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
