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Article(id=1324427102421918324, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1324426994615727048, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1007-7294.2026.09.013, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1776268800000, receivedDateStr=2026-04-16, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793697627883, onlineDateStr=2026-11-03, pubDate=1789401600000, pubDateStr=2026-09-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793697627883, onlineIssueDateStr=2026-11-03, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793697627883, creator=13701087609, updateTime=1793697627883, updator=13701087609, issue=Issue{id=1324426994615727048, tenantId=1146029695717560320, journalId=1240685776644648972, year='2026', volume='30', issue='9', pageStart='1397', pageEnd='1576', issueExtLink='null', onlineDate='null', pubDate='1789401600000', pubDateStr='2026-09-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1793697602180, creator='13701087609', updateTime=1793699937016, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1324436787699000005, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1324426994615727048, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1324436787699000006, tenantId=1146029695717560320, journalId=1240685776644648972, issueId=1324426994615727048, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=1543, endPage=1554, ext={EN=ArticleExt(id=1324427102648410741, articleId=1324427102421918324, tenantId=1146029695717560320, journalId=1240685776644648972, language=EN, title=Creep buckling analysis of PMMA submersible pressure resistant shells, columnId=1242129251223274417, journalTitle=Journal of Ship Mechanics, columnName=Structural Mechanics, runingTitle=null, highlight=null, articleAbstract=

Polymethyl Methacrylate (PMMA) has become a key material for pressure-resistant shells of full-view manned submersibles due to its high transparency, light weight and excellent pressure resistance. However, the viscoelastic creep behavior of PMMA material itself has a significant impact on the long-term reliability of the structure. Therefore, the creep buckling mechanism of PMMA pressure spherical shells and their remaining ultimate load carrying capacity were investigated based on the viscoelastic properties of PMMA. Firstly, the non-linear influence law of stress level and time on the creep behavior of PMMA was revealed through creep tensile tests. Based on short-term test data, creep curves applicable to different stress levels were obtained by applying the time-stress equivalence principle while the applicability of the Burgers model and the modified Burgers model was discussed and analyzed. Subsequently, based on the modified Burgers model and numerical simulations, the influence of key factors, like initial geometric defects, the thickness-to-diameter ratio and working depth on the residual ultimate load of spherical shells after different creep durations was analyzed. The research results can provide certain theoretical basis and data support for the design, safety assessment and life prediction of full-view PMMA pressure-resistant structures.

, authors=Yong-mei ZHU, Guan-jie XU, Li-hui WANG, authorsList=Yong-mei ZHU, Guan-jie XU, Li-hui WANG, authorCompany=null, correspAuthors=null, authorNote=null, correspAuthorsNote=null, copyrightStatement=Copyright ©2026 Journal of Ship Mechanics. All rights reserved., 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, fund=null), CN=ArticleExt(id=1324427108944061117, articleId=1324427102421918324, tenantId=1146029695717560320, journalId=1240685776644648972, language=CN, title=PMMA潜水器耐压壳蠕变屈曲分析, columnId=1241023038926410098, journalTitle=船舶力学, columnName=结构力学, runingTitle=null, highlight=null, articleAbstract=

有机玻璃（PMMA）因其高透明度、轻量化及优良的耐压性能，已成为全通透载人潜水器耐压壳的关键材料。然而，PMMA材料本身的粘弹性蠕变行为对结构的长期可靠性具有显著影响，因此本文基于有机玻璃的粘弹性特性，探究PMMA耐压球壳的蠕变屈曲机理及其剩余极限承载能力。首先，通过蠕变拉伸试验，揭示应力水平和时间对PMMA蠕变行为的非线性影响规律。基于短期试验数据，运用时间−应力等效原理获得适用于不同应力水平的蠕变曲线，并讨论分析Burgers模型与修正Burgers模型的适用性。随后，基于修正的Burgers模型与数值模拟，分析初始几何缺陷、厚径比及工作深度等关键因素在不同蠕变时长下对球壳剩余极限载荷的影响规律。研究成果可为全通透PMMA耐压结构的设计、安全评估与寿命预测提供一定的理论依据和数据支撑。

, authors=朱永梅, 许冠杰, 王黎辉, authorsList=朱永梅, 许冠杰, 王黎辉, authorCompany=null, correspAuthors=null, authorNote=

朱永梅（1969–），女，博士，教授，E-mail：

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朱永梅（1969–），女，博士，教授，E-mail：

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朱永梅（1969–），女，博士，教授，E-mail：

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tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=CN, orderNo=2, keyword=球形耐压壳), Keyword(id=1324427422568952672, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=CN, orderNo=3, keyword=蠕变行为), Keyword(id=1324427422627672929, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=CN, orderNo=4, keyword=剩余极限载荷)], refs=[Reference(id=1324427429116261258, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=1, rfOrder=0, authorNames=null, journalName=null, refType=null, unstructuredReference=刘 帅, 叶 聪, 汤国伟, 等. 国内首型全通透载客潜水器的设计与研制[J]. 中国造船, 2019, 60(3): 113‒120., articleTitle=null, refAbstract=null), Reference(id=1324427430823342987, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=1, rfOrder=1, authorNames=null, journalName=null, refType=null, unstructuredReference=Liu S, Ye C, Tang G W et al. Design and development of the first acrylic-hulled submersible in China[J]. Shipbuilding of China, 2019, 60(3): 113‒120. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1324427431116944268, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=2, rfOrder=2, authorNames=null, journalName=null, refType=null, unstructuredReference=He Z H, Wang F, Wang H X, et al. Parametric analysis on creep deformation of deep-sea PMMA observation window[J]. Applied Sciences, 2024, 14: 2076-3417., articleTitle=null, refAbstract=null), Reference(id=1324427431192441741, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=3, rfOrder=3, authorNames=null, journalName=null, refType=null, unstructuredReference=穆霞英. 蠕变力学[M]. 西安: 西安交通大学出版社, 2022., articleTitle=null, refAbstract=null), Reference(id=1324427431297299342, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=3, rfOrder=4, authorNames=null, journalName=null, refType=null, unstructuredReference=Mu X Y. Creep mechanics[M]. Xi'an: Xi'an Jiaotong University Press, 2022. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1324427431561540495, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=4, rfOrder=5, authorNames=null, journalName=null, refType=null, unstructuredReference=Lin L, Hui L, Tao J, et al. Experimental study on the effects of hygrothermal aging on the indentation creep behaviors of PMMA[J]. Polymer Testing, 2021, 94(106991): 0142-9418., articleTitle=null, refAbstract=null), Reference(id=1324427431653815184, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=5, rfOrder=6, authorNames=null, journalName=null, refType=null, unstructuredReference=陈 薇, 屈 平, 张爱锋. 基于压缩蠕变试验的观察窗蠕变特性研究[J]. 船舶力学, 2021, 25(1): 73‒79., articleTitle=null, refAbstract=null), Reference(id=1324427431725118353, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=5, rfOrder=7, authorNames=null, journalName=null, refType=null, unstructuredReference=Chen W, Qu P, Zhang A F. Study on viewport creep characteristics based on compression creep test[J]. Journal of Ship Mechanics, 2021, 25(1): 73‒79. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1324427431800615826, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=6, rfOrder=8, authorNames=null, journalName=null, refType=null, unstructuredReference=陈 薇, 万正权, 屈 平, 等. 考虑温度和应力影响的有机玻璃加速蠕变试验方法[J]. 船舶力学, 2025, 29(5): 755‒766., articleTitle=null, refAbstract=null), Reference(id=1324427431871918995, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=6, rfOrder=9, authorNames=null, journalName=null, refType=null, unstructuredReference=Chen W, Wan Z Q, Qu P, et al. Accelerated creep test method of PMMA considering the influence of temperature and stress[J]. Journal of Ship Mechanics, 2025, 29(5): 755‒766. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1324427432018719636, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=7, rfOrder=10, authorNames=null, journalName=null, refType=null, unstructuredReference=Adibeig S V T F. Optimum creep lifetime of Polymethyl Methacrylate (PMMA) tube using rheological creep constitutive models based on experimental data[J]. Polymer Testing, 2019, 75: 107-116., articleTitle=null, refAbstract=null), Reference(id=1324427432106800021, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=8, rfOrder=11, authorNames=null, journalName=null, refType=null, unstructuredReference=Xu S X, Lin J P, et al. Experimental and numerical buckling analysis of cylindrical pressure hulls with multi-circular openings[J]. Ocean Engineering, 2020, 214: 0029-8018., articleTitle=null, refAbstract=null), Reference(id=1324427432194880406, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=9, rfOrder=12, authorNames=null, journalName=null, refType=null, unstructuredReference=曹嘉庆. 基于蠕变特性的有机玻璃耐压球壳稳定性研究[D]. 哈尔滨: 哈尔滨工程大学, 2021., articleTitle=null, refAbstract=null), Reference(id=1324427432270377879, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=9, rfOrder=13, authorNames=null, journalName=null, refType=null, unstructuredReference=Cao J Q. Research on the stability of PMMA pressure spherical shell based on creep characteristics[D]. Harbin: Harbin Engineering University, 2021. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1324427432341681048, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=10, rfOrder=14, authorNames=null, journalName=null, refType=null, unstructuredReference=何志豪, 王 芳, 李友洁. 深海全通透耐压壳蠕变分析[J]. 力学与实践, 2024, 46(3): 559‒569., articleTitle=null, refAbstract=null), Reference(id=1324427432429761433, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=10, rfOrder=15, authorNames=null, journalName=null, refType=null, unstructuredReference=He Z H, Wang F, Li Y J. Analysis on creep deformation of deep-sea fullytransparent pressure-resistant hull[J]. Mechanics in Engineering, 2024, 46(3): 559‒569. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1324427432513647514, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=11, rfOrder=16, authorNames=null, journalName=null, refType=null, unstructuredReference=Zhou F, Du Y, Chen Z P, et al. Creep buckling analysis of PMMA pressure vessels for application in neutrino detectors[J]. International Journal of Pressure Vessels and Piping, 2019, 169: 170-176., articleTitle=null, refAbstract=null), Reference(id=1324427432584950683, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=12, rfOrder=17, authorNames=null, journalName=null, refType=null, unstructuredReference=Zhou F, Hou S J, Qian X H, et al. Creep behavior and lifetime prediction of PMMA immersed in liquid scintillator[J]. Polymer Testing, 2016, 53: 323-328., articleTitle=null, refAbstract=null), Reference(id=1324427432677225372, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=13, rfOrder=18, authorNames=null, journalName=null, refType=null, unstructuredReference=Wang L H, Zhu Y M, Zhao X L, et al. Buckling analysis of PMMA hemispherical pressure shells with thickness variation[J]. International Journal of Solids and Structures, 2025, 306: 113109., articleTitle=null, refAbstract=null), Reference(id=1324427432844997533, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=14, rfOrder=19, authorNames=null, journalName=null, refType=null, unstructuredReference=中国船级社. 潜水系统和潜水器入级与建造规范[S]. 北京: 人民交通出版社, 2018., articleTitle=null, refAbstract=null), Reference(id=1324427432924689310, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=14, rfOrder=20, authorNames=null, journalName=null, refType=null, unstructuredReference=China Classification Society. Rules for classification of diving systems and submersibles[S]. Beijing: China Communications Press, 2018. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1324427432991798175, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=15, rfOrder=21, authorNames=null, journalName=null, refType=null, unstructuredReference=高 杰. 深海球形耐压壳力学特性及试验研究[D]. 镇江: 江苏科技大学, 2017., articleTitle=null, refAbstract=null), Reference(id=1324427433079878560, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=15, rfOrder=22, authorNames=null, journalName=null, refType=null, unstructuredReference=Gao Jie. Investigation on mechanical properties of deep sea spherical pressure hull and experimental study[D]. Zhenjiang: Jiangsu University of Science and Technology, 2017. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1324427433151181729, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=16, rfOrder=23, authorNames=null, journalName=null, refType=null, unstructuredReference=ASTM D2990. Standard test methods for tensile, compressive, and flexural creep and creep-rupture of plastics[S]. West Conshohocken: ASTM International, 2017., articleTitle=null, refAbstract=null), Reference(id=1324427433226679202, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=17, rfOrder=24, authorNames=null, journalName=null, refType=null, unstructuredReference=Williams M L, Landel R F, Ferry J D. The temperature dependence of relaxation mechanisms in amorphous liquids[J]. Journal of the American Chemical Society, 1955, 77(14): 3701-3707., articleTitle=null, refAbstract=null), Reference(id=1324427433297982371, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=18, rfOrder=25, authorNames=null, journalName=null, refType=null, unstructuredReference=罗文波, 杨挺青, 安群力. 非线性粘弹体的时间−温度−应力等效原理及其应用[J]. 固体力学学报, 2001(3): 219‒224., articleTitle=null, refAbstract=null), Reference(id=1324427433411228580, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=18, rfOrder=26, authorNames=null, journalName=null, refType=null, unstructuredReference=Luo W B, Yang T Q, An Q L. Time-temperature-stress equivalence principle for nonlinear viscoelastic bodies and its application[J]. Chinese Journal of Solid Mechanics, 2001(3): 219‒224. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1324427433486726053, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=19, rfOrder=27, authorNames=null, journalName=null, refType=null, unstructuredReference=Findley W N, Lai J S, Onaran K. Creep and relaxation of nonlinear viscoelastic materials: with an introduction to linear viscoelasticity[M]. Amsterdam: North-Holland, 1976., articleTitle=null, refAbstract=null), Reference(id=1324427433562223526, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=20, rfOrder=28, authorNames=null, journalName=null, refType=null, unstructuredReference=周华樟. 旋切板胶合木的蠕变及其对结构稳定性的影响[D]. 哈尔滨: 哈尔滨工业大学, 2009., articleTitle=null, refAbstract=null), Reference(id=1324427433637720999, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=20, rfOrder=29, authorNames=null, journalName=null, refType=null, unstructuredReference=Zhou H Z. Creep of laminated veneer lumber and its influence on structural stability[D]. Harbin: Harbin Institute of Technology, 2009. (in Chinese), articleTitle=null, refAbstract=null), Reference(id=1324427435328025513, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, doi=null, pmid=null, pmcid=null, year=null, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=21, rfOrder=30, authorNames=null, journalName=null, refType=null, unstructuredReference=Hoff N J. Rules and methods of stress and stability calculations in the presence of creep[J]. 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Fitting parameters of the Burgers model at different stresses

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应力 /MPa蠕变模型参数相关系数
E1 /MPaE2 /MPaη2 /（MPa·s）η1 /（MPa·s）
26.18333593694.066×1067.454×1070.9913
29.22311872802.972×1065.753×1070.9987
32.14292264252.604×1063.893×1070.9983
35.06263259002.493×1062.933×1070.9965
38234143431.381×1061.819×1070.9973
41.0120721002.564×1068.969×10320.9843
29.22（长期）2068−16224.165×10888.969×10320.9727
), ArticleFig(id=1324427426729702269, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=CN, label=表1, caption=

Burgers模型在不同应力下的拟合参数

, figureFileSmall=null, figureFileBig=null, tableContent=
应力 /MPa蠕变模型参数相关系数
E1 /MPaE2 /MPaη2 /（MPa·s）η1 /（MPa·s）
26.18333593694.066×1067.454×1070.9913
29.22311872802.972×1065.753×1070.9987
32.14292264252.604×1063.893×1070.9983
35.06263259002.493×1062.933×1070.9965
38234143431.381×1061.819×1070.9973
41.0120721002.564×1068.969×10320.9843
29.22（长期）2068−16224.165×10888.969×10320.9727
), ArticleFig(id=1324427426993943422, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=EN, label=Tab.2, caption=

Fitting parameters of the modified Burgers model

, figureFileSmall=null, figureFileBig=null, tableContent=
应力 /MPa蠕变模型参数相关系数
E1 /MPaE2 /MPaη2 /（MPa·s）A /（MPa·s）B /s−1
26.18319369914.865×1062.911×1075.012×10−40.9898
29.22306020212.542×1061.700×1072.759×10−40.9875
32.14292784622.418×1061.667×1072.749×10−40.9999
35.06263595502.254×1061.199×1072.725×10−40.9998
38.00232361671.328×1069.273×1062.064×10−40.9997
41.01207256181.069×1064.753×106−1.933×10−40.9998
29.22（长期）311835711.229×1067.986×107−7.549×10−60.9913
), ArticleFig(id=1324427427077829503, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=CN, label=表2, caption=

修正的Burgers模型的拟合参数

, figureFileSmall=null, figureFileBig=null, tableContent=
应力 /MPa蠕变模型参数相关系数
E1 /MPaE2 /MPaη2 /（MPa·s）A /（MPa·s）B /s−1
26.18319369914.865×1062.911×1075.012×10−40.9898
29.22306020212.542×1061.700×1072.759×10−40.9875
32.14292784622.418×1061.667×1072.749×10−40.9999
35.06263595502.254×1061.199×1072.725×10−40.9998
38.00232361671.328×1069.273×1062.064×10−40.9997
41.01207256181.069×1064.753×106−1.933×10−40.9998
29.22（长期）311835711.229×1067.986×107−7.549×10−60.9913
), ArticleFig(id=1324427427149132672, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=EN, label=Tab.3, caption=

Parameter fitting results of the modified Burgers model

, figureFileSmall=null, figureFileBig=null, tableContent=
应力 /MPa蠕变模型参数相关系数
E1 /MPaE2 /MPaη2 /（MPa·s）A /（MPa·s）B /s−1
18.221376623984.718×1081.766×1010−2.988×10−80.9863
21.407356923822.351×1085.097×109−6.459×10−80.9849
), ArticleFig(id=1324427427237213057, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=CN, label=表3, caption=

修正的Burgers模型参数拟合

, figureFileSmall=null, figureFileBig=null, tableContent=
应力 /MPa蠕变模型参数相关系数
E1 /MPaE2 /MPaη2 /（MPa·s）A /（MPa·s）B /s−1
18.221376623984.718×1081.766×1010−2.988×10−80.9863
21.407356923822.351×1085.097×109−6.459×10−80.9849
), ArticleFig(id=1324427427438539650, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=EN, label=Tab.4, caption=

Residual ultimate loads of spherical shell based on different modal imperfections

, figureFileSmall=null, figureFileBig=null, tableContent=
蠕变时间
$ {T}_{i} $ /天		模态缺陷大小δ /mm
12345
注：括号中为缺陷因子k1，表示考虑蠕变变形后的极限载荷与未考虑蠕变变形的极限载荷的比值。
04.2543.673.2652.9512.705
0.54.165（0.979）3.542（0.965）3.106（0.951）2.761（0.936）2.469（0.913）
14.157（0.977）3.526（0.961）3.084（0.945）2.73（0.925）2.425（0.896）
24.138（0.973）3.499（0.953）3.052（0.935）2.688（0.911）2.373（0.877）
44.112（0.967）3.463（0.944）3.009（0.922）2.640（0.895）2.331（0.862）
64.092（0.962）3.442（0.938）2.985（0.914）2.619（0.887）2.312（0.855）
84.085（0.960）3.431（0.935）2.970（0.910）2.608（0.884）2.298（0.850）
104.078（0.959）3.422（0.932）2.962（0.907）2.600（0.881）2.285（0.845）
204.065（0.956）3.409（0.929）2.942（0.901）2.574（0.872）2.220（0.821）
304.061（0.955）3.402（0.927）2.929（0.897）2.552（0.864）2.152（0.796）
404.056（0.953）3.395（0.925）2.916（0.893）2.529（0.857）2.083（0.770）
504.048（0.952）3.388（0.923）2.903（0.889）2.503（0.848）2.015（0.745）
), ArticleFig(id=1324427427803444099, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=CN, label=表4, caption=

基于不同模态缺陷的球壳剩余极限载荷（MPa）

, figureFileSmall=null, figureFileBig=null, tableContent=
蠕变时间
$ {T}_{i} $ /天		模态缺陷大小δ /mm
12345
注：括号中为缺陷因子k1，表示考虑蠕变变形后的极限载荷与未考虑蠕变变形的极限载荷的比值。
04.2543.673.2652.9512.705
0.54.165（0.979）3.542（0.965）3.106（0.951）2.761（0.936）2.469（0.913）
14.157（0.977）3.526（0.961）3.084（0.945）2.73（0.925）2.425（0.896）
24.138（0.973）3.499（0.953）3.052（0.935）2.688（0.911）2.373（0.877）
44.112（0.967）3.463（0.944）3.009（0.922）2.640（0.895）2.331（0.862）
64.092（0.962）3.442（0.938）2.985（0.914）2.619（0.887）2.312（0.855）
84.085（0.960）3.431（0.935）2.970（0.910）2.608（0.884）2.298（0.850）
104.078（0.959）3.422（0.932）2.962（0.907）2.600（0.881）2.285（0.845）
204.065（0.956）3.409（0.929）2.942（0.901）2.574（0.872）2.220（0.821）
304.061（0.955）3.402（0.927）2.929（0.897）2.552（0.864）2.152（0.796）
404.056（0.953）3.395（0.925）2.916（0.893）2.529（0.857）2.083（0.770）
504.048（0.952）3.388（0.923）2.903（0.889）2.503（0.848）2.015（0.745）
), ArticleFig(id=1324427427912496004, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=EN, label=Tab.5, caption=

Residual ultimate loads of spherical shell based on t/R

, figureFileSmall=null, figureFileBig=null, tableContent=
蠕变时间
Ti /天		厚径比 t/R
0.030.0350.040.0450.05
注：括号中是几何因子k2，表示考虑蠕变变形后的极限载荷与未考虑蠕变变形的极限载荷的比值。
02.2362.8943.674.5565.349
0.52.098（0.938）2.769（0.957）3.542（0.965）4.487（0.985）5.290（0.989）
12.065（0.924）2.737（0.946）3.526（0.961）4.480（0.983）5.284（0.988）
22.045（0.915）2.706（0.935）3.499（0.953）4.467（0.980）5.271（0.985）
41.999（0.894）2.656（0.918）3.463（0.944）4.442（0.975）5.254（0.982）
61.980（0.886）2.636（0.911）3.442（0.938）4.420（0.970）5.238（0.979）
81.960（0.877）2.621（0.906）3.431（0.935）4.412（0.968）5.232（0.978）
101.939（0.867）2.611（0.902）3.422（0.932）4.407（0.967）5.228（0.977）
201.834（0.820）2.589（0.895）3.409（0.929）4.394（0.964）5.216（0.975）
301.714（0.766）2.568（0.887）3.402（0.927）4.390（0.964）5.212（0.974）
401.582（0.708）2.553（0.882）3.395（0.925）4.387（0.963）5.211（0.974）
501.439（0.644）2.537（0.877）3.388（0.923）4.383（0.962）5.210（0.974）
), ArticleFig(id=1324427428222874501, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=CN, label=表5, caption=

基于不同厚径比t/R的球壳剩余极限载荷（MPa）

, figureFileSmall=null, figureFileBig=null, tableContent=
蠕变时间
Ti /天		厚径比 t/R
0.030.0350.040.0450.05
注：括号中是几何因子k2，表示考虑蠕变变形后的极限载荷与未考虑蠕变变形的极限载荷的比值。
02.2362.8943.674.5565.349
0.52.098（0.938）2.769（0.957）3.542（0.965）4.487（0.985）5.290（0.989）
12.065（0.924）2.737（0.946）3.526（0.961）4.480（0.983）5.284（0.988）
22.045（0.915）2.706（0.935）3.499（0.953）4.467（0.980）5.271（0.985）
41.999（0.894）2.656（0.918）3.463（0.944）4.442（0.975）5.254（0.982）
61.980（0.886）2.636（0.911）3.442（0.938）4.420（0.970）5.238（0.979）
81.960（0.877）2.621（0.906）3.431（0.935）4.412（0.968）5.232（0.978）
101.939（0.867）2.611（0.902）3.422（0.932）4.407（0.967）5.228（0.977）
201.834（0.820）2.589（0.895）3.409（0.929）4.394（0.964）5.216（0.975）
301.714（0.766）2.568（0.887）3.402（0.927）4.390（0.964）5.212（0.974）
401.582（0.708）2.553（0.882）3.395（0.925）4.387（0.963）5.211（0.974）
501.439（0.644）2.537（0.877）3.388（0.923）4.383（0.962）5.210（0.974）
), ArticleFig(id=1324427428591973254, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=EN, label=Tab.6, caption=

Residual ultimate loads of spherical shell based on different working depths

, figureFileSmall=null, figureFileBig=null, tableContent=
蠕变时间
Ti /天		工作深度 H /m
6080100120140
注：括号中是水深因子k3，表示考虑蠕变变形后的极限载荷与未考虑蠕变变形的极限载荷的比值。
03.670
0.53.648（0.995）3.621（0.987）3.542（0.965）3.463（0.944）3.282（0.894）
13.644（0.993）3.614（0.985）3.526（0.961）3.441（0.938）3.228（0.880）
23.636（0.991）3.601（0.981）3.499（0.953）3.402（0.927）3.158（0.860）
43.624（0.987）3.579（0.975）3.463（0.944）3.357（0.915）3.108（0.847）
63.614（0.985）3.566（0.972）3.442（0.938）3.331（0.908）3.082（0.840）
83.608（0.983）3.558（0.969）3.431（0.935）3.321（0.905）3.056（0.833）
103.604（0.982）3.550（0.967）3.422（0.932）3.317（0.904）3.036（0.827）
203.594（0.979）3.535（0.963）3.409（0.929）3.297（0.898）2.931（0.799）
303.592（0.979）3.531（0.962）3.402（0.927）3.278（0.893）2.799（0.762）
403.591（0.978）3.529（0.962）3.395（0.925）3.259（0.888）2.685（0.732）
503.590（0.978）3.528（0.961）3.388（0.923）3.239（0.883）2.544（0.693）
), ArticleFig(id=1324427428667470727, tenantId=1146029695717560320, journalId=1240685776644648972, articleId=1324427102421918324, language=CN, label=表6, caption=

基于不同工作深度的球壳剩余极限载荷（MPa）

, figureFileSmall=null, figureFileBig=null, tableContent=
蠕变时间
Ti /天		工作深度 H /m
6080100120140
注：括号中是水深因子k3，表示考虑蠕变变形后的极限载荷与未考虑蠕变变形的极限载荷的比值。
03.670
0.53.648（0.995）3.621（0.987）3.542（0.965）3.463（0.944）3.282（0.894）
13.644（0.993）3.614（0.985）3.526（0.961）3.441（0.938）3.228（0.880）
23.636（0.991）3.601（0.981）3.499（0.953）3.402（0.927）3.158（0.860）
43.624（0.987）3.579（0.975）3.463（0.944）3.357（0.915）3.108（0.847）
63.614（0.985）3.566（0.972）3.442（0.938）3.331（0.908）3.082（0.840）
83.608（0.983）3.558（0.969）3.431（0.935）3.321（0.905）3.056（0.833）
103.604（0.982）3.550（0.967）3.422（0.932）3.317（0.904）3.036（0.827）
203.594（0.979）3.535（0.963）3.409（0.929）3.297（0.898）2.931（0.799）
303.592（0.979）3.531（0.962）3.402（0.927）3.278（0.893）2.799（0.762）
403.591（0.978）3.529（0.962）3.395（0.925）3.259（0.888）2.685（0.732）
503.590（0.978）3.528（0.961）3.388（0.923）3.239（0.883）2.544（0.693）
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PMMA潜水器耐压壳蠕变屈曲分析
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朱永梅 , 许冠杰 , 王黎辉
船舶力学 | 结构力学 2026,30(9): 1543-1554
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船舶力学 |结构力学 2026 , 30 (9) : 1543 -1554
PMMA潜水器耐压壳蠕变屈曲分析
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朱永梅 , 许冠杰, 王黎辉
作者信息
  • 江苏科技大学，江苏 镇江 212100
作者简介:

朱永梅（1969–），女，博士，教授，E-mail：

Creep buckling analysis of PMMA submersible pressure resistant shells
Yong-mei ZHU , Guan-jie XU, Li-hui WANG
Affiliations
  • Jiangsu University of Science and Technology, Zhenjiang 212100, China
出版时间: 2026-09-15 doi: 10.3969/j.issn.1007-7294.2026.09.013
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摘要
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有机玻璃（PMMA）因其高透明度、轻量化及优良的耐压性能，已成为全通透载人潜水器耐压壳的关键材料。然而，PMMA材料本身的粘弹性蠕变行为对结构的长期可靠性具有显著影响，因此本文基于有机玻璃的粘弹性特性，探究PMMA耐压球壳的蠕变屈曲机理及其剩余极限承载能力。首先，通过蠕变拉伸试验，揭示应力水平和时间对PMMA蠕变行为的非线性影响规律。基于短期试验数据，运用时间−应力等效原理获得适用于不同应力水平的蠕变曲线，并讨论分析Burgers模型与修正Burgers模型的适用性。随后，基于修正的Burgers模型与数值模拟，分析初始几何缺陷、厚径比及工作深度等关键因素在不同蠕变时长下对球壳剩余极限载荷的影响规律。研究成果可为全通透PMMA耐压结构的设计、安全评估与寿命预测提供一定的理论依据和数据支撑。

有机玻璃  /  球形耐压壳  /  蠕变行为  /  剩余极限载荷

Polymethyl Methacrylate (PMMA) has become a key material for pressure-resistant shells of full-view manned submersibles due to its high transparency, light weight and excellent pressure resistance. However, the viscoelastic creep behavior of PMMA material itself has a significant impact on the long-term reliability of the structure. Therefore, the creep buckling mechanism of PMMA pressure spherical shells and their remaining ultimate load carrying capacity were investigated based on the viscoelastic properties of PMMA. Firstly, the non-linear influence law of stress level and time on the creep behavior of PMMA was revealed through creep tensile tests. Based on short-term test data, creep curves applicable to different stress levels were obtained by applying the time-stress equivalence principle while the applicability of the Burgers model and the modified Burgers model was discussed and analyzed. Subsequently, based on the modified Burgers model and numerical simulations, the influence of key factors, like initial geometric defects, the thickness-to-diameter ratio and working depth on the residual ultimate load of spherical shells after different creep durations was analyzed. The research results can provide certain theoretical basis and data support for the design, safety assessment and life prediction of full-view PMMA pressure-resistant structures.

PMMA  /  spherical pressure shell  /  creep behavior  /  residual ultimate load
朱永梅, 许冠杰, 王黎辉. PMMA潜水器耐压壳蠕变屈曲分析. 船舶力学, 2026 , 30 (9) : 1543 -1554 . DOI: 10.3969/j.issn.1007-7294.2026.09.013
Yong-mei ZHU, Guan-jie XU, Li-hui WANG. Creep buckling analysis of PMMA submersible pressure resistant shells[J]. Journal of Ship Mechanics, 2026 , 30 (9) : 1543 -1554 . DOI: 10.3969/j.issn.1007-7294.2026.09.013
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0　引言
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随着海洋资源开发的推进与海底旅游产业的不断发展，对水下观光潜水器（图1）的需求也愈发迫切[1]。由于传统金属材料壳体存在视野盲区、视野狭窄等缺点，逐渐被有机玻璃代替。聚甲基丙烯酸甲酯（PMMA），俗称有机玻璃，因其具备高透光率、低密度、优良的力学性能和耐腐蚀性，成为制造全通透载人舱体的首选材料[2]。
然而，耐压壳作为潜水器的核心承压部件，其长期结构安全与可靠性是设计的根本前提。PMMA属于典型的粘弹性高分子材料，在持续载荷作用下，即便处于常温环境中也会表现出明显的蠕变行为，进而影响结构的安全性能[3]。因此，研究粘弹性材料的蠕变问题及粘弹性结构的蠕变屈曲问题非常有必要。Lin等[4]基于压痕蠕变试验发现，PMMA的蠕变位移会随湿热老化处理时间的增加而增大；陈薇等[5−6]基于YB-3有机玻璃蠕变试验数据，采用最小二乘法拟合压缩蠕变本构方程，并结合有限元分析了不同观察窗的蠕变特性；Adibeig等[7]通过仿真结合试验，提出了可以估算PMMA旋转加压管蠕变寿命的Burgers模型；Xu等[8]研究了不同蠕变时间后圆柱壳的极限承载能力，发现蠕变行为会导致圆柱壳的极限载荷显著降低；曹嘉庆[9]基于有限元方法，研究了载荷大小和厚径比对球壳蠕变屈曲临界时间的影响；何志豪等[10]基于有机玻璃试验数据，对完整球壳、单开孔球壳、双开孔球壳及三开孔球壳在不同载荷与温度下应变及位移进行了分析；周凡等[11-12]基于浸入液体闪烁体中的PMMA 蠕变试验数据，揭示了PMMA球形压力容器最大应力与蠕变屈曲时间之间的关系。
尽管目前已有一些研究关注PMMA材料的蠕变特性及其在海洋环境中的应用，但仍存在以下问题：（1）现有研究多集中于短期蠕变行为，对长期蠕变效应及其引起的结构极限承载能力下降问题研究不足；（2）初始几何缺陷、厚径比及工作深度等关键因素在不同蠕变时长下对球壳剩余极限载荷的影响规律，目前尚缺乏系统性分析。因此，本文首先在室温下进行多组恒定载荷蠕变拉伸试验，分析应力水平和时间对PMMA材料蠕变行为的影响，获得蠕变本构模型，并建立修正的Burgers蠕变本构模型；同时，将该修正模型用于蠕变屈曲有限元分析；最后，基于蠕变变形，采用数值分析方法，系统研究初始几何缺陷、厚径比及工作深度对PMMA球壳在不同蠕变时间后剩余极限载荷的影响规律。
1　PMMA球壳屈曲分析
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本文选择300 m为设计深度。参考传统载人潜水器的设计，研究对象为直径2 m的球壳。有机玻璃材料属性通过拉伸试验测得：弹性模量E=3078 MPa，泊松比μ=0.38，抗拉强度σb =63.9 MPa。
根据式（1）计算得到300 m水深压强为
$ {P}_{\sigma }=k{\rho }_{{\mathrm{w}}}gH/0.9 $
式中：k为安全系数；$ {\rho }_{{\mathrm{w}}} $为海水密度；g为重力加速度；H为海水深度。为保证人员安全，这里k取为1.4，$ {\rho }_{{\mathrm{w}}} $=1.025 g/cm3，g=9.8 m/s2，H=300 m。
通过计算，300 m工作水深下球壳的外压载荷为$ {P}_{\sigma } $=4.688 MPa。对于PMMA中厚度球壳，当R/t低于31.173时，强度失效成为评估的重点[13]，因此根据式（2）计算球壳的最大半径厚度比R/t。
$ \dfrac{2{\sigma }_{{\mathrm{i}}}\left[{\left(2+\dfrac{1}{R/t}\right)}^{3}-{\left(2-\dfrac{1}{R/t}\right)}^{3}\right]}{3{\left(2+\dfrac{1}{R/t}\right)}^{3}}\geq {P}_{\sigma } $
式中：R为球壳的半径；σi为球壳内表面应力，这里取σi=$ {\sigma }_{{\mathrm{b}}} $=63.9 MPa。
计算得出球壳的半径厚度比R/t ≤ 25.64。这里半径厚度比R/t取25。
根据中国船级社《潜水系统与潜水器入级规范》[14]中关于壳体整体圆度容差要求与极限承载力有限元分析方法的相关规定，本文基于模态缺陷法对球壳设置初始几何缺陷大小并进行有限元分析。高杰[15]研究发现1阶模态缺陷并不能代表球形耐压壳的最差缺陷。为此，本文基于前50阶特征值屈曲模态，采用修正的Riks分析法计算了2 mm缺陷下的非线性屈曲载荷，以确定最差模态。
有限元模型采用ABAQUS软件中的8节点3D线性体单元。在进行数值分析前，研究了7种网格尺寸对线性屈曲分析结果的影响，网格尺寸分别为20 mm、30 mm、40 mm、50 mm、60 mm、70 mm和80 mm。边界条件选择三点约束[15]。从图2可以看出，网格尺寸对线性屈曲分析结果有着显著影响。当网格尺寸小于30 mm时，临界屈曲载荷值变化小于3%。因此，数值模型网格尺寸选择30 mm。同时为保证厚度方向的计算精度，沿厚度方向至少划分2个以上单元，对应厚度方向单元尺寸不超过模型实际厚度的1/2，这里取15 mm。
几何缺陷为2 mm时，不同模态阶数的非线性屈曲载荷PNLBA和线性屈曲载荷PLBA之比如图3所示。可以看出，以1阶模态为初始缺陷的非线性临界屈曲载荷为3.71 MPa，是对应线性屈曲载荷（7.40 MPa）的50.1%，但不是最小。对于前50阶模态，27阶模态缺陷是导致极限承载力下降幅度最大的阶数，其非线性临界屈曲载荷为3.67 MPa，仅是线性屈曲计算结果（7.64 MPa）的48%。因此，在后续蠕变分析以及蠕变屈曲分析中均以27阶模态为初始缺陷进行计算。
2　PMMA球壳蠕变屈曲分析
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2.1　PMMA蠕变本构模型
为研究有机玻璃的蠕变行为，蠕变拉伸载荷设置为拉伸极限强度的40%~65%。拉伸及蠕变试验试样均按照ASME-D2990[16]加工成标准样件，尺寸如图4所示。按照ASME-D2990[16]标准，进行了六个不同载荷水平的蠕变试验。蠕变拉伸载荷分别为450 N、500 N、550 N、600 N、650 N和700 N，对应的应力水平分别为26.18 MPa、29.22 MPa、32.14 MPa、35.06 MPa、38 MPa、41.01 MPa。每个应力水平进行了2次拉伸蠕变试验。其中，针对应力水平29.22 MPa开展了长期蠕变测试。试验在恒温恒湿条件下进行，温度控制在25±1 ℃，相对湿度控制在50±5％。加载阶段以50 N/s的加载速度开始，在10 s内加载完成，达到目标载荷后保持恒定。在试样损坏或持续加载5000 s时停止试验，并记录各时段的蠕变位移数据，从而计算出相应的蠕变应变。将得到的测试数据通过位移−时间曲线转换为应变−时间曲线，如图4所示。其中红色符号“×”表示不到5000 s就发生蠕变断裂的试件。
为了准确描述有机玻璃这一蠕变变形特性，本文采用Burgers本构模型，如式（3）所示
$ \varepsilon (t)=\frac{{\sigma }_{0}}{{E}_{1}}+\frac{{\sigma }_{0}}{{E}_{2}}\left(1-{{\mathrm{e}}}^{-\tfrac{{E}_{2}}{{\eta }_{2}}t}\right)+\frac{{\sigma }_{0}}{{\eta }_{1}}t $
式中：$ \varepsilon \left(t\right) $为总蠕变应变；$ {\sigma }_{0} $为恒定应力；t为蠕变时间；$ {E}_{1} $为瞬时弹性模量；$ {E}_{2} $为延迟弹性模量；$ {\eta }_{1} $为Maxwell体中的粘度系数；$ {\eta }_{2} $为Kelvin体中的粘度系数。
根据Burgers蠕变本构方程，使用MATLAB软件的非线性拟合工具箱对7组蠕变试验数据进行拟合。拟合曲线与模型参数结果分别如图5及表1所示。尽管拟合结果表现出较高的相关性，对于29.22 MPa的长期蠕变试验数据以及41.01 MPa高应力下的蠕变试验数据，拟合曲线近似呈直线上升，并未能有效描述试验数据变化特征，即蠕变三个阶段的特征。
由此可以看出Burgers模型只适合描述蠕变的减速和稳定蠕变阶段，在表征非线性加速蠕变行为方面存在显著局限性。为了准确描述有机玻璃这一蠕变变形特性，将Burgers 模型的外部粘壶$ {\eta }_{1} $修正为时间的函数，且使其粘度与时间有关，$ {\eta }_{1}=A{{\mathrm{e}}}^{-Bt} $，式（3）修正为
$ \varepsilon (t)=\frac{{\sigma }_{0}}{{E}_{1}}+\frac{{\sigma }_{0}}{{E}_{2}}\left(1-{{\mathrm{e}}}^{-\tfrac{{E}_{2}}{{\eta }_{2}}t}\right)+\int \frac{{\sigma }_{0}}{{\eta }_{1}(t)}{\mathrm{d}}t $
将$ {\eta }_{1}=A{{\mathrm{e}}}^{-Bt} $代入式（4）中，修正的本构模型为
$ \varepsilon (t)=\frac{{\sigma }_{0}}{{E}_{1}}+\frac{{\sigma }_{0}}{{E}_{2}}\left(1-{{\mathrm{e}}}^{-\tfrac{{E}_{2}}{{\eta }_{2}}t}\right)+\frac{{\sigma }_{0}}{AB}(1-{{\mathrm{e}}}^{-Bt}) $
将修正的模型分别与两组应力水平下的试验数据拟合，拟合曲线与参数拟合值分别如图6和表2所示。由结果可知，两组应力水平下的拟合曲线与试验数据相关系数均大于0.99，可以认为修正的Burgers模型能够正确区分减速、稳定以及加速蠕变阶段，能够准确反映出有机玻璃的变形特性。因此，后续蠕变屈曲分析均基于修正的Burgers模型开展。
2.2　有限元模型参数确定
对于球壳的蠕变屈曲分析，选取外压下结构的最大应力作为蠕变参考应力。以球壳工作水深140 m为例，对应的均布外压载荷为1.4063 MPa。首先进行静力分析以确定该外压作用下的最大结构应力。对于受均匀外压作用的理想球形耐压壳，其内表面应力最大。然而，含有初始几何缺陷的球壳，其最大应力不一定位于内表面。图7是140 m水深下完美球壳和含有模态缺陷球壳的结构应力分布云图。完美球壳的应力沿厚度方向由内至外逐渐减小，内表面的最大峰值应力为18.221 MPa。而当球壳存在初始缺陷时，耐压壳的应力分布呈现出与缺陷位置一致的趋势，但由于外压载荷为均匀分布，仅在凹陷处因局部弯矩作用而产生明显的应力集中，最大峰值应力为21.407 MPa。因此，本文以完美球壳和含有模态缺陷的球壳为研究对象进行分析。
2.3　蠕变屈曲有限元分析
由完美球壳和模态缺陷球壳计算得到的最大峰值应力分别为18.221 MPa与21.407 MPa，均低于蠕变拉伸试验的应力区间，无法直接获得对应的蠕变本构参数。因此，本文引入时间−应力等效原理[17−18]，对未测参考应力水平下的材料参数进行外推。具体流程为：（1）通过Findley经验方程[19]构建参考应力条件下的短期蠕变响应曲线；（2）依据公式（6）计算29.22 MPa至目标应力水平的位移因子，随后将29.22 MPa下的主曲线沿时间坐标轴向右平移相应的平移量，得到参考应力的蠕变主曲线；（3）采用修正后的Burgers方程式（5）对生成的应力水平主曲线进行方程拟合，最终得到的模型参数如表3所示。
$ \mathrm{\lg }{\varphi }_{\sigma }=\frac{-7.15(\sigma -{\sigma }_{{\mathrm{o}}})}{52.62+(\sigma -{\sigma }_{{\mathrm{o}}})} $
式中：$ {\varphi }_{\sigma } $为应力时间平移因子；$\sigma $为对应的应力水平。
蠕变屈曲的分析步中Visco分析步中的时间为实际的蠕变时间，需要设置一个较大的总分析步时间。分析步增量设置为3600 s，以确保获取不同时刻球壳变形后的网格节点信息以节约计算时间。其网格信息和边界条件设置均与第1节中屈曲分析部分相同。
图8是球壳在蠕变屈曲过程中的变形云图。为了分析两种球壳结构在不同蠕变时间下的变形行为，图8（a）展示了完美球壳在蠕变时间为0 h、125 h、675 h、1250 h、2500 h、7500 h、12500 h和14990 h时的位移云图。图8（b） 则展示了含有2 mm模态缺陷的球壳在蠕变时间分别为0 h、24 h、120 h、240 h、480 h、1200 h、2400 h和3176 h时的位移云图。通过图中的变形图可见，完美球壳在初期的变形位移呈现随机分布，且具有高度对称性；而在存在模态缺陷的情况下，蠕变变形后的位移呈现出增大初始缺陷幅度的趋势，且表现出非均匀分布的特征，其中凹陷区域的位移最大值为184.864 mm，这与耐压壳的初始应力分布密切相关。因此，蠕变变形不仅会导致几何缺陷的扩大，还会进一步降低球壳的极限承载能力。
由图8可知，含有缺陷的球壳的变形幅度随着时间的延长逐渐增大，当时间达到3176 h时，位移增大幅值在短时间内开始迅速增大，表明球壳此时发生了蠕变屈曲。相对而言，完美球壳在3176 h时仍处于稳定蠕变阶段，直至14990 h才出现蠕变屈曲现象。图9是两种球壳蠕变屈曲最大塌陷处的位移−时间曲线图。基于变形速率判别准则[20−21]可知，当发现变形或变形速率显著增加时，可以认为结构发生了蠕变屈曲。值得注意的是，含缺陷球壳的蠕变屈曲临界时间仅为完美球壳总时间的21.2%。这表明，含有初始缺陷的球壳在相同外载荷下，其蠕变屈曲临界时间显著缩短。由此可见，有机玻璃材料的蠕变特性对球壳的工作寿命具有显著影响。
3　有机玻璃球壳蠕变变形对极限载荷的影响因素分析
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3.1　初始几何缺陷影响分析
为深入分析初始几何缺陷对有机玻璃球壳极限载荷的影响，本文将特征值屈曲模态作为球壳的初始几何缺陷。分别取缺陷大小为1 mm、2 mm、3 mm、4 mm和5 mm，设定50天为蠕变时间上限，蠕变时间（天）$ {T}_{i} $取值为0、0.5、1、2、4、6、8、10、20、30、40和50。球壳剩余极限载荷如表4和图10所示。将不同缺陷下考虑蠕变变形的极限载荷与未考虑蠕变变形的极限载荷的比值称为缺陷因子k1，见表4括号中的结果。可以看出，随着蠕变时间的增长，耐压壳结构的非线性屈曲载荷下降幅度越来越显著。其中，缺陷为5 mm、蠕变时间为0.5天时，球壳的剩余极限载荷为2.469 MPa，而未考虑蠕变效应时的计算结果则为2.705 MPa，考虑蠕变效应后数值下降幅度为8.7%。而蠕变时间达到50天时，球壳的剩余极限载荷为2.015 MPa，下降幅度达到25.5%。
从图10（b）的曲线形态来看，缺陷因子k1均表现出明显的非线性下降趋势，特别是在缺陷较大和蠕变时间较长的情况下，下降速度加快。这一变化趋势与幂律衰减模型非常吻合，表明蠕变过程对球壳材料的强度退化具有累积效应。这一结果表明，初始缺陷的大小是影响球壳极限载荷的重要因素，缺陷的增大导致了球壳的结构强度进一步减弱。
不同蠕变时间下的非线性极限载荷−最大位移曲线如图11所示。可以看出，虽然壳体变形分布相似，但蠕变效应会显著改变位移场梯度特性。对比此时位移数据，不考虑蠕变时模型的最大位移量为21.19 mm，引入蠕变因素（50天）后该位移量增至33.97 mm，增幅达60.3%。这一结果表明，蠕变作用不仅会放大结构初始缺陷的几何幅值，更会通过位移场重构机制增强缺陷敏感性，增大应力集中的效果，最终导致结构极限承载性能发生显著弱化。
3.2　厚径比影响分析
本节研究了不同厚径比对有机玻璃球壳临界载荷的影响。厚径比t/R分别为0.03、0.035、0.04、0.045和0.05。初始缺陷大小设置为2 mm。蠕变时间（天）取值为0、0.5、1、2、4、6、8、10、20、30、40和50。球壳的剩余极限载荷列于表5。几何因子k2定义为不同厚径比下考虑蠕变变形的临界载荷与未考虑蠕变变形的临界载荷之比，如表5括号中的结果所示。
从表5和图12可以看出，随着厚径比t/R的增大，球壳的极限载荷呈现出上升趋势，这是因为较厚的球壳具有更强的结构刚度，因此能够承受更高的载荷。另外，蠕变时间的延长导致极限载荷下降，但随着厚径比t/R的增加，极限载荷下降幅度逐渐减小。例如，蠕变时间为50天后，5种球壳的极限载荷分别下降了35.6%、12.3%、7.7%、3.8%和2.6%，表明蠕变效应逐渐削弱了有机玻璃球壳的承载能力，尤其是在薄壁球壳中，蠕变效应的影响更为显著。而较大的厚径比（0.05）在经历长时间蠕变后，仍能保持较高的承载能力，表现出更强的抗蠕变能力。
3.3　工作深度影响分析
本节以不同工作水深（60 m、80 m、100 m、120 m和140 m）为例，分析考虑初始模态缺陷后有机玻璃球壳的耐压结构蠕变响应。这里厚径比为0.04，初始模态缺陷为2 mm，蠕变时间（天）分别设为0、0.5、1、2、4、6、8、10、20、30、40和50。球壳的剩余极限载荷如表6所示。水深因子k3定义为不同水深下考虑蠕变变形的临界载荷与未考虑蠕变变形的临界载荷比值，如表6括号中的结果所示。
由表6和图13可以看出，剩余极限载荷和k3均随工作深度增加呈指数衰减，且随着蠕变时间延长，这一衰减趋势加速。当蠕变时间为50天后，工作深度（m）为60、80、100、120和140的极限载荷分别下降了2.2%、3.9%、7.7%、11.7%和30.7%。说明较深的工作深度导致球壳在相同蠕变时间下发生了更显著的变形，进而导致剩余极限载荷衰减加剧。
4　结论
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本文深入探讨了有机玻璃（PMMA）潜水器耐压壳的蠕变屈曲行为及其剩余极限承载能力，基于粘弹性特性分析，得出以下主要结论：
（1）基于时间−应力等效原理和短期蠕变试验数据，构建了适用于不同应力水平的PMMA材料蠕变曲线。对比Burgers模型发现，修正的Burgers模型因引入与时间相关的粘度系数，能够更精确地表征PMMA材料的减速、稳态及加速蠕变三阶段全特征。
（2）以直径2 m、壁厚40 mm的PMMA球壳为例，通过追踪球壳蠕变位移−时间曲线发现，当曲线斜率出现急剧增大时，结构发生失稳。据此判定在工作水深140 m的条件下，完美球壳的蠕变屈曲临界时间为14990小时，而含有2 mm初始几何缺陷的球壳该时间缩短至3176小时，仅为完美球壳的21.2%，表明初始缺陷会急剧削弱球壳的长期稳定性。
（3）初始缺陷的增加会显著加剧蠕变效应，导致极限载荷大幅下降，5 mm缺陷球壳蠕变50天后剩余极限载荷仅为1 mm缺陷球壳的49.8%。而增大厚径比能有效延缓蠕变变形对极限载荷的衰减，当厚径比t/R从0.03增加至0.05时，蠕变50天后的剩余极限载荷衰减率由35.6%降至2.6%。此外，工作深度增加引起的蠕变也使剩余极限载荷显著降低，从60 m工况到140 m工况，极限载荷衰减率由2.2%增加至30.7%。这些发现可为PMMA耐压壳的设计优化和安全评估提供重要的理论依据。
基金
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  • 国家自然科学基金资助项目（52271277）
文献
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参考文献 引证文献
排序方式：
1
刘 帅, 叶 聪, 汤国伟, 等. 国内首型全通透载客潜水器的设计与研制[J]. 中国造船, 2019, 60(3): 113‒120.
Liu S, Ye C, Tang G W et al. Design and development of the first acrylic-hulled submersible in China[J]. Shipbuilding of China, 2019, 60(3): 113‒120. (in Chinese)
2
He Z H, Wang F, Wang H X, et al. Parametric analysis on creep deformation of deep-sea PMMA observation window[J]. Applied Sciences, 2024, 14: 2076-3417.
3
穆霞英. 蠕变力学[M]. 西安: 西安交通大学出版社, 2022.
Mu X Y. Creep mechanics[M]. Xi'an: Xi'an Jiaotong University Press, 2022. (in Chinese)
4
Lin L, Hui L, Tao J, et al. Experimental study on the effects of hygrothermal aging on the indentation creep behaviors of PMMA[J]. Polymer Testing, 2021, 94(106991): 0142-9418.
5
陈 薇, 屈 平, 张爱锋. 基于压缩蠕变试验的观察窗蠕变特性研究[J]. 船舶力学, 2021, 25(1): 73‒79.
Chen W, Qu P, Zhang A F. Study on viewport creep characteristics based on compression creep test[J]. Journal of Ship Mechanics, 2021, 25(1): 73‒79. (in Chinese)
6
陈 薇, 万正权, 屈 平, 等. 考虑温度和应力影响的有机玻璃加速蠕变试验方法[J]. 船舶力学, 2025, 29(5): 755‒766.
Chen W, Wan Z Q, Qu P, et al. Accelerated creep test method of PMMA considering the influence of temperature and stress[J]. Journal of Ship Mechanics, 2025, 29(5): 755‒766. (in Chinese)
7
Adibeig S V T F. Optimum creep lifetime of Polymethyl Methacrylate (PMMA) tube using rheological creep constitutive models based on experimental data[J]. Polymer Testing, 2019, 75: 107-116.
8
Xu S X, Lin J P, et al. Experimental and numerical buckling analysis of cylindrical pressure hulls with multi-circular openings[J]. Ocean Engineering, 2020, 214: 0029-8018.
9
曹嘉庆. 基于蠕变特性的有机玻璃耐压球壳稳定性研究[D]. 哈尔滨: 哈尔滨工程大学, 2021.
Cao J Q. Research on the stability of PMMA pressure spherical shell based on creep characteristics[D]. Harbin: Harbin Engineering University, 2021. (in Chinese)
10
何志豪, 王 芳, 李友洁. 深海全通透耐压壳蠕变分析[J]. 力学与实践, 2024, 46(3): 559‒569.
He Z H, Wang F, Li Y J. Analysis on creep deformation of deep-sea fullytransparent pressure-resistant hull[J]. Mechanics in Engineering, 2024, 46(3): 559‒569. (in Chinese)
11
Zhou F, Du Y, Chen Z P, et al. Creep buckling analysis of PMMA pressure vessels for application in neutrino detectors[J]. International Journal of Pressure Vessels and Piping, 2019, 169: 170-176.
12
Zhou F, Hou S J, Qian X H, et al. Creep behavior and lifetime prediction of PMMA immersed in liquid scintillator[J]. Polymer Testing, 2016, 53: 323-328.
13
Wang L H, Zhu Y M, Zhao X L, et al. Buckling analysis of PMMA hemispherical pressure shells with thickness variation[J]. International Journal of Solids and Structures, 2025, 306: 113109.
14
中国船级社. 潜水系统和潜水器入级与建造规范[S]. 北京: 人民交通出版社, 2018.
China Classification Society. Rules for classification of diving systems and submersibles[S]. Beijing: China Communications Press, 2018. (in Chinese)
15
高 杰. 深海球形耐压壳力学特性及试验研究[D]. 镇江: 江苏科技大学, 2017.
Gao Jie. Investigation on mechanical properties of deep sea spherical pressure hull and experimental study[D]. Zhenjiang: Jiangsu University of Science and Technology, 2017. (in Chinese)
16
ASTM D2990. Standard test methods for tensile, compressive, and flexural creep and creep-rupture of plastics[S]. West Conshohocken: ASTM International, 2017.
17
Williams M L, Landel R F, Ferry J D. The temperature dependence of relaxation mechanisms in amorphous liquids[J]. Journal of the American Chemical Society, 1955, 77(14): 3701-3707.
18
罗文波, 杨挺青, 安群力. 非线性粘弹体的时间−温度−应力等效原理及其应用[J]. 固体力学学报, 2001(3): 219‒224.
Luo W B, Yang T Q, An Q L. Time-temperature-stress equivalence principle for nonlinear viscoelastic bodies and its application[J]. Chinese Journal of Solid Mechanics, 2001(3): 219‒224. (in Chinese)
19
Findley W N, Lai J S, Onaran K. Creep and relaxation of nonlinear viscoelastic materials: with an introduction to linear viscoelasticity[M]. Amsterdam: North-Holland, 1976.
20
周华樟. 旋切板胶合木的蠕变及其对结构稳定性的影响[D]. 哈尔滨: 哈尔滨工业大学, 2009.
Zhou H Z. Creep of laminated veneer lumber and its influence on structural stability[D]. Harbin: Harbin Institute of Technology, 2009. (in Chinese)
21
Hoff N J. Rules and methods of stress and stability calculations in the presence of creep[J]. Journal of Applied Mechanics, 1978, 45(3): 669-675.
2026年第30卷第9期
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doi: 10.3969/j.issn.1007-7294.2026.09.013
  • 接收时间：2026-04-16
  • 首发时间：2026-11-03
  • 出版时间：2026-09-15
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  • 收稿日期：2026-04-16
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国家自然科学基金资助项目（52271277）
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    江苏科技大学，江苏 镇江 212100
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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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