(Solved): Question-1 A popular model of hardening in metals is the Ramberg-Osgood power ...

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Question-1 A popular model of hardening in metals is the Ramberg-Osgood power law. The plastic strain was related by a power law to the stress. However, this would mean that there is no clearly defined yield limit, and an arbirtrarily low applied stress always produces some plastic strain. A modified version of the Ramberg-Osgood hardening model preserves a nonvanishing elastic domain by relating the plastic strain to the difference between the current yield stress (after hardening) \( \sigma_{\mathrm{Y}} \), and the initial yield stress, \( \sigma_{0} \). The Ramberg-Osgood equation is \[ \sigma_{Y}=\sigma_{0}+K\left(\boldsymbol{\varepsilon}_{p}\right)^{m} \] Construct the stress-strain diagram when the total stress reaches \( \varepsilon=0.05 \) for an alloy with \( \mathrm{E}=350 \mathrm{GPa}, \sigma_{0}=700 \mathrm{MPa}, \mathrm{K}=900 \mathrm{MPa} \) and \( \mathrm{m}=0.21 \) * Show also the behavior of the model during unloading after reaching \( \varepsilon=0.05 \)