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Article(id=1246031926096675464, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246031922707677827, articleNumber=null, orderNo=null, doi=10.19636/j.cnki.cjsm42-1250/o3.2024.012, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1710086400000, receivedDateStr=2024-03-11, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1775006761334, onlineDateStr=2026-04-01, pubDate=1724515200000, pubDateStr=2024-08-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1775006761334, onlineIssueDateStr=2026-04-01, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1775006761334, creator=13701087609, updateTime=1775006761334, updator=13701087609, issue=Issue{id=1246031922707677827, tenantId=1146029695717560320, journalId=1241755870837649424, year='2024', volume='45', issue='4', pageStart='427', pageEnd='564', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1775006760527, creator=13701087609, updateTime=1775006830786, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1246032217470779944, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246031922707677827, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1246032217470779945, tenantId=1146029695717560320, journalId=1241755870837649424, issueId=1246031922707677827, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=488, endPage=495, ext={EN=ArticleExt(id=1246031926327362188, articleId=1246031926096675464, tenantId=1146029695717560320, journalId=1241755870837649424, language=EN, title=Ultra-high Cycle Fatigue Life Prediction Considering Loading Frequency, columnId=1244229834482757770, journalTitle=Chinese Journal of Solid Mechanics, columnName=Research Paper, runingTitle=null, highlight=null, articleAbstract=

Ultra-high cycle fatigue experiments can be conducted using traditional testing methods such as electromagnetic vibration (30-3000 Hz) and ultrasonic vibration (20 kHz). Differences in fatigue life for the same material may arise when tested under varying loading frequencies. To fully utilize the ultra-high cycle fatigue life data obtained from different testing systems, the impact of loading frequency on the ultra-high cycle fatigue life of materials needs to be studied imperatively. This paper presents novel prediction models for ultra-high cycle fatigue life, taking into account loading frequency. The models incorporate the crack initiation life prediction model based on Tanaka's dislocation theory and the Paris crack growth life prediction model. The influence of loading frequency is integrated into effective stress and fatigue strength. The proposed models are verified using available very high cycle fatigue test data for titanium alloy TC17 and nickel-based superalloy GH4169 under different loading frequencies. The results show that the models proposed in this work can reasonably characterize the ultra-high cycle fatigue test data of materials under varying loading frequencies, establishing the correlation of fatigue life data under different loading frequencies.

, correspAuthors=Zhen Zhang, 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=Lili Shu, Yonghui Chen, Kai Pan, Qiangang Xu, Kai Guo, Zhen Zhang), CN=ArticleExt(id=1246031932245525271, articleId=1246031926096675464, tenantId=1146029695717560320, journalId=1241755870837649424, language=CN, title=考虑加载频率的超高周疲劳寿命预测, columnId=1241831201896469478, journalTitle=固体力学学报, columnName=研究论文, runingTitle=null, highlight=null, articleAbstract=

超高周疲劳试验可以通过传统的电磁振动（30-3000 Hz）、超声振动（20 kHz）等测试方法实现. 对于同一材料，采用不同加载频率的测试方法得到的疲劳寿命可能存在差异. 为了充分利用不同测试系统得到的超高周疲劳寿命数据，关于考虑加载频率的超高周疲劳寿命预测方法亟待研究. 本文结合基于Tanaka的位错理论的裂纹萌生寿命预测模型以及Paris裂纹扩展的寿命预测模型，引入频率对有效应力及疲劳强度的影响，得到超高周疲劳寿命预测模型. 利用本文提出的模型，针对钛合金TC17和镍基高温合金GH4169在不同加载频率下的超高周疲劳试验数据进行寿命预测验证，结果显示本文模型能较好地表征不同加载频率下材料的超高周疲劳特性. 本文模型建立了不同加载频率下的疲劳寿命数据的关联.

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** E-mail：.
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journalId=1241755870837649424, articleId=1246031926096675464, language=CN, label=图2, caption=Fatigue life prediction of TC17, figureFileSmall=MdqJCGLABLDIJg0LPpwGxA==, figureFileBig=ajQL39H9ObV+Q/waDfe34A==, tableContent=null), ArticleFig(id=1246042378151248323, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031926096675464, language=EN, label=Table 1, caption=

Mechanical properties of nickel-based alloy GH4169 at room temperature[17]

, figureFileSmall=null, figureFileBig=null, tableContent=
0.2%屈服应（MPa）拉伸强度（MPa）伸长率（%）收缩率（%）维氏硬度（kgf/mm2）
122013902339.5426
), ArticleFig(id=1246042378230940106, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031926096675464, language=CN, label=表1, caption=

高温镍基合金GH4169室温下力学性能[17]

, figureFileSmall=null, figureFileBig=null, tableContent=
0.2%屈服应（MPa）拉伸强度（MPa）伸长率（%）收缩率（%）维氏硬度（kgf/mm2）
122013902339.5426
), ArticleFig(id=1246042378327409102, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031926096675464, language=EN, label=Table 2, caption=

Fitting results of frequency correction parameters of GH4169

, figureFileSmall=null, figureFileBig=null, tableContent=
修正参数ab
参数值-5.23×10-5-4.06×10-4
), ArticleFig(id=1246042378394517972, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031926096675464, language=CN, label=表2, caption=

GH4169频率修正参数拟合结果

, figureFileSmall=null, figureFileBig=null, tableContent=
修正参数ab
参数值-5.23×10-5-4.06×10-4
), ArticleFig(id=1246042378470015450, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031926096675464, language=EN, label=Table 3, caption=

Mechanical properties of titanium alloy TC17 at room temperature[21]

, figureFileSmall=null, figureFileBig=null, tableContent=
0.2%屈服应力（MPa）拉伸强度（MPa）弹性模量（GPa）密度（kg/m3）维氏硬度（kgf/mm2）
1060.51108.5111.54680356
), ArticleFig(id=1246042378562290144, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031926096675464, language=CN, label=表3, caption=

钛合金TC17室温下基本力学性能[21]

, figureFileSmall=null, figureFileBig=null, tableContent=
0.2%屈服应力（MPa）拉伸强度（MPa）弹性模量（GPa）密度（kg/m3）维氏硬度（kgf/mm2）
1060.51108.5111.54680356
), ArticleFig(id=1246042378671342052, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031926096675464, language=EN, label=Table 4, caption=

Fitting results of frequency correction parameters of TC17

, figureFileSmall=null, figureFileBig=null, tableContent=
修正参数ab
参数值-4.32×10-53.50×10-3
), ArticleFig(id=1246042378755228135, tenantId=1146029695717560320, journalId=1241755870837649424, articleId=1246031926096675464, language=CN, label=表4, caption=

TC17频率修正参数拟合结果

, figureFileSmall=null, figureFileBig=null, tableContent=
修正参数ab
参数值-4.32×10-53.50×10-3
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考虑加载频率的超高周疲劳寿命预测
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舒力力 1 , 陈永辉 3 , 潘凯 4 , 徐乾罡 1 , 郭凯 1 , 张桢 1, 2, **
固体力学学报 | 研究论文 2024,45(4): 488-495
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固体力学学报 | 研究论文 2024, 45(4): 488-495
考虑加载频率的超高周疲劳寿命预测
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舒力力1, 陈永辉3, 潘凯4, 徐乾罡1, 郭凯1, 张桢1, 2, **
作者信息
  • 1华中科技大学航空航天学院，工程力学系，武汉，430074
  • 2华中科技大学工程结构分析与安全评定湖北省重点实验室，武汉，430074
  • 3中国飞机强度研究所强度与结构完整性全国重点实验室，西安，710065
  • 4中国航空研究院，北京，100012

通讯作者:

** E-mail：.
Ultra-high Cycle Fatigue Life Prediction Considering Loading Frequency
Lili Shu1, Yonghui Chen3, Kai Pan4, Qiangang Xu1, Kai Guo1, Zhen Zhang1, 2, **
Affiliations
  • 1Department of Engineering Mechanics, School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan, 430074
  • 2Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, Wuhan, 430074
  • 3National Key Laboratory of Strength and Structural Integrity, Aircraft Strength Research Institute of China, Xi'an, 710065
  • 4Chinese Aeronautical Establishment, Beijing, 100012
出版时间: 2024-08-25 doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.012
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摘要
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超高周疲劳试验可以通过传统的电磁振动（30-3000 Hz）、超声振动（20 kHz）等测试方法实现. 对于同一材料，采用不同加载频率的测试方法得到的疲劳寿命可能存在差异. 为了充分利用不同测试系统得到的超高周疲劳寿命数据，关于考虑加载频率的超高周疲劳寿命预测方法亟待研究. 本文结合基于Tanaka的位错理论的裂纹萌生寿命预测模型以及Paris裂纹扩展的寿命预测模型，引入频率对有效应力及疲劳强度的影响，得到超高周疲劳寿命预测模型. 利用本文提出的模型，针对钛合金TC17和镍基高温合金GH4169在不同加载频率下的超高周疲劳试验数据进行寿命预测验证，结果显示本文模型能较好地表征不同加载频率下材料的超高周疲劳特性. 本文模型建立了不同加载频率下的疲劳寿命数据的关联.

加载频率  /  超高周疲劳  /  寿命预测

Ultra-high cycle fatigue experiments can be conducted using traditional testing methods such as electromagnetic vibration (30-3000 Hz) and ultrasonic vibration (20 kHz). Differences in fatigue life for the same material may arise when tested under varying loading frequencies. To fully utilize the ultra-high cycle fatigue life data obtained from different testing systems, the impact of loading frequency on the ultra-high cycle fatigue life of materials needs to be studied imperatively. This paper presents novel prediction models for ultra-high cycle fatigue life, taking into account loading frequency. The models incorporate the crack initiation life prediction model based on Tanaka's dislocation theory and the Paris crack growth life prediction model. The influence of loading frequency is integrated into effective stress and fatigue strength. The proposed models are verified using available very high cycle fatigue test data for titanium alloy TC17 and nickel-based superalloy GH4169 under different loading frequencies. The results show that the models proposed in this work can reasonably characterize the ultra-high cycle fatigue test data of materials under varying loading frequencies, establishing the correlation of fatigue life data under different loading frequencies.

loading frequency  /  very high cycle fatigue  /  life prediction
舒力力, 陈永辉, 潘凯, 徐乾罡, 郭凯, 张桢. 考虑加载频率的超高周疲劳寿命预测. 固体力学学报, 2024 , 45 (4) : 488 -495 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.012
Lili Shu, Yonghui Chen, Kai Pan, Qiangang Xu, Kai Guo, Zhen Zhang. Ultra-high Cycle Fatigue Life Prediction Considering Loading Frequency[J]. Chinese Journal of Solid Mechanics, 2024 , 45 (4) : 488 -495 . DOI: 10.19636/j.cnki.cjsm42-1250/o3.2024.012
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0　引言
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随着航空与铁路等运输业的蓬勃发展，运输服务高质量的需求持续提升，飞机、高铁等运输工具的长寿命服役安全也越来越受到重视. 例如，典型航空发动机叶盘、涡轮叶片材料往往需要承受高频荷载，循环周次可达109次，超高周疲劳失效也逐渐成为不可忽视的主要失效模式之一. 为了验证材料的疲劳寿命是否满足工程需求，利用超高周疲劳试验开展疲劳性能和寿命研究是简单直接的方式. 传统的疲劳试验机的工作频率通常不到100 Hz，对一个试件完成109次以上的超高周疲劳试验，至少需要4个月[1]. 而且，由于疲劳试验受到材料处理工艺，环境温度等各种影响，结果的分散性非常大. 实际测试需要对大量的试样进行疲劳试验之后才能获得较为可靠的疲劳寿命曲线. 因此，超高周疲劳试验时间和效率成为疲劳测试的主要限制因素. 所以有学者提出采用高频加载的方式缩短超高周疲劳试验周期. 目前国内外较为普遍的方式是利用超声振动来完成超高周疲劳实验[2]. 以20 kHz频率的超声振动完成109循环周次的疲劳试验仅需不到14小时[3].
材料在进行超高周疲劳测试时，高频加载带来的频率效应问题不容忽视. 加载频率效应对于材料疲劳性能的影响受到研究人员的广泛关注，如Sun等通过旋转弯曲疲劳试验和超声疲劳试验研究不同加载频率下钛合金的疲劳性能，结果表明高频加载下材料疲劳裂纹倾向于从试样内部产生，同种材料的疲劳性能在超声高频加载下显著优于旋转弯曲低频加载[4]. 对于不同类型的材料，频率高低造成的影响不同，如Zhang等开展了不同频率下镍基合金的疲劳试验，并通过损伤累积理论定性地分析了加载频率对材料疲劳寿命的影响，试验结果显示疲劳寿命随加载频率升高而变长[5]. Premanand等研究发现复合材料在不同频率加载下得到的疲劳寿命不同，而部分金属材料却不受影响[6]. 针对加载频率对材料疲劳性能影响，部分学者已进行了相关理论研究. Guennec等研究多种碳钢的疲劳性能，发现铁素体晶粒对材料的加载频率效应影响较大，提出了一种考虑屈服应力和温度影响的疲劳强度寿命预测模型[7]. Zhao等从位错运动与加载频率的关系出发，通过位错速度在四分之一个加载周期下的积分计算出位错距离，他们发现加载频率与位错距离成反比，频率越高，位错越小，即塑性应变越小，因此疲劳寿命会随加载频率的提高而变长[8]. 但该理论是以位错自由移动的假设为前提，在含有足够密集障碍物的材料中，加载频率效应会大大减弱. 同样对于循环加载，有效应力大小也是会随着加载频率而改变的[9]. 目前针对超高周疲劳加载频率效应的研究还处于实验探索和理论发展阶段，基于考虑加载频率效应建立的超高周疲劳寿命预测模型也比较少. 因此，研究加载频率与超高周疲劳寿命的联系，建立考虑频率效应的超高周疲劳寿命预测模型，对超高周疲劳理论的发展和工程实践具有重要意义.
材料在疲劳过程中会经历裂纹萌生和扩展多阶段的断裂过程，Wang等考虑裂纹萌生和扩展寿命，在超高周寿命预测方面提出了有效的理论模型[10]. 本文基于裂纹萌生和扩展过程结合Tanaka位错偶极子堆积理论的超高周疲劳裂纹萌生寿命预测模型，并考虑Paris裂纹扩展公式的疲劳寿命预测模型，引入加载频率对有效应力和疲劳强度的影响，建立考虑加载频率效应的包含疲劳裂纹萌生、扩展的超高周疲劳寿命预测模型. 利用提出的模型，本文对钛合金TC17和镍基高温合金GH4169在不同加载频率下的超高周疲劳寿命进行预测，以检验模型的合理性和工程适用性.
1　考虑加载频率效应的超高周疲劳寿命预测模型
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本文的疲劳寿命预测模型包括裂纹萌生和扩展两个阶段，建立考虑加载频率效应的超高周疲劳寿命预测模型. 工程材料疲劳寿命预测是工程结构设计需要解决的关键问题之一. 长期以来，研究人员对材料疲劳行为进行了大量研究，基于物理现象或变形机制建立了多种多样的寿命预测模型. 其中基于裂纹扩展的Paris寿命预测模型在工程中得到了广泛的应用. 20世纪60年代，Paris完成了大量裂纹扩展试验，发现裂纹扩展速率与裂纹尖端应力强度因子范围存在对数线性关系：
方程（1）即为描述裂纹扩展与寿命关系的Paris公式，其中，ΔK为应力强度因子范围，C和n为材料常数，通过裂纹扩展试验数据拟合得到. 因此，ΔK与裂纹扩展驱动力机制有关. 当Kmax超过材料的断裂韧性Kc时，材料将发生断裂，裂纹扩展速率快速增大；当ΔK的值小于应力强度因子范围门槛ΔKth时，认为裂纹停止扩展. 这也是传统意义上疲劳极限的来源. Paris建立的裂纹扩展与寿命的联系对目前的超高周疲劳寿命预测具有很好的启发性和借鉴意义.
另一方面，考虑到疲劳裂纹萌生过程中的位错能量变化，Mura和Nakasone等[11]研究了裂纹尺寸对裂纹萌生的影响，提出基于位错的裂纹萌生寿命预测模型：
其中，σa为循环加载应力幅值，M为最优取向晶粒的泰勒因子，k为位错的摩擦应力，α为疲劳寿命指数，满足0<α≤1，G为剪切模量，ν为泊松比，h为滑移带宽度，d为晶粒尺寸，c为初始裂纹半长，试验数据和仿真结果表明α不是一个常数，其值取决于材料位错堆积能力和滑移的不可逆性.
Hong等[12]基于Tanaka和Mura的简化位错模型[13]，引入不可逆位错因子p，并假设其与应力水平有关，基于Mises屈服准则，得到裂纹萌生寿命预测模型：
其中，σR是疲劳极限应力，A和α是实验拟合参数，aInc为夹杂物尺寸. 该模型针对夹杂物尺寸对疲劳性能影响大的材料更为实用.
基于Tanaka和Mura材料均匀夹杂假设提出的位错偶极子模型[13]，Wang等[10]提出了一种建立在裂纹萌生和裂纹扩展基础上的寿命预测模型，其中裂纹萌生部分为：
其中，Ws为比断裂能，为应力比为R时的疲劳极限，a0为裂纹初始尺寸. 基于Paris公式，Wang等考虑到长裂纹和短裂纹的扩展特点，从短裂纹扩展到长裂纹的寿命远远小于从初始裂纹扩展到短裂纹的寿命，并且初始裂纹长度远远小于短裂纹长度. 因此在n>2的情况下，疲劳寿命预测模型为：
该模型所涉及的参数均为材料常数或能从简单疲劳试验拟合得到，能够较好地预测超高周疲劳寿命，模型包括材料裂纹萌生和裂纹扩展两阶段的疲劳寿命预测. Wang等研究表明，材料在低周情况下裂纹扩展寿命占据主导，在高周及其以上情况由裂纹萌生寿命占据主导[10]. 该模型综合考虑了裂纹萌生和扩展疲劳寿命对总疲劳寿命的贡献，能够针对从低周到超高周所对应不同应力幅值下材料的疲劳寿命进行预测，更好地表征材料的疲劳性能. 而且，该模型在描述夹杂物对次表面裂纹萌生及对超高周疲劳性能的影响方面具有一定可靠性. 但在实际工程中，由于对次表面裂纹萌生的认识不够全面，裂纹萌生阶段存在不确定性. 为了更好地预测超高周疲劳寿命，需要了解材料不均匀性的随机变化，夹杂物或缺陷的尺寸和分布，以及它们在超高周疲劳损伤过程中的作用.
上述模型从宏观的裂纹扩展理论到微观的裂纹萌生理论均有所涉略，但由于没有针对加载频率的物理量，不能对不同频率下的超高周疲劳试验结果进行关联，无法将超声加速超高周疲劳实验结果与现有的低频试验测试结果有效地结合利用. 值得注意的是，目前考虑了上述加载频率效应问题的理论模型还比较少.
随着超声疲劳试验机等高频试验设备的推广应用，材料在高频疲劳试验中产生的加载频率效应问题越来越受到关注. 研究材料在不同加载频率下的S-N曲线特性、疲劳寿命等迫在眉睫. 本文通过分析现有文献试验数据，提出一种考虑加载频率的超高周疲劳寿命预测模型[10]. 该模型从疲劳裂纹萌生和裂纹扩展两个方面，分别考虑加载频率对疲劳寿命的影响.
1.1　超高周疲劳裂纹扩展寿命预测模型
本文考虑裂纹扩展速率与加载频率相关，基于Paris公式，裂纹扩展速率可以表示为：
其中，g1（f）为加载频率有关的修正函数. 对式（6）从裂纹的初始长度a0到极限长度af进行积分得到裂纹扩展寿命：
其中，af为裂纹最终长度，等于试样半径，超过半径则认为试样发生断裂，同式（5）本文的裂纹扩展寿命修正模型可以简化为：
1.2　超高周疲劳裂纹萌生寿命预测模型
基于Tanaka和Mura的位错模型[13]，在不同频率加载条件下，材料受到的有效外加应力与频率大小相关，因此，裂纹萌生寿命模型可表示为：
其中，g2（f）为加载频率有关的函数. 对该模型的进一步简化，假设材料应力状态服从Mises准则：
简化后的裂纹萌生寿命预测模型如下：
结合式（8）和（11）得到疲劳裂纹萌生和裂纹扩展的寿命模型为：
1.3　超高周疲劳全寿命预测模型
超高周疲劳裂纹萌生与金属循环局部塑性变形、位错运动以及加载频率密切相关[7,12]. 裂纹形成后，在裂纹扩展过程中，试件刚度降低导致系统谐振频率发生变化，因此，加载频率也与裂纹扩展速率紧密关联[14]. 加载频率对裂纹萌生和扩展机理显著不同，为了简化上述影响因素，可假设疲劳寿命与频率的关系为线性关系：
其中，a，b为加载频率参数，f为循环加载频率，f0为参考振动频率. 将式（13）、（14）代入式（12）中得到一个考虑加载频率效应的超高周疲劳寿命预测模型如下：
需要注意的是，该模型仅考虑了加载应力幅值与加载频率的线性关系，式（15）简称频率线性模型（Frequency linear model）. 另外，目前已有学者提出理论公式，阐明加载频率效应对材料疲劳强度产生影响的具体机制. 针对高频加载下材料位错的热激活现象，Guennec等基于热激活位错位移理论，考虑在正弦加载下的平均应变率与加载频率成线性相关[7]，得到材料疲劳强度与频率的关系：
其中，σ0为屈服强度，T为当前环境测试温度，T0为室温一般取293 K，c0是与能量耗散相关的模型系数，f0可取为传统伺服液压振动频率. 结合式（16）本文提出的超高周疲劳寿命预测模型可以扩展为：
通过该模型同样可以对材料超高周疲劳寿命进行预测，其中σF为材料在不同加载频率下的疲劳极限，可由式（16）预测得到，式（17）简称频率强度模型（Frequency strength model）.
2　不同加载频率下疲劳寿命模型的预测结果及分析
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镍基高温合金GH4169和钛合金TC17是广泛应用于航空发动机涡轮叶片和涡轮盘等部件的重要原材料. 为了验证本文提出的考虑频率效应的超高周疲劳寿命预测模型的有效性，本文将通过文献已有的镍基高温合金GH4169和钛合金TC17两种材料高频加载下的超高周疲劳寿命测试数据，采用提出的超高周疲劳寿命预测模型对低频加载下的疲劳寿命进行预测，并与已有实验数据进行比较分析.
2.1　GH4169超高周疲劳寿命预测
首先针对GH4169不同加载频率下的超高周疲劳寿命数据进行分析. 考虑Zhang等[9]和Kawagoishi等[15,16]对高温镍基合金GH4169分别在20 kHz和52.5 Hz下的超高周疲劳试验数据，试验均为室温条件下的20 kHz超声疲劳试验和52.5 Hz的旋转弯曲疲劳试验. 根据文献确定GH4169材料的基本物理参数，再对部分模型参数进行拟合得到最终的材料疲劳寿命预测模型.
2.1.1　GH4169模型参数确定
从文献可得到GH4169部分物理参数，基本力学性能见表1[17]，Paris疲劳试验参数为n=4，C=6×10-13，初始裂纹长度为15 μm左右[18]. 采用本文模型对GH4169进行预测时，参考振动频率f0取10 Hz. 从疲劳数据可以确定在20 kHz加载频率下的疲劳极限约为575 MPa，通过对20 kHz下的疲劳试验数据进行拟合得到频率线性模型模型参数结果，如表2所示. 频率强度模型的模型参数c0分别为0.74，0.53. 该参数是在试验频率20 kHz和52.5 Hz下相对于参考频率10 Hz测试时材料的强度变化系数，该参数小于1意味着在两种频率相对于参考频率下的测试存在能量耗散的差别.
2.1.2　GH4169模型预测结果
如图1所示，本文提出的两个模型的预测结果表明，考虑了加载频率效应后，模型可以根据频率的变化，根据高频下的疲劳寿命数据预测低频下GH4169的超高周疲劳寿命. 采用本文模型得到的预测结果与试验得到的低频加载下的疲劳数据趋势基本一致.
从图1可以看出，频率线性模型的预测结果与试验数据基本吻合. 因此，对于具有和GH4169合金类似S-N曲线特性的材料，均可通过本文所述模型获得可靠的基于频率效应的超高周疲劳寿命预测结果. 同时，根据频率强度模型的物理意义可以发现，材料超高周疲劳寿命预测结果中，在不同加载频率下的疲劳极限的变化与高频加载导致的热应力从而产生位错的激活有关，频率越高，热效应越明显，位错就会越活跃[7]. 但在低周下材料的热效应不明显，因此疲劳寿命提升幅值较小. 考虑低周情况下载荷应力水平较高，且疲劳寿命由裂纹扩展占据主导，而频率强度模型目前仅仅引入频率与疲劳强度相关，针对材料超高周疲劳裂纹扩展寿命需进一步考虑裂纹扩展预测方法.
2.2　TC17超高周疲劳寿命预测
为了进一步验证模型的可靠性，本文针对TC17钛合金材料不同加载频率下的超高周疲劳试验数据进行分析. TC17疲劳试验数据由Li等[19]在50 Hz下的高周轴向疲劳试验及王金龙等[20]在20 kHz下的超高周轴向疲劳试验得到. 同样根据文献确定TC17材料的基本物理参数，再对部分模型参数进行拟合优化得到最终的材料疲劳寿命预测曲线.
2.2.1　TC17模型参数确定
从文献可得到TC17钛合金基本力学性能见表3[21]，Paris疲劳试验参数为n=4，C=8.5×10-13，初始裂纹长度为12 μm左右[22]. 采用本文模型对TC17进行预测时，参考振动频率f0取10 Hz. 从疲劳数据可以确定在20 kHz下的疲劳极限为615 MPa，通过对20 kHz下的疲劳试验数据进行拟合得到频率线性模型的模型参数结果见表4. 频率强度模型的模型参数c0分别为0.93，0.66.
2.2.2　TC17模型预测结果
如图2所示，本文提出的两个模型对TC17材料低频下超高周疲劳寿命的预测结果也基本符合原始数据的S-N曲线特性. 可以认为模型可以预测具有类似S-N曲线特性的不同加载频率下超高周疲劳寿命. 并且，通过图1和图2可以发现两种材料对在不同加载频率下疲劳寿命均呈现与频率正相关的现象. 对于频率强度模型体现出了比GH4169更好的预测结果，考虑到由于TC17为钛合金，热效应没有镍基高温合金明显，在高应力水平下也出现良好的预测趋势.
3　结论与展望
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本文基于超高周疲劳裂纹萌生和扩展两阶段的现象，针对加载频率对超高周疲劳寿命的影响进行了研究，提出了考虑加载频率效应的超高周疲劳寿命预测模型. 与实验对比结果显示，本文模型均具有一定的可靠性. 而且，对于GH4169和TC17两种材料的文献实验数据，本文模型预测结果表明疲劳极限与频率大小呈正相关. 对于具有类似超高周疲劳S-N曲线特性的材料均可通过本文提出的模型，获得可靠的考虑频率效应的超高周疲劳寿命预测结果. 但是现有材料的超高周疲劳寿命曲线呈现双线型和阶梯下降型等多种趋势，针对这些复杂情况，考虑加载频率的超高周疲劳寿命预测模型还需进一步研究.
基金
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  • 国家科技重大专项(J2019-IV-0010-0078)
  • 国家自然科学基金项目(12172139)
文献
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2024年第45卷第4期
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doi: 10.19636/j.cnki.cjsm42-1250/o3.2024.012
  • 接收时间：2024-03-11
  • 首发时间：2026-04-01
  • 出版时间：2024-08-25
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  • 收稿日期：2024-03-11
基金
国家科技重大专项(J2019-IV-0010-0078)
国家自然科学基金项目(12172139)
作者信息
    1华中科技大学航空航天学院，工程力学系，武汉，430074
    2华中科技大学工程结构分析与安全评定湖北省重点实验室，武汉，430074
    3中国飞机强度研究所强度与结构完整性全国重点实验室，西安，710065
    4中国航空研究院，北京，100012

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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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