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

Xianglin Huang, Q. M. Li
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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.
根据离散实验数据确定动态流动应力方程:第 1 部分 方法和动态流动应力与应变速率的关系
本研究提出了一种基于分体式霍普金森压力棒(SHPB)实验中变化(或瞬时)应变速率离散数据来确定材料动态流动应力方程的框架。为了生成在塑性应变和应变率空间中分布广泛且多样化的丰富动态流动应力数据,特意放宽了 SHPB 试验中的传统恒定应变率要求。在室温下,对 C54400 磷青铜合金进行了两组独立的 SHPB 试验,即 A 组(无整形器)和 B 组(有整形器),获得了流动应力数据(FSD)(二维(2D)矩阵)。提出了筛选 FSD 的数据鉴定标准,并根据这些标准获得了合格的 FSD。对 A 组的合格 FSD 进行缺失数据粗填充,并通过人工神经网络(ANN)进行重建。结果得到了 A 组的精细填充 FSD,并用 B 组的合格 FSD 对其进行了仔细评估。接下来,用正弦值分解(SVD)方法对 A 组的精细填充 FSD 进行分解。最后,建立了基于传统方法的流动应力方程(f(strain, strain-rate)_MJC)。确定了传统方法在确定流动应力方程时固有的五个不确定性。通过对 f(应变、应变率)_ana 和 f(应变、应变率)_MJC 的比较,证明了拟议方法得到的流动应力方程的有效性和可靠性。
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