留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于三维弹性理论的任意铺层FRP管热变形及残余应力计算方法

张恒铭 李峰

张恒铭, 李峰. 基于三维弹性理论的任意铺层FRP管热变形及残余应力计算方法[J]. 复合材料学报, 2021, 39(0): 1-18
引用本文: 张恒铭, 李峰. 基于三维弹性理论的任意铺层FRP管热变形及残余应力计算方法[J]. 复合材料学报, 2021, 39(0): 1-18
Hengming ZHANG, Feng LI. Calculation method of thermal deformation and residual stress of arbitrarily laminated FRP tube based on three-dimensional elastic theory[J]. Acta Materiae Compositae Sinica.
Citation: Hengming ZHANG, Feng LI. Calculation method of thermal deformation and residual stress of arbitrarily laminated FRP tube based on three-dimensional elastic theory[J]. Acta Materiae Compositae Sinica.

基于三维弹性理论的任意铺层FRP管热变形及残余应力计算方法

基金项目: 国家自然科学基金 (51778620);国家重点研发计划 (2017YFC0703008)
详细信息
    通讯作者:

    李峰,副教授,博士生导师,研究方向为复合材料结构与力学  E-mail: 83812546@qq.com

  • 中图分类号: TB330.1

Calculation method of thermal deformation and residual stress of arbitrarily laminated FRP tube based on three-dimensional elastic theory

  • 摘要: 为了解决纤维增强树脂复合材料(FRP)圆管在工程中热变形和热残余应力的问题,提出了一种针对任意铺层FRP圆管等效热膨胀系数和热残余应力的计算方法,该方法是综合考虑了层合效应、各向异性材料三维本构关系的三维弹性理论。通过与本文试验和ANSYS数值模型的多组数据进行对比分析,验证了理论的正确性。并以此理论模型为基础,首先对多种铺层FRP圆管等效热膨胀系数进行研究,其次结合Hashin失效准则的强度比方程,对由热残余应力引起FRP圆管强度失效进行分析。结果表明:FRP圆管铺层角度对等效热膨胀系数的影响在热缩阶段、热胀阶段表现不同,且存在等效热膨胀系数为零的铺层方式;径厚比仅对等效径向热膨胀系数影响较大,对等效轴向热膨胀系数无影响;温差大小及温差方向影响FRP圆管的破坏模式及破坏位置,热残余应力引起的FRP圆管的强度破坏均为基体破坏。

     

  • 图  1  FRP层合管坐标系、铺层角度、铺层参数

    Figure  1.  FRP laminated tube coordinate system, layer angle, layer parameters

    图  2  FRP层合管铺层节点

    Figure  2.  Layer node point of FRP laminated tube

    图  3  MATLAB函数流程图

    Figure  3.  Flow chart of MATLAB function

    图  4  纤维和基体失效模式与失效界面

    Figure  4.  Failure modes and failure planes of fiber and matrix

    图  5  FRP层合管试件制备过程

    Figure  5.  FRP laminated tube specimen preparation process

    图  6  试验开展过程

    Figure  6.  Test development process

    图  7  应变测试点布置方案

    Figure  7.  Strain test point layout scheme

    图  8  FRP层合管试件的时间-应变曲线

    Figure  8.  Time-strain curve of FRP laminated tube specimen

    图  9  FRP层合管试件TubeB变形协调机制示意图

    Figure  9.  Schematic diagram of deformation coordination of FRP laminated tube specimen TubeB

    图  10  ANSYS定义材料参数、铺层参数

    Figure  10.  ANSYS defines material parameters and layering parameters

    图  11  FRP圆管的铺层信息和模型的端部约束方式

    Figure  11.  Layup information of FRP circular tube and the end constraint mode of the model

    图  12  ANSYS数值模型计算结果的查看方法

    Figure  12.  View method of ANSYS numerical model calculation results

    图  13  FRP层合管ANSYS数值模型应变计算结果

    Figure  13.  ANSYS numerical model strain calculation results of FRP laminated tubes

    图  15  约束铺层位于不同位置时FRP层合管等效热膨胀系数随约束铺层θ的变化关系(ΔT=100℃)

    Figure  15.  Relation of the equivalent thermal expansion coefficient with θ of FRP laminated tubes when the constraint layer is located at different positions(ΔT=100℃)

    (a)Equivalent axial thermal expansion coefficient (b) Equivalent radial thermal expansion coefficient

    图  14  FRP层合管试件TubeB应力应变沿壁厚分布图

    Figure  14.  Distribution diagram of stress and strain along wall thickness of FRP laminated tube specimen TubeB

    图  16  FRP层合管等效热膨胀系数$\bar \alpha $随环向约束铺层层数n增加的变化曲线

    Figure  16.  Curve of equivalent thermal expansion coefficient $\bar \alpha $ with the increase of the constraint layer n of FRP laminated tube

    图  17  圆形变形的几何关系

    Figure  17.  Geometric relation of circular deformation

    图  18  不同径厚比FRP圆管等效热膨胀系数与铺层角度θ的关系

    Figure  18.  Relationship between equivalent thermal expansion coefficient of FRP tubes with different diameter-thickness ratios and layer angle θ

    图  19  FRP层合管等效热膨胀系数与径厚比λ的关系

    Figure  19.  Relationship between equivalent thermal expansion coefficient and diameter-thickness ratio λ of FRP laminated tube

    图  20  FRP层合管强度比和极限温差的计算方法流程图

    Figure  20.  Flow chart of calculation method of strength ratio and limit temperature difference of FRP laminated tube

    图  21  FRP层合管试件TubeB应力沿壁厚分布

    Figure  21.  Stress distribution along wall thickness of FRP laminated tube specimen TubeB

    图  22  FRP层合管试件TubeB节点的坐标位置

    Figure  22.  Coordinates of node point of FRP laminated tube specimen TubeB

    图  23  FRP层合管试件TubeB破坏点处的应力单元体

    Figure  23.  Stress element at failure point of FRP laminated tube specimen TubeB

    (a) ΔT=100℃ (b) ΔT=-100℃

    图  24  FRP圆管强度比R与铺层角度θ的关系

    Figure  24.  Relationship between the strength ratio R of FRP laminated tubes and ply anglesθ

    图  25  FRP圆管垂直纤维方向的变形协调

    Figure  25.  Deformation coordination of FRP laminated tubes in vertical fiber direction

    图  26  FRP圆管纤维方向的变形协调

    Figure  26.  Deformation coordination of FRP laminated tubes in fiber direction

    表  1  T700SC-12K-50C碳纤维/YPH-307环氧树脂预浸料基本力学性能参数

    Table  1.   Basic mechanical property parameters of T700SC-12K-50C carbon fber/YPH-307 epoxy prepreg

    Engineering
    Constants
    ValueStrength
    Parameters
    Value
    E1/GPa95Xt/MPa2448
    E2/GPa7.4Xc/MPa835
    G12/GPa3.6Yt/MPa31
    G23/GPa2.74Yc/MPa103.9
    v120.3Q/MPa45
    v230.35S/MPa53.2
    αL/(10−6·℃−1)−15
    αT/(10−6·℃−1)23
    Notes: the symbols E, G, and ν represent elastic modulus, shear modulus and Poisson; Subscripts 1, 2 and 3 indicate the axial, radial and circumferential directions of the fiber respectively. αL is the axial thermal expansion coefficient; αT is the transverse thermal expansion coefficient; Xt is the tensile failure stress in fiber direction; Xc is the compressive failure stress in fiber direction (absolute value); Yt is the tensile failure stress transverse to fiber direction; Yc is the compressive failure stress transverse to fiber direction (absolute value); Q is the transverse failure shear, σnt in Fig. 4(b); S is the axial failure shear, σln in Fig. 4(a).
    下载: 导出CSV

    表  2  FRP层合管试件表观应变值(×10-6)

    Table  2.   Apparent strain of FRP laminated tube specimens(×10-6)

    SpecimenMeasuring pointsMeasured strainMean strain
    TubeA1850875
    2900
    3−1474−1381
    4−1288
    TubeB1594629
    2664
    3114167
    4220
    下载: 导出CSV

    表  3  FRP层合管试验、理论、ANSYS结果对比(×10-6)

    Table  3.   Comparison of experimental, theoretical and ANSYS results of FRP laminated tubes (×10-6)

    SpecimenTest
    results
    ANSYS
    results
    Theoretical
    results
    Relative error/%
    TubeAAxial strain8759009002.9
    Hoop strain−1381−1380−13800.1
    TubeBAxial strain6296396391.4
    Hoop strain167413413146
    下载: 导出CSV

    表  4  FRP圆管破坏位置及破坏模式

    Table  4.   Location and mode of failure of FRP laminated tubes

    LaminatedθFailure LayerFailure ModeTemperature Difference
    [04θ]0°~90°
    (exclude 0°)
    Fifth LayerTransverse Tensile Failure of Matrix−100℃
    Transverse Compression Failure of Matrix100℃
    θ]30°~90°
    (exclude 0°、90°)
    First LayerTransverse Tensile Failure of Matrix−100℃
    Transverse Compression Failure of Matrix100℃
    θ/θ]s0°~10°
    (exclude 0°)
    Fifth LayerTransverse Tensile Failure of Matrix−100℃
    Transverse Compression Failure of Matrix100℃
    11°~90°
    (exclude 90°)
    Second LayerTransverse Tensile Failure of Matrix−100℃
    Transverse Compression Failure of Matrix100℃
    下载: 导出CSV
  • [1] ZHANG D, YUAN J, LI F, et al. Experimental Characterization of Static Behavior of a New GFRP–Metal Space Truss Deployable Bridge: Comparative Case Study[J]. Journal of Bridge Engineering,2021,26:5020011. doi: 10.1061/(ASCE)BE.1943-5592.0001650
    [2] ZHANG D. Static performance of a new GFRP-metal string truss bridge subjected to unsymmetrical loads[J]. Steel and Composite Structures,2020,35:641-657.
    [3] ZHANG D, LV Y, ZHAO Q, et al. Development of lightweight emergency bridge using GFRP–metal composite plate-truss girder[J]. Engineering Structures,2019,196:109291. doi: 10.1016/j.engstruct.2019.109291
    [4] GAO J, ZHAO Q, LI F, et al. Fatigue failure investigation of pultruded GFRP pre-tightened single-tooth connector (PTSTC)[J]. Engineering Failure Analysis,2019,106:104191. doi: 10.1016/j.engfailanal.2019.104191
    [5] ZHANG D, LI F, SHAO F, et al. Evaluation of Equivalent Bending Stiffness by Simplified Theoretical Solution for an FRP–aluminum Deck–truss Structure[J]. KSCE Journal of Civil Engineering,2018:23.
    [6] ZHU R, LI F, CHEN Y, et al. The effect of Tube-in-Tube buckling-restrained device on performance of hybrid PFRP-Aluminium space truss structure[J]. Composite Structures,2021,260:113260. doi: 10.1016/j.compstruct.2020.113260
    [7] ZHU R, LI F, CHEN Y, et al. A hybrid beam-column element for direct second-order nonlinear analysis of PFRP frame structures[J]. Composite Structures,2021,271:114171. doi: 10.1016/j.compstruct.2021.114171
    [8] ZHU R, LI F, SHAO F, et al. Static and dynamic behaviour of a hybrid PFRP-aluminium space truss girder: Experimental and numerical study[J]. Composite Structures,2020,243:112226. doi: 10.1016/j.compstruct.2020.112226
    [9] 吴杰, 肖正航. 碳纤维复合材料残余应力消除方法探讨[J]. 航天制造技术, 2012(04):38-40.

    WU Jie, XIAO Zhenghang. Discussion on carbon fiber composite residual stress relief[J]. Aerospace Maunfacturing Technology,2012(04):38-40(in Chinese).
    [10] 赵启林, 高一峰, 李飞. 复合材料预紧力齿连接技术研究现状与进展[J]. 玻璃钢/复合材料, 2014(12):52-56.

    ZHAO Qilin, GAO Yifeng, LI Fei. Current reseach and development of the application of the pre-tightened tooth connection[J]. Fiber Reinforced Plastics/Composites,2014(12):52-56(in Chinese).
    [11] 左扬, 李飞, 赵启林, 等. 基于挤压法的复合材料预紧力齿连接预紧力计算方法研究[J]. 复合材料科学与工程, 2020(05):32-39. doi: 10.3969/j.issn.1003-0999.2020.05.005

    ZUO Yang, LI Fei, ZHAO Qilin, et al. Study on the calculation method of preload for composite pre-tightened tooth connections based on extrusion method[J]. Composites Science and Engineering,2020(05):32-39(in Chinese). doi: 10.3969/j.issn.1003-0999.2020.05.005
    [12] 孙宝玉. 轻型大视场光学遥感器结构动态特性研究[D]. 长春: 中国科学院研究生院(长春光学精密机械与物理研究所), 2004.

    SUN Baoyu. Research on dynamic characteristic of the light-duty great visual field optical remote sensor [D]. Changchun : Chinese Academy of Sciences (Changchun Institute of Optics, Fine Mechanics and Physics), 2014(in Chinese).
    [13] 王建花. 复合材料身管残余应力研究[D]. 南京: 南京理工大学, 2007.

    WANG Jianhua. Study on residual stress of the composite materials barrel [D]. Nanjing : Nanjing University of Science & Technology, 2007(in Chinese).
    [14] MAIER G, HOFMANN F. Performance enhancements of polymer–matrix composites by changing of residual stresses[J]. Composites science and technology,2008,68(9):2056-2065. doi: 10.1016/j.compscitech.2008.03.001
    [15] SHOKRIEH M M, AKBARI S, DANESHVAR A. A comparison between the slitting method and the classical lamination theory in determination of macro-residual stresses in laminated composites[J]. Composite structures,2013,96:708-715. doi: 10.1016/j.compstruct.2012.10.001
    [16] 梁群, 冯喜平. 复合材料壳体固化成型过程残余应力和形变分析[J]. 固体火箭技术, 2019, 42(05):628-634.

    LIANG Qun, FENG Xiping. Residual stress and structural distortion analysis for the curing process of srm composite case[J]. Journal of Solid Rocket Technology,2019,42(05):628-634(in Chinese).
    [17] 刘加顺, 李峰, 张恒铭. 树脂基碳纤维卷铺管件热残余应力分析[J]. 玻璃钢/复合材料, 2016(02):18-23.

    LIU Jiashun, LI Feng, ZHANG Hengming. Thermal residual stress analysis of polymer matrix carbon fiber reinforced composite winding tubes[J]. Fiber Reinforced Plastics/Composites,2016(02):18-23(in Chinese).
    [18] 娄菊红, 杨延清. 基体性能对复合材料热残余应力的影响[J]. 材料研究学报, 2016, 30(07):503-508.

    LOU Juhong, YANG Yanqing. Effect of matrix properties on thermal residual stress of fiber reinforced ti-matrix composities[J]. Chinese Journal Of Materials Research,2016,30(07):503-508(in Chinese).
    [19] 杨雷, 武湛君. 热残余应力对纤维增强树脂基复合材料横向力学性能的影响: 中国力学大会-2015[C], 中国上海, 2015.

    YANG Lei, WU Zhanjun. Effect of thermal residual stress on transverse mechanical properties of fiber reinforced resin matrix composites: Chinese Conference on Mechanics, 2015[C], Shanghai, China, 2015(in Chinese).
    [20] PETRUSHIN S I. Calculation of Thermal Residual Stresses in Multilayer Composite Materials[J]. Applied Mechanics and Materials,2013,379:95-100. doi: 10.4028/www.scientific.net/AMM.379.95
    [21] 徐亮工. 缠绕玻璃钢管道的残余热应力[J]. 玻璃钢/复合材料, 1997(01):11-12.

    XU Lianggong. Thermal residual stress in filament winding frp pipe[J]. Fiber Reinforced Plastics/Composites,1997(01):11-12(in Chinese).
    [22] 王建花, 钱林方, 袁人枢. 复合材料身管的热残余应力[J]. 弹道学报, 2007(01):82-85. doi: 10.3969/j.issn.1004-499X.2007.01.023

    WANG Jianhua, QIAN Linfang, YUAN Renshu. Thermal residual stresses in composite material barrel[J]. Journal of Ballistics,2007(01):82-85(in Chinese). doi: 10.3969/j.issn.1004-499X.2007.01.023
    [23] WANG J, QIAN L, YUAN R. The Residual Stresses and Strains in the Composite Material Barrel: Proceedings of the International Conference on Mechanical Engineering and Mechanics 2005 vol. 2[C], 2005.
    [24] 徐芝纶. 弹性力学简明教程(第五版)[J]. 北京:高等教育出版社, 2018:167-172.

    Xu Zhilun. Concise Course of Elasticity (Fifth Edition)[J]. Beijing:Higher Education Press,2018:167-172(in Chinese).
    [25] 李峰, 李若愚. 复合材料力学与圆管计算方法[J]. 北京:科学出版社, 2021:170-172.

    LI Feng, LI Ruoyu. Mechanics of Composite Materials and Calculation Methods for Circular Tubes[J]. Beijing:Science Press,2021:170-172(in Chinese).
    [26] 国家质量技术监督局. 定向纤维增强塑料拉伸性能试验方法: GB/T 3354-1999[S]. 北京: 中国标准出版社, 1999. The state bureau of quality and technical supervision. Test method for tensile properties of oriented fiber reinforced plastics: GB/T 3354-1999[S]. Beijing: China Standards Press, 1999(in Chinese). [27] 中华人民共和国国家质量监督检验检疫总局. 单向纤维增强塑料平板压缩性能试验方法: GB/T 3856-2005[S]. 北京: 中国标准出版社, 2005.

    General administration of quality supervision, inspection and quarantine of the People's Republic of China. Test method for compression properties of unidirectional fiber reinforced plastics: GB/T 3856-2005[S]. Beijing: China Standards Press, 1999(in Chinese).
    [27] ASTM International. ASTM D7078/D7078M-12 Standard test method for shear properties of composite materials by V-notched rail shear method[S]. West Conshohocken: ASTM International, 2012
    [28] 张恒铭, 李峰, 潘大荣. 基于三维梁理论的复合材料层合管等效抗弯刚度[J]. 复合材料学报, 2016, 33(08):1694-1701.

    ZHANG Hengming, LI Feng, PANG Darong. Equivalent bending stiffness of composite laminated tube based on 3D beam theory[J]. Acta Materiae Compositae Sinica,2016,33(08):1694-1701(in Chinese).
    [29] 姜海林. 基于等效位移法的低速冲击载荷下复合材料层合板损伤力学模型[D]. 大连: 大连理工大学, 2020.

    JIANG Hailin. Damage mechanics model of composite laminates under low speed impact loading based on equivalent displacement method[D]. Dalian : Dalian University of Technology, 2020(in Chinese).
    [30] 沈观林, 胡更开, 刘彬. 复合材料力学(第二版)[J]. 北京:清华大学出版社, 2013:129-133.

    SHEN Guanlin, HU Gengkai, LIU Bin. Mechanics of Composite Materials(Second Edition)[J]. Beijing:Tsinghua University Press,2013:129-133(in Chinese).
  • 加载中
计量
  • 文章访问数:  124
  • HTML全文浏览量:  63
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-10-25
  • 录用日期:  2021-12-16
  • 修回日期:  2021-12-05
  • 网络出版日期:  2022-01-05

目录

    /

    返回文章
    返回