Rank the following iron-carbon alloys and associated microstructures from the hardest to the softest: (a) 0.25 wt\% C with coarse pearlite, (b) 0.80 wt\% \(C\) with spheroidite, (c) \(0.25 \mathrm{wt} \% \mathrm{C}\) with spheroidite, and (d) 0.80 wt\% C with fine pearlite. Justify this ranking.

Briefly explain why fine pearlite is harder and stronger than coarse pearlite, which in turn is harder and stronger than spheroidite.

The kinetics of the austenite-to-pearlite transformation obey the Avrami relationship. Using the fraction transformed-time data given here, determine the total time required for \(95 \%\) of the austenite to transform to pearlite: $$\begin{array}{cc} \hline \text {Fraction Transformed} & \text {Time (s)} \\ \hline 0.2 & 280 \\ 0.6 & 425 \\ \hline \end{array}$$

For a eutectoid steel, describe isothermal heat treatments that would be required to yield specimens having the following Brinell hardnesses: (a) \(180 \mathrm{HB}\) (b) \(220 \mathrm{HB}\), and (c) 500 HB.

Briefly cite the differences between pearlite, bainite, and spheroidite relative to microstructure and mechanical properties

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