碳纤维增强复合材料螺栓连接力学特性分析

doi:10.12068/j.issn.1005-3026.2025.20230301

摘要/Abstract

摘要：

针对碳纤维增强复合材料（CFRP）螺栓连接承受横向载荷时的变形以及受载情况，基于三维Hashin失效准则，建立了CFRP板钛合金螺栓连接抗拉强度预测模型，将CFRP板螺栓连接从加载开始到彻底破坏的载荷-位移曲线划分为静止阶段、滑移阶段、完全滑移阶段、螺栓杆承载阶段和破坏阶段共5个阶段，对每个阶段接触状态以及载荷传递方式进行了分析，研究了螺栓连接处在不同阶段弯矩、剪力的大小以及分布，并分析了CFRP板厚与螺栓预紧力对连接强度、连接处弯矩和剪力的影响.结果表明，螺栓连接处在滑移阶段和完全滑移阶段弯矩和剪力理论计算与仿真结果的最大误差不超过20%，在螺栓杆承载阶段和破坏阶段最大误差不超过15%.

关键词: CFRP, 螺栓连接, 数值模拟, 横向载荷, 力学特性

Abstract:

Aiming at the deformation of carbon fiber reinforced polymer （CFRP） bolted joints subjected to transverse load as well as the loading situation， a model is established to predict the tensile strength of a titanium alloy bolted joint with CFRP plates based on the three-dimensional Hashin failure criterion， in which the load-displacement curve of the CFRP bolted joint from the beginning of loading to complete destruction is divided into five stages， i.e. the stationary stage， the slip stage， the complete slip stage， the bolted rod load-bearing stage and the failure stage. Then， the contact state as well as the mode of load transfer in each stage are analyzed， the magnitude of bending moment and shear force as well as the distribution of the bolted joint at different stages are investigated， and the effects of CFRP thickness and bolt preload on the strength of the joint， bending moment and shear force at the joint are analyzed. The results show that the maximum error between theoretical calculations and simulation results for bending moment and shear force at the bolted joint does not exceed 20% in the slip stage and the complete slip stage， and the maximum error does not exceed 15% in the bolted rod load-bearing stage and the failure stage.

Key words: CFRP, bolted joint, numerical simulation, transverse load, mechanical characteristic

中图分类号:

TB 33

王海艳, 冯岩, 王庆超, 于万春. 碳纤维增强复合材料螺栓连接力学特性分析[J]. 东北大学学报（自然科学版）, 2025, 46(5): 71-79.

Hai-yan WANG, Yan FENG, Qing-chao WANG, Wan-chun YU. Mechanical Characteristic Analysis of Carbon Fiber Reinforced Polymer Bolted Joints[J]. Journal of Northeastern University(Natural Science), 2025, 46(5): 71-79.

图/表 10

表1 CFRP在不同模式下的失效准则

Table 1 Failure criteria for CFRP in different modes

损伤类型	失效准则
纤维拉伸破坏 $σ 11 ≥ 0$	$e f t = σ 11 X t 2 + σ 12 S 12 2 + σ 13 S 13 2 ≥ 1 e f c = σ 11 X c 2 ≥ 1 e m t = σ 22 + σ 33 Y t 2 + σ 23 2 - σ 22 σ 33 S 232 + σ 12 S 12 2 + σ 13 S 13 2 ≥ 1 e m c = σ 22 + σ 33 Y c Y c 2 S 23 2 - 1 + σ 22 + σ 33 2 S 23 2 + σ 23 2 - σ 22 σ 33 S 232 + σ 12 S 12 2 + σ 13 S 13 2 ≥ 1$
纤维压缩破坏 $σ 11 < 0$
基体拉伸破坏 $σ 22 + σ 33 ≥ 0$
基体压缩破坏 $σ 22 + σ 33 < 0$

表1 CFRP在不同模式下的失效准则

Table 1 Failure criteria for CFRP in different modes

损伤类型	失效准则
纤维拉伸破坏 $σ 11 ≥ 0$	$e f t = σ 11 X t 2 + σ 12 S 12 2 + σ 13 S 13 2 ≥ 1 e f c = σ 11 X c 2 ≥ 1 e m t = σ 22 + σ 33 Y t 2 + σ 23 2 - σ 22 σ 33 S 232 + σ 12 S 12 2 + σ 13 S 13 2 ≥ 1 e m c = σ 22 + σ 33 Y c Y c 2 S 23 2 - 1 + σ 22 + σ 33 2 S 23 2 + σ 23 2 - σ 22 σ 33 S 232 + σ 12 S 12 2 + σ 13 S 13 2 ≥ 1$
纤维压缩破坏 $σ 11 < 0$
基体拉伸破坏 $σ 22 + σ 33 ≥ 0$
基体压缩破坏 $σ 22 + σ 33 < 0$

图1 单搭接螺栓连接零件几何尺寸

Fig.1 Geometry of single-lap bolted parts

图2 载荷-位移曲线仿真与实验结果对比

Fig.2 Comparison between simulated and experimental results of load-displacement curves

图3 载荷-位移曲线阶段划分

Fig.3 Load-displacement curve stages division

图4 螺栓连接在不同阶段的接触状态（a）—Ⅰ静止阶段；（b）—Ⅱ滑移阶段；（c）—Ⅲ完全滑移阶段；（d）—Ⅳ螺栓杆承载阶段.

Fig.4 Contact state of bolted connections at different stages

图5 旋转约束因子随CFRP板厚和螺栓扭矩变化（a）—CFRP板厚；（b）—螺栓扭矩.

Fig.5 Variation of rotational restraint factor with CFRP plate thickness and bolt torque

图6 不同CFRP板厚的连接处弯矩、剪力对比（a）—Ⅱ阶段弯矩；（b）—Ⅱ阶段剪力；（c）—Ⅲ阶段弯矩；（d）—Ⅲ阶段剪力；（e）—Ⅳ阶段弯矩；（f）—Ⅳ阶段剪力；（g）—Ⅴ阶段弯矩；（h）—Ⅴ阶段剪力.

Fig.6 Comparison of bending moment and shear force at the joint for different CFRP plate thicknesses

图7 不同CFRP板厚的载荷-位移曲线

Fig.7 Load-displacement curves for different CFRP plate thicknesses

图8 不同螺栓扭矩的载荷-位移曲线

Fig.8 Load-displacement curves for different bolt torques

图9 不同螺栓扭矩的连接处弯矩、剪力对比（a）—连接处弯矩；（b）—连接处剪力.

Fig.9 Comparison of bending moment and shear force at the joint for different bolt torques

参考文献 17

[1]	李晖，徐忠浩，王东升，等.基于集中质量法的纤维增强复合材料的损伤定位［J］.东北大学学报（自然科学版）， 2020，41（2）： 234-240.
	Li Hui， Xu Zhong-hao， Wang Dong-sheng，et al. Damage location of fiber-reinforced composites based on lumped mass approach［J］. Journal of Northeastern University （Natural Science）， 2020，41（2）： 234-240.
[2]	Li X， Li Y Z， Li F， et al. Failure analysis and experimental study on bolted composite joints based on continuum damage mechanics［J］. Composite Structures， 2023， 303： 116274.
[3]	山美娟，赵丽滨. CFRP复合材料螺栓连接失效载荷不确定性的评估方法［J］.复合材料学报，2021，38（5）： 1468-1475.
	Shan Mei-juan， Zhao Li-bin. An evaluation method for uncertainty in failure load of CFRP composite bolted joints ［J］. Acta Materiae Compositae Sinica， 2021， 38（5）： 1468-1475.
[4]	Xu G H， Cheng H， Zhang K F， et al. Modeling of damage behavior of carbon fiber reinforced plastic composites interference bolting with sleeve［J］. Materials & Design， 2020， 194： 108904.
[5]	Pinho S T， Darvizeh R， Robinson P， et al. Material and structural response of polymer-matrix fibre-reinforced composites［J］. Journal of Composite Materials， 2012， 46（19/20）： 2313-2341.
[6]	Liu Z F， Zheng M P， Guo J F， et al. Experimental study on performance characterization of bolted joint under transverse loading［J］. Measurement， 2021， 182： 109608.
[7]	Liang Y C， Xu F， Zhang X Y， et al. An analytically improved four-stage model for single-lap torqued bolted joints accounting for preload relaxation［J］. Thin-Walled Structures， 2023， 182： 110252.
[8]	Krishnadasan C K， Shanmugam N S， Sivasubramonian B， et al. Analytical studies and numerical predictions of stresses in shear joints of layered composite panels for aerospace applications［J］. Composite Structures， 2021， 255： 112927.
[9]	Zhao L B， Xin A， Liu F R， et al. Secondary bending effects in progressively damaged single-lap， single-bolt composite joints［J］. Results in Physics， 2016， 6： 704-711.
[10]	Hashi Z. Failure criteria for unidirectional fiber composite［J］. Journal of Applied Mechanics， 1980， 47： 3292334.
[11]	Zhang H Y， Zhang L， Liu Z， et al. Numerical analysis of hybrid （bonded/bolted） FRP composite joints： a review［J］. Composite Structures， 2021， 262： 113606.
[12]	Zheng Y P， Zhang C Y， Ying T I E， et al. Tensile properties analysis of CFRP-titanium plate multi-bolt hybrid joints［J］. Chinese Journal of Aeronautics， 2022， 35（3）： 464-474.
[13]	El Zaroug M， Kadioglu F， Demiral M， et al. Experimental and numerical investigation into strength of bolted， bonded and hybrid single lap joints： effects of adherend material type and thickness［J］. International Journal of Adhesion and Adhesives， 2018， 87： 130-141.
[14]	Kou J F， Xu F， Xie W， et al. A theoretical 4-stage shear model for single-lap torqued bolted-joint with clearances［J］. Composite Structures， 2018， 186： 1-16.
[15]	Blau P J. The significance and use of the friction coefficient［J］. Tribology International， 2001， 34（9）： 585-591.
[16]	Kapidžić Z， Granados D L Á， Arias J A M， et al. Bolt fatigue in CFRP joints［J］. International Journal of Fatigue， 2022， 164： 107138.
[17]	Barrois W. Stresses and displacements due to load transfer by fasteners in structural assemblies［J］. Engineering Fracture Mechanics， 1978， 10（1）： 115-176.