Question$-4-40$ Marks

$1\mathrm{.}1$ Six specimens of $10$ mm diameter made from single crystal of pure Zn are prepared

and subjected to tensile testing. The tensile data is collected as shown in table below, but

unfortunately one of your fellow group mate has lost some of his data, thus incomplete

data.

a$)$ Calculate the resolved shear stress and normal stress acting on the slip plane in each

case and provide your result in table form.

b$)$ Based on the calculation in $($a$)$ explain which stress controls yielding and why.

c$)$ Use the results obtain in $($a$)$ to calculate the estimated values of A$,$ B and C$.$

$1\mathrm{.}2$ During tensile testing of a steel alloy, the strain hardening exponent was found to $0\mathrm{.}2$

and a true yield strength at $0\mathrm{.}2\%$ offset was $450$ MPa $.$ Calculate the ultimate tensile strength

of the steel alloy.

$1\mathrm{.}3$ A metal crystal $($grey$)$ is being rolled between two rollers such that the long transverse

$($LT$)$ is along $[1\frac{?}{\text{b}\text{a}\text{r}}(2)1]$ direction and short transverse $($ST$)$ is along $[\frac{?}{\text{b}\text{a}\text{r}}(1)01$ direction. During

rolling, the polycrystalline grains tend to align themselves along the rolling direction $($RD$).$

Determine what is likely to be the orientation of grains after rolling.

$(10)$