霍普金森杆实验方法中材料弹性阶段杨氏模量及其曲线准确性分析

周玄 王伯通 武一丁 陆文成 马铭辉 余毅磊 高光发

周玄, 王伯通, 武一丁, 陆文成, 马铭辉, 余毅磊, 高光发. 霍普金森杆实验方法中材料弹性阶段杨氏模量及其曲线准确性分析[J]. 爆炸与冲击. doi: 10.11883/bzycj-2023-0380
引用本文: 周玄, 王伯通, 武一丁, 陆文成, 马铭辉, 余毅磊, 高光发. 霍普金森杆实验方法中材料弹性阶段杨氏模量及其曲线准确性分析[J]. 爆炸与冲击. doi: 10.11883/bzycj-2023-0380
ZHOU Xuan, WANG Botong, WU Yiding, LU Wencheng, MA Minghui, YU Yilei, GAO Guangfa. Accuracy analysis of Young’s modulus and stress-strain curve in the elastic stage of materials using Hopkinson bar experimental method[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2023-0380
Citation: ZHOU Xuan, WANG Botong, WU Yiding, LU Wencheng, MA Minghui, YU Yilei, GAO Guangfa. Accuracy analysis of Young’s modulus and stress-strain curve in the elastic stage of materials using Hopkinson bar experimental method[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2023-0380

霍普金森杆实验方法中材料弹性阶段杨氏模量及其曲线准确性分析

doi: 10.11883/bzycj-2023-0380
基金项目: 国家自然科学基金(12172179,11772160,11472008)
详细信息
    作者简介:

    周 玄(1999- ),男,博士研究生,zhoux@njust.edu.cn

    通讯作者:

    高光发(1980- ),男,博士,教授,博士生导师,gfgao@ustc.edu.cn

  • 中图分类号: O347.4

Accuracy analysis of Young’s modulus and stress-strain curve in the elastic stage of materials using Hopkinson bar experimental method

  • 摘要: 霍普金森压杆(split Hopkinson pressure bar,SHPB)实验中试件的应力不均匀对应力-应变曲线的弹性阶段有显著影响,而弹性阶段是研究混凝土等低声速材料或高应变率加载条件下某些金属材料的关键。针对一维杆系统,利用一维弹性增量波理论,推导了线性入射波作用时应力应变和杨氏模量的解析式,研究了试件两端应力差和速度差对试件弹性阶段曲线及杨氏模量准确性的影响;进一步给出了任意形状入射波作用下试件弹性阶段曲线和切线杨氏模量的求解方法,分析了入射波斜率和形状特征对试件应力均匀性及曲线的影响。结果表明:试件弹性阶段曲线及杨氏模量的准确性与试件两端应力差的变化趋势有关,但并不完全依赖试件两端应力差,与入射波斜率、形状特征以及试件屈服强度等因素耦合相关;线性加载波斜率增大,切线模量和割线模量与实际值的差异均增大,在斜率较大时,割线模量的准确性要高于切线模量;入射波形状以正弦波为参考,曲线的初始斜率低时,切线模量的准确性高于割线模量,曲线的初始斜率高时则相反。
  • 图  1  SHPB模型示意图

    Figure  1.  SHPB model schematic diagram

    图  2  铝合金双线性本构模型

    Figure  2.  Bilinear constitutive model of aluminum alloy

    图  3  实际入射波

    Figure  3.  Actual incident wave

    图  4  仿真输入线性波

    Figure  4.  Simulated input linear waves

    图  5  “三波法”应力-应变曲线

    Figure  5.  Stress-strain curves using the three-wave method

    图  6  “二波法”应力-应变曲线

    Figure  6.  Stress-strain curves using the two-wave method

    图  7  不同上升沿时长时应力-应变曲线的拟合模量和割线模量

    Figure  7.  Fitted modulus and secant modulus of stress-strain curves with different rise times

    图  8  理想SHPB示意图

    Figure  8.  Ideal SHPB schematic

    图  9  一维应力波条件下数值模拟与理论计算的应力-应变曲线

    Figure  9.  Stress-strain curves for numerical simulation and theoretical calculation under one-dimensional stress wave conditions

    图  10  “三波法”与“二波法”计算结果

    Figure  10.  Calculation results of the three-wave method and two-wave method

    图  11  采用“三波法”计算得到的应力-应变曲线Fig.11 Stress-strain curves using the three-wave method

    图  12  采用“三波法”计算得到的三种模量无量纲时程曲线

    Figure  12.  Dimensionless time history curves for three moduli in the three-wave method

    图  13  不同波长线性入射波计算结果

    Figure  13.  Calculation results by using different wavelength of the linear incident wave

    图  14  不同波长时切线模量和无量纲应力差曲线

    Figure  14.  Tangent modulus and dimensionless stress difference curves at different wavelengths

    图  15  不同波长时切线模量与质点速度差曲线

    Figure  15.  Tangent modulus and particle velocity difference curves at different wavelengths

    图  16  正弦和线性入射波示意图

    Figure  16.  Schematic of sinusoidal and linear incident waves

    图  17  无量纲时间分别为4和1的线性波和正弦波计算结果

    Figure  17.  Calculated results for linear and sinusoidal waves at dimensionless times 4 and 1

    图  18  正弦入射波分段

    Figure  18.  Segmentation of sinusoidal incident waves

    图  19  不同形状特征入射波得出的试件两端应力差

    Figure  19.  Stress difference at both ends of specimens resulting from incident waves of different shapes

    图  20  入射波上升沿无量纲时间为4时,4种曲线的计算结果

    Figure  20.  Calculation results of four curves when dimensionless time of incident wave rise time is 4

    图  21  入射波上升沿无量纲时间为1时,4种曲线的计算结果

    Figure  21.  Calculation results of four curves when dimensionless time of incident wave rise time is 1

    图  22  无量纲时间为4时三种波形切线和割线杨氏模量曲线对比

    Figure  22.  Comparison of tangent and secant Young’s modulus curves for three waveforms at a dimensionless time of 4

    图  23  不同波形作用下试件达到准确的实验杨氏模量所需无量纲时间

    Figure  23.  Dimensionless time required for accurate determination of Young’s modulus in specimens with different waveforms

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  • 收稿日期:  2023-10-17
  • 修回日期:  2024-01-24
  • 网络出版日期:  2024-02-29

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