Question

.If aligned and continuous carbon fibers with a diameter of 6.90 micron are embedded within an epoxy, such that the bond strength across the fiber-epoxy interface is 17 MPa, and the shear yield strength of the epoxy is 68 MPa, compute the minimum fiber length, in millimeters, to guarantee that the fibers are conveying an optimum fraction of force that is applied to the composite. The tensile strength of these carbon fibers is 3960 MPa.

Answer 1

the required minimum fiber length is 0.80365 mm

Step-by-step explanation:

Given the data in the question;

Diameter D = 6.90 microns = 6.90 × 10⁻⁶ m

Bond strength ζ = 17 MPa

Shear yield strength ζ
`_y` = 68 Mpa

tensile strength of carbon fibers
`6t_{fiber` = 3960 MPa.

To determine the minimum fiber length we make use of the following relation;

L = (
`6t_{fiber` × D) / 2ζ

we substitute our given values into the equation;

L = ( 3960 × 6.90 × 10⁻⁶) / (2 × 17 )

L = 0.027324 / 34

L = 0.000803647 m

L = 0.000803647 × (1000) mm

L = 0.80365 mm

Therefore, the required minimum fiber length is 0.80365 mm