III.A$.$ By using the time$-$temperature$-$transformation $($TTT$)$ diagram for a steel of eutectoid composition $($Fe$-$C alloy with $\backslash (0\mathrm{.}77\backslash$mathrm$\{$wt$\}\backslash \%\backslash )$ carbon$)$ given below, answer the following questions: Sketch the cooling path$($s$)$ on the TTT diagram provided below in answering each question and label them clearly.

$($a$-5$ pts$)$ What is meant by the so$-$called critical cooling rate $($CCR$)?$ What happens if this eutectoid steel is quenched from $\backslash (1000^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ at a cooling rate that is faster than the critical cooling rate? Trace the cooling path on the diagram. What is the crystal structure before and after the quenching?

$($b$-5$ pts$)$ What are the effects of alloying elements on the position of the boundaries on a TTT diagram? What are the engineering implications of such effects on the boundaries on a TTT diagram? Concisely elaborate on your answer.

$($c$-5$ pts$)$ A steel that is comprised of $25\backslash \%$ Pearlite, $37\mathrm{.}5\backslash \%$ Bainite and $37\mathrm{.}5\backslash \%$ Martensite is needed for a special application. Design a heat treatment by which such a steel microstructure and be created. Sketch your heat treatment protocol on the TTT diagram provided herein.

$($d$-5$ pts$)$ What do the temperatures $\backslash (\backslash$mathrm$\{$M$\}\_\{\backslash$mathrm$\{$s$\}\}\backslash )$ and $\backslash (\backslash$mathrm$\{$M$\}\_\{\backslash$mathrm$\{$f$\}\}\backslash )$ designate on the TTT diagram? What happens when a eutectoid steel is first quenched to $\backslash (\backslash$mathrm$\{$M$\}\_\{\backslash$mathrm$\{$s$\}\}>\backslash$mathrm$\{$T$\}>\backslash$mathrm$\{$Mf$\}\_\{$f$\}\backslash )$ at a rate faster than the CCR$,$ and then isothermally held for a very long time $(\backslash ($ t$>10^\{4\}\backslash$mathrm$\{$sec$\}\backslash )),$ followed by quenching to room temperature? What phases are present at room temperature?

$($e$-5$ pts$)$ What is the resultant phase or phases present in a eutectoid steel after the following heat treatment cycle: First quenched to $\backslash (\backslash$mathrm$\{$M$\}\_\{3\}>\backslash$mathrm$\{$T$\}>\backslash$mathrm$\{$MF$\}\_\{\backslash$mathrm$\{$F$\}\}\backslash )$ at a cooling rate faster than the critical cooling rate and held for $\backslash (\backslash$mathrm$\{$t$\}>10^\{4\}\backslash$mathrm$\{$sec$\}\backslash ),$ followed by reheating to $\backslash (\backslash$mathrm$\{$T$\}>727^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and held for a long time, and then quenched to $\backslash (\backslash$mathrm$\{$M$\}\_\{\backslash$mathrm$\{$s$\}\}<mi>\backslash </mi>$mathrm$\{$T$\}<mi>\backslash </mi>$mathrm$\{$TN$\}\backslash )$ at a rate faster than the CCR $,$ and held for $\backslash (\backslash$mathrm$\{$t$\}>10^\{4\}\backslash )$ seconds and then quench to room temperature.

$($f$-5$ pts$)$ What are the major characteristics of the eutectoid and martensitic transformations? Briefly compare and contrast them. ANSWER ALL OF THE QUESTIONS