a. From the rule of mixtures, estimate the density of the composite. b. For the

Question

a. From the rule of mixtures, estimate the density of the composite.

b. For the overall composite, compute the stiffness in the transverse direction (this is to say in that stress is ? to the fibre alignment).

c. Compute the stiffness in the longitudinal direction (this is to say that stress is parallel to the fibres)

d. Assume that the component has a (uniform) cross sectional area of 500 mm2 , and is subjected to a longitudinal (parallel to the fibers) load of 47.5 kN. What is the percentage of the 47.5 kN load carried by the aluminum matrix, and what is the percentage of the 47.5 kN load carried by the Borsic fibers?

e. Comment on the difference in longitudinal stiffness versus transverse stiffness (“E” = elastic modulus) as fiber fraction is changed (Hint – refer to problems 15C-7 and 15C-8 from Problem Set #3; one of the configurations is more sensitive to fiber fraction change)

f. Instead of long fibers aligned in one direction, what is the stiffness of the composite if fibers were to be randomly and uniformly distributed within a specific plane, or within a 3D space?

Explanation / Answer

Given, Volume fraction of Fibre is 44% (let it be V2), Hence volume fraction of Aluminium is 56% (Let it be V1)

a) Density of composite: Dc = D1V1 + D2V2 ( D- density, V- volume)

                                            = (2.7*0.56) + (2.36*0.44) = 1.512+1.0384 = 2.55 g/cu.cm

b) stifness in traverse direection : Ec = (E1*E2)/( E1*V2 + E2*V1)

                                                         = (69*379)/(30.36+212.54) = 107.8 GPa

c) stiffness of the composite: Ec = E1V1+E2V2

                                                   = (69*0.56) + (379*0.44) = 38.64+166.76 = 205.4 GPa

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