## 留言板 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

###### 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

 EngineeringConstants Value StrengthParameters Value E1/GPa 95 Xt/MPa 2448 E2/GPa 7.4 Xc/MPa 835 G12/GPa 3.6 Yt/MPa 31 G23/GPa 2.74 Yc/MPa 103.9 v12 0.3 Q/MPa 45 v23 0.35 S/MPa 53.2 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).

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)

 Specimen Measuring points Measured strain Mean strain TubeA 1 850 875 2 900 3 −1474 −1381 4 −1288 TubeB 1 594 629 2 664 3 114 167 4 220

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)

 Specimen Testresults ANSYSresults Theoreticalresults Relative error/% TubeA Axial strain 875 900 900 2.9 Hoop strain −1381 −1380 −1380 0.1 TubeB Axial strain 629 639 639 1.4 Hoop strain 167 413 413 146

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

 Laminated θ Failure Layer Failure Mode Temperature Difference [04/±θ] 0°~90°(exclude 0°) Fifth Layer Transverse Tensile Failure of Matrix −100℃ Transverse Compression Failure of Matrix 100℃ [±θ]3 0°~90°(exclude 0°、90°) First Layer Transverse Tensile Failure of Matrix −100℃ Transverse Compression Failure of Matrix 100℃ [±θ/θ]s 0°~10°(exclude 0°) Fifth Layer Transverse Tensile Failure of Matrix −100℃ Transverse Compression Failure of Matrix 100℃ 11°~90°(exclude 90°) Second Layer Transverse Tensile Failure of Matrix −100℃ Transverse Compression Failure of Matrix 100℃
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##### 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

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