A Phenomenological Constitutive Equation to Describe Various Flow Stress Behaviors of Materials in Wide Strain Rate and Temperature Regimes

A simple phenomenological constitutive model has been proposed to describe dynamic deformation behavior of various metals in wide strain rate, strain, and temperature regimes. The formulation of the model is, $σ=[A+B{1−exp(−Cε)}][Dln(ε̇/ε̇0)+exp(E⋅ε̇/ε̇0)][1−(T−Tref)/(Tm−Tref)]m$⁠, where $σ$ is the flow stress, $ε$ is the strain, $ε̇$ is the strain rate, $ε̇0$ is the reference strain rate, $T$ is the temperature, $Tref$ is the reference temperature, $Tm$ is the melting temperature, and $A$⁠, $B$⁠, $C$⁠, $D$⁠, $E$⁠, and $m$ are the material parameters. The proposed model successfully describes not only the linear rise of flow stress with logarithmic strain rate for many metals, but also the upturn of the flow stress at strain rate over about $104s−1$ for the case of copper. It can also describe the exponential increase in the flow stress with logarithmic strain rate for the case of tantalum, and is capable of predicting thermal softening of various metals at high as well as low temperature. The current model can be used for the practical simulation of many high-strain-rate events with improved precision and as a more rigorous comparison standard in the development of a physical model.