Problem $1$

Data points for the monotonic stress$-$strain curve of $7075-$T$6$ aluminium during axial stress are given in Table $1.$ The elastic modulus for the material is given as $E=73100$MPa.

a$)$ Determine the plastic strain ${}_p$ for each point and plot $$ vs ${}_p$ on a log$-$log graph. Determine the constants $H$ and $n$ for the Ramberg$-$Osgood material model $($Power law hardening model$)$; see Lecture $5.$ Plot the resulting $=f()$ line and test data using a linear$-$linear graph. Determine the $0\mathrm{.}2\%$ offset yield strength $($i$.$e$.,=0\mathrm{.}002).$ Suggestion: remember definition of strain contribution $($total$,$ elastic, plastic$)$; first graph is for only plastic strain, and it could be useful to find H and n $.$

b$)$ If material properties for cyclic stress$-$strain curve are $H^{\text{'}}=970$MPa, and $n^{\text{'}}=0\mathrm{.}11,$ does this material cyclically harden or soften? Construct and compare the monotonic and cyclic stressstrain curves for strain between $0$ and $2\%.$ The $2\%$ strain means $0\mathrm{.}02m\frac{m}{m}m.$

Table $1$ Test data points for the stress$-$strain curve of $7075-$T$6$ aluminium

$\backslash$table$[[$Stress $[MPa],$Strain $[m\frac{m}{m}m]$