Problem $4$: Controlling the Eutectic Reaction

A $1080$ steel was austenitized at $\backslash (775^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ for one hour and quenched to $\backslash (500^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ until it isothermally transformed at $\backslash (500^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

Figure $12-20.$ The phase$-$temperature transformation diagram for $1080$ steel.

Figure $12-23.$ The effect of transformation temperature on the properties of eutectoid $(1080)$ steel.

a$)$ How long must the austenite be held at $\backslash (500^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to complete the transformation?

b$)$ Describe the transformation, in reaction form, that takes place at $\backslash (500^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$

c$)$ Graphically describe in Figure $12-20$ the heat treatment until its completion.

d$)$ What is the expected microstructure $(\backslash (\backslash$mathrm$\{$P$\}=\backslash )$ Pearlite or $\backslash (\backslash$mathrm$\{$B$\}=\backslash )$ Bainite$)$ and hardness $($HRC$)?$

e$)$ What are the expected tensile strength and $\backslash \%$ elongation? $($see Figure $12-23)$