Problem $6.$ Phase Transformation $(16$ points$)$

The complete isothermal transformation diagram for an iron$-$carbon alloy of eutectoid composition is shown on the right. A specimen of such steel is heated to $\backslash (760^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and has been held at this temperature long enough to obtain a homogeneous austenitic structure. You are required to:

$(1)$ Design a heat$-$treatment procedure for each of the following four products $\backslash (\backslash$mathrm$\{$A$\},\backslash$mathrm$\{$B$\},\backslash$mathrm$\{$C$\}\backslash ),$ and D $($you need to draw processing lines in transformation diagram$)(4$ points$)$

$(2)$ Point out the phases present in each product $(4$ points$)$

$(3)$ Point out the microstructures in each product $(4$ points$)$

$(4)$ Compare mechanical properties for the following two pair materials:

a$)$ Products A $/$ B

b$)$ Products C $/$ D

in terms of hardness, strength and ductility

$(4$ points$)$

The four Products:

A$.\backslash (100\backslash \%\backslash )$ coarse pearlite

B$.\backslash (50\backslash \%\backslash )$ fine pearlite and $\backslash (50\backslash \%\backslash )$ martensite

C$.\backslash (100\backslash \%\backslash )$ martensite

D$.\backslash (100\backslash \%\backslash )$ tempered martensite