Question

The boron fibers are produced by chemical vapor deposition of boron onto fine tungsten wires of dW=10μm. The final wire diameter is dB=75μm. The boron coated wires are then added to an aluminum matrix with VW+B=0.35 fiber volume fraction. The Youngs Moduli of the materials are given below:

EW=410GPa

EB=379GPa

EAl=69GPa

Assuming that the rules of mixtures for binary mixtures applies to ternary systems:

Give a numerical value for the elastic modulus (Ecomp) of the composite in GPa, for loading along the length of the fibers

Ecomp=

Answer 1

1.783×10^-6

Answer 2

E=E1*V1+E2*V2+E3*V3 V1=Boron volume fraction,V2= Tungsten Volume fr. V3=AL vol. fr. V1=pi*d^2/4 *h=pi*75^2/4*h V2=pi*10^2/4*h V1/V2=56.25 V1+V2= 0.35 so V1=0.343, V2=0.007 and V3=1-0.35=0.65, E1=EB , E2=EW, E3=EAL
E=379*0.343 + 410*0.007 + 69*0.65 = 177.71 GPA