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Article(id=1241029725443912423, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241029724655383270, articleNumber=null, orderNo=null, doi=10.16579/j.issn.1001.9669.2025.02.004, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1685289600000, receivedDateStr=2023-05-29, revisedDate=1691164800000, revisedDateStr=2023-08-05, acceptedDate=null, acceptedDateStr=null, onlineDate=1773814143762, onlineDateStr=2026-03-18, pubDate=1739548800000, pubDateStr=2025-02-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773814143762, onlineIssueDateStr=2026-03-18, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773814143762, creator=13701087609, updateTime=1773814143762, updator=13701087609, issue=Issue{id=1241029724655383270, tenantId=1146029695717560320, journalId=1227999626482147330, year='2025', volume='47', issue='2', pageStart='1', pageEnd='158', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773814143575, creator=13701087609, updateTime=1773840259815, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241139264176574915, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241029724655383270, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241139264176574916, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241029724655383270, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=28, endPage=36, ext={EN=ArticleExt(id=1241029725682987757, articleId=1241029725443912423, tenantId=1146029695717560320, journalId=1227999626482147330, language=EN, title=Study on the crack expansion law of laminated porous structure, columnId=1241029725523604201, journalTitle=Journal of Mechanical Strength, columnName=Fatigue∙Damage∙Fracture∙Failure Analysis, runingTitle=null, highlight=null, articleAbstract=

Based on two basic configurations of hexagonal and inner concave shapes, by utilizing experimental test and finite element simulation method, the crack expansion law of laminated porous structures under three-point bending was studied, the influence of cellular element angle of laying direction on failure mode, load capacity, and deformation of the laminated porous structures was discussed. The results indicate that the crack expansion path in the bilayer model deviates towards the weaker layer with less crack expansion inhibition capability. The weaker side experiences greater deformation,leading to a deviation of the model towards the stronger side. Under certain angle combinations, the bilayer model shows significantly improved load-bearing capacity and toughness compared to the corresponding single-layer model.

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DENG Qingtian, E-mail：
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基于六边形和内凹形两种基本构型，采用实验测试和有限元仿真的方法，对三点弯曲作用下层合多孔结构裂纹扩展规律进行了研究，讨论了胞元铺设方向的角度对层合多孔结构破坏形式、承载力和变形的影响。结果表明，双层模型的裂纹扩展路径会向裂纹扩展抑制能力较弱层的裂纹扩展路径偏转；强度低的一侧会发生更大的变形，从而导致模型向强度高的一侧偏转；在一些角度组合下，双层模型承载力和韧性相较于对应的单层模型有明显提升。

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邓庆田（通信作者），男，1980年生，陕西咸阳人，博士，副教授；主要研究方向为多孔材料和结构力学性能、损伤检测结构；E-mail：。
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许爽，女，2000年生，陕西渭南人，硕士研究生；主要研究方向为多孔材料和结构力学性能；E-mail：。

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许爽，女，2000年生，陕西渭南人，硕士研究生；主要研究方向为多孔材料和结构力学性能；E-mail：。

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许爽，女，2000年生，陕西渭南人，硕士研究生；主要研究方向为多孔材料和结构力学性能；E-mail：。

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load-displacement curve of the hexagonal double layer model, figureFileSmall=Ng2lVeaBPQd5fGw1rpfZCA==, figureFileBig=LUGfQru/kuZzJ4L8kBR/9Q==, tableContent=null), ArticleFig(id=1241029751649923854, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=CN, label=图12, caption=六边形双层模型拟合载荷-位移曲线, figureFileSmall=Ng2lVeaBPQd5fGw1rpfZCA==, figureFileBig=LUGfQru/kuZzJ4L8kBR/9Q==, tableContent=null), ArticleFig(id=1241029751721227025, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=EN, label=Fig.13, caption=Fitted load-displacement curve of the hexagonal 0°/15° single and double layer model, figureFileSmall=yf4THuFGgwR0/yoZKBFTzA==, figureFileBig=g9rgTOkxnsbwMQGTrOpGeQ==, tableContent=null), ArticleFig(id=1241029751821890324, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=CN, label=图13, caption=六边形0°/15°单双层模型拟合载荷-位移曲线, 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Geometric parameters of basic configurations

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基本构型
Basic configuration		边长
Length
l1/mm		边长
Length
l2/mm		夹角Angle
α/（°）		夹角Angle
β/（°）
正六边形
Hexagon		1.6—1200、15、30
内凹形
Concave		2.91.45600、15、30、45、90
), ArticleFig(id=1241029752144851743, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=CN, label=表1, caption=

基本构型几何参数

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基本构型
Basic configuration		边长
Length
l1/mm		边长
Length
l2/mm		夹角Angle
α/（°）		夹角Angle
β/（°）
正六边形
Hexagon		1.6—1200、15、30
内凹形
Concave		2.91.45600、15、30、45、90
), ArticleFig(id=1241029752220349217, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=EN, label=Tab.2, caption=

Model and abbreviation

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基本构型
Basic configuration		角度Angle
θ/（°）		简称
Abbreviations		角度Angle
θ/（°）		简称
Abbreviations
正六边形
Hexagon		0LBX-1C-015LBX-1C-15
30LBX-1C-300/15LBX-2C-0-15
15/-15LBX-2C-15-150/30LBX-2C-0-30
内凹形
Concave		0NAX-1C-015NAX-1C-15
30NAX-1C-3045NAX-1C-45
90NAX-1C-900/15NAX-2C-0-15
15/-15NAX-2C-15-150/30NAX-2C-0-30
30/-30NAX-2C-30-300/45NAX-2C-0-45
45/-45NAX-2C-45-450/90NAX-2C-0-90
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模型及简称

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基本构型
Basic configuration		角度Angle
θ/（°）		简称
Abbreviations		角度Angle
θ/（°）		简称
Abbreviations
正六边形
Hexagon		0LBX-1C-015LBX-1C-15
30LBX-1C-300/15LBX-2C-0-15
15/-15LBX-2C-15-150/30LBX-2C-0-30
内凹形
Concave		0NAX-1C-015NAX-1C-15
30NAX-1C-3045NAX-1C-45
90NAX-1C-900/15NAX-2C-0-15
15/-15NAX-2C-15-150/30NAX-2C-0-30
30/-30NAX-2C-30-300/45NAX-2C-0-45
45/-45NAX-2C-45-450/90NAX-2C-0-90
), ArticleFig(id=1241029752409092901, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=EN, label=Tab.3, caption=

PLA material parameters

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参数
Parameter		密度
Density
ρ/（g/cm3）		弹性模量
Modulus of elasticity
E/MPa		泊松比
Poisson ratio
μ		塑性应变
Plastic strain
ε		塑性应力
Plastic stress
R/MPa
值
Value		1.252 2000.3040.689 1
0.00645.218 6
0.013 346.791 7
0.019 946.959 9
), ArticleFig(id=1241029752505561895, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=CN, label=表3, caption=

PLA材料参数

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参数
Parameter		密度
Density
ρ/（g/cm3）		弹性模量
Modulus of elasticity
E/MPa		泊松比
Poisson ratio
μ		塑性应变
Plastic strain
ε		塑性应力
Plastic stress
R/MPa
值
Value		1.252 2000.3040.689 1
0.00645.218 6
0.013 346.791 7
0.019 946.959 9
), ArticleFig(id=1241029752585253674, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=EN, label=Tab.4, caption=

Experimental results and simulation results of hexagonal shape model

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模型
Model		实验结果
Experimental result		仿真结果
Simulation result		模型
Model		实验结果
Experimental result		仿真结果
Simulation result
LBX-1C-0LBX-1C-15
LBX-1C-30
LBX-2C-0-15
（0°铺层）
（0° paving）		LBX-2C-0-15
（15°铺层）
（15° paving）
LBX-2C-15-15
（15°铺层）
（15° paving）		LBX-2C-15-15
（-15°铺层）
（-15° paving）
LBX-2C-0-30
（0°铺层）
（0° paving）		LBX-2C-0-30
（30°铺层）
（30° paving）
), ArticleFig(id=1241029752685916974, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=CN, label=表4, caption=

六边形模型实验结果和仿真结果

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模型
Model		实验结果
Experimental result		仿真结果
Simulation result		模型
Model		实验结果
Experimental result		仿真结果
Simulation result
LBX-1C-0LBX-1C-15
LBX-1C-30
LBX-2C-0-15
（0°铺层）
（0° paving）		LBX-2C-0-15
（15°铺层）
（15° paving）
LBX-2C-15-15
（15°铺层）
（15° paving）		LBX-2C-15-15
（-15°铺层）
（-15° paving）
LBX-2C-0-30
（0°铺层）
（0° paving）		LBX-2C-0-30
（30°铺层）
（30° paving）
), ArticleFig(id=1241029752773997358, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=EN, label=Tab.5, caption=

Experimental results and simulation results of inner concave shape model

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模型
Model		实验结果
Experimental result		仿真结果
Simulation result		模型
Model		实验结果
Experimental result		仿真结果
Simulation result
NAX-1C-0NAX-1C-15
NAX-1C-30NAX-1C-45
NAX-1C-90
NAX-2C-0-15
（0°铺层）
（0° paving）		NAX-2C-0-15
（15°铺层）
（15° paving）
NAX-2C-15-15
（15°铺层）
（15° paving）		NAX-2C-15-15
（-15°铺层）
（-15° paving）
NAX-2C-0-30
（0°铺层）
（0° paving）		NAX-2C-0-30
（30°铺层）
（30° paving）
NAX-2C-30-30
（30°铺层）
（30° paving）		NAX-2C-30-30
（-30°铺层）
（-30° paving）
NAX-2C-0-45
（0°铺层）
（0° paving）		NAX-2C-0-45
（45°铺层）
（45° paving）
NAX-2C-45-45
（45°铺层）
（45° paving）		NAX-2C-45-45
（-45°铺层）
（-45° paving）
NAX-2C-0-90
（0°铺层）
（0° paving）		NAX-2C-0-90
（90°铺层）
（90° paving）
), ArticleFig(id=1241029752870466353, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=CN, label=表5, caption=

内凹形模型实验结果和仿真结果

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模型
Model		实验结果
Experimental result		仿真结果
Simulation result		模型
Model		实验结果
Experimental result		仿真结果
Simulation result
NAX-1C-0NAX-1C-15
NAX-1C-30NAX-1C-45
NAX-1C-90
NAX-2C-0-15
（0°铺层）
（0° paving）		NAX-2C-0-15
（15°铺层）
（15° paving）
NAX-2C-15-15
（15°铺层）
（15° paving）		NAX-2C-15-15
（-15°铺层）
（-15° paving）
NAX-2C-0-30
（0°铺层）
（0° paving）		NAX-2C-0-30
（30°铺层）
（30° paving）
NAX-2C-30-30
（30°铺层）
（30° paving）		NAX-2C-30-30
（-30°铺层）
（-30° paving）
NAX-2C-0-45
（0°铺层）
（0° paving）		NAX-2C-0-45
（45°铺层）
（45° paving）
NAX-2C-45-45
（45°铺层）
（45° paving）		NAX-2C-45-45
（-45°铺层）
（-45° paving）
NAX-2C-0-90
（0°铺层）
（0° paving）		NAX-2C-0-90
（90°铺层）
（90° paving）
), ArticleFig(id=1241029752954352436, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=EN, label=Tab.6, caption=

Downforce distance and peak force of the hexagonal model’s indenter

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模型Model下压距离
Downforce distance/mm		峰值力
Peak force/N
LBX-1C-08.925 002.26
LBX-1C-159.845 559.25
LBX-1C-3011.875 610.61
LBX-2C-0-15306 095.67
LBX-2C-15-1510.794 542.54
LBX-2C-0-30306 460.73
), ArticleFig(id=1241029753055015734, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=CN, label=表6, caption=

六边形模型压头下压距离与峰值力

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模型Model下压距离
Downforce distance/mm		峰值力
Peak force/N
LBX-1C-08.925 002.26
LBX-1C-159.845 559.25
LBX-1C-3011.875 610.61
LBX-2C-0-15306 095.67
LBX-2C-15-1510.794 542.54
LBX-2C-0-30306 460.73
), ArticleFig(id=1241029753143096122, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=EN, label=Tab.7, caption=

Downforce distance and peak force of the inner concave shape model’s indenter

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模型Model下压距离
Downforce distance/mm		峰值力Peak force/N
NAX-1C-04.813 041.72
NAX-1C-158.023 055.74
NAX-1C-3017.364 198.10
NAX-1C-4515.253 694.23
NAX-1C-90306 075.97
NAX-2C-0-1522.404 841.12
NAX-2C-15-1517.643 092.35
NAX-2C-0-3010.614 080.50
NAX-2C-30-308.153 373.65
NAX-2C-0-4515.494 224.67
NAX-2C-45-45304 688.84
NAX-2C-0-9023.264 501.68
), ArticleFig(id=1241029753277313857, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241029725443912423, language=CN, label=表7, caption=

内凹形模型压头下压距离与峰值力

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模型Model下压距离
Downforce distance/mm		峰值力Peak force/N
NAX-1C-04.813 041.72
NAX-1C-158.023 055.74
NAX-1C-3017.364 198.10
NAX-1C-4515.253 694.23
NAX-1C-90306 075.97
NAX-2C-0-1522.404 841.12
NAX-2C-15-1517.643 092.35
NAX-2C-0-3010.614 080.50
NAX-2C-30-308.153 373.65
NAX-2C-0-4515.494 224.67
NAX-2C-45-45304 688.84
NAX-2C-0-9023.264 501.68
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层合多孔结构的裂纹扩展规律研究
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许爽 1 , 邓庆田 1, 2 , 李旺斐 1 , 李新波 1, 2 , 宋学力 1, 2 , 温金鹏 3
机械强度 | 疲劳·损伤·断裂·失效分析 2025,47(2): 28-36
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机械强度 | 疲劳·损伤·断裂·失效分析 2025, 47(2): 28-36
层合多孔结构的裂纹扩展规律研究
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许爽1 , 邓庆田1, 2 , 李旺斐1, 李新波1, 2, 宋学力1, 2, 温金鹏3
作者信息
  • 1.长安大学 理学院，西安　710064
  • 2.长安大学 西安市结构损伤数字化检测技术重点实验室，西安　710064
  • 3.中国工程物理研究院总体工程研究所，绵阳　621900

    • 许爽，女，2000年生，陕西渭南人，硕士研究生；主要研究方向为多孔材料和结构力学性能；E-mail：。

通讯作者:

邓庆田（通信作者），男，1980年生，陕西咸阳人，博士，副教授；主要研究方向为多孔材料和结构力学性能、损伤检测结构；E-mail：。
Study on the crack expansion law of laminated porous structure
Shuang XU1 , Qingtian DENG1, 2 , Wangfei LI1, Xinbo LI1, 2, Xueli SONG1, 2, Jinpeng WEN3
Affiliations
  • 1.School of Sciences, Chang’an University, Xi’an 710064, China
  • 2.Xi’an Key Laboratory of Digital Detection Technology for Structure Damage, Chang’an University, Xi’an 710064, China
  • 3.Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang 621900, China
出版时间: 2025-02-15 doi: 10.16579/j.issn.1001.9669.2025.02.004
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摘要
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基于六边形和内凹形两种基本构型，采用实验测试和有限元仿真的方法，对三点弯曲作用下层合多孔结构裂纹扩展规律进行了研究，讨论了胞元铺设方向的角度对层合多孔结构破坏形式、承载力和变形的影响。结果表明，双层模型的裂纹扩展路径会向裂纹扩展抑制能力较弱层的裂纹扩展路径偏转；强度低的一侧会发生更大的变形，从而导致模型向强度高的一侧偏转；在一些角度组合下，双层模型承载力和韧性相较于对应的单层模型有明显提升。

层合多孔结构  /  三点弯曲实验  /  裂纹扩展  /  聚乳酸材料

Based on two basic configurations of hexagonal and inner concave shapes, by utilizing experimental test and finite element simulation method, the crack expansion law of laminated porous structures under three-point bending was studied, the influence of cellular element angle of laying direction on failure mode, load capacity, and deformation of the laminated porous structures was discussed. The results indicate that the crack expansion path in the bilayer model deviates towards the weaker layer with less crack expansion inhibition capability. The weaker side experiences greater deformation,leading to a deviation of the model towards the stronger side. Under certain angle combinations, the bilayer model shows significantly improved load-bearing capacity and toughness compared to the corresponding single-layer model.

Laminated porous structure  /  Three-point bending experiment  /  Crack expansion  /  Polylactic acid LA material
许爽, 邓庆田, 李旺斐, 李新波, 宋学力, 温金鹏. 层合多孔结构的裂纹扩展规律研究. 机械强度, 2025 , 47 (2) : 28 -36 . DOI: 10.16579/j.issn.1001.9669.2025.02.004
Shuang XU, Qingtian DENG, Wangfei LI, Xinbo LI, Xueli SONG, Jinpeng WEN. Study on the crack expansion law of laminated porous structure[J]. Journal of Mechanical Strength, 2025 , 47 (2) : 28 -36 . DOI: 10.16579/j.issn.1001.9669.2025.02.004
正文
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0　引言
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近年来，随着轻质结构的迅速发展，多孔结构因具有质量轻、渗透性好、比强度高等优点，从一系列轻质结构中脱颖而出，广泛应用于工程与医疗领域[1-2]。
迄今为止，现有的研究主要集中于多孔结构的单层模型，大多由相同材料制成的周期性单元组成，许多学者已经使用实验仿真[3]和理论[4-6]方法探究了其裂纹扩展模式。张欣茹等[7-8]基于有限元仿真和实验研究了拓扑形状、单元方向、孔隙率、预制裂纹参数和相对密度对平面多孔结构裂纹扩展的影响。GIBSON等[9]提出了一些经验公式来描述多孔结构的断裂韧性与其孔隙率、孔洞形状和分布等结构参数之间的关系。也有学者探究梯度多孔结构的裂纹扩展模式[10-11]。SHU等[12]提出了在均匀蜂窝结构中改变支板厚度的概念，通过非均质设计提高均匀蜂窝结构的韧性。对多孔复合材料也有较多的研究[13]。LIU等[14]以Si3N4晶须为界面层制备了仿生ZrB2-SiC层状陶瓷，研究其抗弯强度和断裂韧性。也有对复合材料层合板的研究[15-16]。赵丽滨等[17]从试验研究、理论分析和数值模拟3个方面介绍了单向复合材料层间断裂韧性测试方法和原理，对多向层合板分层扩展行为进行了试验研究。牟浩蕾等[18]对纤维增强复合材料层合试验样件进行拉伸、压缩剪切试验，分析其破坏模式。有学者将层合板理论引入多孔结构中，建立层合多孔结构。马南芳[19]采用层合结构的方式提高蜂窝结构的能量吸收性能。贺璞等[20]研究了层合多孔圆柱壳在轴向压缩载荷下的承载力性能和变形破坏模式。鲜有对多孔层合结构裂纹扩展的研究。本文在多孔结构的基础上，以层合板理论为依托，建立层合多孔结构模型，探究了层间效应对多孔结构裂纹扩展规律的影响。
本文基于复合材料力学层合板理论，设计了层合多孔结构板，通过合理调整每层多孔结构板的孔的构型和铺设方向获取等效力学性能。利用SolidWorks软件进行模型设计，导入仿真软件进行模拟计算，并通过3D打印技术制备了实验模型，通过实验和仿真研究结果分析验证设计和方法的合理性。为功能多孔结构的设计和制备提供了一种新的思路和方法。
1　层合多孔结构
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采用复合材料层合板设计方法，以聚乳酸（Polylactic Acid，PLA）材料为基础材料，设计了层合多孔结构板。多孔结构板的基本尺寸为140 mm×70 mm×10 mm（长×宽×厚），单层结构厚度为10 mm，双层结构每层厚度为5 mm。本文引入了正六边形和内凹形2种基本构型，并对构型进行旋转操作，图1为2种基本构型示意图，其夹角α分别为120°和60°，基本构型旋转角度为β，其中，正六边形旋转角度分别为15°和30°，内凹形则包括了15°、30°、45°和90° 4种不同的旋转角度，基本构型的几何参数如表1所示。在双层模型中，对所选取构型进行分层组合，模型及其简称如表2所示。为了分析裂纹的扩展规律，在下边缘中部预置一个长11 mm、宽2 mm的三角形贯穿裂纹，如图2所示。
2　实验测试与有限元仿真
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2.1　实验测试
采用3D打印机熔融丝进行模型制备，打印速度为30 mm/s，如图3所示。通过三点弯曲测试层合多孔结构裂纹扩展规律，实验装置如图4所示（以NAX-1C-0为例），使用微机控制电子万能试验机进行测试，加载速度为1 mm/min，如图5所示。
2.2　有限元仿真
使用Abaqus有限元仿真软件对平面多孔结构板进行了准静态三点弯曲模拟，并选用聚乳酸作为材料，材料参数如表3所示。实验装置底端两支撑间距为120 mm。顶端压头及底端两支撑与平面多孔结构板之间的接触形式均为摩擦接触，摩擦因数为0.3。采用四面体网格对平面多孔结构板进行划分，模型划分网格单元尺寸为2 mm，网格划分如图6所示。设置底端两支撑面固定端约束，并对顶端压头施加分步位移载荷直至50 mm。
3　结果分析
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3.1　破坏形式
六边形模型的实验结果和有限元仿真结果如表4所示。由表4可知，在六边形模型中，LBX-1C-15裂纹扩展方向与竖直方向的夹角大约为15°，LBX-2C-0-15胞元15°铺层的裂纹扩展方向相对于LBX-1C-15的裂纹扩展方向向竖直方向偏转；LBX-1C-30的裂纹扩展方向大致为竖直方向，整个裂纹扩展路径呈“S”形，LBX-2C-0-30胞元30°铺层的裂纹扩展方向为竖直方向，相较于LBX-1C-30的裂纹扩展方向更靠近竖直方向。其他六边形模型的裂纹扩展方向都大致为竖直方向。由于失稳现象，LBX-2C-0-15上方萌生了新裂纹，且每层新裂纹的扩展方向与预置裂纹扩展方向一致，其他六边形模型均未出现此现象。
单层模型和双层反对称模型都在压头附近出现轻微致密化现象，LBX-2C-0-15和LBX-2C-0-30在压头与支座附近均出现明显致密化现象；且由于失稳现象的出现，在LBX-2C-0-15中，压头附近的致密化现象只出现在胞元15°铺层中，0°铺层产生了较大变形但只在支座附近出现轻微致密化现象；在LBX-2C-0-30中，胞元30°铺层的致密化现象较0°铺层更为严重；LBX-2C-0-30在压头下方出现对称“V”形致密化区域，其他六边形模型均未出现此现象。
内凹形模型的实验结果和有限元仿真结果如表5所示。由表5可知，在内凹形模型中，NAX-1C-15、NAX-1C-30裂纹扩展方向与竖直方向的夹角同基本构型转动的角度一致，分别为15°和30°；NAX-1C-45的裂纹扩展方向与竖直方向的夹角大约为20°。NAX-2C-0-15、NAX-2C-0-30和NAX-2C-0-45的非0°铺层裂纹扩展方向相对于对应单层模型的裂纹扩展方向向竖直方向偏转。其余模型的裂纹扩展方向都为竖直方向。由于失稳现象，NAX-2C-0-15上方萌生了新裂纹，且每层新裂纹的扩展方向与预置裂纹扩展方向一致，其他模型均未出现此现象。
在内凹形单层模型中，NAX-1C-90产生了较大变形，在压头两侧与支座附近出现了大面积致密化区域；NAX-1C-30和NAX-1C-45产生了轻微变形，在靠近压头处出现了轻微致密化现象。在内凹形双层模型中，由于失稳现象，NAX-2C-0-15和NAX-2C-0-90的0°铺层出现了较大变形，但未出现致密化区域，非0°铺层则在压头附近产生了严重的致密化现象。
在所有模型中，反对称结构裂纹扩展路径大致为竖直方向，其余模型的非0°层相对于单层模型都发生了向竖直方向的偏转。在双层模型中，0°层总是先出现裂纹，由于层间黏结力的存在，非0°层受到0°层裂纹扩展力的影响，从而使其裂纹扩展方向向0°层裂纹扩展的方向发生偏转。发生失稳现象的模型，均是朝0°层偏转，导致非0°层产生严重致密化现象。这与双层模型两层的强度差有关，强度低的一侧会发生更大的变形，从而导致模型向强度高的一侧偏转。
3.2　承载力和变形
选取压头下压距离和下压过程中的峰值力为判断指标，压头的下压距离越大，则模型韧性越强；压头下压过程中的峰值力越大，则模型的承载力越强；对于压头下压至30 mm前产生严重失稳的模型，选取发生失稳时压头的下压距离为判断指标，发生失稳时压头的下压距离越大，则结构稳定性越好。
在六边形模型中，所有单层模型和LBX-2C-15-15均在压头下压至30 mm之前发生了脆性断裂，导致无法继续加载。六边形模型压头下压距离和下压过程中的峰值力如表6所示，载荷-位移曲线如图7、图8所示。
由表6、图7和图8可知，六边形单层模型中，0°模型承载力和韧性最弱；30°模型承载力和韧性最强，相较于单层0°和15°，承载力分别提升了12.2%和0.9%，韧性分别提升了33.1%和20.6%。六边形双层模型中，LBX-2C-0-15相较于单层0°和15°模型，承载力分别提升了21.9%和9.6%，韧性分别提升了236.3%和204.9%；LBX-2C-15-15的承载力和韧性最弱，承载力相较于单层15°模型下降了18.3%，韧性相较于单层15°模型提升了9.7%；LBX-2C-0-30承载力和韧性最强，承载力相较于单层0°、30°，双层15°/-15°和0°/15°模型分别提升了29.2%、15.2%、42.2%和6%，韧性相较于单层0°、30°和双层15°/-15°模型分别提升了236.3%、204.9%和178%。
在内凹形模型中，NAX-2C-0-15和NAX-2C-0-90在压头下压至30 mm前发生了严重失稳导致不能加载，单层90°模型和NAX-2C-45-45压头下压至30 mm实验停止，其余模型均在压头下压至30 mm之前发生了脆性断裂导致无法继续加载。内凹形模型压头的下压距离和下压过程中的峰值力如表7所示，载荷-位移曲线如图9、图10所示。
由表7、图9可知，内凹形单层模型中，0°模型的承载力和韧性最弱；90°模型的承载力和韧性远大于其他模型，相较于单层0°、15°、30°和45°，承载力分别提升了99.8%、98.8%、44.7%和64.5%，韧性分别提升了523.7%、274.1%、72.8%和96.7%。在内凹形双层模型中，承载力最弱的模型为NAX-2C-15-15，韧性最弱的模型为NAX-2C-30-30；承载力最强的模型为NAX-2C-0-15，韧性最强的模型为NAX-2C-45-45。
由表7和图10可知，内凹形双层模型中，NAX-2C-0-15相较于单层0°和15°，承载力分别提升了59.2%和58.4%，韧性分别提升了365.7%和179.3%；NAX-2C-0-30相较于单层0°，承载力提升了34.2%，韧性提升了120.6%；NAX-2C-0-30和NAX-2C-30-30相较于单层30°，承载力分别降低了2.8%和17.3%，韧性分别降低了38.9%和53.1%；NAX-2C-0-45相较于单层0°和45°，承载力分别提升了38.9%和14.4%，韧性分别提升了222%和1.5%；NAX-2C-45-45相较于单层45°，承载力提升了26.9%，韧性提升了96.7%。NAX-2C-0-90相较于单层0°，承载力提升了48%，韧性提升了383.6%；相较于单层90°，承载力降低了25.9%，韧性降低了22.5%。
3.3　误差分析
图11~图14所示分别为六边形单层、六边形双层、六边形0°/15°单双层对比和六边形0°/30°单双层对比模型拟合载荷-位移曲线。本文有限元仿真仅考虑了弹塑性的本构关系，未考虑材料和结构的断裂属性和损伤规律。由图11~图14可知，弹性阶段的实验和仿真结果较吻合，且规律类似，弹性阶段之后的仿真结果相较于实验结果偏大（图11~14中，T为实验结果，S为仿真结果）。
4　结论
收起
基于六边形和内凹形两种基本构型研究了单元方向、角度组合多孔结构的破坏形式、承载力和变形的影响，经实验测试与有限元分析得到以下主要结论：
1）由于层间黏结力的存在，双层模型的裂纹扩展路径会向裂纹扩展抑制能力较差层的裂纹扩展路径偏转。
2）在双层模型中，强度低的一侧会发生更大的变形，从而导致模型向强度高的一侧偏转，发生失稳现象，进而会导致两侧模型发生不同程度的致密化现象。
3）六边形单层模型中，胞元30°铺层模型承载力和韧性最强；六边形双层模型中，0°与30°层合模型的承载力和韧性最强；内凹形单层模型中，胞元90°铺层模型的承载力和韧性最强；内凹形双层模型中，承载力最强的模型为0°与15°层合模型，韧性最强的模型为45°与-45°层合模型。
4）在一些角度组合下，双层模型承载力和韧性相较于对应的单层模型有明显提升，六边形0°与30°层合模型承载力和韧性提升幅度均最大，内凹形0°与15°层合模型承载力提升幅度最大，内凹形0°与90°层合模型韧性提升幅度最大。
基金
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  • 国家自然科学基金委员会-中国工程物理研究院NSAF联合基金项目(U1930204)
文献
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2025年第47卷第2期
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doi: 10.16579/j.issn.1001.9669.2025.02.004
  • 接收时间：2023-05-29
  • 首发时间：2026-03-18
  • 出版时间：2025-02-15
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  • 收稿日期：2023-05-29
  • 修回日期：2023-08-05
基金
National Natural Science Foundation of China-Chinese Academy of Engineering Physics NSAF Joint Fund(U1930204)
国家自然科学基金委员会-中国工程物理研究院NSAF联合基金项目(U1930204)
作者信息
    1.长安大学 理学院，西安　710064
    2.长安大学 西安市结构损伤数字化检测技术重点实验室，西安　710064
    3.中国工程物理研究院总体工程研究所，绵阳　621900

通讯作者:

邓庆田（通信作者），男，1980年生，陕西咸阳人，博士，副教授；主要研究方向为多孔材料和结构力学性能、损伤检测结构；E-mail：。
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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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