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Article(id=1241446431668622244, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241446328396476740, articleNumber=null, orderNo=null, doi=10.16579/j.issn.1001.9669.2025.07.011, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1700668800000, receivedDateStr=2023-11-23, revisedDate=1705248000000, revisedDateStr=2024-01-15, acceptedDate=null, acceptedDateStr=null, onlineDate=1773913494269, onlineDateStr=2026-03-19, pubDate=1752508800000, pubDateStr=2025-07-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773913494269, onlineIssueDateStr=2026-03-19, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773913494269, creator=13701087609, updateTime=1773913494269, updator=13701087609, issue=Issue{id=1241446328396476740, tenantId=1146029695717560320, journalId=1227999626482147330, year='2025', volume='47', issue='7', 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=1773913469647, creator=13701087609, updateTime=1773916972123, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1241461018921062969, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241446328396476740, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1241461018921062970, tenantId=1146029695717560320, journalId=1227999626482147330, issueId=1241446328396476740, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=86, endPage=92, ext={EN=ArticleExt(id=1241446431962223528, articleId=1241446431668622244, tenantId=1146029695717560320, journalId=1227999626482147330, language=EN, title=Compression-compression fatigue life prediction model of T300/69 laminates under edge impact, columnId=1241446330749481285, journalTitle=Journal of Mechanical Strength, columnName=·Fatigue·Damage·Fracture·Failure Analysis·, runingTitle=null, highlight=null, articleAbstract=

After low-velocity impact at the edge, delamination and matrix extrusion occur inside the composite laminates,which will have a serious impact on the safe use and life of the composite laminates. Therefore, it is of practical engineering significance to establish a fatigue life prediction model for low-velocity impact at the edge. The dent damage size, compressive residual strength and fatigue life of the fatigue life prediction model were obtained by low-speed impact test, compression test and compression-compression fatigue test. Based on the average stress failure criterion, the impact damage area of the laminated plate was equivalent to the corresponding aperture by combining the opening equivalent method, and the equivalent damage coefficient of different impact energy was proposed. A fatigue life prediction model considering the compressive residual strength of impact damaged laminates was established, and the prediction results were compared with the test results.The results show that the fatigue life prediction accuracy of the model is high, the error is controlled within 10%, and the model has good prediction ability.

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LIU Jianhui, E-mail：
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边缘低速冲击后复合材料层合板内部产生分层、基体挤压等损伤，对于复合材料层合板的安全使用和寿命会产生严重影响。因此，建立一种针对边缘低速冲击后的疲劳寿命预测模型具有实际工程意义。通过低速冲击试验、压缩试验和压-压疲劳试验获得疲劳寿命预测模型的凹陷损伤尺寸、压缩剩余强度和疲劳寿命等数据。基于平均应力破坏准则，结合开口等效法，将层合板冲击损伤区域等效为相应孔径，提出不同冲击能量的等效损伤系数，建立了考虑冲击损伤层合板压缩剩余强度的疲劳寿命预测模型，并将预测结果与试验结果进行对比。结果表明，该模型的疲劳寿命预测精度较高，误差控制在10%以内，具有较好的预测能力。

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刘俭辉，男，1985年生，河南商丘人，博士，教授，硕士研究生导师；主要研究方向为机械强度理论；E-mail：。
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张鹏，男，1999年生，甘肃庆阳人，硕士研究生；主要研究方向为复合材料力学性能；E-mail：。

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张鹏，男，1999年生，甘肃庆阳人，硕士研究生；主要研究方向为复合材料力学性能；E-mail：。

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张鹏，男，1999年生，甘肃庆阳人，硕士研究生；主要研究方向为复合材料力学性能；E-mail：。

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Acta Materiae Compositae Sinica，2006，23（2）：150-157.（In Chinese）, articleTitle=Low-velocity impact damage analysis in carbon fiber reinforced composite laminated plates, refAbstract=null), Reference(id=1241446452677890450, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, doi=null, pmid=null, pmcid=null, year=2012, volume=null, issue=null, pageStart=99, pageEnd=101, url=null, language=null, rfNumber=［29］, rfOrder=42, authorNames=朱炜垚, journalName=null, refType=null, unstructuredReference=朱炜垚. 含低速冲击损伤复合材料层板剩余强度及疲劳性能研究[D]. 南京：南京航空航天大学，2012：99-101., articleTitle=含低速冲击损伤复合材料层板剩余强度及疲劳性能研究, refAbstract=null), Reference(id=1241446452757582227, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, doi=null, pmid=null, pmcid=null, year=2012, volume=null, issue=null, pageStart=99, pageEnd=101, url=null, language=null, rfNumber=［29］, rfOrder=43, authorNames=ZHU Weiyao, journalName=null, refType=null, unstructuredReference=ZHU Weiyao. Research on residual strength and fatigue performance of composite laminates with low-velocity impact damage[D]. Nanjing：Nanjing University of Aeronautics and Astronautics，2012：99-101.（In Chinese）, articleTitle=Research on residual strength and fatigue performance of composite laminates with low-velocity impact damage, refAbstract=null)], funds=[Fund(id=1241446447061717231, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, awardId=51605212, language=EN, fundingSource=National Natural Science Foundation of China(51605212), fundOrder=null, country=null), Fund(id=1241446447145603314, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, awardId=51605212, language=CN, fundingSource=国家自然科学基金项目(51605212), fundOrder=null, country=null)], companyList=[AuthorCompany(id=1241446439436472357, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, xref=null, ext=[AuthorCompanyExt(id=1241446439444860966, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, 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figureFileBig=CYiZ4tMzhKuvpyJIaXQYuQ==, tableContent=null), ArticleFig(id=1241446444339613876, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=CN, label=图8, caption=应力水平与疲劳寿命关系, figureFileSmall=G+0C8WK6l8nn2ie4FD3ROQ==, figureFileBig=CYiZ4tMzhKuvpyJIaXQYuQ==, tableContent=null), ArticleFig(id=1241446444444471480, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=EN, label=Tab. 1, caption=

Elastic performance parameters and strength performance parameters of T300/69 laminates

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E1/MPaE2/MPaE3/MPaν12ν13ν23G12/MPaG13/MPaG23/MPa
140 0009 0009 0000.320.280.214 6004 6003 082
XT/MPaXC/MPaYT/MPaYC/MPaSxy/MPaSxz/MPaSyz/MPa
1 7601 10051130706060
), ArticleFig(id=1241446444536746170, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=CN, label=表1, caption=

T300/69层合板弹性性能参数与强度性能参数

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E1/MPaE2/MPaE3/MPaν12ν13ν23G12/MPaG13/MPaG23/MPa
140 0009 0009 0000.320.280.214 6004 6003 082
XT/MPaXC/MPaYT/MPaYC/MPaSxy/MPaSxz/MPaSyz/MPa
1 7601 10051130706060
), ArticleFig(id=1241446444612243650, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=EN, label=Tab. 2, caption=

Damage morphology size of laminates under different impact energies

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冲击能量
Impact energy/J		试件编号
Specimen number		凹陷长度
Dent length/mm		凹陷长度平均值
Average length of dent/mm		凹陷宽度
Dent width/mm		凹陷宽度平均值
Average width of dent/mm
55 J-16.816.774.233.88
5 J-26.353.56
5 J-37.153.86
1515 J-111.2711.474.154.95
15 J-211.055.65
15 J-312.105.05
), ArticleFig(id=1241446444721295559, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=CN, label=表2, caption=

不同冲击能量下层合板损伤形貌尺寸

, figureFileSmall=null, figureFileBig=null, tableContent=
冲击能量
Impact energy/J		试件编号
Specimen number		凹陷长度
Dent length/mm		凹陷长度平均值
Average length of dent/mm		凹陷宽度
Dent width/mm		凹陷宽度平均值
Average width of dent/mm
55 J-16.816.774.233.88
5 J-26.353.56
5 J-37.153.86
1515 J-111.2711.474.154.95
15 J-211.055.65
15 J-312.105.05
), ArticleFig(id=1241446444817764555, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=EN, label=Tab. 3, caption=

Maximum compressive load and residual strength

, figureFileSmall=null, figureFileBig=null, tableContent=
冲击能量
Impact energy/J		试件编号
Specimen number		破坏载荷
Breaking load/kN		平均压缩载荷
Average compressive load/kN		压缩剩余强度
Compressive residual strength/MPa		平均压缩剩余强度
Average compressive residual strength/MPa
55 J-135.331.4280.1249.2
5 J-227.6219.0
5 J-331.2249.2
1515 J-126.824.5212.7194.4
15 J-225.2200.0
15 J-321.6171.4
), ArticleFig(id=1241446444893262028, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=CN, label=表3, caption=

最大压缩载荷及剩余强度

, figureFileSmall=null, figureFileBig=null, tableContent=
冲击能量
Impact energy/J		试件编号
Specimen number		破坏载荷
Breaking load/kN		平均压缩载荷
Average compressive load/kN		压缩剩余强度
Compressive residual strength/MPa		平均压缩剩余强度
Average compressive residual strength/MPa
55 J-135.331.4280.1249.2
5 J-227.6219.0
5 J-331.2249.2
1515 J-126.824.5212.7194.4
15 J-225.2200.0
15 J-321.6171.4
), ArticleFig(id=1241446444993925328, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=EN, label=Tab. 4, caption=

Characteristic length of the edge of impact compression load

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冲击能量
Impact energy/J		孔径
Aperture/mm		特征长度
Characteristic length a0/mm
53.38510.730
155.7356.030
), ArticleFig(id=1241446445111365846, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=CN, label=表4, caption=

边缘冲击压缩载荷下特征长度

, figureFileSmall=null, figureFileBig=null, tableContent=
冲击能量
Impact energy/J		孔径
Aperture/mm		特征长度
Characteristic length a0/mm
53.38510.730
155.7356.030
), ArticleFig(id=1241446445220417755, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=EN, label=Tab. 5, caption=

Compressive fatigue life after impacts

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试件编号
Specimen number		应力水平
Stress level/%		lg N平均lg N
Average of lg N
5 J-1805.231>5.492
5 J-280>5.653
15 J-1605.1065.440
15 J-2605.627
15 J-3705.3455.173
15 J-4704.885
15 J-5802.7023.560
15 J-6804.417
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冲击后压-压疲劳寿命

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试件编号
Specimen number		应力水平
Stress level/%		lg N平均lg N
Average of lg N
5 J-1805.231>5.492
5 J-280>5.653
15 J-1605.1065.440
15 J-2605.627
15 J-3705.3455.173
15 J-4704.885
15 J-5802.7023.560
15 J-6804.417
), ArticleFig(id=1241446446797476068, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=EN, label=Tab. 6, caption=

Equivalent damage coefficient

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冲击能量
Impact energy/J 		应力水平
Stress level/%		疲劳寿命
Fatigue life lg N		σy /MPa α
5805.231302.9880.656
5805.653302.9880.629
15803.560425.5650.542
15705.173372.3690.480
15605.440319.1740.468
), ArticleFig(id=1241446446910722281, tenantId=1146029695717560320, journalId=1227999626482147330, articleId=1241446431668622244, language=CN, label=表6, caption=

等效损伤系数

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冲击能量
Impact energy/J 		应力水平
Stress level/%		疲劳寿命
Fatigue life lg N		σy /MPa α
5805.231302.9880.656
5805.653302.9880.629
15803.560425.5650.542
15705.173372.3690.480
15605.440319.1740.468
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边缘冲击下T300/69层合板压-压疲劳寿命预测模型
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张鹏 , 刘俭辉 , 韦尧兵
机械强度 | ·疲劳·损伤·断裂·失效分析· 2025,47(7): 86-92
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机械强度 | ·疲劳·损伤·断裂·失效分析· 2025, 47(7): 86-92
边缘冲击下T300/69层合板压-压疲劳寿命预测模型
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张鹏 , 刘俭辉 , 韦尧兵
作者信息
  • 兰州理工大学 机电工程学院，兰州　730050

    • 张鹏，男，1999年生，甘肃庆阳人，硕士研究生；主要研究方向为复合材料力学性能；E-mail：。

通讯作者:

刘俭辉，男，1985年生，河南商丘人，博士，教授，硕士研究生导师；主要研究方向为机械强度理论；E-mail：。
Compression-compression fatigue life prediction model of T300/69 laminates under edge impact
Peng ZHANG , Jianhui LIU , Yaobing WEI
Affiliations
  • School of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou 730050, China
出版时间: 2025-07-15 doi: 10.16579/j.issn.1001.9669.2025.07.011
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摘要
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边缘低速冲击后复合材料层合板内部产生分层、基体挤压等损伤，对于复合材料层合板的安全使用和寿命会产生严重影响。因此，建立一种针对边缘低速冲击后的疲劳寿命预测模型具有实际工程意义。通过低速冲击试验、压缩试验和压-压疲劳试验获得疲劳寿命预测模型的凹陷损伤尺寸、压缩剩余强度和疲劳寿命等数据。基于平均应力破坏准则，结合开口等效法，将层合板冲击损伤区域等效为相应孔径，提出不同冲击能量的等效损伤系数，建立了考虑冲击损伤层合板压缩剩余强度的疲劳寿命预测模型，并将预测结果与试验结果进行对比。结果表明，该模型的疲劳寿命预测精度较高，误差控制在10%以内，具有较好的预测能力。

复合材料层合板  /  疲劳寿命预测模型  /  开口等效法  /  边缘低速冲击

After low-velocity impact at the edge, delamination and matrix extrusion occur inside the composite laminates,which will have a serious impact on the safe use and life of the composite laminates. Therefore, it is of practical engineering significance to establish a fatigue life prediction model for low-velocity impact at the edge. The dent damage size, compressive residual strength and fatigue life of the fatigue life prediction model were obtained by low-speed impact test, compression test and compression-compression fatigue test. Based on the average stress failure criterion, the impact damage area of the laminated plate was equivalent to the corresponding aperture by combining the opening equivalent method, and the equivalent damage coefficient of different impact energy was proposed. A fatigue life prediction model considering the compressive residual strength of impact damaged laminates was established, and the prediction results were compared with the test results.The results show that the fatigue life prediction accuracy of the model is high, the error is controlled within 10%, and the model has good prediction ability.

Composite laminate  /  Fatigue life prediction model  /  Opening equivalent method  /  Low-velocity edge impact
张鹏, 刘俭辉, 韦尧兵. 边缘冲击下T300/69层合板压-压疲劳寿命预测模型. 机械强度, 2025 , 47 (7) : 86 -92 . DOI: 10.16579/j.issn.1001.9669.2025.07.011
Peng ZHANG, Jianhui LIU, Yaobing WEI. Compression-compression fatigue life prediction model of T300/69 laminates under edge impact[J]. Journal of Mechanical Strength, 2025 , 47 (7) : 86 -92 . DOI: 10.16579/j.issn.1001.9669.2025.07.011
正文
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0　引言
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复合材料具有强度高、密度低、疲劳性能好等优点，在航空航天、新能源领域得到广泛应用[1-3]。复合材料层合板由单向碳纤维与树脂基体通过层合热压而成，在使用过程中可能会受到冰雹、碎片等撞击。这会导致复合材料层合板的剩余强度和抗疲劳性能显著下降，削减了材料的使用性能[4]。因此，研究复合材料层合板疲劳寿命成为国内外研究的热点之一[5]。复合材料层合板疲劳试验周期长，耗费大量的物力，其最直接、有效的方法就是通过建立疲劳寿命预测模型对疲劳性能进行评价。
复合材料层合板的疲劳损伤机制十分复杂[6-7]。在疲劳过程中，各种损伤相互影响，其材料性能逐渐退化。复合材料层合板的疲劳寿命预测模型分为三大类[8]：①根据S-N曲线来预测特定载荷下的疲劳寿命；②根据复合材料层合板疲劳渐进损伤模型来预测疲劳寿命；③根据剩余强度或剩余模量建立疲劳寿命预测模型。FAWAZ等[9]将S-N疲劳寿命曲线变换为对数形式的表达式。SHEN等[10]研究了准静态和疲劳载荷作用下正交铺设的玻璃纤维复合材料层合板损伤演化规律，分析不同铺设顺序对材料损伤演化的影响。ATTIA等[11]研究了冲击后复合材料在疲劳载荷作用下的损伤扩展问题，利用应变能释放率来预测冲击损伤后复合材料的疲劳寿命。徐颖等[12]针对冲击后复合材料层合板，研究了冲击损伤层合板的压-压疲劳寿命预测方法。刘俭辉等[13]修正了应力场强法，建立了疲劳寿命预测模型，并验证了模型的可靠性。
复合材料层合板疲劳损伤过程十分复杂，得到准确的疲劳寿命通常需要做大量的试验。为了降低试验成本，提高预测模型的精度，考虑冲击损伤层合板的压缩剩余强度，选用开口等效法[14-17]将损伤区域等效为圆形开孔，圆的直径取决于最大损伤尺寸，并认为该区域不再具有承载能力。此外，子层屈曲法[18]将冲击损伤看作多个矩形分层，并认为压缩破坏是各个子层发生屈曲失效的过程，该方法在工程实际中有一定的局限性。软化夹杂法[19-21]将冲击损伤等效为形状规则的软化夹杂，然后用应力准则、应变准则或其他准则判定层合板的失效。损伤累积法[22-25]利用动态有限元模拟层合板的冲击损伤，将对应退化后的刚度作为层合板的初始损伤，再用损伤累积法模拟层合板的压缩破坏过程，并计算剩余压缩强度。
借助低速冲击试验分析损伤区域尺寸，并进行等效孔径计算，通过压缩试验得到压缩剩余强度，进而求解外载荷应力，通过15 J冲击能量下的压-压疲劳试验获得其疲劳寿命。基于以上结果，拟合等效损伤系数，提出适用于低速冲击损伤状态下的T300/69层合板疲劳寿命预测模型，为工程应用提供理论依据。本文只考虑冲击能量对疲劳寿命的影响，未考虑铺层方式、铺层角度、冲击大小及方向对疲劳性能的影响。
1　低速冲击后压缩试验
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1.1　T300/69试验件
T300/69碳纤维复合材料层合板采用热压罐工艺制作而成，单层板厚度为0.15 mm，材料铺层顺序为［0/45/-45/90］3s，共24层。使用线切割技术将复合材料层合板切割成长为75 mm、宽为35 mm的试验件。T300/69层合板弹性性能参数和强度性能参数如表1所示。
1.2　基于冲击试验获取凹陷损伤数据
如图1所示，冲击试验在落锤试验台上完成，通过调整落锤高度来获得冲击能量，冲头的形状可以根据实际的工况进行调整。
复合材料层合板边缘冲击的损伤形貌与冲击能量有显著关系。当冲击能量为5 J时，损伤区域产生椭圆形凹陷，层间出现少量分层；当冲击能量为15 J时，损伤区域的凹陷程度更明显，其部位产生纤维翘起等现象（图2）。
由试验可以得到不同冲击能量下层合板损伤形貌尺寸，如表2所示。冲击产生的凹坑长度和宽度随冲击能量增大而增加。相比于凹陷宽度，损伤区域凹陷长度对于冲击能量的变化更加敏感。观察层合板的损伤区域发现，其主要损伤模式有纤维压缩破坏、基体挤压及基体裂纹扩展导致的分层。
1.3　基于低速冲击后压缩试验获取压缩剩余强度
按照ASTM D7137[26]标准，压缩试验在WDW-300微机控制电子万能试验机上进行。压缩试验采用载荷控制的加载方式，压缩试验加载速率为2 mm/min，试件夹持情况如图3所示。
损伤区域随冲击能量的增大而增大；当冲击能量为5 J时，压缩失效试件基本观察不到因压缩失效而产生的裂纹［图4（a）］；当冲击能量为15 J时，压缩失效试件表面产生裂纹［图4（d）］，在冲击点附近已经造成了剪切损伤。由试件压缩侧面损伤图可以看出，边缘冲击后层合板压缩失效主要是以分层损伤为主，产生的分层对称分布在层合板的两侧。分层损伤是由边缘低能量冲击造成试件的损伤起始，使得层合板在压缩载荷的作用下不断扩展，最终失效。
不同冲击能量后，层合板最大压缩载荷及压缩剩余强度如表3所示。边缘冲击对层合板压缩强度的影响较大；随着冲击能量的增加，压缩剩余强度随之降低。同时也做了无损伤压缩试验，无损伤的压缩强度为333.25 MPa。
2　冲击损伤层合板的失效理论分析
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开孔等效法认为，冲击损伤层合板压缩失效模式和开孔层合板相似，都是由孔（冲击损伤区）边缘应力集中导致纤维屈曲，从而使层合板发生压缩破坏[27]的。
2.1　平均应力判据
平均应力破坏准则是将距离孔边一定距离上的平均应力作为标准来表征开孔层合板的破坏。假设在y轴上从r到r+a0这段距离的平均应力σy等于或者大于无缺口层合板的强度σ0，就认为开孔层合板失效。
式中，为远场应力，即压缩剩余强度；为开孔层合板孔边应力集中系数；r为孔径；a0为特征长度。
2.2　等效孔径与特征长度的确定
运用开口等效法将冲击造成的损伤处理为一圆形开孔，根据表3将损伤区域等效为半圆孔，凹陷长度等效为开孔孔径。
张彦等[28]认为，含孔复合材料层合板特征长度a0与层合板的材料体系有关。
通过层合板冲击后的静压缩强度和平均失效准则便可以推导出不同孔径层合板的特征长度。损伤宽度扩展到层合板宽度的50%时，试件基本失去承载能力，经过少数加载循环后就会失效。试验表明，选择孔径r到50%板宽距离的平均应力会更适用[29]。如表4所示，冲击能量越大，等效孔径越大，特征长度越小。
3　压-压疲劳试验及寿命预测模型
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3.1　基于压-压疲劳试验获取疲劳寿命
复合材料层合板低速冲击后的压-压疲劳试验在试验机（图5）进行，试验均在室温下进行，疲劳加载采用载荷控制的加载方式，载荷波形为等幅正弦波。
T300/69复合材料层合板冲击后压-压疲劳损伤如图6所示。由图6可以看出，应力水平越大，其疲劳损伤越严重，层间分层越明显。在压-压疲劳载荷作用下，试件边缘冲击造成的分层由冲击点附近沿宽度方向向另一侧扩展，这个过程十分缓慢。随着循环次数的增加，直至临近破坏时，整个试件才会发生贯穿式分层和子层屈曲现象。
由表5可知，即使是同一冲击能量、同一应力水平，疲劳寿命也存在分散性。应力水平越高，循环次数越少。从边缘冲击试验到压-压疲劳试验，层合板局部损伤的复杂多样性也对疲劳寿命产生了影响。试验发现，15 J能量冲击后层合板在80%应力水平下寿命相差较大。
3.2　数值分析
建立层合板冲击后的疲劳寿命模型：
式中，σy (x，0)与σs分别为开孔层合板的外载荷应力和无损伤层合板的静压缩强度。为了更加真实地反映出应力-寿命情况，根据等应力等损伤原则对开孔层合板的疲劳寿命模型进行修正，等效损伤系数为α，式（2）变为
根据无损伤层合板疲劳寿命模型的指数函数规律，假设损伤层合板的对数寿命与应力水平之间也存在指数函数规律，用试验数据进行拟合，得到了低速冲击后层合板的疲劳寿命：
1）计算孔径应力集中系数 ，即
2）计算外载荷应力σy，即
等效孔径r和特征长度a0由表4确定，将5 J、15 J能量冲击后的层合板的疲劳寿命代入式（4）得到α值，如表6所示。
将15 J冲击能量在不同应力水平下获得的等效损伤系数求和再取平均值，得到的疲劳模型等效损伤系数α=0.497 0，则疲劳寿命模型为
4　试验验证与分析
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4.1　试验验证
如图7所示，将15 J能量冲击后复合材料层合板所获得的试验结果与预测结果进行对比。结果表明，误差范围较小，具体误差分析见第4.2节。平均应力水平为60%时，相对误差最大为6. 541%；平均应力水平为70%时，相对误差最大为5. 896%。
如图8所示，将低速冲击损伤层合板的疲劳寿命试验值与预测值进行了对比。低速冲击损伤层合板的疲劳寿命预测结果说明，本文所采用的疲劳寿命预测方法是合理的。
4.2　误差分析
误差来源可以归纳为以下几点：①复合材料层合板的疲劳寿命存在一定的分散性，疲劳性能易受到冲击载荷、环境温度和湿度的影响。边缘冲击后的压-压疲劳试验，层合板局部损伤的复杂多样性也对疲劳寿命产生了影响。②试验发现，层合板在80%应力水平下的寿命相差较大。一方面，因为层合板对分层损伤较为敏感，15 J能量的低速冲击造成的分层损伤严重影响了复合材料层合板的疲劳性能；另一方面，边缘冲击能量越高，层合板损伤区域越大，层合板承受的压缩载荷变弱，应力集中使得损伤区域的应力变大，从而影响层合板的疲劳寿命。③碳纤维复合材料本身为各向异性材料，存在一定的分散性。④将冲击损伤区域等效为圆形孔，虽然两者的力学特性相似但并不完全相同，导致等效过程存在差异。
5　结论
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针对低速边缘冲击下的T300/69复合材料层合板疲劳寿命开展一些研究。考虑层合板压缩剩余强度对疲劳寿命的影响，基于开口等效法建立了疲劳寿命预测模型；通过预测值与试验值，验证了该方法的合理性和可靠性，得出以下结论：
1）考虑低速冲击后复合材料层合板复杂的损伤机制，将边缘冲击损伤层合板等效为开孔层合板，通过测量凹陷损伤尺寸，确定开孔孔径及特征长度，其计算过程简洁高效。
2）考虑压缩剩余强度对疲劳寿命的影响，结合平均应力准则计算外载荷应力，通过试验数据拟合疲劳寿命模型，得到损伤参数，从而获得T300/69复合材料层合板的疲劳寿命预测模型。
3）将疲劳寿命预测与疲劳寿命试验相比，验证该方法可以准确地预测边缘低速冲击下的层合板疲劳寿命，且预测精度较高，预测误差在10%以内。
基金
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  • 国家自然科学基金项目(51605212)
文献
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2025年第47卷第7期
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doi: 10.16579/j.issn.1001.9669.2025.07.011
  • 接收时间：2023-11-23
  • 首发时间：2026-03-19
  • 出版时间：2025-07-15
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  • 收稿日期：2023-11-23
  • 修回日期：2024-01-15
基金
National Natural Science Foundation of China(51605212)
国家自然科学基金项目(51605212)
作者信息
    兰州理工大学 机电工程学院，兰州　730050

通讯作者:

刘俭辉，男，1985年生，河南商丘人，博士，教授，硕士研究生导师；主要研究方向为机械强度理论；E-mail：。
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2种不同金属材料的力学参数
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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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