$12\mathrm{.}32$ For completely reversed strain cycling $\backslash (\backslash$left$(\backslash$sigma$\_\{$m$\}\backslash$approx $0\backslash$right$)\backslash )$ of $7075-$T$6$ Al alloy,. This alloy has tensile properties of yield strength $469$ MPa $,$ ultimate strength $578$ MPa $,$ and $\backslash (51\backslash \%\backslash )$ reduction in area.

$($a$)$ Make a stress$-$strain plot of these data. Then fit the data to obtain a cyclic stressstrain curve of the Ramberg$-$Osgood form, Eq$.12\mathrm{.}54,$ for which $\backslash ($ E$=710\backslash$mathrm$\{$GPa$\}\backslash ).$ Add your fitted curve to the plot of the data, and comment on how well it fits the data.

$($b$)$ Representative points from a typical monotonic stress$-$strain curve for this material are given in Table P$12\mathrm{.}32($b$).$ Add these data to the stress$-$strain plot from $($a$)$ and comment on the behavior of the material.

Table P$12\mathrm{.}32($a$)$

Source: Data in $[$Leese $85].$

Table P$12\mathrm{.}32($b$)$