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Article(id=1246046389315154366, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246046388547596731, articleNumber=null, orderNo=null, doi=10.19636/j.cnki.cjsm42-1250/o3.2024.022, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1716825600000, receivedDateStr=2024-05-28, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1775010209635, onlineDateStr=2026-04-01, pubDate=1735056000000, pubDateStr=2024-12-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1775010209635, onlineIssueDateStr=2026-04-01, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1775010209635, creator=13701087609, updateTime=1775010209635, updator=13701087609, issue=Issue{id=1246046388547596731, tenantId=1146029695717560320, journalId=1241755870837649424, year='2024', volume='45', issue='6', pageStart='709', pageEnd='856', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1775010209451, creator=13701087609, updateTime=1775010293319, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1246046740390986227, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246046388547596731, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1246046740390986228, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246046388547596731, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=724, endPage=734, ext={EN=ArticleExt(id=1246046389554229698, articleId=1246046389315154366, tenantId=1146029695717560320, journalId=1241755870837649424, language=EN, title=Development of Ultrasonic Fatigue Test Method on Biaxial Bending, columnId=1244229834482757770, journalTitle=Chinese Journal of Solid Mechanics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

Thin-walled metal components frequently undergo multiaxial bending fatigue during operation, necessitating an experimental method to replicate loading conditions for investigating material properties. In this study, a novel biaxial bending test method using ultrasonic fatigue technology was proposed. The design involved a cruciform TC4 titanium alloy specimen tuned to a natural frequency of 20 kHz based on the principle of harmonic vibration, featuring vertically superimposed fourth-order and third-order bending modes to ensure the maximum stress region remained in the test section. Arc transitions were utilized in other regions to mitigate stress concentration. Finite element simulations and strain gauge tests were conducted to calibrate stress amplitudes in the specimens. Analysis of S-N curves, crack propagation paths, and fracture morphologies revealed the failure mechanisms of biaxial bending fatigue in the very high cycle regime under varied loading conditions. It was found that TC4 titanium alloy exhibited no fatigue limit in the very high cycle regime, showing a continuous downward trend. Owing to gradient stress distribution, biaxial bending fatigue demonstrated significantly longer fatigue life compared to uniaxial ultrasonic fatigue. Meanwhile, crack propagation behavior resembled conventional biaxial fatigue, producing H-shaped or Y-shaped cracks. Fracture surfaces exhibited a brittle characteristic in a large area of the crack initiation zone, with morphology primarily characterized by facets and tearing ridges formed through facet coalescence. In contrast to uniaxial bending fatigue, the facets in biaxial bending showed a batten pattern akin to multiaxial fatigue failure.

, correspAuthors=Dongtong Yang, Chong Wang, 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=Xinyu Wang, Dongtong Yang, Sen Tang, Beihai Huang, Bo Xu, Chong Wang, Qingyuan Wang), CN=ArticleExt(id=1246046393392017942, articleId=1246046389315154366, tenantId=1146029695717560320, journalId=1241755870837649424, language=CN, title=双轴弯曲超声疲劳实验方法, columnId=1241831201896469478, journalTitle=固体力学学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

面向航空发动机叶片等薄壁材料长寿命耐久性测试需求，本文提出了一种适合双轴弯曲疲劳试验的超声加速疲劳实验方法. 从简谐振动原理出发设计了固有频率为20 kHz的四阶和三阶弯曲垂直叠加TC4十字双轴超声疲劳试样. 通过应变片测量对该方法的振动频率和振动模态进行了测定，并结合激光传感器对超声弯曲疲劳的应力进行了标定. 开展了双轴弯曲加载下的超高周疲劳性能验证性实验. 通过对不同加载条件下的S-N曲线、裂纹扩展路径和断口形貌分析，揭示了双轴弯曲超高周疲劳失效破坏行为的特征. 结果表明，TC4钛合金在超高周阶段仍然呈持续下降趋势. 由于梯度应力分布，双轴弯曲疲劳寿命明显高于单轴超声疲劳寿命. 裂纹扩展行为与常规双轴疲劳时相似，均形成“H”型或“Y”型裂纹. 断口分析表明裂纹萌生区呈现出大面积的脆性断裂特征，形态主要表现为面片和由面片合并形成的撕裂脊. 双轴弯曲疲劳时出现的板条状刻面特征与航空发动机多轴疲劳失效实际案例特征相同，说明该方法有效的再现了实际工况下的多轴弯曲疲劳载荷加载.

, correspAuthors=阳东彤, 王宠, authorNote=null, correspAuthorsNote=
** E-mail：.
*** E-mail：.
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Chemical composition of TC4 titanium alloy

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化学元素AlVFeTi
wt（%）5.984.250.23余量
), ArticleFig(id=1246046404926354184, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246046389315154366, language=CN, label=表1, caption=

TC4化学成分

, figureFileSmall=null, figureFileBig=null, tableContent=
化学元素AlVFeTi
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双轴弯曲超声疲劳实验方法
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汪歆彧 1 , 阳东彤 1, ** , 唐森 1 , 黄北海 1 , 徐波 1, 2 , 王宠 1, 2, *** , 王清远 1, 2, 3
固体力学学报 | 研究论文 2024,45(6): 724-734
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固体力学学报 | 研究论文 2024, 45(6): 724-734
双轴弯曲超声疲劳实验方法
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汪歆彧1, 阳东彤1, ** , 唐森1, 黄北海1, 徐波1, 2, 王宠1, 2, *** , 王清远1, 2, 3
作者信息
  • 1四川大学灾变力学与工程防灾四川省重点实验室，成都，610065
  • 2四川大学深地科学与工程教育省重点实验室，成都，610065
  • 3成都大学机械工程学院力学系，成都，610106

通讯作者:

Development of Ultrasonic Fatigue Test Method on Biaxial Bending
Xinyu Wang1, Dongtong Yang1, ** , Sen Tang1, Beihai Huang1, Bo Xu1, 2, Chong Wang1, 2, *** , Qingyuan Wang1, 2, 3
Affiliations
  • 1Failure Mechanics and Engineering Disaster Prevention Key Laboratory of Sichuan Province, Sichuan University, Chengdu, 610065
  • 2Key Laboratory of Deep Underground Science and Engineering, Sichuan University, Chengdu, 610065
  • 3School of Mechanical Engineering, Chengdu University, Chengdu, 610106
出版时间: 2024-12-25 doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.022
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摘要
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面向航空发动机叶片等薄壁材料长寿命耐久性测试需求，本文提出了一种适合双轴弯曲疲劳试验的超声加速疲劳实验方法. 从简谐振动原理出发设计了固有频率为20 kHz的四阶和三阶弯曲垂直叠加TC4十字双轴超声疲劳试样. 通过应变片测量对该方法的振动频率和振动模态进行了测定，并结合激光传感器对超声弯曲疲劳的应力进行了标定. 开展了双轴弯曲加载下的超高周疲劳性能验证性实验. 通过对不同加载条件下的S-N曲线、裂纹扩展路径和断口形貌分析，揭示了双轴弯曲超高周疲劳失效破坏行为的特征. 结果表明，TC4钛合金在超高周阶段仍然呈持续下降趋势. 由于梯度应力分布，双轴弯曲疲劳寿命明显高于单轴超声疲劳寿命. 裂纹扩展行为与常规双轴疲劳时相似，均形成“H”型或“Y”型裂纹. 断口分析表明裂纹萌生区呈现出大面积的脆性断裂特征，形态主要表现为面片和由面片合并形成的撕裂脊. 双轴弯曲疲劳时出现的板条状刻面特征与航空发动机多轴疲劳失效实际案例特征相同，说明该方法有效的再现了实际工况下的多轴弯曲疲劳载荷加载.

超高周疲劳  /  双轴疲劳  /  弯曲疲劳  /  裂纹萌生  /  裂纹路径

Thin-walled metal components frequently undergo multiaxial bending fatigue during operation, necessitating an experimental method to replicate loading conditions for investigating material properties. In this study, a novel biaxial bending test method using ultrasonic fatigue technology was proposed. The design involved a cruciform TC4 titanium alloy specimen tuned to a natural frequency of 20 kHz based on the principle of harmonic vibration, featuring vertically superimposed fourth-order and third-order bending modes to ensure the maximum stress region remained in the test section. Arc transitions were utilized in other regions to mitigate stress concentration. Finite element simulations and strain gauge tests were conducted to calibrate stress amplitudes in the specimens. Analysis of S-N curves, crack propagation paths, and fracture morphologies revealed the failure mechanisms of biaxial bending fatigue in the very high cycle regime under varied loading conditions. It was found that TC4 titanium alloy exhibited no fatigue limit in the very high cycle regime, showing a continuous downward trend. Owing to gradient stress distribution, biaxial bending fatigue demonstrated significantly longer fatigue life compared to uniaxial ultrasonic fatigue. Meanwhile, crack propagation behavior resembled conventional biaxial fatigue, producing H-shaped or Y-shaped cracks. Fracture surfaces exhibited a brittle characteristic in a large area of the crack initiation zone, with morphology primarily characterized by facets and tearing ridges formed through facet coalescence. In contrast to uniaxial bending fatigue, the facets in biaxial bending showed a batten pattern akin to multiaxial fatigue failure.

very high cycle fatigue  /  biaxial fatigue  /  bending fatigue  /  crack initiation  /  crack path
汪歆彧, 阳东彤, 唐森, 黄北海, 徐波, 王宠, 王清远. 双轴弯曲超声疲劳实验方法. 固体力学学报, 2024 , 45 (6) : 724 -734 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.022
Xinyu Wang, Dongtong Yang, Sen Tang, Beihai Huang, Bo Xu, Chong Wang, Qingyuan Wang. Development of Ultrasonic Fatigue Test Method on Biaxial Bending[J]. Chinese Journal of Solid Mechanics, 2024 , 45 (6) : 724 -734 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.022
正文
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0　引言
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随着先进航空发动机对关键部件长寿命、可靠性需求的不断提升，对相关材料疲劳性能考核要求也在不断向真实服役状态靠近. 例如作为高压压气机中典型薄板构件的高压叶片，由于长期受到高速高压气动载荷的影响，容易发生高阶弯曲共振，进而引发超高周疲劳破坏，导致叶片尖角等部位断裂损毁[1-3]. 而由于叶片曲面的典型外形，其发生高阶共振时最大应力点往往处于多轴弯曲变形状态[4]. 因此了解材料在超高周（Very High Cycle Fatigue，VHCF）条件下的多轴弯曲疲劳行为变得越来越重要. 目前，对于弯曲疲劳研究常常使用悬弯、三点弯或四点弯曲疲劳试验机来完成，但由于传统疲劳实验加载频率较低且不能实现多轴加载，无法有效完成多轴弯曲变形下的超高周疲劳实验，制约了针对薄壁平板的多轴弯曲超高周疲劳研究的进展.
弯曲变形有效地体现了振动加载时的梯度应力分布，这实际上与疲劳的体积效应息息相关，同时也是薄壁构件高频振动的疲劳失效主要模式[5-7]. 针对上述问题，近年来，许多学者开展了VHCF下的弯曲疲劳试验方法研究. Xu等[8]利用电磁振动驱动器对TC17钛合金的弯曲振动VHCF进行了研究. Jiao等[9]提出了一种悬臂梁与超声弯曲实验联立研究TC17钛合金在VHCF下弯曲疲劳行为的方法. Wang等[4]设计了三点弯曲的试样模型利用超声加载装置研究了梯度结构材料在VHCF下的疲劳性能和裂纹起裂机理. 虽然不断有学者结合超声加速疲劳实验的方法研究弯曲疲劳，有效的缩短了时间成本，但目前弯曲VHCF研究仍然属于多轴单轴加载，仅在厚度方向存在弯曲应力分布梯度，最大应力处为沿正应力方向的单轴应力状态. 将多轴加载与弯曲超高周疲劳相结合的相关文献鲜有报道.
多轴疲劳的失效寿命与仅依赖单轴疲劳数据的预测结果存在较大差距. 为了更好地适应复杂的实际载荷工况，建立多轴疲劳寿命预测模型是非常重要的. 建立多轴加载的疲劳实验方法是开展多轴疲劳研究的第一步. 在圆柱体试样单轴拉压疲劳的基础上增加往复扭转载荷是最早被提出的多轴疲劳实验技术[10]. 为了更加贴近容易发生多轴疲劳的薄壁构件，随后又逐渐发展出了薄壁管拉扭多轴和十字形平面双轴加载等实验方法. 基于上述得多轴实验方法得到的实验数据推动了多轴疲劳寿命预测模型的建立和发展. 如Findley[11]提出的多轴失效准则，该准则认为疲劳断裂发生在法向和剪应力线性组合达到最大值的临界平面上.
Brown和Miller提出了以最大切应变和正应变为参数的断裂模型[12,13]. 通过这些方法获得的疲劳寿命评估结果相比于单轴寿命数据更加贴切复杂环境下的实际工况，寿命预测结果也更加准确[14].
综上所述，无论是弯曲变形还是多轴加载，更加贴近实际服役状态的疲劳研究有助于更好的开展强度分析和寿命预测. 因此开展多轴弯曲疲劳研究对于支撑薄壁类构件的设计研制具有重要意义. 为此本文旨在发展一种新的超声疲劳方法，设计适合超声谐振加载的多轴弯曲试样，采用应变测量和激光测振的方式完成对多轴弯曲超声疲劳方法的校准和测试. 并通过该方法进行了不同应力水平下得多轴弯曲疲劳试验，以探究双轴弯曲超高周疲劳的失效破坏行为.
1　实验方法
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1.1　超声加载技术
超声疲劳已被证明是开展金属超高周疲劳研究的一种有效方法. 图1为典型的超声疲劳试验平台. 它由五个主要部分组成：超声波发生器、压电换能器、位移放大器、计算机控制系统和冷却系统. 本设备能够实现20 kHz频率范围内的疲劳快速测试. 与传统加载方法相比较，超声加载大大节省了进行高周及超高周疲劳试验所需的时间.
超声疲劳的振动应力传导主要通过压电换能器、位移放大器和试样本身三个核心部件组成的谐振系统进行[15]. 因此在发展超声疲劳加载技术时需要满足达到以下几点要求：首先整个系统在给定超声频率下发生共振；其次三个核心振动部件最好分别都可以在给定的频率下产生共振，这样才能保证在部件连接处不产生过约束；最后设计试样的的几何形状使得试验段达到足够的应力水平，并保证该处应力明显高于系统其他受载部位.
1.2　双轴弯曲超声试样设计
超声疲劳的加载原理是通过压电换能器将高频的电信号转换为机械信号，从而对试样进行高频的激励，让其产生谐振，激发试样的自由模态破坏从而达到试验的目的. 因此试样的设计是实现方法创新的关键. 优化或者特异性的设计可以更加有效地模拟实际工作条件下材料地疲劳行为，从而提高实验数据的实用性和准确性. 受平面十字双轴疲劳试验方法的启发，本文在转角为零的截面进行加载使得试样产生多轴应力场. 如图2（a）所示，考虑两个分别满足20 kHz模态四阶弯曲和三阶弯曲的共振长条形薄板，将其相互垂直布置. 首先考虑到连接的需要，本文试件有两个关键的区域，一个是位移激励加载区，另一个是双轴受力的试验段，这两个区域的转角要为零所以将试样设计成多阶弯曲，考虑到其共振频率为20 kHz左右，因此较低的弯曲模态会使得试样尺寸过大，综合考虑本文采用四阶和三阶相结合的试样. 具体设计可采用有限元分析（FEA）考虑前述三个要点来开展双轴弯曲谐振疲劳试样的设计优化. 以TC4钛合金材料为例，其弹性模量为110 GPa，密度为4.5 g/cm2，泊松比为0.35. 模态分析使用线性简化的八节点六面体积分单元C3D8R，网格划分采用中性轴扫略方式. 考虑到网格密度对有限元结果精度的重要影响[16,17]，增加网格密度可以获得相对准确的结果. 然而，也需要平衡增加的网格密度和相关的计算成本. 最终，本文采用全局大小0.8 mm的网格，以优化计算效率，同时保持可接受的精度水平.
在获得初步的模态及相应几何尺寸后，需要开展谐响应分析. 如图2（b）所示，在试样加载段施加1 μm的垂直于平板方向的位移载荷激励，最大应力出现在加载区而非试验段，不利于实验的进行. 因此，有必要对试样进行优化，以实现以确保疲劳断裂发生在试样中部的试验段. 优化的路线也是在平面十字多轴试样中常见的方式，包括倒角处理和中心部位减薄[18].
本文双轴弯曲疲劳试样的厚度设计为1.2 mm，通过减薄试样试验区的横截面来增加应力水平. 为了减少其它区域的应力集中，采用了过渡角，如图3（a）所示. 有限元分析表明，优化后试样最大应力出现在试验段中心位置，在单位位移幅值加载条件下，双轴弯曲超声疲劳试样的最大应力为70.75 MPa，即应力-位移系数比为70.75 MPa/μm，如图3（b）所示. 双轴弯曲试样在加载段通过双孔螺栓连接与超声疲劳测试平台的位移放大器相连，实现纵波振动信号向横波振动信号的振动位移传递. 在加载段的应力远低于试验段应力，确保即使考虑加载孔洞的应力系数后，最大应力仍然出现在试验段. 从图3（c）可以看出，试样夹持端的位移转角为零. 最大离面位移发生在试验段中心处，此处位移、位移梯度、转角和应力均为最大值. 图4为双轴弯曲共振时沿长轴和短轴两个正交方向的应力分布图. 其中Sx和Sy方向的最大应力幅值分别为72.58 MPa和67.20 MPa，其双轴应力比值r为1.08. 从图4（d）可以看出长轴为四阶弯曲，短轴为三阶弯曲.
1.3　实验验证
本文首先使用正交布置的应变片验证低加载幅值下的试样实际应力. 由于加载为弯曲变形，因此在试验段处平板的上下两面具有90°相位差. 当上表面为最大拉应力时，下表面为最大压应力. 反之亦然. 因此分别在双轴弯曲试样的试验段正反两面的长轴和短轴方向粘贴应变片，测量这两个方向的应变幅值，根据两个方向的应变计算出应力后，由于最大应力点为双向应力状态，因此可以由Mises应力计算公式计算出应力，如图5所示.
然而，由于应变片中的金属敏感栅在测试时也会因为循环载荷发生灵敏度衰减，因此在高应力幅值的测试中采用激光测振的方法进行应力测量. 具体测量方法可参考作者已发表的单轴弯曲超声疲劳实验方法[19]. 图6包括了低应力幅值下的应变片测量结果、激光测量结果和有限元仿真结果. 由图可知，在低应力幅值段激光测量数据和应变片获得的应力数据具有很好的重合性，说明了激光测量方法的有效性. 由于激光测量为非接触测量方式，因此可以获得包括高应力幅值段的全域应力结果. 在全域范围内离散加载幅值实测的弯曲应力幅值与有限元数值计算结果接近，最大误差不超过5%，进一步验证了试样设计的合理性，在后续试验中可以根据有限元法计算的应力幅值来进行加载.
2　实验结果和分析
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基于上述发展的多轴弯曲超声疲劳实验方法，本文对TC4钛合金材料进行了双轴弯曲超高周疲劳试验. 所使用TC4钛合金微观组织为于α+β型双相钛合金，平均晶粒约为30 μm，如图7所示. 屈服强度为1.012 GPa，弹性模量E=110 GPa，其化学成分如表1所列. 实验开始前，试样表面用砂纸进行机械抛光处理，又粗及细直至2000目砂纸，以确保表面光滑无划痕. 尽管钛合金在20 kHz频率超声载荷下不会产生明显的温升现象，为了尽量接近室温实验条件[20]，在疲劳试验中，采用冷却喷枪对试样和螺纹界面进行冷却，使试样的表面温度保持在环境温度范围内. 考虑到在超高周疲劳条件下，试样的裂纹萌生阶段寿命占据大部分的疲劳寿命，裂纹扩展阶段寿命仅占疲劳总寿命的一小部分[21]. 当试样没有发生疲劳裂纹扩展时，共振频率基本保持不变，既振动稳定. 当裂纹进入快速扩展，谐振频率的突然下降，此时实验停止.
2.1　S-N曲线
基于上面提出的双轴弯曲超声实验方法和试样设计，本文开展了TC4钛合金疲劳双轴弯曲疲劳性能的测试. 并将双轴弯曲的超高周疲劳实验结果与已发表的同样经超声疲劳加载的单轴弯曲疲劳的结果进行了对比.
图8中为双轴弯曲疲劳和相同材料、相同加载频率下的单轴弯曲疲劳在超高周范围的结果. 由于TC4钛合金是一种典型的钛合金产品，成分及性能稳定，因此采用了参考文献中，单轴拉压超声疲劳的结果进行对比分析. 其中红色曲线为双轴弯曲疲劳性能拟合曲线，黄色为单轴弯曲疲劳性能拟合曲线，黑色为单轴拉压弯曲疲劳性能拟合曲线. 由图可知，无论是弯曲还是拉压，抑或是单轴及双轴，TC4钛合金在超高周范围均不存在疲劳极限，都呈现出连续下降趋势. 此外，单轴拉压的疲劳性能在108次方之前显著低于弯曲疲劳. 这是因为在相同的最大应力下，单轴拉压超声疲劳试样的整个截面承受相同水平的循环载荷幅值，而弯曲疲劳试样仅在上下表面与最大弯矩截面的两个交线处具有相同的载荷幅值，随着应力在厚度方向的梯度分布，弯曲试样试验段其他位置的应力均小于最大应力. 根据疲劳断裂所特有的微观及缺陷敏感性，造成相同的最大应力幅值下，单轴拉压疲劳相较于弯曲疲劳更容易发生疲劳断裂. 而在108次方之后，此时由于超高周疲劳裂纹萌生阶段的寿命占据了总寿命的99%以上[21]，因此初始损伤的萌生及形核长大对疲劳寿命的影响更加明显. 在弯曲载荷作用下，由于在近表面处还存在切应力的作用. 在疲劳的在疲劳裂纹萌生过程中，切应力的确扮演着关键角色. 切应力会引起位错的形成和移动，导致局部微观塑性变形的累积，最终促进疲劳裂纹在材料中的萌生和扩展[22-24]. 弯曲载荷和拉压载荷在应力分布和应力状态上是不同的. 在弯曲载荷作用下，材料表面和近表面区域通常承受最大拉应力和压应力，同时在这些区域会存在显著的剪应力. 相对而言，纯拉压载荷下，材料的整个截面承受的是均匀的拉或压应力，剪应力可能较小或者不存在，因此导致了弯曲疲劳性能低于拉压疲劳的情况. 对比双轴弯曲和单轴弯曲，可见在本文给定的幅值应力比R=-1下，两者的下降趋势接近. 但双轴弯曲的疲劳性能要优于其在单轴弯曲载荷下的性能. 这一差异被认识是由于两轴方向的应力比值为1.08，导致两轴应力水平分布相对均匀，因此与萌生相关的循环切应力要小于单轴弯曲下的循环切应力，进而萌生周期更长，疲劳性能更好. 由于该部分数据仅用于验证本文提出的双轴弯曲超声疲劳实验方法，双轴应力比对疲劳性能的影响规律需要进一步开展研究.
2.2　裂纹扩展研究
双轴弯曲疲劳与单轴疲劳弯曲的差异不仅体现在疲劳寿命曲线上，由于应力状态的不同，其裂纹扩展也不同于单轴弯曲疲劳下的简单平直的裂纹扩展路径. 如图9所示，双轴弯曲疲劳裂纹扩展路径表现出典型的双轴裂纹扩展特征，类似于传统拉扭双轴和十字平面双轴中的裂纹扩展特征[10,25-28]. 根据裂纹形态的分布规律，可将双轴弯曲的裂纹形态分为“H型”裂纹和“Y型”裂纹.
根据Griffith断裂准则，从应力场和能量场角度分析[29]，当裂纹在萌生和扩展的初始阶段，断裂过程中的裂尖塑性不明显. 由于扩展的裂纹长度有限，两个主应力相互抑制对方方向上的裂纹扩展，且各自的能量释放率G1和G2都小于裂纹扩展所需的两倍表面自由能γ（G≤2γ）. 因此当裂纹扩展时需要两方向上的主应力矢量叠加为一个方向的应力，使应力水平提高并同时增大了能量释放率G，进而有利于裂纹的扩展. 所以裂纹的走向在早期呈现出单一的裂纹路径，即单向裂纹. 而在扩展后期时，扩展的裂纹长度增大，导致两个主应力方向上的应力强度因子ΔK1和ΔK2皆大于裂纹扩展门槛值ΔKth. 因此，两个主应力方向上的裂纹可以独立开启并扩展，导致裂纹路径由单向变为双向，形成“分叉”或双向裂纹模式. 这种从单一裂纹路径到双向裂纹路径的转变是在双轴加载条件下随着裂纹的扩展而不断变化的应力状态影响的结果. 与传统双轴疲劳不同的是，由于超高周阶段对应的载荷水平较低，单一裂纹的长度占比也更加明显.
图10为双轴弯曲试样的裂纹扩展形貌. 可以看出，早期单向裂纹的扩展路径是呈现小幅锯齿状. 可能的原因是早期扩展裂纹的长度较小导致ΔK较小，这使得裂纹扩展受晶粒尺寸以及晶界的影响，当裂纹从一个晶粒或者至另一个晶粒时，由于微观晶粒差异，导致裂纹的扩展路径发生了偏折，在整体上表现出晶粒尺度的小幅锯齿状. 相反，后期的双向裂纹路径更加笔直，这可能是由于后期的裂纹长度增加（导致ΔK1和ΔK2增加），使得有较高的应力水平去推动裂纹尖端穿过晶粒. 而对于长裂纹来说，晶界阻碍相对较小，裂纹扩展受应力的影响大于受材料特性的影响. 试验表明在后续裂纹扩展过程中，随着能量释放率G的增大，单向裂纹逐渐演化为双向裂纹. 两类裂纹的形成情况如下：当裂纹扩展足够时，单向裂纹路径可发展为双向裂纹，形成“H”型裂纹（如图10（a）（b）（d）所示），而当单向裂纹的一个方向的扩展受到严重阻碍时，相对于另一个方向的裂纹可能发展较慢，可能形成双向分叉裂纹或“Y”型裂纹（如图10（a））.
2.3　断口分析
双轴弯曲的载荷特征同样可以在断口图中表现出来. 图11为双轴弯曲试样（σa=555 MPa，Nf=1.3×107）和单轴弯曲试样（σa=555 MPa，Nf=3.82×106）近萌生区域的扫描电镜形貌.
从图11（a）（b）可以看出单轴和双轴弯曲疲劳的裂纹源均来自表面，并初步向厚度方向扩展. 在超高周疲劳载荷下，解决萌生区的断口无明显塑性. 断裂方式主要为小刻面及其贯通时撕裂形成的撕裂棱. 进而呈现出在扩展过程中呈河流形状. 与TC4钛合金单轴拉压疲劳超高周疲劳断口类似，在萌生处以小刻面为主，说明TC4钛合金在超高周疲劳载荷下均是由于切应变形成的解理断口. 但是不同于单轴弯曲的是，双轴弯曲疲劳小刻面面积更大，裂纹在扩展的过程中受多轴应力的影响. 同时双轴弯曲试样的断口存在大量的台阶和不同方向的疲劳条纹，如图11（d）黄色和橙色箭头所示.
除了与单轴弯曲表现出的差异外，本文所提出双轴弯曲超声疲劳的断口特征与文献报道的事故调查钛合金涡轮盘双轴疲劳裂纹萌生处的特征相似如图12，均可见长条形解理刻面的扩展形貌，在双轴弯曲载荷作用下，由于多个方向的应力共同作用，会刺激更多解理面产生，使得沿这些解理面的破裂更为显著，从而形成长条形刻面. 在弯曲变形下最外侧表面内的应力水平要高于沿着深度方向的应力水平，这可能是造成解理刻面在平行于试件方向要长于垂直于试件平面的厚度方向的原因. 文献认为这是双轴超高周疲劳所特有的断口特征. 表面本文方法所得到的断口与发动机部件实际多轴载荷下的损伤演化行为一致.
通过以上TC4双轴弯曲超高周疲劳验证实验可知，本文提出的基于超声谐振原理设计的双轴弯曲超声谐振试样设计可应用于类似工况下的疲劳性能验证测试. 但同时需要考虑服役工况的环境条件，例如高温环境等. 这也是本方法的优势之一，因为本文提出的双轴弯曲超声加载仅在试样的一个截面处施加循环位移振幅. 除超声测试系统的位移放大器外，不与其他设备链接，这非常有利于将其置于高温炉等环境箱中开展实验. 但具体的研究工作和影响因素有待进一步研究.
3　结论
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本文研究了适合双轴弯曲疲劳试验的超声疲劳系统，并通过有限元方法设计了双轴弯曲疲劳试样. 采用应变片和激光测振对试样试验段的应力水平进行了测量和校准. 通过双轴弯曲超高周疲劳实验，验证了该实验方法的有效性. 通过对S-N曲线的分析，发现相对于双轴弯曲，单轴弯曲和单轴拉压加载的结果用于设计均偏保守. 扫描电镜断口分析表明，在超高周疲劳阶段，双轴弯曲载荷下裂纹萌生仍然是有解理断口为主，裂纹扩展行为类似于传统双轴疲劳实验，单向裂缝总是向双向裂缝演化，形成了“H型”裂纹或“Y型”裂纹.
文献
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参考文献 引证文献
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2024年第45卷第6期
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doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.022
  • 接收时间：2024-05-28
  • 首发时间：2026-04-01
  • 出版时间：2024-12-25
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  • 收稿日期：2024-05-28
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    1四川大学灾变力学与工程防灾四川省重点实验室，成都，610065
    2四川大学深地科学与工程教育省重点实验室，成都，610065
    3成都大学机械工程学院力学系，成都，610106

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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
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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