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Article(id=1149779600915525955, tenantId=1146029695717560320, journalId=1146120084050784272, issueId=1149779599254581563, articleNumber=null, orderNo=null, doi=10.19562/j.chinasae.qcgc.2025.02.018, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1719763200000, receivedDateStr=2024-07-01, revisedDate=1724860800000, revisedDateStr=2024-08-29, acceptedDate=null, acceptedDateStr=null, onlineDate=1752058418730, onlineDateStr=2025-07-09, pubDate=1740412800000, pubDateStr=2025-02-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1752058418730, onlineIssueDateStr=2025-07-09, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1752058418730, creator=13701087609, updateTime=1752058418730, updator=13701087609, issue=Issue{id=1149779599254581563, tenantId=1146029695717560320, journalId=1146120084050784272, year='2025', volume='47', issue='2', pageStart='201', pageEnd='390', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=0, createTime=1752058418334, creator=13701087609, updateTime=1753780722751, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1157003467609956875, tenantId=1146029695717560320, journalId=1146120084050784272, issueId=1149779599254581563, language=EN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1157003467609956876, tenantId=1146029695717560320, journalId=1146120084050784272, issueId=1149779599254581563, language=CN, specialIssueTitle=, coverIllustrator=, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=376, endPage=382, ext={EN=ArticleExt(id=1149779601083298116, articleId=1149779600915525955, tenantId=1146029695717560320, journalId=1146120084050784272, language=EN, title=A Prediction Model for Compression Instability Folds of Thin-Walled Tubes Based on Energy Method, columnId=null, journalTitle=Automotive Engineering, columnName=null, runingTitle=null, highlight=

Thin-walled tubes，commonly used structures in automobile lightweight and industrial production，have the advantages of lightweight and high strength. The study of the axial compression instability characteristics of thin-walled tubes is helpful for its application in optimizing structural design and safety. Therefore，a novel axial compression fold model of thin-walled tubes is proposed to describe the morphological characteristics and average compressive load of deformation folds for thin-walled tubes based on the energy method. The prediction accuracy of the new theoretical model and the plastic hinge model for the fold length and compressive average load is validated by experiments and finite element simulation. The results show that the fold length predicted by the new theoretical model is closer to the experimental and finite element results compared with the plastic hinge model，with the average prediction error reduced by 55.2%. The prediction accuracy for compressive average load is improved by 29.7% after the friction coefficient correction. When guiding engineering practice，a fold prediction model considering friction effect correction should be adopted.

, articleAbstract=

Thin-walled tubes, commonly used structures in automobile lightweight and industrial production, have the advantages of lightweight and high strength. The study of the axial compression instability characteristics of thin-walled tubes is helpful for its application in optimizing structural design and safety. Therefore, a novel axial compression fold model of thin-walled tubes is proposed to describe the morphological characteristics and average compressive load of deformation folds for thin-walled tubes based on the energy method. The prediction accuracy of the new theoretical model and the plastic hinge model for the fold length and compressive average load is validated by experiments and finite element simulation. The results show that the fold length predicted by the new theoretical model is closer to the experimental and finite element results compared with the plastic hinge model, with the average prediction error reduced by 55.2%. The prediction accuracy for compressive average load is improved by 29.7% after the friction coefficient correction. When guiding engineering practice, a fold prediction model considering friction effect correction should be adopted.

, correspAuthors=Haiyan Yu, 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=Hongwei He, Hangyu Wu, Haiyan Yu), CN=ArticleExt(id=1149779615855636997, articleId=1149779600915525955, tenantId=1146029695717560320, journalId=1146120084050784272, language=CN, title=基于能量法的薄壁管压缩失稳褶皱预测模型*, columnId=null, journalTitle=汽车工程, columnName=null, runingTitle=null, highlight=

薄壁管具有质量轻、强度高等优势，是汽车轻量化和工业生产的常用结构。研究薄壁管的轴压失稳特性有助于其在优化结构设计和安全性上的应用。因此，本文基于能量法提出了一种新的薄壁圆管轴压褶皱模型，用于描述薄壁管轴压变形褶皱的形貌特征和平均压缩载荷。通过试验和有限元模拟验证了新理论模型和塑性铰模型对褶皱长度和压缩平均载荷的预测精度。结果表明：相比塑性铰模型，新理论模型预测的褶皱长度更接近试验和有限元结果，预测平均误差减少55.2%。采用摩擦因数修正后，新理论模型对压缩平均载荷的预测精度提升29.7%。指导工程实践时，应采用考虑摩擦效应修正的褶皱预测模型。

, articleAbstract=

薄壁管具有质量轻、强度高等优势,是汽车轻量化和工业生产的常用结构。研究薄壁管的轴压失稳特性有助于其在优化结构设计和安全性上的应用。因此,本文基于能量法提出了一种新的薄壁圆管轴压褶皱模型,用于描述薄壁管轴压变形褶皱的形貌特征和平均压缩载荷。通过试验和有限元模拟验证了新理论模型和塑性铰模型对褶皱长度和压缩平均载荷的预测精度。结果表明:相比塑性铰模型,新理论模型预测的褶皱长度更接近试验和有限元结果,预测平均误差减少55.2%。采用摩擦因数修正后,新理论模型对压缩平均载荷的预测精度提升29.7%。指导工程实践时,应采用考虑摩擦效应修正的褶皱预测模型。

, correspAuthors=余海燕, authorNote=null, correspAuthorsNote=
余海燕，教授，博士，E-mail：。
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参数 数值
密度/（kg·m-3） 7 850
弹性模量/GPa 210
泊松比 0.28
屈服强度/MPa 278.8
极限强度/MPa 454.6
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DC01钢管材料参数

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参数 数值
密度/（kg·m-3） 7 850
弹性模量/GPa 210
泊松比 0.28
屈服强度/MPa 278.8
极限强度/MPa 454.6
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半径/mm 厚度/mm 褶皱长度 压缩平均载荷
16 1.0 试验值/mm 计算值/mm 误差/% 试验值/kN 计算值/kN 误差/%
5.85 塑性铰模型 6.19 5.81 15.73 塑性铰链模型 10.55 32.93
新理论模型 6.01 2.74 新理论模型 15.70 0.13
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试验测量结果与不同预测模型预测结果对比

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半径/mm 厚度/mm 褶皱长度 压缩平均载荷
16 1.0 试验值/mm 计算值/mm 误差/% 试验值/kN 计算值/kN 误差/%
5.85 塑性铰模型 6.19 5.81 15.73 塑性铰链模型 10.55 32.93
新理论模型 6.01 2.74 新理论模型 15.70 0.13
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数值模拟方案编号 圆管半径/mm 厚度/mm 径厚比
1 20 1.0 20.0
2 20 1.5 13.3
3 20 2.0 10.0
4 25 1.0 25.0
5 25 1.5 16.7
6 25 2.0 12.5
7 30 1.0 30.0
8 30 1.5 20.0
9 30 2.0 15.0
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数值模拟方案

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数值模拟方案编号 圆管半径/mm 厚度/mm 径厚比
1 20 1.0 20.0
2 20 1.5 13.3
3 20 2.0 10.0
4 25 1.0 25.0
5 25 1.5 16.7
6 25 2.0 12.5
7 30 1.0 30.0
8 30 1.5 20.0
9 30 2.0 15.0
), ArticleFig(id=1170299393753231484, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1149779600915525955, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
编号

褶皱长度

数值结果/mm

塑性铰模型

计算值/mm

塑性铰

模型

误差/%

新理论

模型

计算值/mm

新理论

模型

误差/%
1 6.33 6.93 9.48 6.53 3.16
2 8.26 8.72 5.57 8.46 2.42
3 9.86 10.28 4.26 10.21 3.55
4 6.80 7.65 12.50 7.10 4.41
5 8.75 9.60 9.71 9.16 4.68
6 10.45 11.31 8.23 11.02 5.45
7 7.23 8.30 14.80 7.62 5.39
8 9.18 10.40 13.29 9.79 6.64
9 11.55 12.23 5.89 11.76 1.82
), ArticleFig(id=1170299393824534654, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1149779600915525955, language=CN, label=表4, caption=

理论模型预测褶皱长度与数值结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
编号

褶皱长度

数值结果/mm

塑性铰模型

计算值/mm

塑性铰

模型

误差/%

新理论

模型

计算值/mm

新理论

模型

误差/%
1 6.33 6.93 9.48 6.53 3.16
2 8.26 8.72 5.57 8.46 2.42
3 9.86 10.28 4.26 10.21 3.55
4 6.80 7.65 12.50 7.10 4.41
5 8.75 9.60 9.71 9.16 4.68
6 10.45 11.31 8.23 11.02 5.45
7 7.23 8.30 14.80 7.62 5.39
8 9.18 10.40 13.29 9.79 6.64
9 11.55 12.23 5.89 11.76 1.82
), ArticleFig(id=1170299393933586560, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1149779600915525955, language=EN, label=null, caption=null, figureFileSmall=null, figureFileBig=null, tableContent=
编号

平均压缩载荷

数值结果/kN

塑性铰模型

计算值/kN

 误差/%

不考虑摩擦效应的

新理论模型计算值/kN

 误差/%

考虑摩擦效应的

新理论模型计算值/kN

 误差/%
1 18.36 13.74 25.16 13.40 27.05 17.77 3.21
2 35.98 25.08 30.29 25.52 29.08 33.86 5.90
3 58.58 38.36 34.52 40.46 30.93 53.68 8.36
4 19.67 15.40 21.71 15.72 20.08 19.52 0.74
5 39.44 28.15 28.63 27.95 29.14 37.08 5.99
6 63.18 43.12 31.75 44.20 30.04 58.64 7.18
7 21.11 16.90 19.94 16.91 19.89 21.10 0.04
8 43.11 30.92 28.28 32.14 25.45 39.98 7.24
9 65.85 47.39 28.03 47.58 27.74 63.13 4.12
), ArticleFig(id=1170299394042638466, tenantId=1146029695717560320, journalId=1146120084050784272, articleId=1149779600915525955, language=CN, label=表 5, caption=

理论模型预测平均压缩载荷与数值结果对比

, figureFileSmall=null, figureFileBig=null, tableContent=
编号

平均压缩载荷

数值结果/kN

塑性铰模型

计算值/kN

 误差/%

不考虑摩擦效应的

新理论模型计算值/kN

 误差/%

考虑摩擦效应的

新理论模型计算值/kN

 误差/%
1 18.36 13.74 25.16 13.40 27.05 17.77 3.21
2 35.98 25.08 30.29 25.52 29.08 33.86 5.90
3 58.58 38.36 34.52 40.46 30.93 53.68 8.36
4 19.67 15.40 21.71 15.72 20.08 19.52 0.74
5 39.44 28.15 28.63 27.95 29.14 37.08 5.99
6 63.18 43.12 31.75 44.20 30.04 58.64 7.18
7 21.11 16.90 19.94 16.91 19.89 21.10 0.04
8 43.11 30.92 28.28 32.14 25.45 39.98 7.24
9 65.85 47.39 28.03 47.58 27.74 63.13 4.12
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基于能量法的薄壁管压缩失稳褶皱预测模型*
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贺宏伟 , 吴航宇 , 余海燕
汽车工程 | 2025,47(2): 376-382
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汽车工程 | 2025, 47(2): 376-382
基于能量法的薄壁管压缩失稳褶皱预测模型*
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贺宏伟, 吴航宇, 余海燕
作者信息
  • 同济大学汽车学院，上海 201804

通讯作者:

余海燕，教授，博士，E-mail：。
A Prediction Model for Compression Instability Folds of Thin-Walled Tubes Based on Energy Method
Hongwei He, Hangyu Wu, Haiyan Yu
Affiliations
  • School of Automotive Studies，Tongji University，Shanghai 201804
出版时间: 2025-02-25 doi: 10.19562/j.chinasae.qcgc.2025.02.018
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摘要
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薄壁管具有质量轻、强度高等优势,是汽车轻量化和工业生产的常用结构。研究薄壁管的轴压失稳特性有助于其在优化结构设计和安全性上的应用。因此,本文基于能量法提出了一种新的薄壁圆管轴压褶皱模型,用于描述薄壁管轴压变形褶皱的形貌特征和平均压缩载荷。通过试验和有限元模拟验证了新理论模型和塑性铰模型对褶皱长度和压缩平均载荷的预测精度。结果表明:相比塑性铰模型,新理论模型预测的褶皱长度更接近试验和有限元结果,预测平均误差减少55.2%。采用摩擦因数修正后,新理论模型对压缩平均载荷的预测精度提升29.7%。指导工程实践时,应采用考虑摩擦效应修正的褶皱预测模型。

褶皱预测模型  /  薄壁圆管  /  能量法  /  轴压失稳  /  压缩载荷

Thin-walled tubes, commonly used structures in automobile lightweight and industrial production, have the advantages of lightweight and high strength. The study of the axial compression instability characteristics of thin-walled tubes is helpful for its application in optimizing structural design and safety. Therefore, a novel axial compression fold model of thin-walled tubes is proposed to describe the morphological characteristics and average compressive load of deformation folds for thin-walled tubes based on the energy method. The prediction accuracy of the new theoretical model and the plastic hinge model for the fold length and compressive average load is validated by experiments and finite element simulation. The results show that the fold length predicted by the new theoretical model is closer to the experimental and finite element results compared with the plastic hinge model, with the average prediction error reduced by 55.2%. The prediction accuracy for compressive average load is improved by 29.7% after the friction coefficient correction. When guiding engineering practice, a fold prediction model considering friction effect correction should be adopted.

fold prediction model  /  thin-walled circular tube  /  energy method  /  axial instability  /  compressive load
贺宏伟, 吴航宇, 余海燕. 基于能量法的薄壁管压缩失稳褶皱预测模型*. 汽车工程, 2025 , 47 (2) : 376 -382 . DOI: 10.19562/j.chinasae.qcgc.2025.02.018
Hongwei He, Hangyu Wu, Haiyan Yu. A Prediction Model for Compression Instability Folds of Thin-Walled Tubes Based on Energy Method[J]. Automotive Engineering, 2025 , 47 (2) : 376 -382 . DOI: 10.19562/j.chinasae.qcgc.2025.02.018
正文
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前言
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为了实现中国式现代化要求和“双碳”目标，汽车工业对汽车的轻量化提出了更高的要求[1]。金属薄壁管结构具有质量轻、强度高、易于加工、吸能性好等优点，被广泛用于车身安全结构件的制造[2-3]。在发生碰撞时，这些构件通常承受轴向载荷而发生塑性变形。研究薄壁管在轴向压缩下的塑性变形和褶皱形貌有助于优化结构设计和安全性应用。
金属薄壁圆管在轴向载荷的作用下发生轴对称变形，这种变形是在管的长度方向形成相互堆叠的褶皱。由于这种变形模式吸能效果显著，许多研究学者对这种变形模式进行了大量的理论和试验研究。Alexander[4-5]第一个提出了圆管在轴对称变形模式下形成褶皱的理论模型。整个轴对称变形过程可简化成图1所示的模型。在压缩过程中，管壁在轴截面上会形成四段塑性铰。这些塑性铰会绕着铰点发生变形。忽略材料的弹性变形，并假设金属圆管在轴向压缩过程中以固定的塑性铰长度发生轴对称变形。此时塑性铰的长度可由最小势能原理确定。后来的研究者在Alexander理论模型的基础上不断改进和拓展。Abramowicz等[6]和Dubey等[7]认为压缩褶皱在子午线方向应该拟合成曲线而不是由塑性铰点连接构成的直线段。Wierzbicki等[8]、Singace等[9]和 Koloushani等[10]则提出了含有偏心率效应的塑性铰模型，并认为偏心率对平均压缩载荷的影响不大。Hu等[11]和Kuleyin等[12]认为多个堆叠褶皱之间存在倾角，并在Alexander理论的基础上对褶皱的形貌进行了修正。Liu等[13]则考虑了管材料的应变硬化效应来修正轴压褶皱的压缩载荷。徐峰祥等[14]在现有薄壁圆管压溃模型的基础上发展出双变属性管的压溃力计算公式。姚如洋等[15]考虑了管材的应变强化效应提出了一种基于Alexander理论的开孔圆管轴对称压溃模型。还有研究者通过大量的试验和仿真，建立了薄壁圆管轴压的经验方程。比如基于圆管几何尺寸参数建立的铝合金圆管屈曲载荷公式[16]，基于虚功原理的薄壁管大变形的平均载荷预测模型[17]，马梦娇[18]的波纹管轴压吸能公式，Yu等[19]的塑性变形长度预测公式等。
然而，Alexander模型的预测效果与实际仍存在较大差异。研究表明，Alexander模型预测的单位长度的能量吸收比实际结果小40%左右[20-21]。尽管后来的研究者对Alexander提出的塑性铰模型做出了许多改进，但这些模型仍然存在局限性：首先，模型对褶皱的形貌过于简化，没有对压缩褶皱的过渡区域做出正确的模拟。在塑性铰点处存在曲率突变的情况。同时，整个模型没有考虑薄壁管壁之间的摩擦力，这会使模型计算的平均载荷低于实际载荷。
针对Alexander模型的局限性，本文基于能量法提出一种新的描述薄壁圆管轴对称褶皱的理论模型。根据最小势能原理计算压缩褶皱的长度，并引入摩擦因数对平均压缩载荷进行修正。最后通过试验和有限元仿真结果验证该理论模型的准确性和有效性。研究结果可以为薄壁管的轴对称变形模式及吸能特性预测提供参考。
1 理论模型
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1.1 Alexander塑性铰模型
在Alexander模型中，形成一个压缩褶皱单元所做的外力功转化为两部分，一部分为塑性铰处的弯曲变形能E1，另一部分为塑性铰之间金属被拉伸所消耗的拉伸变形能E2。两种能量的计算公式分别为
E1=4πM0(πR+H)
E2=2πYtH2
式中：R、t分别为管的半径和厚度；H为轴截面上塑性铰的长度；M0是管壁单位长度的塑性极限弯矩；Y为材料的屈服应力。根据能量法可得平均载荷Fav与塑性耗散能的关系为
Fav∙2H=E1+E2
根据最小势能原理有∂(Fav)/∂(H)=0，可以求得H的表达式为
H=π230.5(2Rt)0.5≈1.3435(Rt)0.5
联立式（3）和式（4），可得平均载荷Fav的近似取值为
Fav=8.4853YtRt
1.2 新薄壁圆管轴压褶皱模型
1.2.1 基本假设
为了简化分析过程，本文对薄壁管压缩过程的理论分析提出两个假设：
（1） 在Alexander模型中，管材视为理想刚塑性材料，没有考虑材料的应变硬化效应，这会使模型计算的平均载荷低于实际载荷。在理论分析中，可以参考张婉琪等[22-23]在建立薄壁管外翻理论模型中流动应力σ0的计算方法：
σ0=σy+σu2
式中：σy为屈服强度；σu为抗拉强度。
（2） 在薄壁圆管柱面上取一微元进行分析，如图2所示。其中x轴平行于圆管的轴线，φ为横截面的圆心角。该微元体作用的力矩有薄膜力Nx、Nφ，弯矩Mx、Mφ。
对于轴压过程中的塑性能量耗散，有学者通过理论分析得到子午线方向的弯曲应变和周向拉伸应变远大于其他应变分量[24]。在薄壁管的变形区域取微元的长度dS，微元的弯曲曲率为K，微元dS变形前后的薄壁管对应半径分别为Rini和Rend。因此，长度为dS的微元塑性能量耗散为
dE=dEb+dEt=1tMxK∙2πRt∙dS+1tNφ∙RendRini∙2πRt∙dS
式中：R为薄壁管子午线的半径；t为薄壁管厚度；dEb和dEt分别为子午线方向的弯曲变形能和圆周方向的拉伸变形能。Mx和Nφ可由式（8）和式（9）得到：
Mx=∫-t/2t/2σ0zdz=14σ0t2
Nφ=∫-t/2t/2σ0dz=σ0t
（3）随着压缩位移的增加，假设轴压褶皱发生了完全的压缩，如图3所示，此时褶皱内部没有任何间隙。同时考虑到塑性铰模型的局限性，对变形褶皱的过渡区域采用圆弧进行模拟，修正后的褶皱轮廓如图4所示，褶皱的变形区域可以分为AB、BC、CD和DE 4个部分。其中AB段为半径r1的1/4圆弧，CD段为半径r2的1/2圆弧。BC段和DE段分别为长度H1、H2的直线段。
由图4的几何关系可知：
r2=t2
H1+r1+t2=H2
关于r1的取值，可以参考板材冲压成形理论中板料弯曲90°时的最小弯曲半径[25]：
r1=t
1.2.2 变形能量分析
根据式（7），分别计算各变形区域的塑性能。
AB段为半径t的圆弧段，曲率为1t，圆心角为π2，子午线上的弯曲变形能为
EbAB=∫0π21tMxK∙2πRt∙dS=14σ0π2Rt2
圆周方向的拉伸变形能为
EtAB=∫0π21tNφεR∙2πRt∙dS=σ0π2t3-2σ0πt3
同样，CD段为半径t2的圆弧段，曲率为2t，圆心角为π，弯曲变形能和拉伸变形能为
EbCD=∫0π1tMpK∙2πRt∙dS=12σ0π2Rt2
EtCD=∫0π1tNpεR∙2πRt∙dS=32σ0π2t3+σ0π2t2H-σ0πt3
在BC段和DE段，弯曲曲率为0，因此弯曲变形能为0，即
EbBC=EbDE=0
BC段和DE段的拉伸变形能为
EtBC=2σ0πt2H+σ0πtH2
EbDE=σ0πtH2+2σ0πt2H+34t2
根据能量守恒可得：
W=Fav∙L=EbAB+EtAB+EbCD+EtCD+EbBC+EtBC+EbDE+EtDE
式中L为压缩位移。根据最小势能原理求解参数H，方程表达为dFav/dH=0。将式（13） ~式（19）代入式（20），求微分可得参数H，进而计算出褶皱长度和平均压缩载荷。
1.3 摩擦因数修正
在1.2.2节中的变形能量分析中，没有考虑由管壁之间摩擦而耗散的能量。但在实际褶皱形成过程中，摩擦耗能对压缩载荷有较大影响。参照翻管理论研究中对摩擦效应的考虑，假设摩擦耗能独立于塑性耗能，得到考虑摩擦效应的压缩平均载荷：
Favf=eπ2fFav
式中f为薄壁管压缩时与管壁之间的摩擦因数。
2 试验验证
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2.1 应力应变曲线拟合
为确保后续有限元和理论模型的准确性，须测定压缩管材的材料参数，根据ASTM-E8标准从DC01薄壁管上切割拉伸试样，试样尺寸参数如图5所示，拉伸速度为2 mm/min，并采用幂指数强化模型进行拟合，材料的真实应力应变关系和拟合结果如图6所示，式（22）为拟合得到的表达式。
σ=278.8+319.2ε0.425
表1给出了DC01的材料参数。将拟合曲线用于本文提出的理论模型计算和数值模型中，进一步分析模型的合理性。
2.2 试验样本及试验机描述
本文选用半径R=16 mm、厚度t=1 mm的DC01钢管进行压缩试验。试验机如图7所示。准静态薄壁圆管轴压试验在MTS万能拉伸材料试验机上进行。最大工作载荷为100 kN，梁位移速度可以设置为0.005-750 mm/min。压缩速率为2 mm/min。
2.3 试验结果
图8给出了DC01钢管在轴向压缩过程中的载荷-位移曲线。随着压缩位移的增加，载荷会迅速到达峰值，随后圆管发生塑性失稳并逐渐形成褶皱。这一阶段载荷将逐渐下降，直到褶皱被完全压缩。此时压缩载荷也达到极小值。此时的压缩载荷约为峰值载荷的15.5%。继续增加压缩位移，载荷重新开始上升，此时在第1个褶皱的上方开始堆叠第2个褶皱。可以看出，随着褶皱数目的增加，压缩载荷呈周期性变化。图8给出了完全压缩的褶皱轴截面形态，可以看到在相邻褶皱的过渡区域呈圆弧状，这验证了理论模型中对褶皱过渡区域的模拟假设。说明了本文提出的模型具有合理性。
表2给出了压缩褶皱的褶皱长度和压缩平均载荷的试验值和模型计算结果。相比塑性铰模型，本文提出的轴压褶皱模型具有更高的精度。在褶皱长度的预测上，新理论模型的精度比Alexander的塑性铰模型提升了53%，对于压缩平均载荷，新理论模型将预测误差从32.93%降至0.13%。新模型预测值与试验结果基本一致，说明对压缩过程和褶皱形貌的预测是准确的。
3 数值模拟
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3.1 有限元建模
为了进一步验证新理论模型的合理性，使用有限元软件对圆管轴压过程进行数值模拟。压缩板和地面均定义为离散刚体。圆管采用轴对称模型，将拉伸试验得到的应力应变曲线应用至数值计算中。采用四节点双线性轴对称四边形单元对圆管进行网格划分，沿厚度方向划分5个单元。对压缩板和地面施加边界条件，其中上板约束除轴向位移以外的所有自由度，地面约束所有自由度。为整个变形过程定义通用接触，其中摩擦因数设为0.16。根据正交试验设计方法，选择薄壁圆管的半径和厚度为影响因素，以褶皱长度和压缩平均载荷为考察指标，设计2因素3水平正交试验。表3给出了9种数值模拟方案。
3.2 数值分析结果
图9为有限元软件中模拟的薄壁管轴压褶皱形成过程。随着压缩力逐渐增大，薄壁管发生塑性失稳，直至形成褶皱。仿真中的压缩过程与试验基本吻合。本文以压缩过程中形成的第1个褶皱为对象分析理论模型预测值和数值模拟结果的误差。
表4为各个数值模拟方案的褶皱长度数值结果及理论模型计算值。其中塑性铰模型计算结果由式（4）得到，本文提出的褶皱长度理论模型计算结果由式（20）计算得到。随着圆管径厚比的增加，两个模型计算的褶皱长度误差变大。塑性铰模型计算得到的褶皱长度最大误差为14.8%，最小误差为5.89%。本文提出的理论模型计算得到的褶皱长度最大误差为6.64%，最小误差为1.82%。同时，每个方案使用单一褶皱理论模型计算褶皱长度的误差都低于塑性铰模型，说明本文提出的褶皱长度计算理论模型有更高的精确度，与数值模拟结果更加吻合。
压缩平均载荷是衡量薄壁圆管吸能特性的一个重要指标。表5为各个数值模拟方案对压缩平均载荷的数值结果及理论模型的计算值。其中塑性铰模型计算由式（5）得到，本文理论模型平均载荷由式（20）计算得到，考虑摩擦效应修正的理论模型由式（20）和式（21）计算得到。为了消除流动应力的不同选择造成的影响，将塑性铰模型中的流动应力替换为本文采用的流动应力。由于塑性铰模型没有对褶皱的过渡区域进行建模以及忽略摩擦效应，平均载荷计算结果与数值模拟结果误差较大，平均误差为27.5%，最大误差达到了47.58%。在新理论模型中，不考虑摩擦效应的平均压缩载荷计算值与仿真结果存在较大误差。平均误差为26.6%，最大误差为30.93%。进行摩擦修正后，预测误差显著下降，平均误差为4.75%，最大误差为8.36%，说明摩擦因数对压缩平均载荷的预测影响较大。考虑摩擦因数修正后的理论模型与数值模拟结果基本一致，相比于塑性铰模型和不考虑摩擦效应的理论模型预测结果更为准确。
4 结论
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本文根据薄壁圆管轴压失稳变形的特点，建立了一个新的薄壁圆管轴压褶皱预测模型。该模型基于曲率变化来计算薄壁管在轴压过程中的塑性耗散能。通过与试验和有限元结果的对比验证了新理论模型的可靠性。本文得到的主要结论如下。
（1）本文基于能量法，提出了一种新的轴对称薄壁管压缩褶皱的理论模型。相比塑性铰模型，该模型考虑了褶皱曲率的连续性、管材的应变硬化效应和压缩过程中的摩擦效应。
（2）本文理论模型预测的褶皱长度相比塑性铰模型结果更接近试验和有限元结果，预测平均误差减少55.2%。
（3）在新理论模型中，摩擦效应对压缩平均载荷的计算影响较大。不考虑摩擦效应时，理论模型对压缩平均载荷的最小预测误差为19.89%，考虑摩擦效应后模型的最大预测误差为8.36%。在指导工程实践时，应采用考虑摩擦效应修正的褶皱预测模型。
基金
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  • *国家重点研发计划项目(2022YFE0208000)
文献
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doi: 10.19562/j.chinasae.qcgc.2025.02.018
  • 接收时间：2024-07-01
  • 首发时间：2025-07-09
  • 出版时间：2025-02-25
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  • 收稿日期：2024-07-01
  • 修回日期：2024-08-29
基金
*国家重点研发计划项目(2022YFE0208000)
作者信息
    同济大学汽车学院，上海 201804

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余海燕，教授，博士，E-mail：。
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2种不同金属材料的力学参数
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