A unified mechanics theory-based model for temperature and strain rate dependent proportionality limit stress of mild steel

Strain rate and temperature dependent elastic limit of mild steel is investigated by developing a dislocation incipient motion-based proportionality limit stress model. Temperature effect on strain energy of an edge dislocation is modeled by using unified mechanics theory. Unified mechanics theory-based index, called thermodynamic state index, is used to model thermally assisted degradation of strain energy. Kinetic energy due to thermal vibrations is added to the kinetic energy of an accelerating dislocation. It is shown that, prior to the onset of observable plastic slip at the macrolevel, dislocation incipient motion is dominated by inertial effects within the elastic limit, rather than drag controlled mechanisms, that are normally observed in the post-yield response of metals. A new model for temperature and strain rate dependent critical shear stress is derived. Validation of the derived model with experimental data and comparison of model predictions with Johnson-Cook model predictions for mild steel at zero plastic strain shows that the micromechanics of rate and temperature dependence of the elastic response of mild steel involve inertia dominated mechanism at higher temperatures.