A bar with a rectangular cross section that has a width of $24\mathrm{.}5$ mm $,$ a thickness of $6\mathrm{.}1$ mm and a gauge length of $75$ mm was tested in tension to fracture. Use the load$-$elongation characteristics shown in the following table to complete parts $($a$)$ through $($k$).$

$($a$)$ Plot the data as engineering stress versus engineering strain.

$($b$)$ Compute the modulus of elasticity $($by using best fit approach and show on the enlarged initial portion of the diagram$).$

$($c$)$ Determine the yield strength at a strain offset of $0\mathrm{.}002($show on the enlarged diagram$).$

$($d$)$ Determine the tensile strength $($ultimate strength$)$ of this material.

$($e$)$ What is the approximate ductility, in percent elongation $($show on the diagram$)?$

$($f$)$ Compute the modulus of resilience $($explain how it is found$).$

$($g$)$ Compute toughness $($Use numerical analysis method and give the calculations$)$

$($h$)$ Five tensile tests were carried out on the specimens cut from this material and the following ultimate forces were obtained:

$58\mathrm{.}6-59\mathrm{.}1-60\mathrm{.}2-61\mathrm{.}7-63\mathrm{.}0$ kN

Find the average ultimate strength and its standard deviation and coefficient of variation.

$($i$)$ Make a guess about the type of this material $($Mention how this prediction is made$).$ Mention the fields of usage of this material in constructions $($mention at least one reference$).$

$($j$)$ If the material is loaded up to $59$ kN and then unloaded, find the modulus, yield strength, ultimate strength and ductility of the material for the subsequent loading. Draw its stress$-$strain diagram.

$($k$)$ Draw the true stress$-$strain curve on the same page with the engineering stress$-$strain curve. NOTE: Excel program can be used.

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