Buckling and postbuckling behaviour of laminated composite plates with a cutout
composite concrete-steel plate walls
The idea of using composite steel and concrete walls to resist offshore loads was introduced a decade ago by the Hitachi Shipbuilding and Engineering Company (Adams 1987). Composite construction utilizes exterior steel plates with concrete infill. This has many advantages relative to built-up steel-plate or reinforced-concrete construction. For instance, a relatively thin plate can be used since local buckling is restrained by the concrete. Detailing consists of straight line weldments. This is much simpler than the substantial details required for built-up steel walls. Because of concrete confinement and the properties of the steel plates, composite walls should exhibit a high degree of strength and ductility. Both are desirable characteristics for exterior walls on offshore structures. A significant research project financed by the Center for Frontier Engineering Research (CFER) was concluded in 1990. The project investigated simple sandwich walls with internal diaphragms. These walls were intended for use in shallow water that is 20.0 to 30.0 m deep. The walls form an enclosed volume infilled with sand. This results in an artificial island that can be used as a base of operations for offshore explorations. Proposed systems would have typical configurations in which the ocean side walls span 5.0 to 6.0 m between bulkheads. Each span would have a 1.0 m depth, comprising three or four cells (Fig. 1). Steel-plate thickness would be of the order of 25 mm or more to avoid tearing during major loading events. These dimensions would appear to point to shear compression failure rather than flexural failure. The descriptor "composite" should be interpreted loosely. Separation and slippage between the concrete infill and the steel plate occurs on the tension side under flexural loading. Positive composite action can be provided by imbedded stiffeners or shear studs (O'Flynn 1987). The advantage obtained from composite action is offset by the complexity of the construction and details. A typical offshore structure is designed to withstand the 100-yr loading without significant permanent damage. The structure must also be able to resist a 1O,000-yr load event without total collapse (CSA 1989). In order that structural integrity is maintained for this event, two requirements have to be met. First, after the event has occurred, global collapse must not occur to the damaged structure under the application of permanent gravity and hydrostatic loading. Second, individual members that are overloaded are detailed so that adequate energy absorption capacity through large deformations is maintained. Adequate energy absorption is defined as the ability of the members to sustain six times the yield deflection while maintaining 50% of the yield load. This translates into a ductility requirement and a residual load capacity in the postpeak strength region of behavior. There are currently four different methods commonly used to predict the strength of composite walls. Traditional reinforced concrete design requires the existence of strain compatibility between the concrete and the tensile reinforcing steel. This assumption is not true in the case of concrete sandwich panels, since significant slip occurs between the steel and concrete. Empirical design equations were proposed based on dimensional analysis and statistical regression applied to multiple sets of test data (Adams and Zimmerman 1987). Although potentially useful in the range of parameters tested, the applicability of empirical design approaches outside of that range
制孔分层损伤对CF
第52卷第7期表面技术2023年7月SURFACE TECHNOLOGY·239·制孔分层损伤对CF/PEEK复合材料拉伸性能和表面应变分布的影响杜宇1,2，刘畅1，原文慧1（1.天津工业大学 机械工程学院，天津 300387；2.数字化学习技术集成与应用教育部工程研究中心，北京 100039）摘要：目的研究钻削制孔表面分层损伤与拉伸载荷下开孔碳纤维增强聚醚醚酮（CF/PEEK）复合材料表面应变分布的相关性。
方法通过对CF/PEEK复合材料层合板进行钻削制孔实验，分析不同进给速度对钻削温度、钻削轴向力、制孔出口表面分层和孔壁表面损伤的影响。
采用数字图像相关技术（DIC）和力学实验相结合的方法，研究分层损伤程度对开孔CF/PEEK复合材料层合板拉伸性能和表面应变分布的影响。
使用扫描电镜观测开孔试件的断裂形貌，分析开孔试件受拉伸载荷时的破坏模式。
结果随着进给速度的增加，钻削温度降低，钻削轴向力提高，出口表面分层和孔壁损伤程度加剧。
随着分层损伤程度的增加，层合板的拉伸强度呈现出降低的趋势，试件的拉伸强度从558.4 MPa降低到525.63 MPa，降低了5.87%。
在中应力和高应力状态下，试件x方向的最大负应变随着分层损伤程度的增加而增加。
在高应力状态下，试件y方向的最大正应变随着分层损伤程度的增加而增加。
试件的断裂方式主要是基体开裂、分层和纤维撕裂，断口有纤维脱落和纤维拔出，垂直于载荷方向的纤维破坏模式为剥离破坏，与载荷方向一致的纤维破坏模式为拉伸破坏。
结论钻削制孔表面分层损伤会降低开孔CF/PEEK复合材料的拉伸强度。
不同分层损伤程度的开孔层合板表面应变分布表现出明显的差异性。
关键词：CF/PEEK复合材料；制孔损伤；拉伸性能；数字图像相关技术；表面应变中图分类号：TG506.7文献标识码：A 文章编号：1001-3660(2023)07-0239-11DOI：10.16490/ki.issn.1001-3660.2023.07.021Effect of Delamination Damage on Tensile Properties and SurfaceStrain of Open-hole CF/PEEK CompositesDU Yu1,2, LIU Chang1, YUAN Wen-hui1(1. School of Mechanical Engineering, Tiangong University, Tianjin 300387, China; 2. Engineering Research Center ofIntegration and Application of Digital Learning Technology, Ministry of Education, Beijing 100039, China)收稿日期：2022–09–19；修订日期：2023–01–12Received：2022-09-19；Revised：2023-01-12基金项目：天津市131创新型人才团队（201916）；天津市自然科学基金（20JCQNJC00050）；数字化学习技术集成与应用教育部工程研究中心创新基金（1221007）Fund：Tianjin 131 Research Team of Innovative Talents(201916); Natural Science Foundation of Tianjin(20JCQNJC00050); Innovation Foundation of Engineering Research Center of Integration and Application of Digital Learning Technology, Ministry of Education (1221007)作者简介：杜宇（1988—），男，硕士，高级实验师，主要研究方向为切削加工技术。
超高性能混凝土铺层提升钢桥面板疲劳性能试验研究
第49
卷第8期
2021年8月
Vol. 49 No. 8Aug. 2021同济大学学报(自然科学版)
JOURNAL OF TONGJI UNIVERSITY (
NATURAL SC'IENCE
)
文章编号：
0253-374X(2021 )08-1097-10
DOI： 10.11908/j.
issn.
0253-374x. 21164
超高性能混凝土铺层提升钢桥面板疲劳性能试验研究程斌I,田亮
2,孙斌
3,徐晨彳
(1.上海交通大学船舶海洋与建筑T.程学院，上海200240；2.天津城建大学天津市土木建筑结构防护与加周重点实验室，天津300384；3.同
济大学土木工程学院，上海200092)
摘要：为明确超高性能混凝土
(UHPC)铺层对钢桥面板疲劳
性能的定量提升效果，考虑单轮和双轮两种加载模式，对正
交异性钢桥面板典型的U肋盖板-横隔板焊接节点在 UHPC铺装前后的疲劳性能开展试验研究。首先基于静载
试验得到焊接节点关键区域的热点应力分布.随后开展高周 常幅疲劳试验，得到节点试件的疲劳裂纹萌生及扩展过程、 疲劳破坏模式、刚度退化以及疲劳寿命等关键性能指标。结
果表明：
同等荷载作用下
，钢
UHPC组合节点焊趾处热点应
力值显著降低.最大降幅达58 %;与无UHPC铺层节点相 比,钢-UHPC组合节点的疲劳裂纹数量减少，裂纹扩展速率 和刚度退化速度得到了有效抑制，特征疲劳寿命也得到了大
幅提高。国际焊接协会疲劳设计指南中的FAT 90.FAT100
级S-N(应力幅疲劳寿命)曲线可适用于UHPC铺装前后钢
桥面板的疲劳寿命评估。
关键词：正交异性钢桥面板；疲劳性能;超高性能混凝土
(UHPC)；热点应力;疲劳寿命;裂纹扩展
中图分类号：
U443. 32
文献标志码：
A
Experimental Study of Fatigue
Behaviors of
Orthotropic
Steel
Bridge
Decks Enhanced by the Ultra-High
T800H级环氧基复合材料热力学性能测试
第1期纤维复合材料㊀No.1㊀252024年3月FIBER ㊀COMPOSITES ㊀Mar.2024T800H 级环氧基复合材料热力学性能测试乔㊀巍,贾佳乐,路明坤(中建材(上海)航空技术有限公司,上海200120)摘㊀要㊀开展了T800H 级树脂基复合材料的热力学性能测量㊂采用热膨胀分析仪测量了0ħ~170ħ温度范围内复合材料热膨胀系数;对E1806树脂进行了恒温和动态DSC 扫描,基于自催化模型,建立了E1806树脂的固化动力学方程;利用旋转流变仪测量出E1806树脂的凝胶固化度为0.62;采用TMA 法测量出凝胶后单向层合板厚度方向上的收缩应变为0.88%㊂关键词㊀热力学性能;固化动力学方程;收缩应变;试验Thermodynamic Performance Test of T 800H Grade EpoxyMatrix Composite MaterialsQIAO Wei,JIA Jiale,LU Mingkun(CNBM (Shanghai)Aviation Technology Co.,Ltd.,Shanghai 200120)ABSTRACT ㊀This article conducted thermodynamic performance measurements of T800H resin based composite materials.The thermal expansion coefficient of composite materials was measured using a thermal expansion analyzer within the temper-ature range of 0ħto 170ħ;The constant temperature and dynamic DSC scanning were performed on E1806resin,and the curing kinetics equation of E1806resin was established based on an autocatalytic model;The gel curing degree of E1806resin was 0.62measured by rotary rheometer;The shrinkage strain in the thickness direction of unidirectional laminates af-ter gel is 0.88%measured by TMA method.KEYWORDS ㊀thermodynamic performance;curing kinetics equation;shrinkage strain;test基金项目:中国建材集团攻关专项资助(2021YCJS02)通讯作者:乔巍,博士㊂研究方向为复合材料结构设计及固化变形控制㊂E -mail:qiaow@1㊀引言复合材料具有高比强度,高比刚度,且具有良好的可设计性,因此,复合材料越来越多地应用于飞机机身㊁机翼等结构中[1-3]㊂复合材料热力学性能是复合材料固化过程模拟㊁残余应力和固化变形预测的基础,因此需要通过试验获得复合材料热力学性能及在固化过程中的固化反应行为㊂固化动力学方程主要描述固化过程中树脂基体固化反应程度与温度和时间的函数关系㊂众多学者对不同树脂体系固化反应行为进行了大量的理论和试验研究㊂李伟东等[4]和张晨乾等[5]研究了热压罐固化的双马聚酰亚胺树脂固化动力学行为,并绘制了树脂的时间-温度-转变(TTT)图㊂李自强等[6]在Kamal 动力学模型的基础上,通过差示扫描量热分析法(Differential Scanning Calorimetry,纤维复合材料2024年㊀DSC)获得了微波固化的环氧树脂固化反应动力方程㊂江天等[7]研究了热压罐固化的T800/环氧树脂体系的复合材料性能,其中树脂固化动力学方程和玻璃化转变温度方程的研究方法为DSC法㊂贾丽杰[8]利用江天试验测量的材料性能和固化动力学方程建立了复合材料固化变形的有限元模型,研究了结构因素对固化变形的影响㊂在固化过程中,复合材料化学收缩反应会产生收缩应变,目前获得树脂化学收缩应变的方法主要是试验法㊂Li等[9]采用重量法测量了MY750树脂凝胶前后的化学收缩率㊂杨喜等[10]采用王荣秋教授发明的毛细管膨胀计法实时监测了环氧树脂固化过程中化学收缩率的变化㊂丁安心[11]和Hu等[12]将光纤布拉格光栅传感器埋入预浸料内部,测量了固化过程中材料内应变的变化情况㊂Garstka等[13]采用静态热机械分析仪(Thermomechanical Analy-sis,TMA)测量了AS4/8552复合材料的收缩应变,江天等[7]采用了相同的方法监测了T800/环氧预浸料固化过程中的厚度变化情况㊂TMA法是目前比较主流的化学收缩应变测量方法,预浸料在一定的温度历程(复合材料厂推荐的固化工艺温度曲线)下,且在预浸料表面的特定方向上施加一定的机械力以模拟固化压力,这时测量在该方向上预浸料尺寸变化量随温度和时间的变化情况㊂目前研制的T800H环氧基复合材料的材料性能和固化动力学参数等尚不完善,亟需进行相关试验测量材料参数,为后续复合材料固化变形模拟提供输入条件㊂本文利用电液伺服试验机和热膨胀仪分别测量了复合材料力学性能和热膨胀系数,通过差示扫描量热分析仪和旋转流变仪分别研究了E1806环氧树脂的固化动力学方程和凝胶固化度,采用静态热机械分析仪研究了固化过程中T800H/E1806单向预浸料在厚度方向上的收缩应变㊂2㊀热膨胀系数测量复合材料试验件的材料牌号为T800H/E1806,纤维为T800级增强碳纤维,基体为E1806环氧基树脂,采用热压罐固化工艺成型㊂采用MST370系列电液伺服试验机测量复合材料的力学性能,其中复合材料纵向(沿着纤维方向)和横向(垂直纤维方向)弹性模量的试验标准为ASTM D3039,复合材料剪切模量和泊松比的试验标准为ASTM D7078㊂通过NETZSCH公司的DIL402Expedis热膨胀分析仪测量不同温度下复合材料热膨胀系数,试验件为固化好的单向层合板,试验标准为ASTM D696,测量范围为0ħ~170ħ,试验结果如图1所示㊂试验结果表明,复合材料横向热膨胀系数β2远大于纵向热膨胀系数β1,且β1的值很小,这是由于复合材料的纵向性能主要是由纤维性能决定的,且纤维的热膨胀系数很小㊂β1的试验结果随温度变化很小,因此可取均值-0.35με/ħ㊂β2的试验结果随温度的增加而增大,采用一次函数拟合该试验数据,拟合结果如公式(1)所示,拟合优度R2为0.978,接近于1,表明拟合效果良好㊂β2=(0.018T+30.642)με/ħ(1)式中,T为温度㊂图1㊀T800H复合材料热膨胀系数的试验结果3㊀固化动力学方程采用DSC法研究E1806树脂的固化动力学方程,获得树脂在固化过程中固化度随温度和时间的变化历程,为后续的固化变形仿真分析奠定试验基础㊂首先,采用德国NETZSCH公司的DSC200F3型号设备对树脂样品进行变温扫描,DSC试验测量设备如图2所示,样品质量为3mg,流速设定为50ml/min,时间设定为50min,升温速率有两种,分别为5ħ/min和10ħ/min㊂变温下DSC测量的热流-时间曲线如图3所示,获得了单位质量树脂固化反应释放的总热量Hr为452kJ/kg㊂在此基础上,采用DSC进行等温扫描,树脂样品质量约562㊀1期T800H 级环氧基复合材料热力学性能测试mg,流速设定为50ml /min,时间设定为60min,温度分别为165ħ㊁175ħ及185ħ,测量获得的热流-时间曲线如图4所示㊂图2㊀DSC试验测量设备图3㊀DSC 测量的热流-时间曲线图4㊀恒温下DSC 测量的热流-时间曲线假设树脂的固化率与热流变化率成正比,即[14]如公式(2)所示㊂dαdt =1H r dHdt(2)式中,t 为时间;α为固化度;dα/dt 为固化率;H 为热量;dH /dt 为热流变化率㊂将图4中的瞬时热量除以总热量Hr,再对时间进行积分,得到了固化度-固化率曲线,如图5所示㊂目前,固化动力学模型主要有宏观尺度上的唯象模型和细观尺度上的机理模型㊂由于固化反应过程过于复杂,采用机理模型进行建模和计算的难度高,因此现有的固化动力学研究主要以唯象模型为基础,再通过非线性拟合得到模型参数㊂目前常用的固化动力学模型主要有n 级动力学模型㊁Kamal 模型及自催化模型等㊂本文采用自催化模型对E1806树脂的固化反应进行动力学分析,自催化模型的表达式如公式(3)所示㊂dαdt =A exp (-ΔERT)αm (1-α)n (3)式中,A 为频率因子;ΔE 为活化能;m 和n 为动力学常数;R 为普适气体常数㊂根据图5中的固化度-固化率试验结果,采用神经网络优化算法对公式(3)进行非线性拟合,即可得到固化动力学参数㊂拟合优度R 2㊂图5同时给出了试验结果和自催化模型的拟合结果,结果表明,在固化反应阶段,自催化模型的拟合结果与试验结果吻合良好,拟合得到的E1806树脂固化动力学参数如表1所示㊂图5㊀不同温度下固化度-固化率的自催化模型拟合结果与试验结果对比表1㊀拟合的E1806树脂自催化模型固化动力学参数A /minΔE /(J /mol)mn4.824ˑ104 6.544ˑ1040.1636 1.33264㊀凝胶固化度测量随着固化的进行,树脂黏度逐渐增大,基体分子链逐渐增长,开始形成三维网状结构,此时会出72纤维复合材料2024年㊀现凝胶现象,其中树脂的凝胶点是固化反应到达一定程度的标准㊂在等温凝胶试验中,将固化反应到达凝胶点所需要的时间定义为凝胶时间t gel ,此时的固化度称为凝胶固化度αgel ㊂本文采用旋转流变仪研究了E1806树脂的凝胶固化度㊂采用美国TA 仪器公司的ARES -G2旋转流变仪在170ħ和180ħ两种温度下对树脂进行了等温扫描,获得的E1806树脂存储模量和损耗模量变化曲线如图6所示㊂结果表明,随着固化反应的进行,树脂存储模量E 和损耗模量Eᶄ均逐渐增加㊂此外,固化反应开始时E 小于Eᶄ,但到达某个时间点后E 将超过Eᶄ,且通常将E =Eᶄ对应的时刻定义为该温度下树脂的凝胶时间t gel [7],这样170ħ和180ħ对应的凝胶时间t gel 分别为31.05min 和21.12min㊂利用E1806树脂的固化动力学公式(3),计算出在170ħ和180ħ恒温下的凝胶固化度αgel 分别为0.61和0.63,因此本文通过旋转流变仪法测量得到的E1806树脂凝胶固化度取值为0.62㊂图6㊀旋转流变仪测量的E1806树脂存储模量和损耗模量曲线化学收缩应变测量采用TMA 法测量固化过程中T800H /E1806复合材料的化学收缩应变㊂试验所用TMA 为美国热流变科学仪器公司的Q400,如图7(a)所示,其温度精度为ʃ1ħ,位移精度为ʃ0.5nm㊂试验件为单向铺层的预浸料,如图7(b)所示,其面内尺寸4mm ˑ4mm,初始厚度为4.04mm㊂T800H /E1806复合材料的固化工艺温度曲线为:从室温升温至130ħ,保温一个小时,再升温至185ħ,保温两个小时,最后降至室温,升温和降温速率分别为2ħ/min 和-2ħ/min,如图8所示㊂此外,热压罐的固化压力为0.6MPa,真空袋压力为0.1MPa㊂采用TMA 进行测试时,将测量频率设定为1Hz,压头施加压强设定为0.7MPa,温度历程按工艺温度曲线,测量固化过程中试验件在厚度方向上的收缩应变历程㊂图7㊀TMA 试验仪器和试验件通过E1806树脂的固化动力学方程,计算得到135min 时的树脂固化度为0.62,即135min 时树脂将发生凝胶反应㊂由于凝胶前树脂的流动性较好,通常认为凝胶前复合材料内部的残余应变和残余应力都会随着树脂的流动而消失[13],因此可合理假设135min 时的应变为0㊂在此基础上,通过TMA 获得了固化过程中试验件厚度方向上的收缩应变变化曲线,如图8所示㊂结果表明,135min 前试验件厚度方向上的收缩应变为0;135min 至245min 时,试验件厚度方向上的收缩应变绝对值逐渐增加,需要注意的是,这里的收缩应变不仅包含了化学收缩应变,还包含了该时间段内产生的少量热应变;245min 后收缩应变保持恒定,试验件厚度方向上的收缩应变最终达到了-0.88%㊂采用一个三次多项式拟合固化过程中收缩应变的试验结果,获得的拟合式如公式(4)所示,图8表明拟合曲线与试验结果吻合较好㊂εsh 2=εsh3=0,tɤ135min -9.1076ˑ10-9t 3+6.025ˑ10-6t 2-0.00136t +0.0962,135<t <245min -0.0088,tȡ245minìîíïïïïï(4)式中,εsh 2和εsh3分别为复合材料面内横向和厚度方向上的化学收缩应变㊂由于纵向化学收缩应变εsh1主要由纤维性能决定,而纤维发生化学收缩,82㊀1期T800H 级环氧基复合材料热力学性能测试因此εsh1的值非常小,通常取为0㊂图8㊀固化过程中试验件厚度方向上的收缩应变变化曲线6㊀结语采用试验方法研究了T800H 级树脂基复合材料的热力学性能,结论如下:(1)采用热膨胀分析仪测量了E1806树脂0ħ~170ħ温度范围内复合材料热膨胀系数;(2)对E1806树脂进行了恒温和动态DSC 扫描,基于自催化模型,建立了E1806树脂的固化动力学方程;(3)利用旋转流变仪测量出E1806树脂的凝胶固化度为0.62;(4)采用TMA 法测量出凝胶后单向层合板厚度方向上的收缩应变为0.88%㊂参考文献[1]杜善义,关志东.我国大型客机先进复合材料技术应对策略思考[J].复合材料学报,2008(01):1-10.[2]王衡.先进复合材料在军用固定翼飞机上的发展历程及前景展望[J].纤维复合材料,2014,31(04):41-45.[3]张兴金,邓忠林.浅谈纤维复合材料与中国大飞机[J].纤维复合材料,2009,26(02):24-26.[4]李伟东,张金栋,刘刚,等.高韧性双马来酰亚胺树脂的固化反应动力学和TTT 图[J].复合材料学报.2016,33(07):1475-1483.[5]张晨乾,陈蔚,叶宏军,等.具有双峰反应特性的高韧性双马来酰亚胺树脂固化动力学和TTT 图[J].材料工程.2016,44(10):17-23.[6]李自强,湛利华,常腾飞,等.基于微波固化工艺的碳纤维T800/环氧树脂复合材料固化反应动力学[J].复合材料学报.2018,35(09):162-168.[7]江天,徐吉峰,刘卫平,等.整体化复合材料结构分阶段固化变形预报方法及其实验验证[J].复合材料学报.2013,30(5):61-66.[8]贾丽杰,叶金蕊,刘卫平,等.结构因素对复合材料典型结构件固化变形影响[J].复合材料学报.2013(s1):261-265.[9]Li C,Potter K,Wisnom M R,et al.In -situ measurement of chem-ical shrinkage of MY750epoxy resin by a novel gravimetric method [J].Composites Science 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纳米纤维素对CFRP界面及损伤演化行为的影响
DOI：10.19936/ki.2096-8000.20220528.010纳米纤维素对CFRP界面及损伤演化行为的影响杨飒123,周伟123*,姬晓龙123,刘佳123,马连华123(1.河北大学质量技术监督学院，保定071002；2•计量仪器与系统国家地方联合工程研究中心，保定071002；3.河北省能源计量与安全检测技术重点实验室(筹)，保定071002)摘要：纳米纤维素作为一种低成本的可再生资源，在复合材料的增强改性中显示出独特的优势。
本文使用纳米纤维素对碳纤维复合材料进行辅助增强，在弯曲加载下开展声发射监测实验。
基于k-means方法确定不同损伤模式的特征频率范围和累积声发射能量，并采用扫描电镜对增强后复合材料的界面强度进行表征。
结果表明：纳米纤维素增强后复合材料的损伤起始得到延缓,损伤演化过程中出现较少的声发射信号；且断裂时声发射信号的能量显著下降，基体开裂和纤维/基体脱黏的累积声发射能量分别减少了78.1%和87.6%。
扫描电镜结果表明：纳米纤维素提高了纤维/基体界面的结合强度，改善了复合材料的界面性能，从而提高了其抗弯强度。
关键词：纳米纤维素；碳纤维增强聚合物；声发射监测；纤维/基体界面；损伤演化中图分类号：TB332文献标识码：A文章编号：2096-8000(2022)05-0071-07Effects of cellulose nanofibers on CFRP interface and damage evolution behaviorYANG Sa1，2,3,ZHOU Wei1，2,3*,JI Xiao-long1，2,3,LIU Jia1，2,3,MA Lian-hua1，2,3(1.College of Quality and Technical Supervision,Hebei University,Baoding071002,China;2.National&Local Joint Engineering Research Center of Metrology Instrument and System,Hebei University,Baoding071002,China; 3.Hebei Key Laboratory ofEnergy Metering and Safety Testing Technology,Hebei University,Baoding071002,China) Abstract:As a low-cost renewable resource,cellulose nanofibers(CNF)have shown unique advantages in the reinforcement and modification of composite materials.In this paper,cellulose nanofibers were used to reinforce carbon fiber composites.Bending test was carried out,and acoustic emission technology was used for damage assessment.Based on k-means method,the characteristic frequency range and cumulative acoustic emission energy of different damage modes were determined,and the interface strength of reinforced composites was characterized by scanning electron microscope.Results show that the damage initiation of cellulose nanofibers reinforced composites was delayed,and less acoustic emission signals appear in damage evolution.The energy of acoustic emission signals decrease during damage,and the cumulative acoustic emission energy of matrix cracking and fibeMmatrix debonding decrease by78.1%and87.6%,respectively.Scanning electron microscope results show that cellulose nanofibers improve the interfacial properties of fibeMmatrix,consequently improving the bending strength.Key words:cellulose nanofibers;carbon fiber reinforced polymer；acoustic emission monitoring；fiber/matrix interface;damage evolution1前言环氧基碳纤维增强聚合物(CFRP)是以碳纤维为增强相,以环氧树脂为基体相的两相复合材料。
无限长预应力弹性地基梁后屈曲问题的数值解
无限长预应力弹性地基梁后屈曲问题的数值解于永平;王中强;孙维鹏【摘要】The nonlinear integral-deferential governing equation of a pre-stressed infinite beam bonded to a linear elastic foundation was first extended by introducing a new variable and then solved by applying the shooting method. The results show that the postbuckling load and curve of deflection depend on the positive slope in position without deflection and the corresponding post-buckling wavelength does not change with the increase of the slope.%基于无限长预应力弹性地基梁的积-微分方程控制方程,通过引进新变量将其扩展成微分方程组,再利用打靶法求解该扩展系统进而得到该问题的数值解.结果表明:后屈曲载荷与后屈曲挠度曲线都依赖于梁挠度为零点的正斜率;而后屈曲波长不随此斜率的增加而变化.【期刊名称】《吉林大学学报（理学版）》【年(卷),期】2011(049)001【总页数】4页(P37-40)【关键词】后屈曲;无限梁;预应力;弹性地基;打靶法【作者】于永平;王中强;孙维鹏【作者单位】吉林大学,建设工程学院,长春,130026;长春师范学院,数学学院,长春,130032;吉林大学,数学学院,长春,130012【正文语种】中文【中图分类】O343.9弹性地基梁-柱问题具有重要的应用背景. 例如, 弹性地基梁模型在钢轨、低桁架桥的顶部弦、埋在海底的管道、盾构隧道纵向设计等领域应用广泛. Timoshenko等[1]研究了轴向受压的简支有限长弹性地基梁的线性屈曲问题. 而对于足够长的梁, 梁长对临界状态的影响可以忽略, 此问题可以视为无限长梁的屈曲问题. Hetenyi[2]给出了无限长弹性地基梁的临界状态解, 并证明了在此状态下挠曲波形一定是周期的. 预应力弹性地基梁的后屈曲响应是非线性的, 文献[3-5]运用数值或解析逼近的方法研究了弹性地基梁的后屈曲响应. Hunt等[6]已证明了对于非线性的弹性地基及小的后屈曲挠度情况, 预应力梁的响应是周期的, 而没有局部化现象的产生.Abu-Salih等[5]研究了无限长预应力弹性地基梁后屈曲问题, 在挠度梯度较小的情况下得到了此问题的解析逼近解.本文只考虑线性的弹性地基梁, 由于考虑了弹性伸展, 所以平衡方程增加了一个非线性项. 在这种情形下, 预应力梁的后屈曲响应具有周期性[5], 此时的周期解可用寻找非线性振动周期解的方法[7-8]得到. 本文通过先将原方程变形再用打靶技术得到数值解.1 问题求解预应力弹性地基梁如图1所示, 控制该系统的后屈曲响应平衡方程由下式给出[5,9]：(1)其中: x∈[0,L]为沿杆长的水平坐标； y为描述梁后屈曲挠度的纵坐标；D=Eh3/[12(1-υ2)]为单位宽度梁的弯曲刚度； E为杨氏弹性模量；υ为泊松比; L 为梁的长度(对于无限长的梁L→∞)；σ为轴向内部预应力； kf为地基的弹性模量, 单位是N/m3. 如果把地基视为杨氏模量为Ef、泊松比为υf=0、厚度为hf的弹性材料, 则有kf=Ef/hf. 由于对梁的伸展项用了近似表达式, 所以平衡方程(1)在挠度梯度较小(即0<(dy/dx)2≪1)的情况下有效.图1 无限长预应力弹性地基梁的示意图Fig.1 Schematic view of a compressively stressed beam bonded to an elastic foundation在后屈曲挠度为周期的假设下, 可以通过研究弹性地基梁挠度的一个单独周期研究无限长地基梁的后屈曲响应, 即通过考虑具有周期边界条件的有限长梁实现. 如果解为周期的, 则无限长梁的挠度即为具有周期边界条件的有限长梁挠度的周期重复. 不妨取弹性地基梁后屈曲状态的一个周期波长作为有限梁长度L(未知).为方便, 可将平衡方程(1)写成如下无量纲形式[5]：(2)其中无量纲参数定义如下：α为规范化的有限梁长度；β为载荷参数； S为无量纲的量, 表示梁的轴向刚度与弯曲和弹性地基刚度之积开方的比, 该比值控制后屈曲挠度[5].为了数值求解无限长预应力弹性地基后屈曲平衡方程(2), 可将其加上周期边界条件：‴‴(α),(3)则变形后梁的挠度曲线载荷参数β以及波长α都依赖于下面通过打靶方法[10]求解方程(2)和(3). 因为积分项上限中含有未知波长α, 所以应将其变形后才能应用打靶法. 将方程(2)和(3)改写成如下形式：(4)Y(0)=Y(2π)=0, Y′(0)=Y′(2π)=A, Y″(0)=Y″(2π), Y‴(0)=Y‴(2π).(5)方程中的无量纲量重新定义如下：通过上面的变换, 原方程的积分项可化成与未知波长α无关的常量这时可以通过引进新变量将积-微分方程(4)转化为扩展的微分方程组, 再应用打靶方法求解. 引进如下扩展的微分方程组初值问题：从初始向量m=(ξ,ω,β,α,ζ)T及A开始的轨迹记为[Y(X,m,A),φ(X,m,A)], 要求其满足X=2π时的边界条件：(9)可以用牛顿迭代法求解非线性代数方程组(9). 对于每个A, 令m0为初始的迭代向量, mk是第k步迭代向量, 则可以由(k-1)步计算得到, 即mk=mk-1-[Fm(mk-1,A)]-1F(mk-1,A),(10)其中(11)这里及以后的所有变量在(m,A)=(mk-1,A)处取值符号均省略“mk-1,A”. 式(11)中的元素可以由下面的扩展系统求得. 为简便, 记将方程(6)-(8)分别对ξ,ω,β,α及ζ求导数, 可得如下方程组：(12)同时求解方程组(6)-(8)和(12), 可得式(11)中的系数矩阵. 再应用方程(10), 执行迭代程序, 可以得到后屈曲无量纲化的载荷参数β、波长α及相应的后屈曲变形挠度Y(X), 这些后屈曲参数及挠度曲线都是A的函数.2 数值结果与讨论波长α随挠曲斜率幅值A的变化情况列于表1. 由表1可见, 对于小挠度幅值的情况, 无量纲波长α并不随挠曲斜率幅值的增加而变化, 即梁的一个周期波长L就等于临界屈曲波长Λcr. 图2为载荷参数β随后屈曲挠曲斜率幅值A的变化曲线. 图3为当A=0.4时, 一个周期内的后屈曲变形挠度曲线Y(X). 这里只列出了无量纲参数及后屈曲变形曲线中有代表性的几个数值结果, 也可以通过无量纲化定义式反解出真实荷载、挠度曲线, 研究它们与该结构的物理、几何参数的依赖关系.表1 波长α随挠曲斜率幅值A的变化Table 1 Change of wavelength α with AA00.050.100.150.200.250.300.350.40α111111111图2 载荷参数β随挠曲斜率幅值A的变化Fig.2 Change of load parameter β with A图3 后屈曲变形挠度Y曲线(A=0.4)Fig.3 Post-buckling deflection Y(A=0.4) 参考文献【相关文献】[1] Timoshenko S P, Gere J. Theory of Elastic Stability [M]. New York: McGraw-Hill, 1936.[2] Hetenyi M. Beams on Elastic Foundation: Theory with Applications in the Fields of Civil and Mechanical Engineering [M]. Ann Arbor: The University of Michigan Press, 1946. [3] Wadee M K, Hunt G W, Whiting A I M. Asymptotic and Rayleigh-Ritz Routes to Localized Buckling Solutions in an Elastic Instability Problem [J]. Proc Roy Soc London Ser A: Math Phys Eng Sci, 1997, 453: 2085-2107.[4] Chen G, Baker G. Rayleigh-Ritz Analysis for Localized Buckling of a Strut on a Softening Foundation by Hermite Functions [J]. Int J Solids Struct, 2003, 40(26): 7463-7474.[5] Abu-Salih S, Elata D. Analytic Postbuckling Solution of a Pre-stressed Infinite Beam Bonded to a Linear Elastic Foundation [J]. Int J Solids Struct, 2005, 42(23): 6048-6058.[6] Hunt G W, Bolt H M, Thompson J M T. Structural Localization Phenomena and the Dynamical Phase-Space Analogy [J]. Proc Roy Soc London Ser A: Math Phys Eng Sci, 1989, 425: 245-267.[7] LI Peng-song, SUN Wei-peng. Construction of Analytical Approximate Solutions to Buckling of Euler’s Column with Large Deflectio n [J]. Journal of Jilin University: Science Edition, 2009, 47(1): 40-43. (李鹏松, 孙维鹏. Euler杆大挠度屈曲解析逼近解的构造 [J]. 吉林大学学报: 理学版, 2009, 47(1): 40-43.)[8] LI Peng-song, SUN Wei-peng. A New Method for Analytical Approximate Solutions to the Duffing-Harmonic Oscillator [J]. Journal of Jilin University: Science Edition, 2006, 44(2): 170-174. (李鹏松, 孙维鹏. 达芬-谐波振子解析逼近的新方法 [J]. 吉林大学学报: 理学版, 2006,44(2): 170-174.)[9] Brush D O, Almroth B O. Buckling of Bars, Plates, and Shells [M]. New York: McGraw-Hill, 1975.[10] Seydel R. Practical Bifurcation and Stability Analysis: From Equilibrium to Chaos [M]. 2nd ed. New York: Springer Verlag, 1994.。
不同载荷形式下复合材料层合板渐进失效行为研究
第43卷第5期2021年5月舰船科学技术SHIP SCIENCE AND TECHNOLOGYVol.43,No.5May,2021不同载荷形式下复合材料层合板渐进失效行为研究袁昱超，赵新豪，王艺伟，薛鸿祥，唐文勇(上海交通大学海洋工程国家重点实验室，上海200240)摘要：近年来复合材料在船舶与海洋工程领域得到快速发展。
船舶在服役周期内受载复杂，主要承载板材除受典型的面内拉压外载外，免不了遭受横向波浪载荷作用。
研究复合材料层合板在不同载荷形式下结构的响应特征与损伤演化特性，有助于先进复合材料的性能评估及优化设计。
本文采用三维实体单元及内聚力单元建立复合材料层合板模型进行计算分析，考察拉压载荷下层合板的极限承载能力与渐进失效过程，研究在横向载荷下层合板结构强度，对比分析其层内及层间损伤模式的差异性。
关键词：复合材料；层合板；不同载荷形式；渐进失效；内聚力单元中图分类号：TV35文献标识码：A文章编号：1672-7649(2021)05-0001-09doi：10.3404/j.issn.l672-7649.2021.05.001Progressive failure behavior of composite laminates under different load forms YUAN Yu-chao,ZHAO Xin-hao,WANG Yi-wei,XUE Hong-xiang,TANG Wen-yong (State Key Laboratory of Ocean Engineering,Shanghai Jiaotong University,Shanghai200240,China)Abstract:Composite materials have been developed rapidly in the naval architecture and ocean engineering over recent years.During the service period,ships experience complicated loads.The primary plates suffer not only in-plane tension and compression but also transverse wave loads.Researches on the structural response and damage evolution characteristics of composite laminate plates under different load forms are helpful for the performance evaluation and optimization design of advanced composite materials.This paper adopts three-dimensional solid elements and cohesive elements to establish a composite laminate plate model.Firstly,the ultimate bearing capacity progressive failure process of the laminate plate with tension and compression loads are analyzed.Then,the structure strength of the laminated plate with transverse loads is investigated,and the differences of the inter-and interior-layer damage modes under different load forms are discussed in detail.Key words:composite material；laminate plate；different load forms；progressive failure；cohesive elemento引言复合材料在结构工程中的应用日益广泛，复合材料的损伤与失效问题也受到人们的关注。
patran错误日志及解决方法
2. USER WARNING MESSAGE 4124 (IFS3P)
THE SPCADD OR MPCADD UNION CONSISTS OF A SINGLE SET 在图中用了 RB3 的 MPC，其中 dependent node (ux,uy,uz), independent(ux,uy,uz,rx,ry,rz),有可 能是这里的问题。不过这个倒不影响计算结果。
^^^ RUN TERMINATED DUE TO EXCESSIVE PIVOT RATIOS IN MATRIX KLL. ^^^ USER ACTION: CONSTRAIN MECHANISMS WITH SPCI OR SUPORTI ENTRIES OR SPECIFY PARAM,BAILOUT,-1 TO CONTINUE THE RUN WITH MECHANISMS. 以前也遇到这种情况，这次遇到后，又在一节点加载了位移约束，就解决了。看来这 种错误主要是由于约束不够，线性方程组无解造成的。 还有可能是没有 equivalence，This should solve your problem or reduce the number of failed ratios.有一次就遇到此情况。
7. 常用材料定义对比表
MAT1 MAT2 MAT3 MAT8 MAT9
isotropic anisotropic(2) orthotropic(3) orthotropic(2) anisotropic(3) • Use a FORCE entry if you want to define a static, concentrated force at a grid point by 一个点的力 specifying a vector. • Use a FORCE1 entry if the direction is determined by a vector connecting two grid points. 两个点的力 • Use a FORCE2 entry if the direction is specified by the cross product of two such vectors. 以上的乘积
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Abstract This paper addresses the effects of a cutout on the buckling and postbuckling behavior of rectangular plates made of advanced composite materials. An overview of past research is presented, and several key findings and behavioral characteristics are discussed. These findings include the effects of cutout size, shape, eccentricity, and orientation; plate aspect and slenderness ratios; loading and boundary conditions; and plate orthotropy and anisotropy. Some overall important findings of these studies are that plates that have a cutout can buckle at loads higher than the buckling loads for corresponding plates without a cutout and can exhibit substantial postbuckling load-carrying capability. In addition, laminate construction, coupled with cutout geometry, offers a viable means for tailoring structural response.
NASA
Technical
Paper
3587
Buckling Laminated
Michael Langley P. Nemeth Research
and Postbuckling Behavior of Composite Plates With a Cutout
Center • Hampton, Virginia
Introduction Two research topics of great practical importance are the buckling behavior and the postbuckling behavior of thin plates that have a cutout and are made of advanced composite materials. For example, composite plate-like subcomponents that have a cutout are being considered for use in many types of aerospace structures because of their high stiffness-to-weight and strength-to-weight properties. These properties could ultimately yield substantial weight savings for aircraft structures. The need for a cutout in a subcomponent is typically required by practical concerns. For example, cutouts in wing spars and cover panels of commercial transport wings and military fighter wings are needed to provide access for hydraulic lines and for damage inspection. In some applications, these structural elements are required primarily to resist buckling, and in other cases they must carry a load well into the postbuckling range in order to yield weight savings. Thus, understanding their buckling and postbuckling behavior is needed for their design. Plate-like subcomponents come in many forms such as an annular plate or a rectangular plate that has a circular cutout. The present study focuses on rectangular plates that have a single unreinforced cutout. Developing a thorough understanding of the behavior of this subcomponent is a fundamental step toward understanding the behavior of complex structures with cutouts such as airplane wing ribs. Knowledge of the basic response of the subcomponent provides useful information for the preliminary design of complex structures. In addition, this basic knowledge provides valuable insight into modeling complex structures with general purpose finite element codes, a step that takes place at a later phase in the design process. Furthermore, knowledge of the subcomponent response is very useful for identifying erroneous results that may be obtained because of improper finite element modeling.
One objective results of research
of the present study is to describe the that has been conducted on the buck-
ling and postbuckling behavior of rectangular composite plates that have a cutout. Another objective is to describe several of the key behavioral characteristics and trends in a coherent manner. To achieve this goal, the present paper is structured as follows: Nomenclature is established for concisely describing plate geometry, loading conditions, and support conditions. An overview of past research is presented that identifies the analytical approach that is used and then describes what particular aspects of the behavior were investigated. For convenience, the primary studies conducted on buckling and postbuckling behavior are also summarized in tables 1 and 2, respectively. Next, several key findings on the buckling and postbuckling behavior of composite plates that have been identified since the early 1970's are described and discussed. Several subsections are included that address specific issues such as the effects of cutout shape and plate anisotropy. Last, some closing comments about future research are given. Problem Description and Terminology