Fillers and Reinforcements Questions and Answers

Answer: D

The Young's modulus is \(2.77 \times 10^{4}\) kg/cm².

Since the curve is linear up to the break, the modulus is the breaking stress over the breaking strain:

\[ \begin{aligned} \varepsilon &= \frac{0.03}{4} = 0.0075 \\ E &= \frac{208.3}{0.0075} = 2.78 \times 10^{4}\ \text{kg/cm}^{2} \end{aligned} \]

which is the key's \(2.77 \times 10^{4}\) within rounding. The lower options would require a larger strain or a smaller stress than the data give.

Answer: C

The keyed explanation is The surface functional groups of the filler formed hydrogen bonds with the antioxidant.

The hydroxyl groups were grafted onto the clay so that the filler would interact with the polar amide groups of Nylon 6, wetting well and transferring load across the interface. Common antioxidants, such as hindered phenols, are themselves polar and carry hydrogen-bonding groups. When they hydrogen-bond to the hydroxylated clay surface, they occupy the sites meant to bond with the nylon, so the filler-matrix interface stays weak; at the same time the antioxidant is held on the filler instead of protecting the polymer. Either way the composite is mechanically poor.

A reaction between the filler's groups and Nylon 6 is what the modification aims for, and it would improve, not weaken, the composite. Nothing in the case points to the antioxidant degrading or reacting with the nylon; the observation turns on the competition at the filler surface.

Answer: B

The profiles are P - Glass fibre ; Q - Composite ; R - Matrix.

In longitudinal loading of a unidirectional lamina with perfect bonding, fibre and matrix strain together, so the composite modulus follows the rule of mixtures:

\[ E_{c} = E_{f}V_{f} + E_{m}(1-V_{f}) \]

This lies between the fibre modulus and the matrix modulus. Glass fibre (about 70 GPa) is far stiffer than a brittle polymer matrix (a few GPa), so the steepest line P is the glass fibre, the least steep R is the matrix, and the intermediate Q is the composite.

Any option giving the composite the steepest or the shallowest line contradicts the rule of mixtures, and putting the matrix above the glass fibre reverses their stiffnesses.