Question

Compute the longitudinal tensile strength of an aligned glass fiber-epoxy matrix composite in which the average fiber diameter and length are 0.010 mm and 2.5 mm, respectively, and the volume fraction of fibers is 0.40. Assume that thefiber-matrixbondstrengthis75MPa, the fracture strength of the fibers is 3500 MPa and the matrix stress at fiber failure is 8.0 MPa.

Answer 1

Answer:

Explanation:

Given that,

Average fiber diameter is 0.01mm

d = 0.01mm = 1 × 10^-5m

The average fiber length is 2.5mm

L = 2.5mm = 0.0025m

Volume of the fraction of fibers is 0.40

Vf = 0.40

Fiber matrix bond strengths is 75MPa

τ = 75 MPa

The fraction strength of the fibers is 3500 Mpa

σf = 3500 MPa

The matrix street fiber is 8 MPa

σm = 8 MPa

We need to find the critical fiber length and compare it to original fiber length

Ic = σf•d / 2τ

Ic = 3500 × 0.01 / 75 × 2

Ic = 0.233 mm

Since the critical fiber length of 0.233 mm is much less than the provided length of the fiber (2.5mm) , so we can use the following equation to find the longitudinal tensile strength

σcd = σf•Vf(1—Ic / 2L) + σm(1—Vf)

σcd = 3500×0.4[1—0.233/(2 × 2.5)] + 8(1—0.4)

σcd = 1400(1—0.0467) + (8 × 0.6)

σcd = 1334.67 + 4.8

σcd = 1339.47 MPa

The longitudinal tensile strength of the aligned glass fiber-epoxy matrix composite is 1339.47 MPa