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Chapter 16: Problem 18

\(16.18\) (a) From the moduli of elasticity data in Table \(16.2\) for glass fiber-reinforced polycarbonate composites, determine the value of the fiber efficiency parameter for each of 20,30 , and 40 vol\% fibers. (b) Estimate the modulus of elasticity for 50 vol \% glass fibers.

Short Answer

Expert verified
The purpose of calculating the fiber efficiency parameter (η) for different fiber volume fractions in part (a) is to understand how efficiently the fibers contribute to the overall modulus of elasticity of the composite material at various fiber volume fractions. This information helps us estimate the modulus of elasticity for composites with different fiber volume fractions, such as in part (b) where we need to estimate the modulus of elasticity for a composite with 50 vol% glass fibers.

Step by step solution

01

Extract the data from Table 16.2

We need to find the required data from Table 16.2, which contains information about the modulus of elasticity for different fiber volume fractions. For this exercise, we need the following data: 1. Modulus of elasticity of the glass fibers, Ef 2. Modulus of elasticity of the polycarbonate matrix, Em 3. Modulus of elasticity of the composites, Ec, for 20, 30, and 40 vol% fibers
02

Calculate the fiber efficiency parameter η for each fiber volume fraction

Using the rule of mixtures equation, we will solve for the fiber efficiency parameter η for each fiber volume fraction in part (a): η = (Ec - Em * Vm) / (Vf * Ef) For each fiber volume fraction, we will plug in the values from Table 16.2 and solve for η.
03

Estimate the modulus of elasticity for 50 vol% glass fibers

In part (b), we need to estimate the modulus of elasticity Ec for a composite with 50 vol% glass fibers. To do this, we will assume that the fiber efficiency parameter η remains constant as the fiber volume fraction increases. We can average the fiber efficiency parameter η for the three fiber volume fractions in part (a) and use the rule of mixtures to estimate the modulus of elasticity Ec for 50 vol% glass fibers: Ec = η_avg * Vf * Ef + Em * Vm After plugging in the values, we can solve for the modulus of elasticity Ec for 50 vol% glass fibers.

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Most popular questions from this chapter

Cite the distinction between carbon and graphite.

16.30 (a) Briefly describe sandwich panels. (b) What is the prime reason for fabricating these structural composites? (c) What are the functions of the faces and the core? to be aligned parallel to the tube axis. The applied load, maximum fiber volume fracuser is allowed to input values for the foltion, elastic moduli of matrix and all fiber lowing parameters: inside and outside tube materials, densities of matrix and fiber diameters, tube length, maximum deflecmaterials, and cost per unit mass for the tion at the axial midpoint for some given matrix and all fiber materials.

16.8 A continuous and aligned fiber-reinforced composite is to be produced consisting of 30 vol \(\%\) aramid fibers and 70 vol\% of a polycarbonate matrix; mechanical characteristics of these two materials are as follows: \begin{tabular}{lcc} \hline & Modulus of Elasticity [GPa (psi)] & Tensile Strength \([\) MPa (psi)] \\\ \hline Aramid fiber & \(131\left(19 \times 10^{6}\right)\) & \(3600(520,000)\) \\ Polycarbonate & \(2.4\left(3.5 \times 10^{5}\right)\) & \(65(9425)\) \\ \hline \end{tabular} Also, the stress on the polycarbonate matrix when the aramid fibers fail is \(45 \mathrm{MPa}\) (6500 psi). For this composite, compute (a) the longitudinal tensile strength, and

16.17 Compute the longitudinal tensile strength of an aligned glass fiber- epoxy matrix composite in which the average fiber diameter and length are \(0.010 \mathrm{~mm}\left(4 \times 10^{-4}\right.\) in.) and \(2.5\) \(\mathrm{mm}(0.10\) in.), respectively, and the volume fraction of fibers is \(0.40\). Assume that (1) the fiber-matrix bond strength is \(75 \mathrm{MPa}(10,900\) \(\mathrm{psi}\) ), (2) the fracture strength of the fibers is \(3500 \mathrm{MPa}(508,000 \mathrm{psi})\), and (3) the matrix stress at fiber failure is \(8.0 \mathrm{MPa}\) (1160 psi).

16.19 For a polymer-matrix fiber-reinforced composite: (a) List three functions of the matrix phase. (b) Compare the desired mechanical characteristics of matrix and fiber phases. (c) Cite two reasons why there must be a strong bond between fiber and matrix at their interface,
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