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  

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

作　　者：周玄 王伯通 武一丁 陆文成 马铭辉 余毅磊 高光发[1] ZHOU Xuan;WANG Botong;WU Yiding;LU Wencheng;MA Minghui;YU Yilei;GAO Guangfa(School of Mechanical Engineering,Nanjing University of Science and Technology,Nanjing 210094,Jiangsu,China)

机构地区：[1]南京理工大学机械工程学院,江苏南京210094

出　　处：《爆炸与冲击》2024年第9期128-141,共14页Explosion and Shock Waves

基　　金：国家自然科学基金(12172179,11772160,11472008)。

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。The stress-strain data obtained from split Hopkinson pressure bar(SHPB)tests include both strain rate effects and structural effects,where the structural effects result in non-uniform stress in the elastic phase of the stress-strain curve.The elastic phase is a critical focus of study for materials like concrete with low sound velocity or certain metals under high strain rate loading conditions.In this paper,we focus on one-dimensional rod systems and employ one-dimensional elastic incremental wave theory to derive analytical expressions for stress-strain curves and Young’s modulus under one-dimensional stress wave conditions with linear incident waves.We investigate the effects and mechanisms of stress difference and velocity difference at both ends of the specimen on the accuracy of stress-strain curves and Young’s modulus.Furthermore,we provide a method for determining stress-strain curves and tangent Young’s modulus during the elastic phase for arbitrary incident waveforms.We analyze the influence of the incident wave slope and shape characteristics on the stress uniformity in specimens and stress-strain curves.We establish the inherent relationship between stress uniformity and experimental stress-strain curves,and clarify the relative accuracy and applicability conditions of tangent modulus and secant modulus.The results indicate that stress uniformity is a key factor affecting the accuracy of stress-strain curves and Young’s modulus.However,the accuracy of Young’s modulus is not solely dependent on the change in stress difference at both ends of the specimen;it is also related to the factors such as the incident wave slope,shape characteristics,and the elastic segment range of the specimen.An increase in the linear wave slope leads to a greater difference between the tangent modulus and the secant modulus from the actual values.For larger slopes,the accuracy of the secant modulus is higher than that of the tangent modulus.When the incident wave shape is considered as a reference,curves with low i

关 键 词：SHPB 杨氏模量 应力均匀性 应力波 

分 类 号：O347.4[理学—固体力学]