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Readme [11.4K]
3 years ago
14

Is it possible to produce a continuous and oriented aramid fiber–epoxy matrix composite having longitudinal and transverse modul

i of elasticity of 35 GPa (5 × 106psi) and 5.17 GPa (7.5 × 105psi), respectively? Why or why not? Assume that the elastic modulus of the epoxy is 3.4 GPa (4.93 × 105psi).The value of Efor aramid fibers is 131 GP

Physics
1 answer:
gregori [183]3 years ago
5 0

Answer:

It is not possible to produce continued and oriented fiber.

Explanation:

To solve the problem it is necessary to take into account the concepts related to Fiber volume ratio. The amount of fiber in a fiber reinforced compound corresponds directly to the mechanical properties of the compound. Given the fiber volume fraction, the theoretical elastic properties of a compound can be determined. The elastic modulus of a compound in the fiber direction of a unidirectional compound can be calculated using the following equation:

E = (1-V_f)E_m+V_fE_f

Where,

E is the longitudinal modulus of Elasticity

V_f is the fiber volume ratio

E_m is the elastic modulus of the matrix

E_f is the elastic modulus of the fibers

We need to consult the table of characteristics of Fibers and Reinforcements of Materials, in which they specify that the modulus of elasticity of the aramid fiber-epoxy is

E_f = 131Gpa

Moreover from the statement,

E = 35Gpa

E_m = 3.4Gpa

Replacing in the previous equation,

35 = 3.4 (1-V_f)+131V_f

V_f = 0.25 \rightarrow longitudinal

To make the comparison we now calculate the Fiber volume ratio through the transverse elastic modulus,

E = \frac{E_mE_f}{(1-V_f)E_f+V_fE_f}

Our values are given in this case as:

E = 5.17Gpa\\E_m = 3.4Gpa \\E_f = 131Gpa

Replacing,

5.17 = \frac{3.4*131}{(1-V_f)(131)+V_f*3.4}

V_f = 0.351 \rightarrow transversal

From both cases it is possible to conclude that it is not possible to produce a fiber of the specified material in a continuous and oriented manner, as long as the volume fraction is different in the different cases.

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