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Article(id=1242150428671025376, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1242150427056222760, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2024.02.010, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1691596800000, receivedDateStr=2023-08-10, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1774081340234, onlineDateStr=2026-03-21, pubDate=1708358400000, pubDateStr=2024-02-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774081340234, onlineIssueDateStr=2026-03-21, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774081340234, creator=13701087609, updateTime=1774081340234, updator=13701087609, issue=Issue{id=1242150427056222760, tenantId=1146029695717560320, journalId=1240685776644648972, year='2024', volume='28', issue='2', pageStart='169', pageEnd='318', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1774081339849, creator=13701087609, updateTime=1774081592202, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1242151485560136680, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1242150427056222760, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1242151485560136681, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1242150427056222760, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=273, endPage=282, ext={EN=ArticleExt(id=1242150428884934884, articleId=1242150428671025376, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Prediction method of fatigue crack growth rate of HTS-A steel at low temperature, columnId=1242129251223274417, journalTitle=Journal of Ship Mechanics, columnName=Structural Mechanics, runingTitle=null, highlight=null, articleAbstract=

Aiming at the fatigue crack growth behavior of marine HTS-A steel at low temperature, the CT sample of HTS-A steel with a thickness of 25 mm was adopted in this paper, and the fatigue crack growth tests at room temperature and different low temperature environments were carried out. On the basis of experimental research, a low-temperature fatigue crack growth prediction method with improved McEvily formula including temperature term was proposed. The results show that the fatigue crack growth rate of HTS-A steel decreases gradually with the temperature decrease. At -60 ℃, the low temperature fatigue crack growth rate of HTS-A steel does not show low temperature brittle fracture, and the test results provide data reference for the low temperature fatigue design of marine HTS-A steel. At the same time, the low temperature test data of HTS-A steel in this paper and the low temperature test data of titanium alloy in the literature were used to verify the rationality and correctness of the low temperature fatigue crack growth rate prediction method. The method can be used to predict the metal fatigue crack growth rate in different low temperature environments.

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针对低温下船用HTS-A钢的疲劳裂纹扩展行为，本文采用25 mm厚HTS-A钢CT试样为研究对象，开展常温及不同低温环境下疲劳裂纹扩展试验。在试验研究的基础上，提出包含温度项的改进McEvily公式的低温疲劳裂纹扩展预报方法。结果表明：随着温度的降低，HTS-A钢的疲劳裂纹扩展速率逐渐降低。在-60 ℃时，HTS-A钢的低温疲劳裂纹扩展速率没有出现低温脆断，试验结果可为船用HTS-A钢低温疲劳设计提供数据参考。同时，分别采用本文HTS-A钢低温试验数据和文献中的钛合金低温试验数据验证低温疲劳裂纹扩展速率预报方法的合理性及正确性，该方法可用于预报不同低温环境下金属疲劳裂纹扩展速率。

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通讯作者，E-mail：
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刘家奇（1996-），男，硕士研究生

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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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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Basic mechanical properties of HTS-A steel

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屈服强度σy/MPa极限强度σy/MPa弹性模量E/MPa泊松比γ
850900200 0000.34
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HTS-A钢基本力学性能

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屈服强度σy/MPa极限强度σy/MPa弹性模量E/MPa泊松比γ
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低温下HTS-A钢疲劳裂纹扩展速率预报方法研究
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刘家奇 1 , 罗广恩 1 , 潘广善 2 , 刘俊成 1 , 李爽 1 , 张帅 1
船舶力学 | 结构力学 2024,28(2): 273-282
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船舶力学 | 结构力学 2024, 28(2): 273-282
低温下HTS-A钢疲劳裂纹扩展速率预报方法研究
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刘家奇1, 罗广恩1 , 潘广善2, 刘俊成1, 李爽1, 张帅1
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.中国船舶科学研究中心，江苏　无锡　214082

    • 刘家奇（1996-），男，硕士研究生

    罗广恩（1980-），男，博士，副教授，通讯作者，E-mail：。

通讯作者:

通讯作者，E-mail：
Prediction method of fatigue crack growth rate of HTS-A steel at low temperature
Jia-qi LIU1, Guang-en LUO1 , Guang-shan PAN2, Jun-cheng LIU1, Shuang LI1, Shuai ZHANG1
Affiliations
  • 1.School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
  • 2.China Ship Scientific Research Center, Wuxi 214082, China
出版时间: 2024-02-20 doi: 10.3969/j.issn.1007-7294.2024.02.010
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摘要
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针对低温下船用HTS-A钢的疲劳裂纹扩展行为，本文采用25 mm厚HTS-A钢CT试样为研究对象，开展常温及不同低温环境下疲劳裂纹扩展试验。在试验研究的基础上，提出包含温度项的改进McEvily公式的低温疲劳裂纹扩展预报方法。结果表明：随着温度的降低，HTS-A钢的疲劳裂纹扩展速率逐渐降低。在-60 ℃时，HTS-A钢的低温疲劳裂纹扩展速率没有出现低温脆断，试验结果可为船用HTS-A钢低温疲劳设计提供数据参考。同时，分别采用本文HTS-A钢低温试验数据和文献中的钛合金低温试验数据验证低温疲劳裂纹扩展速率预报方法的合理性及正确性，该方法可用于预报不同低温环境下金属疲劳裂纹扩展速率。

疲劳裂纹扩展速率  /  HTS-A钢  /  低温疲劳试验  /  预报方法

Aiming at the fatigue crack growth behavior of marine HTS-A steel at low temperature, the CT sample of HTS-A steel with a thickness of 25 mm was adopted in this paper, and the fatigue crack growth tests at room temperature and different low temperature environments were carried out. On the basis of experimental research, a low-temperature fatigue crack growth prediction method with improved McEvily formula including temperature term was proposed. The results show that the fatigue crack growth rate of HTS-A steel decreases gradually with the temperature decrease. At -60 ℃, the low temperature fatigue crack growth rate of HTS-A steel does not show low temperature brittle fracture, and the test results provide data reference for the low temperature fatigue design of marine HTS-A steel. At the same time, the low temperature test data of HTS-A steel in this paper and the low temperature test data of titanium alloy in the literature were used to verify the rationality and correctness of the low temperature fatigue crack growth rate prediction method. The method can be used to predict the metal fatigue crack growth rate in different low temperature environments.

fatigue crack growth rate  /  HTS-A steel  /  low temperature fatigue test  /  prediction method
刘家奇, 罗广恩, 潘广善, 刘俊成, 李爽, 张帅. 低温下HTS-A钢疲劳裂纹扩展速率预报方法研究. 船舶力学, 2024 , 28 (2) : 273 -282 . DOI: 10.3969/j.issn.1007-7294.2024.02.010
Jia-qi LIU, Guang-en LUO, Guang-shan PAN, Jun-cheng LIU, Shuang LI, Shuai ZHANG. Prediction method of fatigue crack growth rate of HTS-A steel at low temperature[J]. Journal of Ship Mechanics, 2024 , 28 (2) : 273 -282 . DOI: 10.3969/j.issn.1007-7294.2024.02.010
正文
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0　引言
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随着北极航线的开发和我国深海战略与极地研究的深入，极地航行的船舶除了需要承受冰载荷外，极地的低温环境也会对船体钢材的力学性能产生较大影响[1]；极地深潜器搭乘母船前往极地开展作业，下潜前和上浮后都要承受极地的低温环境，同时在下潜及上浮过程中潜水器还要承受海水的高压循环载荷，承压结构的焊缝区域容易形成初始裂纹，在低温影响下会发生疲劳裂纹扩展而威胁结构安全[2]。HTS-A钢作为潜水器耐压结构的一种常用高强度钢材，其常温下的疲劳裂纹扩展特性研究较多，而低温环境下的疲劳裂纹扩展研究则较少[3]。因此，针对HTS-A钢开展低温环境下的疲劳裂纹扩展速率试验及低温下疲劳裂纹扩展预报方法研究，对于极地船舶和潜水器的设计和疲劳寿命评估具有重要的工程实用价值。
近年来，国内外许多学者对于材料的低温疲劳性能做了许多研究。Zhao等[4]研究了DH36钢裂纹扩展特性，发现随着温度降低，钢材焊缝以及母材的疲劳裂纹扩展速率低于常温；Lu等[5]研究了低温下16Mn钢的疲劳裂纹扩展问题，指出当温度大于-143 ℃的疲劳脆韧转变温度时，疲劳裂纹扩展速率随温度降低而降低；刘牧东[6]研究了低温下铝合金的裂纹扩展速率，发现-70 ℃时裂纹扩展速率降低，与常温25 ℃时有明显区别，并分别给出了疲劳裂纹扩展速率公式；秦闯[7]研究了不同温度下EH36钢的疲劳裂纹扩展行为，发现低温会降低疲劳裂纹扩展速率；许赞[8]研究了低温和常温下Q355NHC钢的疲劳行为，低温-50 ℃下Q355NHC钢的疲劳寿命整体高于室温条件下疲劳寿命。现有文献是对低温疲劳裂纹扩展进行试验研究，然后对某个特定低温下的扩展速率曲线公式进行参数拟合。扩展速率公式中不包含温度变量，只能用于该低温条件下的裂纹扩展预报。目前，针对HTS-A钢的低温环境下疲劳裂纹扩展性能的研究较少，所提出的裂纹扩展速率公式不包含温度变量，无法预报其他低温环境下的疲劳裂纹扩展速率。
对于疲劳裂纹扩展速率曲线的数学描述，Paris公式因其公式简单、使用方便的优点被广泛使用，但Paris公式只能描述疲劳裂纹扩展三个阶段中的线性阶段。而崔维成等[9-11]提出的改进McEvily模型可以覆盖疲劳裂纹扩展的三个阶段，且改进的McEvily模型可以解释诸多因素对于裂纹扩展的影响，如压压疲劳、载荷次序和应力比等，具有较好的应用前景。
本文选择HTS-A钢作为研究对象，研究分析该材料的低温疲劳裂纹扩展行为，基于20 ℃、-20 ℃、-40 ℃和-60 ℃四个温度开展HTS-A钢的疲劳裂纹扩展速率试验，得到HTS-A钢在指定应力比下的疲劳裂纹扩展速率曲线。在此基础上，进一步提出包含温度参数的改进McEvily模型，确定改进McEvily模型中的相关参数，研究HTS-A钢的低温疲劳裂纹扩展速率的预报方法，将预报曲线与试验曲线进行对比分析。同时，选取-10 ℃这个未试验温度进行单独预报检验，从而确定低温预报方法的合理性和正确性。最后，利用参考文献中的钛合金低温数据再次验证该模型的预报能力，阐明该低温疲劳裂纹速率预报方法可推广至其它金属材料。
1　试验及方法
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1.1　试验材料及基本性能
本次试验采用HTS-A钢，材料的基本力学性能见表1。
板厚B=25 mm，试件宽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》加工准备，试件的尺寸如图1所示。
根据之前研究结果，本次试验选用应力比R为0.1，考虑温度对疲劳裂纹扩展速率的影响。本文试验方案中温度范围定为-60 ℃至20 ℃，在20 ℃、-20 ℃、-40 ℃和-60 ℃四个温度段分别测定HTS-A钢的疲劳裂纹扩展性能。
HTS-A钢的裂纹扩展速率试验在江苏科技大学结构力学试验室完成。仪器设备为Instron 8802高低温试验机，试验试件及仪器如图2~3所示。
实验程序包括疲劳预裂纹阶段和裂纹扩展阶段。疲劳裂纹扩展试验前采用等K法预制初始疲劳裂纹，预制长度为2.5 mm，预制裂纹在于提供足够大小的疲劳裂纹，消除试件因为机加工对后续裂纹扩展速率数据带来的影响。试验采用载荷频率为10 Hz，最大载荷为30 kN，最小载荷为3 kN，应力比为0.1对试件加载。
2　低温下疲劳裂纹扩展速率试验
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本文开展了低温下疲劳裂纹扩展速率试验，试验过程中最大载荷、加载频率各参数无异常变化，试验过程中及试验后的试件如图4~5所示。研究不同温度环境对HTS-A钢的疲劳裂纹扩展速率影响，通过Instron 8802型疲劳试验机配套的计算机软件输出试验结果，得到应力比R=0.1时HTS-A钢的a-N曲线和lg（da/dN）-lg（ΔK）疲劳裂纹扩展速率曲线，如图6~7所示。
根据图6所示的a-N曲线可以看出，在低温环境下，HTS-A钢的疲劳寿命相比较常温环境有明显提高，在-60 ℃时寿命达到最大。只是从a-N曲线难于判断出低温对疲劳裂纹扩展速率的影响，还需要裂纹扩展速率曲线来判断低温带来的影响。
根据图7所示的裂纹扩展速率曲线，随着温度的降低，在中低速区内，低温环境下的疲劳裂纹扩展速率比常温20 ℃时速率有所降低，限于试验条件，第三区域试验数据不太明显。-60 ℃时，裂纹扩展速率比较稳定，未发生明显的低温脆断行为。低温环境下，中低速区疲劳裂纹扩展速率较室温有所下降，表明了在低温环境下HTS-A钢拥有良好的抵抗裂纹扩展的能力；低温情况下的疲劳裂纹扩展速率和裂纹尺寸较大时，HTS-A钢的脆断防止是工程实际中需要注意的问题。
3　低温下疲劳裂纹扩展公式
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3.1　疲劳裂纹扩展理论和低温对材料力学性能的影响
疲劳裂纹扩展寿命计算式中的应力强度因子幅值的计算式为
式中，Y（a）为几何形状因子，计算式为
疲劳寿命预测需要建立正确的裂纹扩展速率关系。自从提出基于线弹性断裂力学的裂纹扩展速率以来，已经取得了许多进展。McEvily与他的同事提出的修正本构关系可以解释不同的疲劳现象，是较好的疲劳裂纹扩展模型之一。
为解释更多的疲劳现象，崔维成等[9-11]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。
式中，KC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，Kmax是最大应力强度因子，ΔKeffth是在门槛值下的有效应力强度因子范围。
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，ΔKth（T）和ΔKth（T0）分别为低温及室温时的疲劳裂纹扩展门槛值，σcy（T）和σcy（T0）分别为低温和常温时的循环屈服强度，σ-1（T0）为常温疲劳极限。
王元清等[13-14]通过大量试验数据统计分析得出，钢材在低温环境下的强度指标可以用e的指数函数进行拟合：
式中，σy（T0）为常温下钢材的屈服应力，σy（T）为环境温度为T ℃条件下的屈服应力，qy为钢材的低温敏感因子。
同时，Butt等[15]研究了NiAl屈服强度随温度变化数据，给出了屈服强度随温度变化关系为
根据公式，赵伟栋等[16]分析了DH36钢的屈服强度对于温度的依赖关系，将-60~-20 ℃分为Ⅰ区，将-20~10 ℃分为Ⅱ区。
Ⅰ区船用DH36钢屈服强度与温度之间关系为
Ⅱ区船用DH36钢屈服强度与温度之间关系为
3.2　低温疲劳裂纹扩展模型
综合考虑低温对材料屈服强度的影响公式（5），以及低温下材料性能对疲劳裂纹扩展门槛值的影响公式（4），引入无量纲量。随后，本文在改进McEvily模型（公式（3））中增加低温下屈服强度对应力强度因子和门槛值的影响项，提出了一种包含温度参数的改进McEvily模型，见公式（9）。
公式（9）能够描述不同低温下的裂纹扩展速率。该模型及其参数估计方法可为研究海洋结构应对低温环境时的疲劳寿命提供参考。
式中，
其中，KC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，Kcf表示材料在疲劳载荷下的断裂韧性，re是固有缺陷长度的经验材料常数，a是修正后裂纹长度，σmax是最大施加应力，σmin是最小施加应力，R是应力比，ΔKeff是有效应力强度因子范围，ΔKeffth是在门槛值处有效应力强度因子范围，Kop是张开裂纹处的应力强度因子，α'是裂纹尖端应力/应变约束比，α是计算虚拟强度参数，σu是材料极限强度，σy是材料屈服强度，n'是材料的硬化指数，n是裂纹扩展速率模型中表明裂纹不稳定指数，ν是泊松比。A0、A1、A2、A3定义了计算fop的系数。
4　低温模型预报讨论分析
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研究讨论低温预报公式时，首先基于常温数据进行拟合得到模型参数A和m，通过一组低温数据拟合确定低温影响下的屈服强度，本文再次运用其余的两组低温数据验证公式的预报效果，讨论公式（9）的正确性以及合理性。再运用文献中钛合金试验数据，验证公式（9）的推广性和适用性。
4.1　HTS-A钢模型参数确定
基于低温下裂纹扩展速率公式（9），运用常温下的试验数据使用最小二乘法拟合获得模型参数A和m，最终获得包含温度参数的HTS-A钢的裂纹扩展速率公式（14），常温下试验数据与拟合数据对比如图8所示。
可以看出，疲劳裂纹扩展速率的试验数据和预报曲线吻合度较好，能够较好地达成期望的预报效果。随着应力强度因子范围ΔK的增加，HTS-A钢疲劳裂纹扩展速率加快。本文提出的模型公式能够预报疲劳裂纹扩展速率。
4.2　低温下HTS-A钢模型的讨论分析
常温下HTS-A钢屈服强度为850 MPa，为获得低温影响因子，根据-20 ℃试验数据和公式（14）进行拟合，-20 ℃时屈服强度为920 MPa。根据公式（5）求得HTS-A钢的低温影响因子，从而计算其余低温下的屈服强度。同时，-20 ℃疲劳裂纹扩展速率试验及预报结果如图9所示。
根据公式（5）计算低温下的屈服强度，得到-40 ℃和-60 ℃下屈服强度分别为958 MPa和997 MPa，运用本文的模型公式（14）对其他温度的裂纹扩展进行预报验证，将其与试验数据对比，结果如图10~11所示。全部的对比曲线如图12所示。
为验证公式对其他未做的试验温度的适用性，运用本文的低温预报公式（14）对-10 ℃时疲劳裂纹扩展速率进行预报，-10 ℃下屈服强度为902 MPa，可以得到-10 ℃时的疲劳裂纹扩展速率曲线，如图13所示。
低温使得HTS-A钢的屈服强度增加，降低了HTS-A钢疲劳裂纹扩展速率。可以看出，低温下疲劳裂纹扩展速率的试验数据和预报曲线吻合度较好。运用公式（14）能够对HTS-A钢低温疲劳裂纹扩展进行预报，可以节省昂贵的低温试验成本。同时，采用本公式对-10 ℃时疲劳裂纹扩展速率进行预报，发现其低于常温时疲劳裂纹扩展速率，符合低温下的疲劳裂纹扩展速率变化规律，因此可以认为公式（14）能够对不同低温环境的HTS-A钢低温疲劳裂纹扩展速率进行预报。
公式（9）只需运用一组常温试验数据以及一组低温试验数据便可完成对不同低温环境的疲劳裂纹扩展速率预报，能够避免大量的低温试验，节省试验成本。试验数据为HTS-A钢运用于深海耐压壳提供了参考。
4.3　钛合金钢预报讨论分析
为验证本文提出的改进McEvily模型的推广性及适用性，选取文献[17]中钛合金疲劳裂纹扩展试验数据，运用公式（9）进行预报分析，A与m值采用最小二乘法进行拟合，得到钛合金低温疲劳裂纹扩展预报公式（15），钛合金常温下试验数据与预测数据对比如图14所示。
钛合金屈服强度为1104 MPa，为获得钛合金低温影响因子，根据-20 ℃时试验数据和公式（15）进行拟合，-20 ℃时屈服强度为1149 MPa。根据公式（15）求得钛合金的低温影响因子，从而计算其余低温下的屈服强度。同时，-20 ℃时疲劳裂纹扩展速率试验及预报结果如图15所示。
根据公式（15）计算低温下屈服强度，得到-40 ℃以及-60 ℃下的屈服强度分别为1172 MPa和1195 MPa。低温下试验数据与预测数据对比如图16~17所示，全部的对比曲线如图18所示。
通过试验与预报结果的对比可知，试验数值与预报数值吻合度较好。中速区钛合金裂纹扩展速率随温度降低而降低，-60 ℃时发生脆断裂纹扩展速率高于-40 ℃时的速率。公式（15）能够对12.5 mm厚钛合金疲劳裂纹扩展进行预报。
本文提出的改进McEvily模型公式（9）不仅适用于HTS-A钢，也适用于钛合金材料，具有良好的适用性和推广性。因此可以认为本文提出的改进McEvily模型可以适用于其他金属材料的预报分析，选用本公式可以避免大量昂贵的低温试验，节省材料的低温疲劳裂纹试验成本。
5　结论
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本文开展HTS-A钢常温及低温下疲劳裂纹扩展试验，提出了包含温度变量的改进McEvily疲劳裂纹扩展模型，利用最小二乘法进行了模型参数拟合，在该模型基础上对HTS-A钢的低温疲劳裂纹扩展速率进行了预报分析，将预报曲线与试验曲线对比分析，验证该模型对低温裂纹扩展速率的预报能力。选用文献中钛合金的低温试验数据，进一步验证该模型在其他金属材料中的推广性与适用性。通过研究得到以下结论：
（1）HTS-A钢具有优良的低温性能。根据HTS-A钢的疲劳裂纹扩展试验测得的不同低温下的a-N曲线和疲劳裂纹扩展速率结果表明，随着温度降低，HTS-A钢的疲劳寿命得到增加，-60 ℃时寿命最大。同时，随着温度降低，裂纹扩展速率会降低，在-60 ℃时未发生低温脆断。
（2）基于本文的HTS-A钢疲劳裂纹扩展速率试验和试验数据，本文提出了包含温度项的疲劳裂纹扩展速率公式。该模型能对不同低温环境下的HTS-A钢疲劳裂纹扩展速率进行较好的预报，对未进行试验的-10 ℃条件下的疲劳裂纹扩展速率也能达到较好的预报效果。通过文献中钛合金材料疲劳试验数据的再次验证，该模型具有应用于其他金属材料的可推广性。
（3）本文提出了包含温度项的疲劳裂纹扩展速率公式，采用此模型只需要一组常温和一组低温共两组疲劳裂纹扩展速率试验数据，便可对不同低温环境下的疲劳裂纹扩展速率进行预报，避免大量低温试验，节省低温试验成本。
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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doi: 10.3969/j.issn.1007-7294.2024.02.010
  • 接收时间：2023-08-10
  • 首发时间：2026-03-21
  • 出版时间：2024-02-20
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  • 收稿日期：2023-08-10
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.中国船舶科学研究中心，江苏　无锡　214082

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