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复合材料加筋板的屈曲与后屈曲研究综述

胡媛媛, 张桂嘉, 陈普会, 童明波, 王芳丽

胡媛媛, 张桂嘉, 陈普会, 等. 复合材料加筋板的屈曲与后屈曲研究综述[J]. 复合材料学报, 2025, 42(5): 2349-2368. DOI: 10.13801/j.cnki.fhclxb.20241030.003
引用本文: 胡媛媛, 张桂嘉, 陈普会, 等. 复合材料加筋板的屈曲与后屈曲研究综述[J]. 复合材料学报, 2025, 42(5): 2349-2368. DOI: 10.13801/j.cnki.fhclxb.20241030.003
HU Yuanyuan, ZHANG Guijia, CHEN Puhui, et al. Review on buckling and post-buckling of stiffened composite panels[J]. Acta Materiae Compositae Sinica, 2025, 42(5): 2349-2368. DOI: 10.13801/j.cnki.fhclxb.20241030.003
Citation: HU Yuanyuan, ZHANG Guijia, CHEN Puhui, et al. Review on buckling and post-buckling of stiffened composite panels[J]. Acta Materiae Compositae Sinica, 2025, 42(5): 2349-2368. DOI: 10.13801/j.cnki.fhclxb.20241030.003

复合材料加筋板的屈曲与后屈曲研究综述

基金项目: 航空科学基金 (20230009052004)
详细信息
    通讯作者:

    童明波,博士,教授,博士生导师,研究方向为复合材料飞机结构设计与分析 E-mail: tongw@nuaa.edu.cn

  • 中图分类号: TB332

Review on buckling and post-buckling of stiffened composite panels

Funds: Aeronautical Science Foundation of China (20230009052004)
  • 摘要:

    复合材料加筋板因其卓越的轻质、高强度和高刚度特性,在航空航天领域的飞机承力构件中得到了广泛应用。随着对材料性能要求的不断提升,深入理解这类结构的屈曲与后屈曲行为变得尤为重要。本文综述了国内外复合材料加筋板屈曲及后屈曲性能的研究进展,系统归纳了理论方法、有限元仿真技术及实验研究方法。研究表明:加筋板的几何参数(如加筋高度和间距)及层合板的铺层顺序显著影响其屈曲性能;同时,考虑材料非线性和几何非线性对准确预测后屈曲行为至关重要。此外,本文探讨了预测复合材料加筋板屈曲和后屈曲失效模式及载荷的关键技术难点。通过分析现有研究的局限性,本文指出了未来可能的研究方向,为复合材料加筋板的屈曲与后屈曲研究及其工程应用提供了理论基础和实践指导。

     

    Abstract:

    Composite stiffened panels are widely used in aircraft load-bearing components in the aerospace field due to their excellent lightweight, high strength and high stiffness properties. With the continuous improvement of material performance requirements, it is particularly important to have a deep understanding of the buckling and post-buckling behavior of such structures. This article reviews the research progress on buckling and post-buckling properties of composite stiffened panels, and systematically summarizes theoretical approach, finite element simulation technology and experimental research methods. Studies have shown that the geometric parameters (such as height and spacing of stiffeners) and lay-up sequence of stiffened panels significantly affect the buckling performance. At the same time, considering material nonlinearity and geometric nonlinearity is crucial to accurately predict post-buckling behavior. In addition, this article explores the key technical difficulties in predicting buckling and post-buckling failure modes and loads of composite stiffened panels. By analyzing the limitations of existing researches, this article points out possible future research directions, providing a theoretical basis and practical guidance for buckling and post-buckling research on composite stiffened panels and their engineering applications.

     

  • 碳纤维增强聚合物复合材料(CFRP)具有轻质高强、耐久和抗疲劳性能好、可设计性强等优点,近年来CFRP已被广泛应用于工程结构的加固中[1-5],相比于混凝土结构加固,采用CFRP加固钢结构的研究和应用虽起步较晚但近年来也正在受到关注。利用粘结剂将CFRP外贴于待加固构件表面是目前较普遍的加固方法,Yousefi等[6]进行了外贴CFRP板加固钢梁的抗弯试验,发现普通外贴加固容易发生CFRP板的剥离失效。如果考虑二次受力等原因,普通外贴CFRP板的加固效果将非常有限,CFRP板的高强度特性不能充分发挥[7-8]。Galal等[9]通过对比带端部锚固与无端部锚固的CFRP加固损伤钢梁,发现端部锚固在一定程度上可以抑制CFRP的剥离。为了更好地解决外贴CFRP板的剥离和加固效果不明显的问题,国内外学者开展了预应力CFRP板加固钢梁抗弯性能的相关研究[10-14],发现预应力CFRP板能更明显地提高钢梁的承载力和刚度,预应力CFRP板的端部锚固也可以很好地改善CFRP板的端部剥离问题。

    现有的预应力CFRP板加固钢梁抗弯性能研究主要集中在有粘结预应力CFRP板加固技术上,加固时由于需要粘结剂,一方面会延长施工周期,另一方由于构件端部机械式锚具(如夹片式锚具)的存在,导致粘结剂厚度比外贴加固大很多,增加加固成本。无粘结预应力CFRP板加固技术则可以很好地避免以上问题,但CFRP板与钢梁的共同工作完全依靠端部锚具,因此采用该技术加固后的构件力学性能和加固效果需要研究。Ghafoori等[15]和Hosseini等[16]设计了张弦式和平板式预应力CFRP板张拉锚固装置,并利用该装置进行了无粘结预应力CFRP板加固钢梁在弹性阶段的抗弯性能试验,结果表明加固后钢梁的承载力显著提高,设计的锚固装置可靠。叶华文等[17]开展了无粘结预应力CFRP板加固损伤钢梁的疲劳试验,发现施加预应力能够降低裂纹扩展速率和受损钢梁残余挠度超过40%,当CFRP板的有效预应力达到900 MPa时,钢梁的疲劳寿命可提高8倍以上。整体上看,目前国内外仅有极少数针对该技术的研究,在工程应用前仍需对该技术进行更多的研究和验证。

    采用CFRP板加固钢梁时,基于是否使用粘结剂及施加预应力可分为不同的加固方法,为了对比不同方法的加固效果,本文对不同预应力水平下的有粘结和无粘结CFRP板加固损伤钢梁的抗弯性能进行试验和有限元分析,通过对比特征荷载、荷载-位移曲线、CFRP板应变及其强度利用率等,评估粘结层和预应力对CFRP板加固效果的影响,为CFRP板在钢梁抗弯加固中的研究和应用提供参考。

    钢梁的钢材等级为Q235 B,根据GB/T 228.1—2010[18]实测的钢梁受拉翼缘主要力学指标如表1所示。CFRP板的截面尺寸为50 mm×2 mm,对于有粘结CFRP板加固试件,采用两组份环氧粘结剂将CFRP板粘贴在钢梁受拉翼缘下表面,粘结剂的A和B组份按质量比2∶1混合,根据GB/T 3354—2014[19]实测的CFRP板主要力学指标及厂家提供的粘结剂主要力学指标见表1

    表  1  材料的主要力学性能
    Table  1.  Main mechanical properties of materials
    Material typeElasticity modulus/GPaYielding stress/MPaTensile strength/MPaElongation/%
    Q235 B steel 207.0 271 429.0 15.78
    CFRP plate 163.0 - 2516.0 1.54
    Adhesive 4.5 - 49.2 1.64
    Note: CFRP—Carbon fiber reinforced polymer.
    下载: 导出CSV 
    | 显示表格

    试验采用热轧H型钢梁制作试件,钢梁的截面尺寸为200 mm×200 mm×8 mm×12 mm,长度为3400 mm,净跨为3000 mm,在支座、加载点及支座与加载点的中点处焊接加劲肋,加劲肋厚度为8 mm。为了模拟初始损伤,在钢梁跨中下翼缘两侧对称切割两条长度为40 mm、宽度为2 mm的缺口,其中缺口端部的尖端长度为5 mm。共设计5根损伤钢梁试件,包括1根未加固钢梁和4根加固钢梁,分别采用有粘结和无粘结方式进行加固,每种加固方式设计了非预应力和预应力2种预应力水平,加固试件的CFRP板长度均为2600 mm,试件的设计参数如表2所示。表中,试件B-0为未加固钢梁;试件B-BR为有粘结无预应力CFRP板加固钢梁,为了避免CFRP板的端部剥离,根据YB/T 4558—2016[20]的构造要求,在CFRP板端部正、负45°方向各粘贴3层碳纤维布,其中碳纤维布宽度为200 mm,单层厚度为0.167 mm,碳纤维布覆盖钢梁受拉翼缘端部下表面并延伸包裹至受拉翼缘上表面;试件B-UR为无粘结无预应力CFRP板加固钢梁,为了保证无粘结CFRP板加固系统的工作,采用楔形夹片式锚具进行锚固(见1.3节);试件B-PBR和B-PUR分别为有粘结预应力和无粘结预应力CFRP板加固钢梁,设计预应力均为850 MPa,采用研发的反向张拉锚固系统进行预应力张拉和CFRP板锚固(见1.3节)。

    表  2  CFRP板加固损伤钢梁试件的加固参数
    Table  2.  Strengthening parameters of damaged steel beam strengthened with the CFRP plate specimens
    SpecimenSectional area of CFRP plate/mm×mmStrengthening methodDesigned prestress/MPa
    B-0-Unstrengthening -
    B-BR50×2Bonded strengthening 0
    B-UR50×2Unbonded strengthening 0
    B-PBR50×2Bonded strengthening850
    B-PUR50×2Unbonded strengthening850
    Notes: In the specimen, the first letter B represents the beam; The number 0 represents the unstrengthening, the letters BR, UR, PBR and PUR represent bonded CFRP plate strengthening, unbonded CFRP plate strengthening, prestressed bonded CFRP plate strengthening, and prestressed unbonded CFRP plate strengthening, respectively.
    下载: 导出CSV 
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    反向张拉锚固系统主要由固定端锚具、固定端支座、张拉端锚具和张拉端支座组成,如图1所示,其中张拉端锚具和固定端锚具均为楔形夹片式锚具,张拉端支座和固定端支座分别通过6个高强螺栓连接到钢梁下翼缘。通过反向张拉工艺进行预应力张拉,即将千斤顶放置在张拉端锚具内侧通过顶推锚具实现预应力张拉,如图1所示。相比于常用的正向张拉工艺,反向张拉工艺所需的端部操作空间大幅降低,即使端部空间受限也能实施张拉,具有更广的工程适用性。施加预应力时,通过监测粘贴在CFRP板表面的应变片数据来控制张拉应力的大小。正式张拉前先取CFRP板张拉控制应力的10%进行预张拉,以确保仪器和张拉系统能正常工作;正式张拉阶段采用分级张拉形式,每级张拉至CFRP板张拉控制应力的20%,达到张拉控制应力后进行5%的超张拉。

    图  1  CFRP板预应力张拉系统
    Figure  1.  Prestress tensioning system of the CFRP plate

    试验在量程为2000 kN的液压伺服加载系统上进行,如图2所示,采用四点弯曲加载,两个加载点之间的距离为500 mm。采用位移控制模式,钢梁屈服前的加载速率为0.2 mm/min,屈服后的加载速率为0.5 mm/min,在试件的跨中挠度达到30 mm时停止加载,此时试件已远超正常使用极限状态和翼缘屈服状态。为了测量试件的挠度和应变,在跨中、加载点和支座对应位置处布置位移计;为了研究应变沿CFRP板-钢梁复合截面的分布,在钢梁跨中沿竖向以40 mm间隔布置应变片,在CFRP板跨中位置也布置应变片;为了研究CFRP板应变沿长度的分布,在CFRP板表面从跨中向两端以250 mm间隔布置应变片。

    图  2  试验加载装置
    Figure  2.  Test setup of the experiment

    在加载过程中,所有试件均经历了弹性和弹塑性两个受力阶段,失效模式均为典型的受弯破坏,如图3(a)所示。在钢梁下翼缘屈服前,荷载随挠度呈线性增加;在下翼缘开始屈服后,未加固试件荷载随着挠度的增大而缓慢增加,而各加固试件由于CFRP板的加固作用,荷载的增加速度比未加固试件的大。对于有粘结加固试件B-BR和B-PBR,当下翼缘屈服范围达到一定程度后,CFRP板在钢梁跨中周围出现了界面剥离现象,如图3(b)所示;界面剥离由下翼缘屈服引起,这是由于随着下翼缘的不断屈服,下翼缘与CFRP板之间的界面相对滑移将逐渐增大,当相对滑移超过最大允许滑移后就会导致剥离[21]。对于无粘结CFRP板加固试件B-UR和B-PUR,由于没有粘结层,钢梁下翼缘与CFRP板之间的距离随加载而不断减小,最终紧密贴合,如图3(c)所示。在整个加载过程中,所有试件均未发生CFRP板端部剥离破坏,验证了试验采用的锚固系统的有效性。

    图  3  典型试验现象照片
    Figure  3.  Photos of typical test phenomena

    以试件B-PBR和B-PUR为例,分析采用有粘结和无粘结CFRP板加固的CFRP板-钢梁复合截面是否满足平截面假定,图4显示了2个试件的跨中截面应变沿竖向的分布。可知,有粘结CFRP板加固试件的复合截面在界面剥离前基本满足平截面假定。然而,无粘结CFRP板加固试件的复合截面无论在弹性阶段还是弹塑性阶段均不满足平截面假定,在加载过程中CFRP板的应变小于钢梁下翼缘应变,且随着荷载的增加两者的应变差越来越大;这主要是由于无粘结CFRP板加固试件的钢梁与CFRP板之间只能依靠两端的锚具传递荷载,导致CFRP板应变增量被“平均”到整个CFRP板长度上,使跨中截面的CFRP板应变明显滞后于钢梁下翼缘的应变。这说明粘结层的存在能够保证CFRP板与钢梁的变形协调,而无粘结CFRP板与钢梁之间不能满足变形协调条件,同时有粘结CFRP板可以更有效地限制钢梁下翼缘的应变发展。

    图  4  CFRP板加固损伤钢梁跨中截面的典型应变分布
    Figure  4.  Typical strain distributions at mid-span section of damaged steel beams strengthened with CFRP plates

    为了定量对比不同加固方式的加固效果,选取特征荷载进行分析。根据GB/T 50017—2017[22]的规定,主梁的挠度容许值为l/400(l为钢梁跨度),针对本试验即为7.5 mm,将该挠度对应的荷载记为P7.5,代表着正常使用极限状态下的荷载,将下翼缘屈服时对应的荷载作为屈服荷载,记为Py,代表着承载能力极限状态下的荷载。本节以P7.5Py作为特征荷载进行分析,表3列出了各试件的特征荷载及相对于未加固试件的提高程度,即α7.5αy。可以看出,与未加固试件相比,各加固试件的特征荷载均有提高,整体上屈服荷载Py的提高幅度远大于正常使用极限状态荷载P7.5的提高幅度,说明CFRP板在钢梁屈服后的加固效果远大于在正常使用阶段的加固效果。当预应力水平相同时,有粘结与无粘结CFRP板加固试件的特征荷载非常接近,相差不超过2%,说明在其他条件相同时,有粘结和无粘结CFRP板具有几乎相同的加固效果。试验还发现,无论采用有粘结还是无粘结CFRP板加固方式,非预应力CFRP板的加固效果均非常有限,尤其是在正常使用阶段的改善效果非常微弱,且屈服荷载的提高幅度也低于20%;相比较而言,施加预应力可以明显提高试件的特征荷载,预应力CFRP板加固试件的特征荷载P7.5Py比未加固试件分别提高了28.7%~30.2%和49.2%~49.8%,比非预应力CFRP板加固试件分别提高了26.1%~29.1%和25.3%~26.7%。

    表  3  CFRP板加固损伤钢梁特征荷载比较
    Table  3.  Comparisons of characteristic loads of damaged steel beams strengthened with CFRP plates
    SpecimenP7.5/kNα7.5/%Py/kNαy/%
    B-0102.5-105.8-
    B-BR104.6 2.0124.617.8
    B-UR103.4 0.9126.519.6
    B-PBR131.928.7157.949.2
    B-PUR133.530.2158.549.8
    Notes: P7.5—Load when the mid-span deflection is 7.5 mm; Py—Yielding load; α7.5 and αy—Ratios between the P7.5 and Py of the strengthened beams and those of the unstrengthened beam, respectively.
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    试件的荷载-挠度曲线如图5所示,图中预应力CFRP板加固试件考虑了预应力产生的初始反拱。可以看出,当预应力水平相同时,有粘结与无粘结CFRP板加固试件的荷载-挠度曲线在弹性阶段基本重合,试件的承载力及抗弯刚度相近。在弹塑性阶段,随着荷载的不断增加,有粘结CFRP板加固试件出现了CFRP板跨中剥离后,荷载发生突然降低,而无粘结CFRP板加固试件没有这个现象。此外,在弹性阶段非预应力CFRP板对钢梁抗弯刚度的影响很小,而只有在达到弹塑性阶段后,CFRP板对钢梁抗弯刚度的提高才逐渐明显。与非预应力CFRP板相比,预应力CFRP板对钢梁抗弯刚度的提高更明显,而且由于初始反拱的引入,相同荷载下对挠度的降低也更明显。可见采用预应力有粘结和无粘结CFRP板加固方法对钢梁抗弯性能的提升更有效,加固效果更显著。

    图  5  CFRP板加固损伤钢梁荷载-挠度曲线
    Figure  5.  Load-deflection curves of damaged steel beams strengthened with CFRP plates

    典型试件CFRP板应变沿长度方向的分布如图6(a)所示。可以看出,有粘结CFRP板加固试件的CFRP板应变由跨中向两侧逐渐降低,而无粘结CFRP板加固试件的CFRP板应变沿长度基本保持不变,而且应变值明显小于相同荷载下有粘结CFRP板在纯弯段的最大应变。这主要是由于有粘结CFRP板加固试件中粘结剂充当钢梁与CFRP板之间的传力介质,CFRP板与下翼缘界面之间的剪应力传递使CFRP板与钢梁的协同工作性能较好,因此CFRP板与下翼缘的应变分布规律接近;而无粘结CFRP板加固试件缺少粘结层,CFRP板与下翼缘界面之间不存在剪应力的传递,因此CFRP板应变沿长度分布均匀,不存在应变梯度。图6(b)为加固试件的CFRP板跨中应变随荷载的变化曲线。可以看出,在钢梁屈服前,CFRP板应变随荷载基本线性增大,当钢梁开始屈服后,CFRP板应变增速开始变快,而且有粘结CFRP板加固试件的CFRP板跨中应变随荷载的增长速率明显大于无粘结CFRP板加固试件。此外,由于预应力CFRP板加固试件存在初始应变,在相同荷载下,其CFRP板应变明显大于非预应力CFRP板加固试件。

    图  6  CFRP板的应变分布
    Figure  6.  Strain distributions of CFRP plates

    CFRP板具有高强优势,在加固时CFRP板强度能发挥多少值得关注。为了说明在不同加载阶段的CFRP板强度利用率,表4列出了各加固试件的CFRP板初始张拉应变(ε0,取千斤顶卸下时的CFRP板应变)、两个特征荷载对应的CFRP板应变(εp7.5εpy)及其与极限应变(εu,数值见表1)的比值。可知,采用非预应力加固时,在正常使用阶段CFRP板的应变很低,其高强度特性远不能发挥,有粘结和无粘结方式的CFRP板强度利用率仅为5.6%和3.8%,即使达到屈服荷载,其强度利用率也仅为8.4%和4.7%。相比较而言,对CFRP板施加预应力是提高其强度利用率的有效方法,有粘结和无粘结方式在正常使用阶段的CFRP板强度分别发挥了44.7%和40.9%,在屈服阶段分别达到47.2%和42.1%。另一方面,通过比较有粘结和无粘结方式可以发现,有粘结方式的CFRP板强度利用率大于无粘结方式,不过在相同的预应力水平下,无粘结和有粘结方式的CFRP板强度利用率相差不大。

    表  4  CFRP板应变及强度利用率比较
    Table  4.  Comparisons of CFRP plate strain and strength utilization
    Specimenε0/10−6εp7.5/10−6εp7.5/εu/%εpy/10−6εpy/εu/%
    B-BR 0 855 5.6 1287 8.4
    B-UR 0 581 3.8 723 4.7
    B-PBR 5605 6877 44.7 7276 47.2
    B-PUR 5542 6300 40.9 6485 42.1
    Notes: ε0—Initial tensioning strain of the CFRP plate; εp7.5—Strain of the CFRP plate at P7.5; εpy—Strain of the CFRP plate at Py; εu—Ultimate strain of the CFRP plate.
    下载: 导出CSV 
    | 显示表格

    对试验试件进行有限元模拟,以预测钢梁的抗弯性能。采用ABAQUS软件建立三维有限元分析模型,其中钢梁、CFRP板及锚具均采用8节点的三维应力减缩积分单元C3D8R进行模拟。对于有粘结CFRP板加固试件B-BR和B-PBR,试验发现在钢梁下翼缘屈服后界面发生了跨中剥离,为了反映界面跨中剥离对抗弯性能的影响,在模型中采用三维粘聚力单元COH3 D8模拟胶层,将钢梁、胶层和CFRP板之间通过绑定相互连接。界面本构关系采用简化的双线性粘结-滑移关系[23],模拟中采用的界面本构关系及参数如图7所示。采用二次名义应力准则作为界面的损伤起始判据,即当界面各个方向的名义应力比的平方和等于1时,界面开始出现损伤,如下式所示:

    {tnt0n}2+{tst0s}2+{ttt0t}2=1 (1)

    式中:tntstt分别为界面在3个方向上的应力;t0nt0st0t分别为界面在3个方向上破坏时的最大名义应力;下标nst分别表示垂直和平行于界面的3个方向。当损伤发生后,界面将进入损伤演化阶段,采用基于能量的线性准则定义界面的损伤演化过程,如下式所示:

    GIGIc+GIIGIIc+GIIIGIIIc=1 (2)

    式中:GIGIIGIII分别是界面在混合模式下I型(张开型)、II型(滑开型)和III型(撕开型)开裂的能量释放率;GIcGIIcGIIIc分别为界面发生纯I型、II型和III型开裂时的临界能量释放率。

    图  7  CFRP板加固损伤钢梁的界面粘结-滑移关系
    Figure  7.  Interfacial bond-slip relationship of damaged steel beams strengthened with CFRP plates

    考虑到锚固系统在整个加载过程中没有发生滑移和锚固失效,为了简化建模过程,在模拟时忽略张拉端和固定端支座,直接将锚具通过绑定与钢梁的下翼缘连接,同时将CFRP板、夹片和锚杯也分别通过绑定进行连接。典型的有限元网格划分如图8所示。在有限元模型中,钢梁按各项同性材料进行定义,采用弹塑性本构模型,使用Von Mises准则作为屈服准则。对于CFRP板,不考虑垂直碳纤维丝方向的材料性能,仅考虑CFRP板沿纤维方向的材料性能,其应力-应变关系为理想的线弹性关系。钢材和CFRP板的材料性能均按表1取值。对于预应力CFRP板加固试件B-PBR和B-PUR,采用降温法对CFRP板施加预应力。试件的边界条件设置为简支,与试验保持一致。在计算时,对有限元模型施加位移荷载,进行非线性分析。

    图  8  CFRP板加固损伤钢梁有限元模型
    Figure  8.  Finite element model of damaged steel beams strengthened with CFRP plates

    有限元得到的荷载-挠度曲线与试验结果的对比如图9所示。可以看出,无论对于无粘结还是有粘结CFRP板加固试件,有限元计算结果与试验结果均符合较好。对于有粘结CFRP板加固试件,有限元也可以模拟出由下翼缘屈服引起的界面跨中剥离。总体上看,建立的有限元模型可以较好地预测不同预应力水平下有粘结和无粘结CFRP板加固损伤钢梁的全过程受力性能。

    表5列出了有限元得到的特征荷载与试验结果的对比。发现两者符合较好,误差在5%以内,说明本文建立的有限元模型可以较好地预测不同预应力水平下有粘结和无粘结CFRP板加固损伤钢梁的特征荷载。

    表  5  CFRP板加固损伤钢梁有限元与试验结果的对比
    Table  5.  Comparisons of finite element and test results of damaged steel beams strengthened with CFRP plates
    SpecimenP7.5Py
    Test/kNFinite element/kNRatioTest/kNFinite element/kNRatio
    B-0102.5104.41.02105.8106.11.00
    B-BR104.6107.41.03124.6131.11.05
    B-UR103.4104.21.01126.5127.81.01
    B-PBR131.9138.31.05157.9164.51.04
    B-PUR133.5137.61.03158.5163.41.03
    下载: 导出CSV 
    | 显示表格
    图  9  CFRP板加固损伤钢梁荷载-挠度曲线对比
    Figure  9.  Comparisons of load-deflection curves of damaged steel beams strengthened with CFRP plates

    图10为有限元得到的试件B-PUR的位移云图和应力云图。可以看出,有限元得到的钢梁竖向位移沿跨中对称分布,CFRP板与钢梁下翼缘贴合,与试验观察到的现象一致。钢梁的应力分布呈现由跨中向两端减小的趋势,应力最大值出现在下翼缘的缺口尖端,可以看出在缺口尖端处表现出明显的应力集中现象。

    图  10  试件B-PUR的位移和应力分布
    Figure  10.  Displacement and stress distributions of the specimen B-PUR

    前述研究发现有粘结和无粘结CFRP板具有相近的加固效果,因此本节以无粘结CFRP板加固钢梁为对象进行参数分析。

    选取CFRP板预应力分别为600 MPa、850 MPa和1100 MPa进行模拟,CFRP板的厚度均保持为2 mm,得到的荷载-挠度曲线如图11所示。可以看出,CFRP板的预应力越大,钢梁的反拱越大,在相同荷载下的挠度越小,同时正常使用极限状态特征荷载和屈服荷载也随着预应力的增大而逐渐增大。总体上看,钢梁的抗弯加固效果随着预应力的增大而提高。

    图  11  CFRP板预应力对CFRP板加固损伤钢梁荷载-挠度曲线的影响
    Figure  11.  Effect of the CFRP plate prestress on the load-deflection curves of damaged steel beams strengthened with CFRP plates

    选取CFRP板厚度分别为1.4 mm、2.0 mm和3.0 mm建立有限元模型,CFRP板预应力均保持为850 MPa,得到的荷载-挠度曲线如图12所示。由于在相同的预应力下,CFRP板的预拉力随着CFRP板厚度的增加而增大,因此随着CFRP板厚度的增加,钢梁的反拱逐渐增大,在相同荷载下的挠度逐渐降低,特征荷载也逐渐提高。因此,钢梁的抗弯加固效果随着CFRP板厚度的增加逐渐增大。

    图  12  CFRP板厚度对CFRP板加固损伤钢梁荷载-挠度曲线的影响
    Figure  12.  Effect of the CFRP plate thickness on the load-deflection curves of damaged steel beams strengthened with CFRP plates

    选取CFRP板弹性模量分别为160 GPa、300 GPa和450 GPa进行分析,CFRP板厚度均为2 mm,预应力均为850 MPa,得到的荷载-挠度曲线如图13所示。可以看出,随着CFRP板弹性模量的增加,钢梁的弹性抗弯刚度变化很小,只有进入弹塑性阶段后抗弯刚度的提高才逐渐明显。由于模型中不同弹性模量CFRP板的截面面积和预应力相同,即CFRP板的预拉力相同,因此弹性模量的增加对反拱没有影响,对正常使用极限状态特征荷载的影响也很小,对屈服荷载的提高也不明显。因此,当CFRP板的预拉力不变时,仅增加CFRP板的弹性模量虽然可以提高抗弯加固效果,但效果并不明显。

    图  13  CFRP板弹性模量对CFRP板加固损伤钢梁荷载-挠度曲线的影响
    Figure  13.  Effect of the CFRP plate elastic modulus on the load-deflection curves of damaged steel beams strengthened with CFRP plates

    以上研究发现,无粘结预应力CFRP板加固技术在钢梁抗弯加固方面显示出良好的性能。该技术的主要特点有:

    (1) 在施工方面,工序少、速度快。一方面该技术在使用时无需对钢梁表面进行打磨或喷砂处理,也不需要填充粘结剂;另一方面在预应力张拉完成后,无需进行粘结层养护即可投入使用。这在灾后等条件下需要快速抢险加固以恢复结构功能时尤其有利;

    (2) 在受力方面,无粘结预应力CFRP板具有与有粘结预应力CFRP板几乎相同的加固效果,显著高于外贴非预应力CFRP板的加固效果,而且在受力过程中CFRP板应变分布更加均匀,避免了界面剥离的不利影响;

    尽管如此,无粘结预应力CFRP板加固技术由于不使用粘结剂,结构与CFRP板之间的传力完全依靠两端的锚具,若锚具失效就意味着加固效果随即丧失。因此,锚具需要有更高的可靠性,设计时应该设定更高的可靠指标。

    (1) 粘结层对钢梁特征荷载和抗弯刚度几乎没有影响,有粘结和无粘结碳纤维增强聚合物复合材料(CFRP)板具有几乎相同的抗弯加固效果。

    (2) 对CFRP板施加预应力可以显著提高钢梁的抗弯加固效果,预应力CFRP板加固试件的屈服荷载相比未加固试件提高了约50%,正常使用极限状态下的荷载提高了约30%,而在正常使用阶段非预应力CFRP板的加固效果非常小。

    (3) 有粘结CFRP板-钢梁复合截面在跨中剥离前基本满足平截面假定,CFRP板沿长度具有明显的应变梯度;而无粘结CFRP板-钢梁复合截面不满足平截面假定,CFRP板应变沿长度保持不变并小于有粘结CFRP板的最大应变值。

    (4) 非预应力CFRP板的高强度特性远不能发挥,对CFRP板施加预应力是提高CFRP板在正常使用阶段和屈服阶段强度利用率的有效方法。有粘结CFRP板的强度利用率略大于无粘结CFRP板。

    (5) 采用ABAQUS软件建立的三维有限元模型可以较好地预测不同预应力水平下有粘结和无粘结CFRP板加固损伤钢梁的抗弯性能。增加CFRP板的预应力、厚度和弹性模量均可以提高损伤钢梁的抗弯加固效果。

  • 图  1   工程算法流程图[11]

    Figure  1.   Flowchart of engineering calculation method[11]

    图  2   有效宽度处理:(a)试验曲板横截面;(b)等效横截面[21]

    Figure  2.   Effective width approach: (a) Test curved panel cross section;(b) Equivalent cross section[21]

    图  3   帽型加筋板3种蒙皮有效宽度[22]

    Figure  3.   Three skin effective widths for omega-stiffened panel[22]

    图  4   加筋板筋条种类

    Figure  4.   Types of stiffeners for stiffened panels

    图  5   后屈曲渐进损伤分析流程图

    Figure  5.   Flowchart of post-buckling progressive damage analysis

    图  6   双线性本构模型[36]

    tn—Normal stress component; ts, tt—Shear stress component; δn, δs, δt—Interface separation deformation displacement; D—Damage coefficient

    Figure  6.   Bilinear constitutive model[36]

    图  7   冲击损伤有限元模型[59]

    Figure  7.   Finite element model of impact damage[59]

    图  8   压缩试验夹具示意图(左)、刀口夹具(右)[64]

    Figure  8.   Schematic diagram of compression test fixture (left), knife edge fixture (right) [64]

    图  9   压缩试验夹具示意图[10]

    Figure  9.   Schematic diagram of compression test fixture[10]

    图  10   剪切试验夹具示意图[10]

    Figure  10.   Schematic diagram of shear test fixture[10]

    图  11   剪切试验夹具现场图[67]

    Figure  11.   Field diagram of shear test fixture[67]

    图  12   压剪混合试验夹具示意图

    F—Force; T1—Shear load; T2—Compression load

    Figure  12.   Schematic diagram of compression-shear test fixture

    图  13   破坏模式:(a)工字型;(b) J型;(c) T型[72]

    Figure  13.   Failure mode: (a) I-type; (b) J-type; (c) T-type[72]

    图  14   数字图像相关(DIC)测量的屈曲模态:(a)未屈曲;(b)局部屈曲;(c)局部屈曲;(d)屈曲模式转变[73]

    Figure  14.   Buckling modes measured by digital image correlation (DIC): (a) Before buckling; (b) Local buckling; (c) Local buckling; (d) Buckling mode transition[73]

    图  15   加筋板剪切破坏[72]

    Figure  15.   Shear failure of stiffened panel[72]

    图  16   加筋板冲击损伤[60]

    Figure  16.   Impact damage of stiffened panel[60]

    图  17   含冲击损伤加筋板的破坏现象:(a)筋条侧;(b)蒙皮侧[60]

    Figure  17.   Failure phenomenon of stiffened panel with impact damage: (a) Stiffeners side; (b) Skin side[60]

    图  18   开裂模式:(a)厚度1.2 mm、载荷60 kN;(b)厚度1.5 mm、载荷80 kN[98]

    Figure  18.   Cracking modes: (a) Thickness 1.2 mm, load-60 kN; (b) Thickness 1.5 mm, load-80 kN[98]

    表  1   Camanho和Matthews的材料性能折减模型[29]

    Table  1   Material property reduction model of Camanho and Matthews[29]

    Failure mode Degradation coefficient
    Fiber tensile failure Ed11=0.07E11
    Fiber compression failure Ed11=0.14E11
    Matrix tensile/shear failure Ed22=0.2E22
    Gd12=0.2G12, Gd23=0.2G23
    Matrix compression/shear failure Ed22=0.4E22
    Gd12=0.4G12, Gd23=0.4G23
    Notes: E11 and E22 are the elastic moduli in the fiber and matrix directions; G12 and G23 are the shear moduli; d stands for degradation.
    下载: 导出CSV

    表  2   Chang和Lessard的材料性能折减模型[30]

    Table  2   Material property reduction model of Chang and Lessard[30]

    Failure mode Degradation coefficient
    Fiber failure Ed11=0, Ed22=0, Gd12=0
    Matrix failure Ed22=0, νd21=0
    Fiber-matrix shear failure Gd12=0, νd12=0, νd21=0
    Notes: Ed11 and Ed22 are the elastic moduli in the fiber and matrix directions after degradation; Gd12 is the shear moduli after degradation; νd12 and νd21 are poisson’s ratios after degradation.
    下载: 导出CSV
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  • 目的 

    复合材料具有轻质、高强度和高刚度、抗疲劳、耐高温、成型工艺优良且成本低等优势,如今广泛应用于航空航天领域。复合材料加筋板是飞机机身的主要部件,筋条能够显著提高层合板的屈曲性能。加筋板的主要失效模式是屈曲,但在结构屈曲后并未完全丧失承载能力,为了能够充分利用复合材料加筋板结构的后屈曲承载能力,研究学者们对屈曲与后屈曲行为做了大量研究。本文对近年来有关复合材料加筋板屈曲与后屈曲问题的研究进行了综述,系统地描述了加筋板屈曲后屈曲的处理方法。

    方法 

    本文从复合材料加筋板结构在工程中最常用的三种方法展开介绍:第一部分为常用理论方法介绍及具体公式,并提供有效宽度的处理方法;第二部分详细介绍有限元方法的分析过程,并分别对复合材料加筋板的层内层间模拟方法展开综述;第三部分分别从夹具设计、加载类型以及屈曲疲劳三个方面介绍了屈曲与后屈曲的试验方法。最后分别对三种方法进行优缺点的总结,并对该领域的研究进行了展望。

    结果 

    理论方法在初步设计阶段具有不可替代的重要性。通过层板理论延伸的分析模型以及工程经验得到的计算公式,可以快速获得加筋板的屈曲与后屈曲载荷,其中最重要的步骤是如何正确地简化模型,这对于加筋板的初步设计具有极高的参考价值。但理论模型和经验公式精度有限,无法完全模拟实际情况,且忽略了复合材料的缺陷。有限元方法能够针对复杂几何形状、特殊边界情况进行求解,选择合适的损伤、失效准则,能够准确模拟加筋板的损伤、失效过程,并得到加筋板的屈曲载荷和极限载荷。其中,渐进损伤分析(Progressive Damage Analysis,PDA)方法是预测复合材料层合板失效过程的有效工具。根据不同情况选取适当的层间损伤模型及失效准则,能够使得有限元分析结果更加精确。试验是研究复合材料加筋板屈曲与后屈曲行为不可或缺的手段。针对不同的载荷类型,包括面内载荷(压缩、剪切、压剪混合)和冲击载荷,通过精心设计的试验夹具、合适的加载方式和先进的试验设备,研究人员能够准确直观地测得加筋板的屈曲/后屈曲失效模式以及关键载荷参数。

    结论 

    深入研究加筋板的屈曲与后屈曲性能,挖掘后屈曲承载能力,能够进一步实现飞机轻量化的目标。理论方法通常用理论分析模型及既定公式对加筋板的屈曲和破坏载荷进行计算。其中工程算法速度较快,但精度较低,没办法考虑复杂的边界条件。因此通常用于加筋板初步设计阶段,为设计人员提供一个大致的范围以供参考。有限元方法可以对各种复杂的加筋板外形以及边界条件进行模拟,选取合适的失效准则和建模方法,可以较为准确地预测出加筋板屈曲和后屈曲载荷。合理地使用有限元工具可以减少试验的成本,一般可用于后期设计及验证阶段。试验可以清晰直观地观测到加筋板受载时的失效过程及破坏模式,可以用于最终试验验证以及对有限元方法进行修正。随着科技的飞速发展,未来复合材料加筋板的屈曲与后屈曲分析方法将持续发展,特别是在数值仿真精度的提高、理论模型的完善以及多尺度分析技术的融合等方面,将有显著进展。

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出版历程
  • 收稿日期:  2024-08-13
  • 修回日期:  2024-10-06
  • 录用日期:  2024-10-22
  • 网络出版日期:  2024-10-31
  • 发布日期:  2024-10-30
  • 刊出日期:  2025-05-14

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