090 Longitudinal modulus 10 psi 58 55.0 31.0 32.0 22 12.4 10.6 Transverse modulus 10 psi 58 0.90 2.0 2.0 0.6 124 10.6 Longitudinal shear modulus 10 psi 24.2 1.1 2.0 1.3 0.42 5.17 4.37 Transverse shear modulus 10 psi 24.2 0.7 1.0 0.7 0.22 5.17 4.37 Longitudinal Poisson's ratio 0.20 0.20 0.20 0.20 0.35 0.20 0.22 Transverse Poisson's ratio" 0.20 0.00327 0.0129 0.0125 0.00954 0.20 0.22 Heat capacity Longitudinal heat conductivity Transverse heat conductivity btu/lb/"F 0.31 0.20 0.20 0.22 0.25 0.17 0.17 btu/h/ft/F/in 22 580 580 580 1.7 21 7.5 btu/h/ft/F/in 22 58 58 58 1.7 21 7.5 Longitudinal thermal expansion coefficient 10-6 in./in./F 2.8 -0.55 -0.55 -0.55 -2.2 2.8 2.8 Transverse thermal expansion coefficient. Longitudinal tensile strength Longitudinal compression strength Shear strength 10- in./in./F 2.8 5.6 5.6 5.6 30 2.8 2.8 ksi 600 250 350 350 400 600 400 ksi 700 200 260 300 75 ksi 100 -