Estimate the upper limit for the specific stiffness of a composite composed of l

Question

Estimate the upper limit for the specific stiffness of a composite composed of large tungsten particles (volume fraction of 0.33) within a silver matrix given the specific gravities of W and Ag are 19.3 and 10.4 and the moduli of elasticity are 407 GPa and 72 GPa for W and Ag, respectively. We need to manufacture a discontinuous, aligned carbon fiber-epoxy matrix composite with a longitudinal tensile strength of 500 MPa. Calculate the volume fraction of fibers necessary given the following information: The average fiber diameter and length are 0.015 mm and 1.0 mm, respectively The fiber fracture strength is 4.2 GPa The fiber-matrix bond strength is 27 MPa The matrix stress at composite failure is 7.2 MPa

Explanation / Answer

two approaches can be used,

Easy approach for calculation , (407)/ (19.3) * 0.33 + (72/10.4)*(0.66)

= 11.52 Gpa

2) l

Fracture = 4.2 Gpa

Failure critical = 4.2*10^3 * ( d/2l) = 4.2*10^3 * 0.015/2 = 31.5 Mpa

27 = 7.2*x + 31.5*(1-x)

x = 0.185

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