Determination of dynamic flow stress equation based on discrete experimental data: Part 1 Methodology and the dependence of dynamic flow stress on strain-rate

Abstract: In this study, a framework to determine the dynamic flow stress equation of materials based on discrete data of varied (or instantaneous) strain-rate from split Hopkinson pressure bar (SHPB) experiments is proposed. The conventional constant strain-rate requirement in SHPB test is purposely relaxed to generate rich dynamic flow stress data which are widely and diversely distributed in plastic strain and strain-rate space. Two groups of independent SHPB tests, i.e. Group A (without shaper) and Group B (with shaper) were conducted on the C54400 phosphor-bronze copper alloy at room temperature, obtaining flow stress data (FSD) (two-dimensional (2D) matrix). Data qualification criteria were proposed to screen the FSD, with which qualified FSD were obtained. The qualified FSD of Group A were coarsely filled with missing data and were reconstructed by the Artificial Neural Network (ANN). As a result, finely-filled FSD of Group A were obtained, which were carefully evaluated by the qualified FSD of Group B. The evaluation proves the effectiveness of ANN in FSD prediction. Next, the finely-filled FSD from Group A were decomposed by Singular Value Decomposition (SVD) method. Discrete and analytical flow stress equation f(strain, strain-rate)_ana were obtained from the SVD results. Finally, flow stress equation (f(strain, strain-rate)_MJC) based on conventional method were established. Five uncertainties inherent in the conventional method in the determination of the flow stress equation were identified. The comparison between f(strain, strain-rate)_ana and f(strain, strain-rate)_MJC demonstrated the effectiveness and reliability of the flow stress equation obtained from the proposed method.