Formula sheet:

Stress: $=\frac{dF}{dA},{}_{\text{a}\text{v}\text{e}}=\frac{F}{A},=\frac{dV}{dA},{}_{\text{a}\text{v}\text{e}}=\frac{V}{A}$

Strain: $lon=\frac{du}{dx},lon=\frac{}{L_0},lon=ln(\frac{L_f}{L_0}),=\frac{du}{dy},=\frac{x}{Y}$

Mechanical Properties: $=Elon,=G,$

$u=-lo\frac{n_{\text{l}\text{a}\text{t}}}{}lo{n}_{\text{l}\text{o}\text{n}\text{g}},G=\frac{E}{2(1+)}$

$u,lon=T$

Axial loading: $={\displaystyle \underset{x=0}{\overset{x=L}{}}}du,={\displaystyle \underset{x=0}{\overset{x=L}{}}}\frac{F(x)dx}{E(x)A(x)},=\frac{FL}{EA},=LT,k=\frac{EA}{L}=\frac{1}{f}$

Problem $1.$ Review the following stress$-$strain diagrams from the tensile tests on

four different materials A$,$ B$,$ C$,$ and D$.$ Please identify: $(6$ points$)$

$($a$)$ Which material has the highest Young's modulus?

$($b$)$ Which material has the highest yielding stress?

$($c$)$ Which material experiences the most strain in yielding region?

$($d$)$ Which material experiences the most strain in strain$-$hardening region?

$($e$)$ Which material experiences the most strain in necking region?

$($f$)$ Which material has the highest fracture stress?