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Article(id=1241023039408755061, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1241023036892172648, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2025.11.008, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1747497600000, receivedDateStr=2025-05-18, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773812549688, onlineDateStr=2026-03-18, pubDate=null, pubDateStr=null, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773812549688, onlineIssueDateStr=2026-03-18, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773812549688, creator=13701087609, updateTime=1773812549688, updator=13701087609, issue=Issue{id=1241023036892172648, tenantId=1146029695717560320, journalId=1240685776644648972, year='2025', volume='29', issue='11', pageStart='1663', pageEnd='1826', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1773812549088, creator=13701087609, updateTime=1773812775651, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241023987245970093, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1241023036892172648, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241023987245970094, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1241023036892172648, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=1746, endPage=1756, ext={EN=ArticleExt(id=1241023041166168442, articleId=1241023039408755061, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Effect of different stress ratios on fatigue crack growth rate of HTS-A steel at low temperature and prediction for crack growth, columnId=1241023038716694896, journalTitle=Journal of Ship Mechanics, columnName=Structural Mechanic, runingTitle=null, highlight=null, articleAbstract=

In order to study the effect of different stress ratios on the fatigue crack growth of HTS-A steel in low temperature environment, low-temperature fatigue crack growth tests of HTS-A steel CT specimens at stress ratios of 0.1 and 0.3 were carried out. The test results show that with decreasing temperature, the crack growth rate decreases and the fatigue life increases. At the same time, with the increase of the stress ratio, the fatigue crack growth rate also increases accordingly. However, with the decrease of temperature, the effect of stress ratio on fatigue crack growth rate becomes smaller and smaller. On the basis of experiments, an improved McEvily model considering the effects of temperature and stress ratio was proposed in this paper. The model can predict the fatigue crack growth rate of HTS-A steel under different low temperatures and different stress ratios. The predicting results were compared with the experimental data. This prediction model lays a foundation for the fatigue life assessment of marine equipment in low temperature environment.

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为研究不同应力比对低温环境下HTS-A钢疲劳裂纹扩展的影响，本文开展了在应力比（R）为0.1和0.3时HTS-A钢CT试件的低温疲劳裂纹扩展试验。试验结果表明，随着温度的降低，裂纹扩展速率降低，疲劳寿命增加；同时，随着应力比的增大，疲劳裂纹扩展速率也相应地增大，但随着温度的降低，应力比对疲劳裂纹扩展速率的影响越来越小。在试验的基础上，本文提出了考虑温度和应力比影响的改进McEvily模型，该模型能够预报不同低温、不同应力比条件下的HTS-A钢疲劳裂纹扩展速率，并与试验结果进行了对比验证。该预报模型可为低温环境下海洋装备的疲劳寿命评估打下基础。

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通讯作者，E-mail：
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罗广恩（1980-），男，博士，副教授，通讯作者，E-mail：

刘家奇（1996-），男，硕士研究生

姜金辉（1977-），女，研究员。

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罗广恩（1980-），男，博士，副教授，通讯作者，E-mail：

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罗广恩（1980-），男，博士，副教授，通讯作者，E-mail：

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刘家奇（1996-），男，硕士研究生

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刘家奇（1996-），男，硕士研究生

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姜金辉（1977-），女，研究员。

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姜金辉（1977-），女，研究员。

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1 The basic mechanical properties of HTS-A steel

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屈服强度极限强度弹性模量泊松比
8509002.0×1050.34
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HTS-A钢基本力学性能

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屈服强度极限强度弹性模量泊松比
8509002.0×1050.34
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Test loading conditions

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应力比R最大载荷Pmax /kN最小载荷Pmin /kN试验频率f /Hz环境温度/℃
0.13031020，-20，-40，-60
0.33091020，-20，-40，-60
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试验工况

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应力比R最大载荷Pmax /kN最小载荷Pmin /kN试验频率f /Hz环境温度/℃
0.13031020，-20，-40，-60
0.33091020，-20，-40，-60
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Test data of final crack sizes and fatigue cycles in different fatigue cases

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环境温度/℃循环次数N /cycles最终裂纹尺寸a /mm
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-20226 220254 31182.8382.58
-40237 534269 20082.6282.48
-60250 228282 08382.6282.49
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各试验工况下的最终裂纹尺寸和循环次数表

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环境温度/℃循环次数N /cycles最终裂纹尺寸a /mm
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20175 730203 29582.8082.52
-20226 220254 31182.8382.58
-40237 534269 20082.6282.48
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不同应力比对HTS-A钢低温疲劳裂纹扩展速率的影响与预报
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罗广恩 1 , 刘家奇 1 , 姜金辉 2
船舶力学 | 结构力学 2025,29(11): 1746-1756
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船舶力学 | 结构力学 2025, 29(11): 1746-1756
不同应力比对HTS-A钢低温疲劳裂纹扩展速率的影响与预报
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罗广恩1 , 刘家奇1, 姜金辉2
作者信息
  • 1.江苏科技大学　船舶与海洋工程学院，江苏　镇江，212003
  • 2.上海船舶运输研究所有限公司　航运技术与安全国家重点实验室/航运技术交通行业重点实验室，上海　200135

    • 罗广恩（1980-），男，博士，副教授，通讯作者，E-mail：

    刘家奇（1996-），男，硕士研究生

    姜金辉（1977-），女，研究员。

通讯作者:

通讯作者，E-mail：
Effect of different stress ratios on fatigue crack growth rate of HTS-A steel at low temperature and prediction for crack growth
Guang-en LUO1 , Jia-qi LIU1, Jin-hui JIANG2
Affiliations
  • 1.School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
  • 2.State Key Laboratory of Navigation and Safety Technology/Key Laboratory of Marine Technology Ministry of Communications, Shanghai Ship and Shipping Research Institute Co. Ltd., Shanghai 200135, China
doi: 10.3969/j.issn.1007-7294.2025.11.008
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摘要
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为研究不同应力比对低温环境下HTS-A钢疲劳裂纹扩展的影响，本文开展了在应力比（R）为0.1和0.3时HTS-A钢CT试件的低温疲劳裂纹扩展试验。试验结果表明，随着温度的降低，裂纹扩展速率降低，疲劳寿命增加；同时，随着应力比的增大，疲劳裂纹扩展速率也相应地增大，但随着温度的降低，应力比对疲劳裂纹扩展速率的影响越来越小。在试验的基础上，本文提出了考虑温度和应力比影响的改进McEvily模型，该模型能够预报不同低温、不同应力比条件下的HTS-A钢疲劳裂纹扩展速率，并与试验结果进行了对比验证。该预报模型可为低温环境下海洋装备的疲劳寿命评估打下基础。

疲劳裂纹扩展速率  /  HTS-A钢  /  应力比  /  低温  /  疲劳试验

In order to study the effect of different stress ratios on the fatigue crack growth of HTS-A steel in low temperature environment, low-temperature fatigue crack growth tests of HTS-A steel CT specimens at stress ratios of 0.1 and 0.3 were carried out. The test results show that with decreasing temperature, the crack growth rate decreases and the fatigue life increases. At the same time, with the increase of the stress ratio, the fatigue crack growth rate also increases accordingly. However, with the decrease of temperature, the effect of stress ratio on fatigue crack growth rate becomes smaller and smaller. On the basis of experiments, an improved McEvily model considering the effects of temperature and stress ratio was proposed in this paper. The model can predict the fatigue crack growth rate of HTS-A steel under different low temperatures and different stress ratios. The predicting results were compared with the experimental data. This prediction model lays a foundation for the fatigue life assessment of marine equipment in low temperature environment.

fatigue crack growth rate  /  HTS-A steel  /  stress ratio  /  low temperature  /  fatigue test
罗广恩, 刘家奇, 姜金辉. 不同应力比对HTS-A钢低温疲劳裂纹扩展速率的影响与预报. 船舶力学, 2025 , 29 (11) : 1746 -1756 . DOI: 10.3969/j.issn.1007-7294.2025.11.008
Guang-en LUO, Jia-qi LIU, Jin-hui JIANG. Effect of different stress ratios on fatigue crack growth rate of HTS-A steel at low temperature and prediction for crack growth[J]. Journal of Ship Mechanics, 2025 , 29 (11) : 1746 -1756 . DOI: 10.3969/j.issn.1007-7294.2025.11.008
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0　引言
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近年来，随着极地航道和极地资源的进一步开发与利用，低温环境下船舶与海洋结构物的安全性引起了广泛的关注。极地船舶与深海潜水器在极地低温海域航行和作业时，会受到低温环境和外部载荷对结构造成的影响[1-2]。低温环境、波浪载荷、冰载荷等不同载荷类型共同作用，会给船舶与海洋结构物的安全带来威胁，有可能引发各种灾难事故，因此，准确评估结构的强度和疲劳寿命是结构安全性评估的重要工作。HTS-A钢是一种船舶与海洋装备常用的高强度钢，研究其在不同应力比和不同低温环境下的疲劳裂纹扩展性能，对于HTS-A钢在极地装备上的应用及其结构安全性的评估具有重要意义。
许多学者针对常温条件的钢材疲劳裂纹扩展性能进行了研究[3]。但是，在不同应力比和低温环境下，针对钢材的疲劳裂纹扩展性能方面的研究还比较少。秦闯[4]对EH36钢在不同温度下的疲劳裂纹扩展速度进行了研究，结果表明不同的温度对疲劳裂纹扩展速度有一定的影响。随着温度的下降，EH36钢的屈服和抗拉强度有一定程度的提高，而且疲劳裂纹扩展速率低于常温。张浩辉[5]测定了DH36钢三种标准件在两种应力水平下的-60℃低温疲劳寿命，通过DH36钢材焊接节点低温疲劳性能试验分析得出T字型在-60℃低温下疲劳性能良好，-60℃低温环境下疲劳寿命比常温环境下的疲劳寿命长。廖小伟等[6]研究了Q345qD钢裂纹扩展特性，结果表明随应力比增大，裂纹扩展速率略有增加。许赞[7]研究了在低温和常温下Q355NHC钢在不同应力比下的疲劳行为，发现低温-50℃下Q355NHC钢的疲劳寿命整体高于室温条件下疲劳寿命。Moore等[8]研究了低温环境下铝合金的疲劳裂纹扩展行为，表明低温会增强铝合金抵抗疲劳和裂纹扩展的能力，延长疲劳寿命。现有研究主要集中在金属疲劳裂纹扩展特性的试验研究上，同时考虑不同应力比和低温环境影响的研究较少，许多研究提出的裂纹扩展速率公式往往只适用于单一的试验场景，无法对不同应力比和不同低温环境下的疲劳裂纹扩展速率进行预报。另外，针对低温环境下，不同应力比的HTS-A钢的疲劳裂纹扩展行为的研究则更少。
本文为研究不同应力比对低温环境下HTS-A钢疲劳裂纹扩展的影响，开展HTS-A钢CT试件低温疲劳裂纹扩展速率试验，得到不同应力比下的低温疲劳裂纹扩展速率曲线，并分析应力比对低温环境下HTS-A钢疲劳裂纹扩展速率的影响。在试验研究的基础上，对Cui等[9-11]提出的改进McEvily模型做进一步改进，提出考虑应力比和低温影响的新的改进McEvily模型。对不同应力比下HTS-A钢的低温疲劳裂纹扩展速率进行预报，并将预报结果与试验结果进行对比，以此验证疲劳裂纹扩展速率模型的有效性。
1　疲劳裂纹扩展速率试验基本情况
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本次试验的对象为HTS-A钢CT试件，钢材的基本力学性能见表1。
CT试件板厚B=25 mm，宽度W=100 mm，初始切口a0=30 mm，试件依据GB/T 6398-2000《金属材料疲劳裂纹扩展速率试验方法》加工制备。试件的尺寸如图1所示。
在低温环境下，试验研究两种不同的应力比R（0.1和0.3）对HTS-A钢疲劳裂纹扩展速率的影响。疲劳裂纹扩展试验的环境温度分别设定为20℃、-20℃、-40℃和-60℃这四个温度。
HTS-A钢CT试件裂纹扩展速率试验在江苏科技大学结构力学实验室完成。使用的仪器为Instron8802高低温试验机，CT试件及试验仪器如图2和图3所示。
试验程序包括疲劳预裂纹阶段和裂纹扩展阶段。为消除试件裂纹前部形状对后续裂纹扩展速率数据带来的影响，在疲劳裂纹扩展试验前采用等K法预制初始疲劳裂纹，预制长度2.5 mm。疲劳试验中，我们采用的是保证最大载荷不变，改变应力比的方式。试验过程中的应力比、最大载荷、最小载荷和环境温度等具体参数见表2。
2　不同应力比条件下的疲劳裂纹扩展速率试验结果与分析
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2.1　裂纹扩展速率试验结果
按照表2的试验工况开展试验，试验过程及试验后试件照片如图4和图5所示。
试验过程中，通过CT试件开口处安装的引伸计来实时检测裂纹张开位移，反馈至Instron8802型疲劳试验机后，系统根据张开位移自动确定实时的裂纹尺寸，当试件裂纹扩展到一定程度或试件断裂时，引伸计能自动脱离试件，疲劳试验机自动停止。试验结束后，从疲劳试验机配套的计算机中输出试验结果。将各工况下的疲劳裂纹扩展试验结果绘制成曲线，得到不同温度、同一应力比条件下的裂纹扩展a-N曲线和裂纹扩展速率曲线，如图6~9所示。整理得到的各试验工况下的最终裂纹尺寸和循环次数见表3。
从图6和图8可以看出，在应力比R不变的条件下，疲劳裂纹扩展寿命均随着温度的降低而增加。从图7和图9可以看出，在应力比R不变的条件下，疲劳裂纹扩展速率均随着温度的降低而减小。从表3中可以看出，每次试验都是由于CT试件裂纹张开位移达到一定值（对应于最终裂纹尺寸达到82.6 mm左右）时，引伸计的自动弹开而机器自动终止试验。表3结果也表明当温度达到-60℃时，HTS-A钢仍然保持有较好的力学性能，没有出现低温脆断的现象。
2.2　不同应力比R对疲劳裂纹扩展速率的影响分析
对试验结果进一步分析，分析不同应力比对疲劳裂纹扩展速率的影响。在相同的温度环境下，对比分析R=0.1和0.3时的裂纹扩展a-N曲线和裂纹扩展速率曲线，分别见图10~17。
从图10、图12、图14和图16和表3中可以看出，各试验工况最终裂纹尺寸均为82.6 mm左右；应力比R=0.1所对应的疲劳裂纹扩展寿命小于R=0.3条件下的疲劳寿命，这是因为在试验过程中仪器的最大载荷不变，始终为30 kN（具体见表2），这样当应力比R增大时，最小载荷相应增大，载荷和应力变化范围则变小，因此R=0.3的疲劳寿命变长。
进一步将a-N曲线试验数据转换成对应的裂纹扩展速率曲线，见图11、图13、图15和图17所示，可以看出各试验工况下的R=0.3对应的裂纹扩展速率曲线高于相应的R=0.1时的扩展速率曲线，说明在相同的环境温度条件下，随着应力比R的增加，裂纹扩展速率增大。从这些图中还可以进一步看出，随着温度的降低，应力比R对裂纹扩展速率的影响程度在逐渐降低，表现为相同温度环境下R=0.1和R=0.3的扩展速率曲线越来越接近，当-60℃时，R=0.1和R=0.3的扩展速率曲线在中部的线性段部分区域接近重合。
3　HTS-A钢疲劳裂纹扩展速率预报及分析
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3.1　改进的McEvily疲劳裂纹扩展模型
疲劳裂纹扩展速率的准确预报首先需要建立恰当的裂纹扩展速率模型。迄今为止，描述疲劳裂纹扩展速率的模型有很多，应用最为广泛的是Paris公式，该公式形式简单，需要确定的模型参数少，但是仅能描述裂纹扩展速率曲线的第二区域——线性段部分。
Cui等[9-11]在McEvily与他的同事提出的扩展速率模型基础上，提出了改进的McEvily模型，能够较好地预报常温下的疲劳裂纹扩展速率，见公式（1）。
式中：是材料的断裂韧性，A是环境敏感尺寸常数，m表示相应疲劳裂纹扩展速率曲线斜率的常数，n是不稳定断裂的常数，是最大应力强度因子，是在门槛值下的有效应力强度因子范围。
本文将在公式（1）的基础上，增加低温和应力比的影响参数，得到新的能够适用于低温环境和不同应力比条件下的疲劳裂纹扩展速率模型。
吕宝铜等[12]提出温度低于室温环境时，低温疲劳裂纹扩展门槛值为
式中：和分别为低温及常温时的疲劳裂纹扩展门槛值，和分别为低温和常温时的循环屈服强度，为常温疲劳极限。
Wang等[13-14]通过大量试验数据的统计分析得出，钢材在低温环境下的强度指标可以用自然对数e的指数函数进行拟合，即
本文将在公式（1）的基础上引入公式（3）以考虑温度引起的材料屈服强度变化，结合公式（2）进一步考虑低温下材料性能对疲劳裂纹扩展门槛值的影响，并进行无量纲化处理。最后，在扩展速率模型公式（1）的基础上，提出了包含温度参数和应力比R影响的新的改进McEvily模型，见公式（4）。其中，模型中的参数计算公式（6）考虑了应力比对低温疲劳裂纹扩展的影响。
其中，
式中：是材料的断裂韧性，A是环境敏感尺寸常数，m表示相应疲劳裂纹扩展速率曲线斜率的常数，n是不稳定断裂的常数，是材料在疲劳载荷下的断裂韧性，是固有缺陷长度的经验材料常数，a是修正后裂纹长度，是最大施加应力，是最小施加应力，R是应力比，是有效应力强度因子范围，是在门槛值处有效应力强度因子范围，是张开裂纹处的应力强度因子，是裂纹尖端应力/应变约束比，是计算虚拟强度参数，是材料极限强度，是材料屈服强度，是材料的硬化指数，是裂纹扩展速率模型中表明裂纹不稳定的指标，是泊松比。定义了计算的系数。
对于本文试验中的CT试件，其应力强度因子K计算过程中用到的几何形状因子Y（a），对应的计算式为公式（9）。若要将扩展速率公式（4）应用到其他形式的裂纹疲劳扩展问题，需要根据具体的裂纹形式查阅应力强度因子手册确定相应的几何形状因子Y（a）。
3.2　疲劳裂纹扩展速率模型的参数确定及裂纹扩展速率预报
为了验证本文提出的改进McEvily疲劳裂纹扩展模型在不同温度、不同应力比条件下的有效性，将2.1节中的疲劳试验数据分为两部分：一部分用于疲劳试验数据进行模型参数确定，另一部分试验数据用于检验模型对裂纹扩展速率的预测能力。
把-20℃和-40℃的试验数据用最小二乘法进行模型参数确定，而把20℃和-60℃的试验数据用于检验模型的预测能力。HTS-A钢断裂韧性为150 MPa，模型中的参数n=6.0，常温下的屈服强度为850 MPa，通过参数拟合确定模型参数A和m，根据公式（3）可以计算得到低温-20℃和-60℃下屈服强度为920 MPa、997 MPa以及-40℃时屈服强度为958 MPa。
公式（4）模型参数拟合如图18~21所示，得到HTS-A钢不同应力比下的低温疲劳扩展速率模型见公式（10）。
运用公式（10）对20℃和-60℃低温环境下、应力比0.1和0.3时的裂纹扩展速率进行预报，并与试验结果对比验证，如图22~25所示。
从图22~25可以看出公式（10）对HTS-A钢在不同温度、不同应力比条件下的疲劳裂纹扩展速率预测结果与试验结果吻合较好，表明本文提出的扩展速率模型能够准确反映HTS-A钢在不同温度、不同应力比条件下的疲劳裂纹扩展速率特性，同时运用少量组的试验数据确定模型参数，就能够预测出其他温度、应力比条件下的疲劳裂纹扩展速率，从而减少大量的低温疲劳试验，节约试验成本。同时该模型也可以为HTS-A钢深海耐压结构的低温疲劳寿命评估提供参考。
4　结论
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本文开展了HTS-A钢CT试件疲劳裂纹扩展试验，研究了不同应力比R对其低温环境下疲劳裂纹扩展速率的影响。在试验研究的基础上，提出了考虑温度和应力比影响的新的改进McEvily模型，通过对试验结果进行最小二乘法拟合确定了模型参数，进一步对HTS-A钢的低温疲劳裂纹扩展速率完成预报分析。通过研究得到以下结论：
（1）随着应力比R的增大，HTS-A钢低温疲劳扩展速率增大；同时，随着温度的降低，应力比R对疲劳裂纹扩展速率的影响越来越小。
（2）基于本文的HTS-A钢疲劳裂纹扩展速率试验和试验数据，本文提出了一种考虑了应力比和温度影响的改进McEvily疲劳裂纹扩展速率公式，可以拟合和预测在不同低温、不同应力比条件下的疲劳裂纹扩展速率，预报结果与试验结果较为吻合。该方法可以减少低温疲劳试验数量，节省试验成本同时可为低温环境下的海洋装备疲劳寿命评估打下基础。
基金
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  • 国家自然科学基金面上项目(52171312)
  • 水路交通控制全国重点实验室开放课题资助项目(QZ2022-Y012)
文献
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2025年第29卷第11期
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doi: 10.3969/j.issn.1007-7294.2025.11.008
  • 接收时间：2025-05-18
  • 首发时间：2026-03-18
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  • 收稿日期：2025-05-18
基金
国家自然科学基金面上项目(52171312)
水路交通控制全国重点实验室开放课题资助项目(QZ2022-Y012)
作者信息
    1.江苏科技大学　船舶与海洋工程学院，江苏　镇江，212003
    2.上海船舶运输研究所有限公司　航运技术与安全国家重点实验室/航运技术交通行业重点实验室，上海　200135

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2种不同金属材料的力学参数
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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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