(Solved): 2.30 For aluminum alloy 2024-T351, the monotonic and cyclic stress-strain curves both fit Ramberg-O ...

2.30 For aluminum alloy 2024-T351, the monotonic and cyclic stress-strain curves both fit Ramberg-Osgood forms, Eqs. \( 12.12 \) and 12.54, respectively. Constants for the monotonic curve are \( E=73.1 \mathrm{GPa}, H=662 \mathrm{MPa} \), and \( n=0.070 \), and those for the cyclic curve are given in Table 12.1. (a) Plot both of these curves on the same linear-linear axes out to a strain of \( \varepsilon=0.01 \). (b) Does this material harden or soften cyclically? How do the yield strengths from the two curves compare? Equations of the Ramberg-Osgood form have this character and are thus commonly used to represent cyclic stress-strain curves: \[ \varepsilon_{a}=\frac{\sigma_{a}}{E}+\left(\frac{\sigma_{a}}{H^{\prime}}\right)^{1 / n^{\prime}} \] \[ \varepsilon=\varepsilon_{e}+\varepsilon_{p}, \quad \varepsilon=\frac{\sigma}{E}+\left(\frac{\sigma}{H}\right)^{1 / n} \]