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A particle-reinforced composite has its reinforcement in a simple cubic array of spherical particles as shown in Figure 6

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A particle-reinforced composite has its reinforcement in a simple cubic array of spherical particles as shown in Figure 6.45. Determine (a) the relationship between the particle center-to-center spacing, s, the particle diameter, d, and the particle volume fraction, υp, (b) the maximum particle packing fraction, υpmax, and (c) the yield strength and the Young’s modulus for a composite having the maximum particle volume fraction υp = υpmax and constituent material properties Ep = 10.2 × 106 psi, Em = 0.25 × 106 psi, Sym = 5 × 103 psi, and bonding angle θ = 45°.