Physics, 20.12.2019 05:31 starr3971

Acontinuous and aligned fiber reinforced composite having a cross-sectional area of 1130 mm^2 (1.75 in.^2) is subjected to an external tensile load. if the stresses sustained by the fiber and matrix phases are 156 mpa (22,600 psi) and 2.75 mpa (400 psi), respectively; the force sustained by the fiber phase is 74,000 n (16,600 lbf); and the total longitudinal strain is 1.25 10^ -3, determine: (a)the force sustained by the matrix phase, (b)the modulus of elasticity of the compos- ite material in the longitudinal direction, and (c) the moduli of elasticity for fiber and matrix phases.

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Answer from: darkcrystal463

a) $F_m=1803.013\ N$

b) $E=53665.84\ MPa$

c) $E_f=124800\ MPa$

$E_m=2200\ MPa$

Explanation:

Given:

cross-sectional area of reinforced composite, $A=1130\ mm^2$ stress sustained by the fiber phase, $\sigma_f=156\ MPa$ force sustained by the fiber phase, $F_f=74000\ N$ Total strain on the composite, $\epsilon=1.25\times 10^{-3}$ stress sustained in the matrix phase, $\sigma_m=2.75\ MPa$

Now, the area of fiber phase:

$A_f=\frac{F_f}{\sigma_f}$

$A_f=\frac{74000}{156}$

$A_f=474.359\ mm^2$

∴Area of matrix phase:

A_m=A-A_f

A_m=1130-474.359

$A_m=655.641\ mm^2$

(a)

Now the force sustained by the matrix phase:

$F_m=\sigma_m\times A_m$

$F_m=2.75\times 655.641$

$F_m=1803.013\ N$

(b)

Total stress on the composite:

$\sigma=\frac{(F_f+F_m)}{A}$

$\sigma=\frac{(74000+1803.013)}{1130}$

$\sigma=67.082\ MPa$

Now,Modulus of elasticity of the composite:

$E=\frac{\sigma}{\epsilon}$

$E=\frac{67.082}{1.25\times 10^{-3}}$

$E=53665.84\ MPa$

(c)

Since, strain will be same in this case throughout the material.

Now the modulus of elasticity of fiber phase:

$E_f=\frac{\sigma_f}{\epsilon}$

$E_f=\frac{156}{1.25\times 10^{-3}}$

$E_f=124800\ MPa$

Now the modulus of elasticity of matrix phase:

$E_m=\frac{\sigma_m}{\epsilon}$

$E_m=\frac{2.75}{1.25\times 10^{-3}}$

$E_m=2200\ MPa$

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the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

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