16.12 In an aligned and continuous glass fiberreinforced nylon 6,6 composite, the fibers are to carry \(94 \%\) of a load applied in the longitudinal direction. (a) Using the data provided, determine the volume fraction of fibers that will be required. (b) What will be the tensile strength of this composite? Assume that the matrix stress at fiber failure is 30 MPa (4350 psi). \begin{tabular}{lcc} \hline & Modulus of Elasticity ofensile [GPa (psi)] & Strength [MPa(psi)] \\ \hline Glass fiber & \(72.5\left(10.5 \times 10^{6}\right)\) & \(3400(490,000)\) \\\ Nylon 6,6 & \(3.0\left(4.35 \times 10^{5}\right)\) & \(76(11,000)\) \\ \hline \end{tabular}

Fiber-reinced composites are engineered materials made from two distinct components: the fibers, which provide strength and stiffness, and the matrix, which supports and binds the fibers together, transferring stress between them. The unique aspect of these composites lies in the way the fiber and the matrix interact to produce a combination of properties that is not present in the individual components.

Fibers, typically made of materials like glass, carbon, or aramid, are embedded in a matrix composed of polymers such as epoxy or nylon. The orientation and length of the fibers influence the mechanical properties of the composite material. For example, in the case of aligned and continuous fiber composites, the fibers are arranged in the same direction, which provides maximum strength and stiffness in that direction, making it ideal for applications where loads are applied longitudinally, such as in aerospace or sporting equipment.

Through the synergy between fibers and matrix, these composites achieve high tensile strength, low weight, and resistance to corrosion, factors crucial in many high-performance and advanced engineering applications.

The volume fraction of fibers, denoted as \(V_{fiber}\), is a critical factor in the design of fiber-reinforced composites. It refers to the ratio of the volume of fibers to the total volume of the composite. In the world of composite materials, the mechanical properties are significantly influenced by this ratio. By adjusting the volume fraction, engineers can tailor the composite to have specific properties suitable for its intended application.

Higher volume fractions of fibers generally lead to composites with greater strength and stiffness, as the fibers bear the majority of the load applied. However, there's a limit to this; beyond a certain point, adding more fibers can lead to issues such as poor fiber wetting, difficulty in composite fabrication, and a potential decrease in toughness. The optimal volume fraction must, therefore, be carefully calculated, which typically involves the use of the rule of mixtures as seen in the example provided where the target was to have the fibers carry 94% of a load in the longitudinal direction. The result of these calculations is critical for ensuring that the composite performs as intended under the specified conditions.

Tensile strength is a measure of a material's ability to resist tension when being pulled apart. For composites, tensile strength is one of the most important mechanical properties, particularly in applications requiring high strength-to-weight ratios, such as automotive, marine, and construction fields.

The tensile strength of a composite is derived from both its constituents, the fiber and matrix, and is influenced by factors like the type of fibers used, their arrangement, the quality of the bond between the fiber and matrix, and the volume fraction of fibers. By using the rule of mixtures, one can predict the tensile strength of the composite based on the volume fraction of the fibers and the individual strengths of the fiber and matrix materials.

In the provided example, by substituting the specific strengths and volume fraction in the rule of mixtures, the tensile strength of the glass fiber-reinforced nylon 6,6 composite can be calculated. This value is a theoretical approximation that assumes optimal bonding and load transfer between the fiber and matrix. In real-world applications, factors such as defects, fiber alignment, and the presence of voids can affect the actual tensile strength of the composite. Therefore, understanding and accurately calculating the tensile strength of composites is vital for predicting how these materials will behave under stress in practical scenarios.