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

TL;DR

This paper introduces a novel framework combining experimental data, neural networks, and mathematical decomposition to accurately determine dynamic flow stress equations from split Hopkinson pressure bar tests with varied strain-rates.

Contribution

It presents a new methodology that relaxes traditional test constraints, uses ANN for data reconstruction, and applies SVD for deriving flow stress equations, improving accuracy and reliability.

Findings

ANN effectively predicts missing flow stress data

Derived flow stress equations match experimental results

Identified uncertainties in conventional methods

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.