A hybrid unidirectional E-glass/T-300 carbon/IMHS epoxy composite is to be designed to have an overall longitudinal thermal expansion coefficient of zero in order to insure the best possible thermal stability under varying service temperatures. It is also required that in order to ensure that the material will be sufficiently stiff, the volume fraction of T-300 carbon fibers is to be twice the volume fraction of the E-glass fibers.

(a) Using the properties in Tables 3.1 and 3.2 and neglecting voids in the material, determine the required volume fractions of T-300 carbon fibers and E-glass fibers.

(b) Assuming that the T-300 carbon fibers and E-glass fibers have approximately the same diameters, and that the fibers are packed in a triangular array, is the composite design of part (a) feasible?

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 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 Transverse heat conductivity btu/h/ft/F/in 22 58 58 58 1.7 21 7.5 Longitudinal thermal expansion coefficient 10- in./in./F 2.8 -0.55 -0.55 -0.55 -2.2 2.8 2.8 Transverse thermal expansion coefficient 10- in./in./F 2.8 5.6 5.6 5.6 30 2.8 2.8 Longitudinal tensile strength Longitudinal compression strength Shear strength ksi 600 250 350 350 400 600 400 ksi 700 200 260 300 75 ksi 100