$3\mathrm{.}18$ A bronze alloy specimen having a diameter of $12\mathrm{.}8$ mm and a gage length of $50$ mm was tested to fracture. Stress and strain data obtained during the test are shown in Fig. P$3\mathrm{.}18.$ Determine:

$($a$)$ the modulus of elasticity.

$($b$)$ the proportional limit$.$

$($c$)$ the ultimate strength.

$($d$)$ the yield strength $(0\mathrm{.}20\%$ offset$).$

$($e$)$ the fracture stress.

$($f$)$ the true fracture stress if the final diameter of the specimen at the location of the fracture was $10\mathrm{.}5$ mm $.$

Fig. P$3\mathrm{.}18$A