Determination of dynamic flow stress equation based on discrete experimental data: Part 2 dynamic flow stress depending on strain, strain-rate and temperature

Abstract

In this study, the effects of strain, strain-rate and temperature on the flow stress of C54400 phosphor copper alloy is investigated experimentally. Artificial neural network (ANN) is used to train the qualified data from the split Hopkinson pressure bar (SHPB) tests, obtaining finely-filled flow stress array (an order-three tensor). CANDECOM/PARAFAC (CP) decomposition method is used to decompose the flow stress array, from which both discrete and analytical expressions of flow stress equations are obtained. It is found that the analytical flow stress equation ($f{\left(\epsilon ,\dot{\epsilon },T\right)}_{\text{Ana}\_R2}$) based on CP Rank-2 decomposition agrees well with the finely-filled data from ANN. Most importantly, the thermal softening effect of the C54400 material is well reproduced by $f{\left(\epsilon ,\dot{\epsilon },T\right)}_{\text{Ana}\_R2}$. Finally, $f{\left(\epsilon ,\dot{\epsilon },T\right)}_{\text{Ana}\_R2}$ is compared with the flow stress equation ($f{\left(\epsilon ,\dot{\epsilon },T\right)}_{\text{MJC}}$) obtained by following the conventional method to determine the dynamic flow stress. Results show the excellent performance of $f{\left(\epsilon ,\dot{\epsilon },T\right)}_{\text{Ana}\_R2}$ in flow stress prediction from low to high temperatures while $f{\left(\epsilon ,\dot{\epsilon },T\right)}_{\text{MJC}}$ fails in the high temperature range. The comparison demonstrates the effectiveness of the proposed framework in the determination of dynamic flow stress equations.