Derive the rule-of-mixtures equation for the coefficient of thermal expansion ?2. Compare the variation of ?2 based on rule-of-mixtures & alternative rule with fiber volume fraction for graphite-reinforced material.

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Use the following numerical values for sample calculation: (vf = 0.6) E = 233 GPa V = v3 = 0.200 G =G3=8.96 GPa a = -0.540 106/K E = E = 23.1 GPa 3 = 0.400 G23 = 8.27 GPa = = 10.10 106/K E = 4.62 GPa am = 41.4 10-6/K v = 0.360 Use the following numerical values for sample calculation: (vf = 0.6) E = 233 GPa V = v3 = 0.200 G =G3=8.96 GPa a = -0.540 106/K E = E = 23.1 GPa 3 = 0.400 G23 = 8.27 GPa = = 10.10 106/K E = 4.62 GPa am = 41.4 10-6/K v = 0.360