$(30)$ The ductility vs$.\%$ of cold work and tensile strength vs$.\%$ of cold work for three metals are shown below. A cylindrical specimen of cold$-$worked brass has ductility of $30\%($Specimen A$).$

$($a$)(13)$ If Specimen A$\text{'}$s cold worked diameter is $1$ in $.,$ what was its diameter before cold work? What is the tensile strength of Specimen A after cold work?

$($b$)(6)$ An annealing process is provided for the sample after cold work, what are the three stages during annealing $($in sequence$)?$

$($c$)(5)$ With annealing, material properties change compared to its cold worked properties. Indicate whether the following properties would increase or decrease with annealing:

a$.$ Ductility

b$.$ Strength

c$.$ Hardness

d$.$ Grain size $($please briefly describe the trend$)$

$($d$)(6)$ Specimen B$,$ with initial diameter $1$ in $.,$ is cold worked to a final diameter of $0\mathrm{.}8$ in$.,$ all other parameters the same as Specimen A$,$ please indicate which specimen $($your answers need to be $A$ or $B)$ has greater value of the following properties during$/$after annealing:

a$.$ Rate of nucleation

b$.$ rate of grain growth

c$.$ Grain size

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