﻿ 一种多钉铆接连接件的疲劳寿命分析方法<sup>*</sup>
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A fatigue life analysis method for multiple riveted joint
ZHANG Tianyu, HE Yuting, CHEN Tao, DU Xu, TAN Xiangfei, LIU Kai
Aeronautic and Astronautic Engineering College, Air Force Engineering University, Xi'an 710038, China
Received: 2017-11-06; Accepted: 2017-11-13; Published online: 2017-12-12
Corresponding author. HE Yuting.E-mail:heyut666@126.com
Abstract: In the analysis of fatigue life of multiple riveted joints, the explicit dynamic analysis of the pressing and riveting process was carried out, and the deformation form and interference after riveting process were obtained. An APDL subroutine was developed to analyze the riveting process of various forms of specimens. Detailed stress was analyzed by using load-displacement curves of fastener. The load-displacement calculation method of riveted joint was proposed based on the three-dimensional elastoplastic finite element method, and compared with the experimental results, the reliability of using this method to obtain load-displacement curves was validated. Riveting units were established in ANSYS by using parametric modeling to carry out the calculation of riveting load. The fatigue life of the joint is estimated by the stress severity coefficient method. The fatigue test of typical aviation riveted joint was carried out. The calculation results are in good agreement with the test results, which indicates the feasibility of this method.
Keywords: multiple riveted joint     riveting process     explicit dynamic analysis     load-displacement curve     rivet unit

Ronsenfeld和Jarfall只是将P-δ曲线看做一条直线[3-4]，用柔度系数来表征紧固件的变形和孔的局部变形。国外多名学者通过大量试验提出紧固件柔度的半经验公式[5-8]。试验表明，紧固件的P-δ曲线并不是一条直线，而是一条曲线。

1 紧固件P-δ曲线获取方法 1.1 铆接过程有限元分析

 图 1 铆钉几何模型 Fig. 1 Geometric model of rivets

 图 2 铆接简化模型 Fig. 2 Simplified model of riveting

 图 3 沙漏能与内能的比值 Fig. 3 Ratio of hourglass energy to internal energys

 图 4 半圆头铆钉铆接过程应力分布 Fig. 4 Stress distribution in riveting process of semicircular head rivet
 图 5 铆接后塑性应变分布 Fig. 5 Plastic strain distribution after riveting
 图 6 镦头部位网格变形 Fig. 6 Grid deformation of heading positon

 图 7 铆接过程有限元分析参数化 Fig. 7 Parametric finite element analysis of riveting process
1.2 铆接连接件有限元分析

 图 8 铆钉连接件几何模型 Fig. 8 Rivet connection geometric model

 图 9 边界条件 Fig. 9 Boundary conditions

 图 10 模型局部应力和变形 Fig. 10 Stress and deformation of part of model

 图 11 P=0 N时x方向应力分布 Fig. 11 Stress distribution along x direction when P=0 N

 图 12 P-δ曲线计算结果与试验结果对比 Fig. 12 Comparison of P-δ curves between calculated and experimental results
2 多钉连接件钉载计算 2.1 建立钉单元简化模型

 图 13 钉单元示意图 Fig. 13 Schematic diagram of rivet unit

 (1)

 (2)
2.2 钉元非线性解法

P-δ曲线是一条非线性变化的曲线，随着钉载的增大，钉元将进入非线性区，其刚度是一个不断变化的量，钉元刚度的改变将影响整个刚度矩阵，导致力的重新分配。采用增量法计算钉载的基本原理为[19-21]：将总外载Pa分为线性部分Pe和非线性部位Pp，即Pa=Pe+PpPe是某一个钉元(或某些钉元)达到Pg(P-δ曲线线性段和非线性段临界点)时所对应的外载；Pe确定之后，根据精度要求将Pp分为相等的m段，每段外载为Pm，每次以Pm作为外载计算出所有钉元的内力，并检查是否进入P-δ曲线的非线性段，如果进入就修改该钉元的刚度系数。作m次计算，得到m段内力，一个钉的钉载就是各段计算结果的累加。

 图 15 细节应力分析系统流程图 Fig. 15 Detailed stress analysis system flowchart
3 典型航空铆接连接件疲劳试验

 图 16 试件结构形式与尺寸 Fig. 16 Structure form and dimension of specimen

 力学性能参数 数值 弹性模量/MPa 85 000 泊松比 0.33 密度/(kg·m-3) 4.83 屈服强度/MPa 880

 图 17 有限元模型及各钉位置 Fig. 17 Finite element model and position of rivets

 图 18 防弯夹具 Fig. 18 Anti-bending fixture

 图 19 试件断裂部位 Fig. 19 Fracture parts of specimen

 组别 中值疲劳寿命/cycles 计算与试验结果相对误差/% 试验结果 计算结果 1 192 909 169 489 12.14 2 72 598 64 937 10.55 3 41 271 35 886 13.05 4 277 469 312 001 12.45 5 121 505 140 670 15.77 6 52 113 59 389 13.96

4 结论

1) 应用显式动力学分析铆接过程是符合实际情况的。

2) 编制APDL子程序计算P-δ曲线的方法与试验相比，误差在合理的范围之内，从而改变了铆钉P-δ曲线的获取必须依赖试验的现状。

3) 建立钉元模型来估算多钉连接结构疲劳寿命的方法与试验结果比较吻合，能较准确地预测疲劳裂纹的初始位置，误差在工程应用允许的范围之内，可以在工程上推广。

 [1] 飞机结构强度研究所. 航空结构连接件疲劳分析手册[M]. 西安: 飞机结构强度研究所, 1985: 21-23. Aircraft Structure Strength Research Institute. Fatigue analysis manual of aircraftjoints[M]. Xi'an: Aircraft Structure Strength Research Institute, 1985: 21-23. (in Chinese) [2] BOFF A.飞机制造工艺学[M].佘公藩, 张钧, 等译.西安: 西北工业大学出版社, 1989: 205-221. BOFF A. Aircraft manufacturing technology[M].SHE G F, ZHANG J, et al., translated. Xi'an: Northwest Industrial University Press, 1989: 205-221(in Chinese). [3] ROSENFELDS J.Analytical and experimental investigation of bolted joints: NACA TN-1458[R].Washington, D.C.: NACA, 1458. [4] JARFALL L E. Optimun design of joints:The stress severity factor concept[J]. Aircraft Fatigue, 1967, 56 (2): 49–63. [5] TATE M B, ROSENFELD S J. Preliminary investigation of theloads carried by individual bolts in bolted joints: NACA TN-10511[R].Washington, D.C.: NACA, 1946. [6] NELSON W D, BUNIN B L, HART-SMITHL J. Critical joints in large composite aircraft structure: NASA CR-3710[R].Washington, D.C.: NASA, 1983. [7] SWIFT T.Fracture analysis of stiffened structure: ASTM STP842[R].New York: ASTM, 1984. [8] HUTH H.Influence of the fastener flexibility on the prediction of load transfer and fatigue life for multi-row joints: ASTM STP927[R].New York: ASTM, 1986. [9] 梁沛权.紧固件载荷-变形曲线的计算方法研究[D].西安: 西北工业大学, 1987. LIANG P Q.Study on the numerical calculations of P-δ curves of fasteners[D]. Xi'an: Northwestern Polytechnical University, 1987(in Chinese). [10] 陈涛, 何宇廷, 韩宏文, 等. 螺栓连接件的紧固件P-δ曲线计算方法研究[J]. 科学技术与工程, 2014, 14 (28): 140–147. CHEN T, HE Y T, HAN H W, et al. Study on the numerical calculations of P-δ curves of fasteners for bolted joints[J]. Science Technology and Engineering, 2014, 14 (28): 140–147. DOI:10.3969/j.issn.1671-1815.2014.28.027 (in Chinese) [11] 师访. ANSYS二次开发及应用实例详解[M]. 北京: 中国水利水电出版社, 2012: 121-126. SHI F. Secondary development of ANSYS and detailed application example[M]. Beijing: China Water Power Press, 2012: 121-126. (in Chinese) [12] 王勖成. 有限单元法[M]. 北京: 清华大学出版社, 2009: 576-579. WANG X C. Finite element method[M]. Beijing: Tsinghua University Press, 2009: 576-579. (in Chinese) [13] 袁立. 航空制造工程手册:飞机装配[M]. 北京: 航空工业出版社, 2010: 390-401. YUAN L. Handbook of aeronautical manufacturing engineering:Aircraft assembly[M]. Beijing: Aviation Industry Press, 2010: 390-401. (in Chinese) [14] 熊竣江. 飞行器结构疲劳与寿命设计[M]. 北京: 北京航空航天大学出版社, 2004: 85-111. XIONG J J. Structure fatigue and life design of aircraft[M]. Beijing: Beihang University Press, 2004: 85-111. (in Chinese) [15] 李艳, 于克杰, 李小雷. 铆钉材料对铆接变形影响的有限元分析[J]. 机床与液压, 2013, 41 (4): 50–52. LI Y, YU K J, LI X L. Finite element analysis for the influence of rivet materials on rivet deformation[J]. Machine Tool and Hydraulics, 2013, 41 (4): 50–52. DOI:10.3969/j.issn.1001-3881.2013.04.015 (in Chinese) [16] BARROIS W. Stresses and displacements due to load-transfer by fasteners instructural assemblies[J]. Engineering Fracture Mechanics, 1978, 10 (1): 115–176. DOI:10.1016/0013-7944(78)90055-3 [17] MCCARTHY M A, MCCARTHY C T, PADHI G S. A simple method for determining theeffects of bolt-hole clearance on load distribution in single-column, multi-bolt composite joints[J]. Composite Structures, 2006, 73 (1): 78–87. DOI:10.1016/j.compstruct.2005.01.028 [18] MCCARTHY C T, GRAY P J. An analytical model for the prediction of loaddistribution in highly torqued multi-bolt composite joints[J]. Composite Structures, 2011, 92 (2): 287–298. [19] 郑晓玲. 民机结构耐久性与损伤容限设计手册[M]. 北京: 航空工业出版社, 2003: 38-44. ZHENG X L. Handbook of civil aircraft structures durability and damage tolerance design[M]. Beijing: Aviation Industry Press, 2003: 38-44. (in Chinese) [20] 薛景川, 杨玉功. 紧固件载荷变形曲线的试验方法[M]. 西安: 飞机结构强度研究所, 1982: 22-26. XUE J C, YANG Y G. Test method for buckling deformation curve of fastener[M]. Xi'an: Aircraft Structure Strength Research Institute, 1982: 22-26. (in Chinese) [21] 薛景川, 杨玉功. 紧固件载荷变形曲线的工程确定方法[M]. 西安: 飞机结构强度研究所, 1984: 23-29. XUE J C, YANG Y G. Engineering determination method for buckling deformation curve of fastener[M]. Xi'an: Aircraft Structure Strength Research Institute, 1984: 23-29. (in Chinese) [22] 刘仁宇.某型飞机外翼下壁板连接件细节应力分析和疲劳性能研究[D].西安: 空军工程大学, 2008: 43-48. LIU R Y.Failure analysis for lap joint panel of an outer wing in fatigue test[D].Xi'an: Air Force Engineering University, 2008: 43-48(in Chinese).

#### 文章信息

ZHANG Tianyu, HE Yuting, CHEN Tao, DU Xu, TAN Xiangfei, LIU Kai

A fatigue life analysis method for multiple riveted joint

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(9): 1933-1940
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0689