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Article(id=1244239608314179905, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1244239603624952467, articleNumber=null, orderNo=null, doi=10.19636/j.cnki.cjsm42-1250/o3.2023.045, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1683129600000, receivedDateStr=2023-05-04, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774579439475, onlineDateStr=2026-03-27, pubDate=1708790400000, pubDateStr=2024-02-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774579439475, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774579439475, creator=13701087609, updateTime=1774579439475, updator=13701087609, issue=Issue{id=1244239603624952467, tenantId=1146029695717560320, journalId=1241755870837649424, year='2024', volume='45', issue='1', pageStart='1', pageEnd='144', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774579438358, creator=13701087609, updateTime=1774590203812, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244284757283025531, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1244239603624952467, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244284757283025532, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1244239603624952467, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1, endPage=15, ext={EN=ArticleExt(id=1244239609056571737, articleId=1244239608314179905, tenantId=1146029695717560320, journalId=1241755870837649424, language=EN, title=Research on Constant-Amplitude Impact Fatigue Test Method Based on Hopkinson Bar, columnId=1244229834482757770, journalTitle=Chinese Journal of Solid Mechanics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

Structural components in the fields of aviation, aerospace, weapons, and energy are often subjected to repeated impacts of small loads (or low energy). This type of load is different from the single-pulse impact of high energy and the conventional low-strain-rate fatigue, which is called impact fatigue. Because the energy-based impact fatigue test methods can only detect the relation between impact energy and fatigue life, the industrial application of impact fatigue test results in structural design and performance evaluation has been limited. Therefore, this paper focuses on exploring a new impact fatigue loading method. First, based on a brief review of the development of existing impact fatigue test methods, this paper affirms the superiority of the stress wave method based on the Hopkinson bar principle, and raises the problem of non-constant amplitude loading in impact fatigue tests. The waveform generated by the Hopkinson bar is controllable and measurable, which is beneficial to realizing constant-amplitude cyclic loading. Then, three impact fatigue loading techniques (namely the one-wave, two-wave, and three-wave techniques) based on the Hopkinson bar are proposed. The feasibility of these methods is verified through experiments, focusing on studying whether there is a non-constant amplitude loading problem caused by secondary loading. The three-wave technique is found to be the most effective impact fatigue loading method because it can achieve constant amplitude loading and obtain comprehensive test data. Finally, a constant-amplitude dynamic shear fatigue test method is developed using the three-wave technique. Impact fatigue performance tests are carried out on the TC4 titanium alloy. The test loading frequency is 0.1 Hz, and the test strain rate ranges from 6800/s to 8400/s. It is proved that this method can realize dynamic shear fatigue testing of metal materials at the strain rate level of 103/s. This study provides a new idea for the constant-amplitude impact fatigue test. By changing the forms of the specimen and the loading bars, the impact fatigue loading in other loading modes (such as tension, compression, etc.) can also be realized.

, correspAuthors=Weiguo Guo, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Kangbo Yuan, Jianhui Yang, Boli Li, Sihan Zhao, Mingjiang Wu, Songmiao Yang, Weiguo Guo), CN=ArticleExt(id=1244239620825789020, articleId=1244239608314179905, tenantId=1146029695717560320, journalId=1241755870837649424, language=CN, title=基于Hopkinson杆的恒幅冲击疲劳试验方法研究, columnId=1241831201896469478, journalTitle=固体力学学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

在航空、航天、武器和能源等领域的结构件经常会受到小载荷（小能量）的重复冲击，不同于大能量的单次冲断和常规准静态疲劳，这种载荷形式被称为冲击疲劳. 冲击疲劳性能的评估需要依赖科学有效的冲击疲劳试验结果. 多年来，受到基于能量法的冲击疲劳试验方法的限制，冲击疲劳试验结果在结构设计和性能评估方面的工业应用十分有限. 因此，本文首先基于对冲击疲劳试验方法的发展历程的简要回顾，肯定了基于Hopkinson杆原理的应力波法的优越性，明确了冲击疲劳试验中普遍存在的非恒幅加载的问题. 同时，提出了几种基于Hopkinson杆原理的冲击疲劳加载技术，并通过试验验证技术的可行性，重点关注是否存在二次加载引起的非恒幅加载问题. 最后，采用经典的分离式Hopkinson压杆技术开发了一套可实现恒幅加载的动态剪切疲劳试验方法，实现了对TC4钛合金的冲击疲劳性能测试，从而验证了新方法的有效性和可行性.

, correspAuthors=郭伟国, authorNote=null, correspAuthorsNote=
**E-mail：
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Comparison of different types of the fatigue load spectrum

, figureFileSmall=null, figureFileBig=null, tableContent=
载荷类型常规准静态疲劳载荷（正弦）谱图恒幅冲击疲劳载荷谱图非恒幅冲击疲劳载荷谱图
载荷谱图
), ArticleFig(id=1244274772801078171, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1244239608314179905, language=CN, label=表1, caption=

不同类型疲劳载荷谱图的比较

, figureFileSmall=null, figureFileBig=null, tableContent=
载荷类型常规准静态疲劳载荷（正弦）谱图恒幅冲击疲劳载荷谱图非恒幅冲击疲劳载荷谱图
载荷谱图
), ArticleFig(id=1244274772880769952, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1244239608314179905, language=EN, label=Table 2, caption=

Comparison of the advantages and disadvantages of the three loading methods

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加载方法是否二次加载优点缺点
一波法否·可避免二次加载，进而实现恒幅冲击疲劳加载；
·试验装置形式简单，有利于实现较高的加载频率		·仅可获得透射数据
二波法是—·无法避免二次加载，不建议采用
三波法否·可避免二次加载，进而实现恒幅冲击疲劳加载；
·可获得完整的入射、反射和透射波形，得到更丰富的试验数据		·试验装置形式较复杂；
·低强度的尼龙入射杆限制了加载率的大小
), ArticleFig(id=1244274772973044644, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1244239608314179905, language=CN, label=表2, caption=

三种加载方法的优缺点比较

, figureFileSmall=null, figureFileBig=null, tableContent=
加载方法是否二次加载优点缺点
一波法否·可避免二次加载，进而实现恒幅冲击疲劳加载；
·试验装置形式简单，有利于实现较高的加载频率		·仅可获得透射数据
二波法是—·无法避免二次加载，不建议采用
三波法否·可避免二次加载，进而实现恒幅冲击疲劳加载；
·可获得完整的入射、反射和透射波形，得到更丰富的试验数据		·试验装置形式较复杂；
·低强度的尼龙入射杆限制了加载率的大小
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基于Hopkinson杆的恒幅冲击疲劳试验方法研究
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袁康博 1 , 杨建辉 2 , 李泊立 2 , 赵思晗 2 , 吴名疆 2 , 杨松淼 2 , 郭伟国 2, **
固体力学学报 | 研究论文 2024,45(1): 1-15
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固体力学学报 | 研究论文 2024, 45(1): 1-15
基于Hopkinson杆的恒幅冲击疲劳试验方法研究
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袁康博1, 杨建辉2, 李泊立2, 赵思晗2, 吴名疆2, 杨松淼2, 郭伟国2, **
作者信息
  • 1西北工业大学力学与土木建筑学院，西安，710129
  • 2西北工业大学航空学院，西安，710072

通讯作者:

Research on Constant-Amplitude Impact Fatigue Test Method Based on Hopkinson Bar
Kangbo Yuan1, Jianhui Yang2, Boli Li2, Sihan Zhao2, Mingjiang Wu2, Songmiao Yang2, Weiguo Guo2, **
Affiliations
  • 1School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an, 710129
  • 2School of Aeronautics, Northwestern Polytechnical University, Xi'an, 710072
出版时间: 2024-02-25 doi: 10.19636/j.cnki.cjsm42-1250/o3.2023.045
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摘要
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在航空、航天、武器和能源等领域的结构件经常会受到小载荷（小能量）的重复冲击，不同于大能量的单次冲断和常规准静态疲劳，这种载荷形式被称为冲击疲劳. 冲击疲劳性能的评估需要依赖科学有效的冲击疲劳试验结果. 多年来，受到基于能量法的冲击疲劳试验方法的限制，冲击疲劳试验结果在结构设计和性能评估方面的工业应用十分有限. 因此，本文首先基于对冲击疲劳试验方法的发展历程的简要回顾，肯定了基于Hopkinson杆原理的应力波法的优越性，明确了冲击疲劳试验中普遍存在的非恒幅加载的问题. 同时，提出了几种基于Hopkinson杆原理的冲击疲劳加载技术，并通过试验验证技术的可行性，重点关注是否存在二次加载引起的非恒幅加载问题. 最后，采用经典的分离式Hopkinson压杆技术开发了一套可实现恒幅加载的动态剪切疲劳试验方法，实现了对TC4钛合金的冲击疲劳性能测试，从而验证了新方法的有效性和可行性.

冲击疲劳  /  Hopkinson杆  /  应力波  /  恒幅  /  动态试验技术

Structural components in the fields of aviation, aerospace, weapons, and energy are often subjected to repeated impacts of small loads (or low energy). This type of load is different from the single-pulse impact of high energy and the conventional low-strain-rate fatigue, which is called impact fatigue. Because the energy-based impact fatigue test methods can only detect the relation between impact energy and fatigue life, the industrial application of impact fatigue test results in structural design and performance evaluation has been limited. Therefore, this paper focuses on exploring a new impact fatigue loading method. First, based on a brief review of the development of existing impact fatigue test methods, this paper affirms the superiority of the stress wave method based on the Hopkinson bar principle, and raises the problem of non-constant amplitude loading in impact fatigue tests. The waveform generated by the Hopkinson bar is controllable and measurable, which is beneficial to realizing constant-amplitude cyclic loading. Then, three impact fatigue loading techniques (namely the one-wave, two-wave, and three-wave techniques) based on the Hopkinson bar are proposed. The feasibility of these methods is verified through experiments, focusing on studying whether there is a non-constant amplitude loading problem caused by secondary loading. The three-wave technique is found to be the most effective impact fatigue loading method because it can achieve constant amplitude loading and obtain comprehensive test data. Finally, a constant-amplitude dynamic shear fatigue test method is developed using the three-wave technique. Impact fatigue performance tests are carried out on the TC4 titanium alloy. The test loading frequency is 0.1 Hz, and the test strain rate ranges from 6800/s to 8400/s. It is proved that this method can realize dynamic shear fatigue testing of metal materials at the strain rate level of 103/s. This study provides a new idea for the constant-amplitude impact fatigue test. By changing the forms of the specimen and the loading bars, the impact fatigue loading in other loading modes (such as tension, compression, etc.) can also be realized.

impact fatigue  /  Hopkinson bar  /  stress wave  /  constant amplitude  /  dynamic test techniques
袁康博, 杨建辉, 李泊立, 赵思晗, 吴名疆, 杨松淼, 郭伟国. 基于Hopkinson杆的恒幅冲击疲劳试验方法研究. 固体力学学报, 2024 , 45 (1) : 1 -15 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2023.045
Kangbo Yuan, Jianhui Yang, Boli Li, Sihan Zhao, Mingjiang Wu, Songmiao Yang, Weiguo Guo. Research on Constant-Amplitude Impact Fatigue Test Method Based on Hopkinson Bar[J]. Chinese Journal of Solid Mechanics, 2024 , 45 (1) : 1 -15 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2023.045
正文
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0　引言
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在航空航天、现代武器以及能源开采等重要工程领域，舰载机的拦阻钩、飞机起落架、火炮炮管、枪械中的自动机、石油开采中的钻头钻杆和冷作模具等结构经常会受到小载荷（小能量）的重复冲击[1,2]. 这种加载形式不同于大能量的单次冲断和常规准静态疲劳，是由重复冲击载荷造成损伤累积，进而引发裂纹萌生、扩展直至失效，被称为冲击疲劳. 冲击疲劳问题的特殊之处在于不能忽视加载率对疲劳损伤和寿命的影响，高加载率可能会引起某些材料的屈服和极限强度，尤其是断裂韧性的变化，进而引发工程部件的过早失效[3]. 工程实践证明，这些结构件的失效破坏大多源于冲击疲劳，如果采用单次冲断的试验结果评估冲击疲劳性能往往对材料韧性的要求过高，评价标准过于保守[4]；而常规准静态疲劳由于没有考虑应变率效应引起的韧性下降，难以预测冲击疲劳引起的材料提前失效. 因此，冲击疲劳性能的评估需要依赖科学的冲击疲劳试验结果.
冲击是两个物体（冲击构件与试样）之间碰撞的结果，冲击力伴随着从接触点开始的应力波的传播和反射，并受到加载条件、试样几何形状和尺寸的影响[5]. 同时，试样中局部应力集中和裂纹萌生，增加了后续应力应变场测试的复杂性[6]. 由于以上复杂性和困难，目前还没有针对材料冲击疲劳性能测试的标准试验方法，已有的各种试验方法都存在其适用范围和局限性，亟待得到进一步研究. 常见的冲击疲劳实验方法大多属于能量法，可获得冲击能量（A）与冲击频次（N）之间的关系. 然而，疲劳寿命与冲击能量之间的关系曲线的力学意义并不清楚，基于能量的评价标准无法解耦载荷和变形，也难以引入加载率的影响. 同时，能量法产生的载荷谱一般不是恒幅循环加载，进而无法与单次冲断和常规准静态疲劳结果直接进行对比. 因此，基于能量法的冲击疲劳试验方法无法提供可用于结构设计的冲击疲劳强度的数据，因而其工程应用受到极大限制. 理想的力学试验方法是可以获得载荷、频率和变形率与变形、疲劳寿命等可测量之间的关系曲线，并且这些可测量与结构几何和材料参数之间没有依赖关系，进而可利用数学模型分析和预测结构在特定载荷条件下的力学响应. Hopkinson杆是一种基于应力波加载的动态性能测试方法，具有以下鲜明优势：1）应力波形可控，可通过改变加载条件，如撞击杆速度、波导杆材料、采用波形整形器等方法定量控制载荷、加载率和时间等；2）应力波形可测，可用于直接推算被测材料的应力、应变和应变率；3）可实现恒应变率加载，从而可直接与常规准静态疲劳结果进行横向对比，评估加载率对疲劳寿命的影响；4）可采用相应措施避免应力波反射引起的二次加载问题；5）可实现对应力状态的精准控制，相比能量法实现的复杂应力状态，Hopkinson杆试验中可通过设计加载方法和优化设计试样几何形式实现不同应力状态，尤其是简单应力状态下的加载，从而有利于将试验数据直接用于力学建模. 因此，可基于Hopkinson杆原理开发冲击疲劳试验方法，从而实现对材料冲击疲劳性能的测试，揭示载荷、加载率、频率和应力状态等因素对材料冲击疲劳性能的影响机制，建立计及这些关键影响因素的冲击疲劳寿命预测模型，形成一套更准确的材料冲击疲劳性能评价体系.
1　冲击疲劳试验方法的研究现状与关键问题
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依据冲击载荷的产生方式或能量转换方式，可以将冲击疲劳试验方法分为重力式、机械式、液压式和气动式等. 依据加载和测试原理则可以将现有的冲击疲劳试验方法主要分为两类：能量法和应力波法. 能量法一般采用摆锤、落锤和弹簧等机械方法直接对试样进行冲击加载，可通过检测撞击部件的速度和力传感器数据获得冲击能量或冲击力的时间历程曲线. 由于能量法可获得的信息有限，其主要以单次冲击能量作为衡量指标，可获得冲击能量（A）与疲劳寿命（N）之间的关系曲线. 应力波法主要通过对传统Hopkinson杆系统进行改进，利用冲击产生的特定构型的应力波实现对试样的多次冲击加载，通过加载杆上的应变信息推算试样的应力、应变和应变率信息，可获得一定加载率下的载荷（S）与疲劳寿命（N）之间的关系曲线. 下面我们将详细回顾已有冲击疲劳试验方法的发展历程和在工程实际测试中存在的关键问题.
1.1　典型冲击疲劳试验原理与方法
冲击疲劳试验机的基本原理可表述为：撞击部件在重力、弹簧力、液压力或气动力等作用下做加速运动，以一定的速度撞击试样，从而使试样发生位移、变形和破坏. 之后撞击部件又在机械力、液压力或气动力等的作用下返回到初始状态，如此反复运行，可实现对试样的多次冲击加载.
在各种能量法中，落锤式和摆锤式冲击疲劳试验方法的应用最为广泛. 根据公开发表的文献，最早的摆锤式冲击疲劳试验装置可追溯到1974年Radhakrishnan等的发明[7]. 与夏比冲击试验类似，利用电机将摆锤提升到一定高度，通过销钉释放摆锤冲击轭式传力机构向右运动，进而对拉伸试样施加拉伸冲击载荷. 如图1罗列了两种不同的摆锤式冲击疲劳装置示意图，图1（a）为由凸轮驱动的摆锤式装置[8]，试样固定在混凝土底座上，由固定在冲锤上的加速度计测试输出加速度历程，进而计算冲击能量. 图1（b）[9]为利用摆锤反复冲击固定于夹具上的板状弯曲试样，类似的装置还可以用来加载板状缺口试样[10].
图2展示了转盘式[11]和偏心轮式[12]冲击疲劳装置. 图2（a）中的装置包含了和试样直接串联的测力杆，通过测力杆上的载荷信息推算试样上的受力情况，和Hopkinson杆原理中的一波法具有类似的原理. 图2（b）中所示为Tanaka等[12]提出的由偏心轮带动的冲击疲劳试验方法，作者在文中提出了冲击疲劳试验机应该遵循的四项原则：1）普通疲劳试验和冲击疲劳试验都可以在该试验机上进行，就像程序和随机载荷疲劳试验机一样，它们通常有能力在基本应力模式下进行常规疲劳试验，以便能够横向比较；2）冲击由两个物体的碰撞产生；3）冲击疲劳试验机应该具有高冲击频率，从而可实现107以上的循环次数；4）试验机最好是推拉式以便获得冲击疲劳强度的基本数据. 对于加载率较低的冲击疲劳试验，可采用与常规疲劳相同的试验机，但对于加载率更高的冲击疲劳试验，就需要采用专用的冲击试验机，如落锤、摆锤和Hopkinson杆等.
Azouaoui等[13-15]采用一种曲柄连杆机构带动的冲击疲劳装置对复合材料板试样进行小能量的多次冲击，研究其冲击疲劳性能及损伤机理. 该装置采用半球形冲头，利用曲柄连杆机构将旋转运动转化为往复的平移运动，进而实现对平板试样中心点的反复加载. 采用测速仪测试冲头撞击试样的速度，并用循环计数器记录冲击次数. Froustey等[16]设计了一种飞轮冲击疲劳实验装置，如图3所示，单次冲击的应变在102-103/s之间，属于中等应变率范围. 该设备上安装了两种摆动加载装置（短摆和长摆系统），试样的一端连接砧座，另一端用螺钉固定在试样架上. 短摆系统中，力的测量是通过位于试样架和框架之间的压电传感器实现的. 长摆系统中，力由细长的测力杆上的8个应变片测量，该测量方法类似于Hopkinson杆原理.
Sun等[17]设计并实现了一种用于冲击疲劳试验的落锤试验台，试样为带缺口的三点弯试样，利用粘贴于缺口处的应变片记录缺口前缘处的应变时间历程，获得每次冲击造成的塑性变形程度，并判断裂纹萌生的循环数. Wang等[18]基于Instron 9350落锤试验机，通过改造夹具和试样实现了一种针对拉伸试样的冲击疲劳方法，冲击能量和速度可达1800 J和24 m/s，其试验装置如图4所示. 实验时，试件顶部与固定支架相连，试件底部与可垂直移动的自由低位夹具相连. 当落锤冲击连接盖板时，载荷将通过低位夹具传递到试样底部，使试样受到拉伸冲击载荷. 由于增加了额外的非标准夹具，因此不能将试验机输出的载荷值作为试样实际受载情况，因此该方法需要借助有限元计算间接获得试样上的实际载荷历程.
1.2　基于Hopkinson杆原理的应力波法
早在1985年，Tanaka等[19]就基于Hopkinson杆原理设计了冲击疲劳试验装置，该装置利用连杆机构驱动套管撞击波导杆，从而产生应力波加载中心孔试样，研究材料的冲击疲劳裂纹扩展行为. Hopkinson杆式装置可通过改变冲击条件，例如子弹和波导杆材料与几何、波形整形器等，有效地控制加载波构型. 如图5所示，我们在之前的研究中设计并搭建了一套基于Hopkinson杆装置的冲击疲劳试验装置，可实现对三点弯曲试样的冲击疲劳加载[20]. 该装置中，利用PLC控制电磁阀实现吸弹-充气-发射工作循环实现可控的循环冲击，通过弹性约束对试验装置中能量传递杆和夹具的限位，最终实现了对316L不锈钢的三点弯曲冲击疲劳加载，冲击力大小为1kN，加载速率为1.1×106MPa/s，冲击频率为0.5Hz. Hopkinson杆上实现高频重复冲击面临着入射杆上的反射波对试样进行二次加载的问题，这会使得单次冲击后产生的加载波形呈现幅值递减的多次加载.
1.3　非恒幅循环加载的问题
在冲击试验中，由于应力波在冲击构件中的反射，会产生对试样的二次或多次加载问题. 如果不对二次加载进行控制，就会出现冲击载荷（能量）逐渐衰减的多次冲击. Dumitru等[5]将这种载荷幅值逐渐衰减的多次冲击加载称为Non-stationary impact fatigue（NSIF），将每次冲击载荷都保持相等的多次冲击加载称为Stationary impact fatigue（SIF）. NSIF和SIF也就是非恒幅冲击疲劳和恒幅冲击疲劳. 表1对比了常规准静态疲劳、恒幅冲击疲劳和非恒幅冲击疲劳的载荷谱图，其中常规疲劳的单次加载脉宽远大于冲击疲劳的单次加载脉宽. 由于冲击中的应力波会在冲击构件中来回反射，或者冲击构件会存在剩余动能，如果不施加控制措施，必然会引起非恒幅冲击疲劳加载. 事实上，非恒幅冲击疲劳加载更接近于实际工程中的载荷形式，但由于循环载荷不相等，且衰减系数难以定量控制，使得试验结果难以直接应用于力学建模和预测，也不能直接与常规疲劳实验结果进行横向比较. 因此，在冲击疲劳试验中更倾向于实现恒幅冲击疲劳加载，那么就需要对二次加载进行有效控制. 在能量法中，当冲击构件与试样碰撞时会出现非恒幅冲击疲劳载荷谱，从冲击时刻到冲击构件离开试样会发生一系列重复冲击，具体取决于试样和支撑的刚度.
2　恒幅冲击疲劳试验方法探讨
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本文采用的冲击疲劳试验装置如图6所示，利用基于PLC控制电磁阀的吸弹-充气-发射工作循环系统实现子弹的循环冲击和复位. 利用两套分别位于炮管底部和炮口的激光感应器来感应子弹的位置，电磁阀A和B可分别启动子弹发射和子弹回吸复位. 安装于透射杆的伺服电机可在每次加载后推动透射杆、试样和入射杆完成复位. 整个循环过程由PLC控制器进行精确地时序控制. 在图6中分别用蓝色方框标出了PLC控制的电磁阀系统和伺服电机系统，这是本文提出的冲击疲劳装置与传统Hopkinson杆系统的显著区别.
该冲击疲劳试验方法在一次冲击中包含的步骤有：子弹发射、子弹回吸复位、以及伺服电机驱动加载杆和试样复位，因此可实现的频率取决于各个步骤所需的时间和对各步骤的时序安排. 同时，如果采用简单的加载杆形式，也会缩减装置复位所需时间，进而提高加载频率.
Hopkinson杆原理的本质在于利用细长的波导杆来传导和检测应力波，实现对试样进行加载和对试样上的载荷和变形信息进行推算. Hopkinson杆系统的设计具有很强的灵活性，可根据测试目的对波导杆的材料、几何、甚至组成进行变化，例如在动态断裂韧性的测试中，可基于一波法、二波法和三波法采用一根[21]、两根[22]甚至三根[23]波导杆来进行测试. 同时，在传统分离式Hopkinson压杆（SHPB）的基础上，也可通过设计优化合适的试样几何构型来实现不同的测试目的，例如采用双剪切试样和帽形试样来进行剪切试验[24]，采用巴西圆盘试样[25]来进行脆性材料的动态拉伸强度测试等. 为了探索可实现恒幅循环加载的试验方法，下面将分别设计和探讨三种基于Hopkinson杆的冲击疲劳加载方式，根据载荷的计算方式可分别命名为一波法、二波法和三波法.
2.1　一波法
在动态三点弯曲试验中，如果仅采用位于三点弯曲试样的后方的透射杆记录透射信号，可将这种方法称为一波法. 如图7所示为一波法的试验方法示意图，利用带有一字尖头的子弹直接冲击三点弯试样，在试样的裂纹尖端前方粘贴应变片记录试样的变形，同时透射杆上的应变片可记录每次冲击的透射波信号. 由于三点弯曲试样的透射波信号较小，且透射杆的直径较大，因此透射杆一般采用金属管，从而降低试样和透射杆的广义波阻抗的差距，使得透射信号容易被测量.
由于在冲击疲劳加载中，加载杆和试样均为弹性变形，因此，加载杆或试样上的应力σ（t）可表示为
式中，E为弹性模量，ε（t）为应变信号. 本试验中，应变片使用的惠斯通电桥采用对臂桥工作方式，从而消除非轴向应变的干扰信号，可由应变片测得的电压信号获得对应的应变信号：
式中，ΔU（t）为输出电压，K1为应变片的灵敏系数，K2为应变仪的放大系数，U0为输入直流电压. 在该方法中，由于三点弯曲试样上各点的应变不均匀，应变片粘贴处的应变率无法代表试样整体获得的加载率，因此试样上的应变片仅用于检验试样是否受到恒幅循环加载. 为衡量加载率大小，基于Hopkinson杆的一维应力波和力平衡假设，可利用透射杆上的应力率作为衡量指标，即
式中，表示对三点弯试样的加载率，σT（t）表示透射杆上的应力信号.
下面对一波法进行试验验证，采用方形截面的炮管和子弹冲击三点弯试样，有利于使子弹加载的方向保持稳定、前缘的一字尖头保持水平，进而保证撞击瞬间子弹前缘与三点弯试样实现标准的水平线接触. 透射杆采用直径为40 mm、长度为1000 mm的钢管，钢管与试样连接的一端安装了三点弯支座，将试样固定在三点弯曲支座上，测试结果如图8所示. 任意选取循环加载中的5次冲击获得的电压信号，如图8（a）所示. 由于仅采用透射杆作为加载杆，一波法实现了约1 Hz的冲击频率，冲击幅值和频率都较为稳定. 如图8（b）所示为单次冲击下试样和透射杆上的应力信号，试样上的信号表明试样仅受到单次加载，第一个加载波之后没有出现其他加载波形；透射杆上的信号显示，前三个压缩波都是依次衰减，压缩波没有叠加，也进一步证明没有出现对试样的二次加载. 根据公式（3），对透射杆上的应力信号的上升沿进行线性拟合，其斜率可衡量单次冲击的加载率，得到相应的加载率约为4.63×106 MPa/s.
2.2　二波法
在Hopkinson杆试验中，基于试样上的应力均匀性假设，也可以用入射杆上应变片检测到的入射波和反射波来推算试样受到的载荷大小，因此设计了如图9所示的二波法加载装置. 同样对三点弯曲试样进行加载，在入射杆杆端加工一字尖头，将试样固定在一字尖头和固定支座中间. 利用常规圆柱炮管发射截面为圆形的子弹，采用波形整形器获得需要的三角加载波，利用入射杆和试样上的应变片同时记录变形信号. 同样，我们搭建了二波法的试验平台，对该方法的有效性进行验证. 由于该装置不包含透射杆，且试样后部直接与固支的支座相连，因此无需增加复位装置. 采用直径为19 mm、长度为1000 mm的钢杆作为入射杆，首先对三点弯试样进行一次冲击加载，验证是否可试验二次加载，试验的典型结果如图10所示. 结果表明，该方式由于采用了固定支座，入射杆选择了高阻抗的钢杆，导致应力波在入射杆中的多次反射会继续作用在试样上，试样上的电压信号表现为多次加载波的叠加. 可见，二波法难以实现对三点弯试样的恒幅冲击疲劳加载.
2.3　三波法
借鉴了二波法试验中造成二次加载的原因，我们设计了如图11所示的三波法加载装置. 首先用可自由水平运动的透射杆代替了固定支座，使得试样在一次加载之后可以随透射杆向右运动. 同时，选用了波阻抗较小的PA66尼龙杆作为入射杆，其弹性波速仅为约1700 m/s，可以使反射波回传引起的压缩波在入射杆中缓慢传播，在试样和透射杆远离入射杆之后再次到达接近试样的入射杆端，并不对试样造成二次加载. 同样，我们搭建了三波法的试验平台对其有效性进行验证. 采用圆管炮管发射圆柱子弹，以PA66尼龙为材质的入射杆直径为26 mm，长度为1000 mm. 为方便测试，采用了直径为14 mm和高度为8 mm的圆柱试样，同样在试样上粘贴应变片验证是否实现单次加载. 透射杆采用直径为19 mm、长度为1000 mm的钢杆.
三波法的冲击疲劳循环试验结果如图12（a）所示，通过自动控制子弹撞击入射杆，得到了入射杆、透射杆和试样在16 s内连续的信号. 比较每次冲击的间隔时间和冲击幅值，可知建立的三波法装置测试的冲击间隔时间约为3 s，并且冲击幅值非常稳定. 由于三波法包含了入射杆和透射杆，并且入射杆为波速较慢的PA66尼龙杆，因此该系统实现的冲击频率仅约为1/3Hz. 为检验三波法是否可有效地避免二次加载，在图12（b）中绘制了采用0.25 MPa冲击气压时获得的单次冲击的试验曲线. 由于采用了不同阻抗的入射和透射杆，为了统一标准进行比较，分别绘制了入射杆、试样和透射杆上检测到的力信号. 可以看出，试样仅受到一次加载，证明了该方法可避免二次加载，进而可用于实现恒幅的冲击疲劳试验. 此外，试样和透射杆上的力信号吻合良好，说明该套装置整体符合力平衡假设. 同样根据公式（3），采用透射波上的应力信号推算相应的加载率，可得该方法实现的加载率为1.10×105 MPa/s.
2.4　三种方法的对比讨论
表2分别从是否二次加载、加载范围和试验数据获取几个方面比较了三种方法的优缺点. 在本文提出的三种基于Hopkinson杆原理的冲击疲劳试验方法中，一波法可避免二次加载引起的非恒幅加载；二波法由于采用了高阻抗入射杆和固定支座，固定支座使得试样不能及时远离入射杆，入射杆上的幅值逐渐衰减的反射波多次加载试样，造成对试样的非恒幅加载；三波法采用了低阻抗的尼龙杆降低入射杆中反射波的回传速度，同时使试样固定在透射杆上，在反射波回传到是试样前，透射杆上的拉伸波将试样带离原位置，成功避免了二次加载问题. 因此，建议采用一波法和三波法进行恒幅冲击疲劳试验.
在验证试验中，一波法采用了三点弯曲试样，三波法采用了压缩试样，二者均实现了稳定幅值和频率的循环加载. 一波法由于设备构成相对简单，可实现相对较高的加载频率. 三波法由于采用了低模量和强度的PA66尼龙杆，要求冲击气压幅值不能过高，限制了加载率幅值的进一步增大. 然而，和一波法相比，三波法可获得完整的入射、反射和透射波形，可用于验证力平衡假设，得到更完备的试验数据.
冲击疲劳要求可实现对试样进行小能量的多次冲击，当试样强度不是很高时，对入射波幅值要求也不高，综合以上横向比较结果，作者认为三波法在加载和数据获取方面具有更好的效果.
3　基于Hopkinson杆原理的动态剪切疲劳试验方法
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3.1　方法原理
基于三波法的基本原理，采用双剪切试样，对TC4钛合金进行动态剪切疲劳性能的测试. 具体试验设备和双剪切试样的示意图如图13所示，子弹和入射杆材料均为PA66尼龙，直径26 mm，子弹为长50 mm的圆柱子弹，入射杆长1000 mm. 透射杆材料为7075铝合金，直径26 mm，杆长1500 mm. 为了尽可能实现纯剪切的应力状态，设计并优化了双剪切试样的几何构型与尺寸. 两个对称的剪切区厚度仅为1 mm，小于三个支撑腿的厚度（5 mm），有利于剪切区的纯剪切变形. 相比2.3节中采用的大尺寸压缩试样，剪切试样的强度非常小，因此需要彻底避免PA66入射杆中应力波来回反射对剪切试验的加载. 为此，在剪切试验中将伺服电机启动的时间适当延后，保证透射杆、试样和入射杆完成复位之前，入射杆中的应力波已彻底衰减至零.
3.2　试验结果
图14所示为这套动态剪切疲劳试验装置的测试结果. 图14（a）中显示了5次连续循环加载获得的透射杆信号，可以看出，透射信号幅值具有良好的稳定性，由于增加了伺服电机的等待时间，两次加载时间间隔约为10 s，实现了约0.1 Hz的连续加载. 为了直观地验证不同冲击循环中波形的稳定性，并且证明不存在二次加载，在图14（b）中，将5次连续冲击获得的透射波绘制在一起进行比较，其中每次冲击都截取了两个波的信号，第一个为透射波，第二个为透射波在透射杆中反射回传形成的波形. 如果透射信号上的第二个波的幅值没有增大，就意味着试样没有被二次加载. 可见我们提出的这套动态剪切疲劳试验装置可以稳定地实现恒幅冲击疲劳加载.
Hopkinson杆试验的基本假设之一是变形均匀性假设，由此可推导出试样两侧的力平衡假设. 对于双剪切试样，其几何形式较为复杂，需要验证这套方法是否满足力平衡假设. 随机选择一次冲击获得的入射、反射和透射波，如图15（a）所示，可以对试样两侧是否实现力平衡进行验证. 由于采用了相同直径的入射杆和透射杆，可直接进行应力平衡的验证. 将入射波和反射波进行截取、移波和叠加，并与透射波进行比较，如图15（b）所示，二者吻合良好，证明了这套试验设备可以满足力（应力）平衡假设.
在0.048 MPa的冲击气压下，对TC4双剪切试样进行频率为0.1 Hz的循环加载，经过774次加载，试样彻底发生剪切断裂. 如图16（a）所示为在不同循环数下的应力应变曲线，可以看出，随着循环数增大，试样整体发生强化，由于冲击气压是恒定的，因此随着应力的上升，卸载应变下降. 如图16（b）通过计算不同循环数下的应变率可见，应变率整体随试样的强化有所下降，但整体仍在6800/s～8400/s的应变率范围内. 由于Hopkinson杆属于开环试验装置，因此无法实时修正加载率，因此这套设备存在着应变率在一定范围内变化的问题，并且应变率变化的程度取决于材料自身应变强化的能力. 对于本文研究的TC4钛合金来说，应变率在七百多次的加载之后下降幅度并不高，仍在103量级范围以内，因此可以得到TC4钛合金在该应变率水平下的动态剪切疲劳寿命为774次的结论.
4　结论
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本文开展了对基于Hopkinson杆原理的冲击疲劳试验方法的研究，通过与多数基于能量法的冲击疲劳试验方法的对比，发现Hopkinson杆式冲击疲劳试验方法具有波形可控可测、有利于实现恒幅循环加载等诸多优势. 因此，基于Hopkinson杆原理提出并利用试验验证了三种冲击疲劳加载技术的可行性，重点探讨各种方法避免二次加载、实现恒幅冲击疲劳加载的能力，并基于三波法搭建了一套动态剪切疲劳试验装置. 获得的重要结论如下：
（1）无论是能量法还是应力波法，都可能存在对试样的二次加载引起的非恒幅加载问题，使得每次冲击的能量和加载率不一致，实验结果难以直接应用于力学建模和性能预测中.
（2）本文提出的三种基于Hopkinson杆原理的冲击疲劳加载技术中，三波法由于采用了波速更小的尼龙入射杆，可完全避免二次加载，进而实现恒幅冲击疲劳加载. 同时，三波法可获得包括入射波、反射波和透射波的全面的试验数据，被认为是最有效的冲击疲劳加载方式.
（3）本文基于三波法搭建了一套可实现恒幅循环加载的动态剪切疲劳试验装置，并对TC4钛合金的动态剪切的冲击疲劳性能进行测试，试验加载频率为0.1 Hz，试验应变率在6800/s～8400/s范围内，动态剪切疲劳寿命为774次，证明了该方法可以实现对金属材料在103/s应变率水平的动态剪切疲劳试验.
基金
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  • 中央高校基本科研业务费专项资金(2022ZYGXZR057)
  • 国家自然科学基金项目(12072287; 12202149)
  • 中国博士后科学基金(2022M711198)
  • 广州市基础研究计划与应用项目(2023A04J1564)
文献
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2024年第45卷第1期
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文章信息
doi: 10.19636/j.cnki.cjsm42-1250/o3.2023.045
  • 接收时间：2023-05-04
  • 首发时间：2026-03-27
  • 出版时间：2024-02-25
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  • 收稿日期：2023-05-04
基金
中央高校基本科研业务费专项资金(2022ZYGXZR057)
国家自然科学基金项目(12072287; 12202149)
中国博士后科学基金(2022M711198)
广州市基础研究计划与应用项目(2023A04J1564)
作者信息
    1西北工业大学力学与土木建筑学院，西安，710129
    2西北工业大学航空学院，西安，710072

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2种不同金属材料的力学参数
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鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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