# Effect of Riveting Angle and Direction on Fatigue Performance of Riveted Lap Joints

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Basic Pressure Riveting Model Simulation and Verification

- Stage 1: This stage starts from the contact between the punch and the rivet. As the displacement of the punch increases, the pressure riveting force gradually increases, the rivet begins to deform, and the shank is upset as a whole. When the nail bar touches the connecting hole, this stage ends. The first stage only involves the deformation of the rivet, as the pressure riveting force has not been transmitted to the riveting part and the riveting joint will naturally not be deformed by force.
- Stage 2: This stage starts from the contact between the rivet rod and the connecting hole. As the displacement of the punch increases, the contact area between the rivet rod and the inner wall of the connecting hole begins to increase. When the rivet rod is in full contact with the inner wall of the connecting hole, this stage ends. In the second stage, there is both the deformation of the rivet and the deformation of the connecting hole.
- Stage 3: The displacement of the punch continues to increase, and the tail of the rivet rod begins to be partially upset form the driven head and in contact with the surface of the connecting piece. Due to the friction in the contact area between the driven head and the connecting piece, the material flow changes. At the same time, the pressure transmits from the driven head to the connecting piece and causes the joint to begin to deform. When the punch moves to the specified position, the stage ends. In the third stage, the deformation and force of the riveting parts are the most complicated in the whole process. There is not only the pressure transmitted to the riveted joint through the hole circumference due to the expansion of the rivet in the connecting hole, but also the pressure generated by the driven head contacting the surface of the plate and the friction caused by extension of the driven head.
- Stage 4: The displacement of the punch begins to decrease and moves away from the riveted joint. During this process, the punch is still in contact with the rivet head, the rivet recovers elastically, and the pressure riveting force begins to gradually decrease. Finally, the punch and the rivet head are separated, and the pressure riveting process ends.

#### 2.1. Finite Element Model of Basic Pressure Riveting

- During the riveting process, the application of the force load and displacement load are completely continuous without interruption.
- The rivet and plates in the connector are isotropic homogeneous materials.
- The initial stress and volume force before riveting are both zero.
- The temperature during riveting is normal and constant.

_{true}) and strain (ε

_{true}) of the aluminum alloy in the plastic deformation stage satisfies

#### 2.2. Riveting Deformation and Stress Analysis of Basic Pressure Riveting Model

#### 2.3. Riveting Test Verification of Basic Pressure Riveting Model

## 3. Influence of Riveting Angle and Direction on Fatigue Performance

^{4}–10

^{5}[18]. The fatigue test in this paper is mainly to compare the fatigue performance of the riveted lap joint when the riveting parameters are different, and the structure of the joint is relatively simple, so the constant amplitude loading method was used.

#### 3.1. Riveting Deformation and Stress Analysis of Different Riveting Angles and Directions

#### 3.2. Experiment Design and Preparation

^{5}during fatigue failure. The stress level on the structural parts that undergo high-cycle fatigue failure is generally lower than the yield limit of the material, and some stress levels are even only about one third of its tensile strength. Low-cycle fatigue refers to fatigue in which the number of stress cycles is less than 10

^{4}to 10

^{5}during fatigue failure. The stress levels on the structural parts that undergo low-cycle fatigue failure are generally relatively high, usually close to or exceeding the yield limit of their materials.

#### 3.3. Fatigue Analysis of Riveted Joints

#### 3.3.1. Analysis of Fatigue Crack Initiation Location

#### 3.3.2. Analysis of the Influence of Riveting Angles on Fatigue Performance of Riveted Joints

#### 3.3.3. Analysis of the Influence of Riveting Direction on Fatigue Performance of Riveted Joints

#### 3.3.4. Analysis of High-Cycle Fatigue and Low-Cycle Fatigue of Riveted Joints

## 4. Discussion and Conclusions

- The change in the angle and direction of the punch downward affects the shape of the driven head directly. The contact area of the driven head and the connecting plates is no longer symmetrically distributed along the connecting hole (or rivet rod) axis, which also causes a stress concentration. The maximum residual stress of the riveted joint also increases, which reduces the fatigue life of the riveted joint.
- The residual tensile stress formed by the tensile load of joints is mainly concentrated on the surface area of the rivet head, and there is a certain degree of stress concentration, causing the fatigue cracks of the riveted part to occur on the surface of the side of the plate with the rivet head mainly.
- The riveting angle will have a great impact on the location of the fatigue crack and fatigue life of the riveted joint. As the riveting angle increases, the position of the fatigue crack on the riveted part moves from the middle of the connecting hole to the left, and the high-cycle fatigue life increases to a certain extent; in the riveting direction of 0°, the low-cycle fatigue life of the riveted joint first increases and then decreases as the riveting angle increases. In the riveting direction of 180°, the low-cycle fatigue life of the riveted joint increases with the increase in the riveting angle.
- The location of fatigue cracks and fatigue life of the riveted joint are closely related to the riveting direction. The crack occurrence position of the riveted connector in the 180° direction is shifted to the right from that of the riveted joint in the 0° direction. The high-cycle fatigue life and low-cycle fatigue life of the riveted joint in the 0° direction are both longer than those in the 180° direction.
- The fatigue performance of each component of the riveted joint is different. The low-cycle fatigue performance of the plate is better than the rivet but the high-cycle fatigue performance of the plate is not as good as the rivet.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Gagg, C.R.; Lewis, P.R. In-Service Fatigue Failure of Engineered Products and Structures—Case Study Review. Eng. Fail. Anal.
**2009**, 16, 1775–1793. [Google Scholar] [CrossRef] - Li, G.; Shi, G.; Bellinger, N.C. Residual Stress/Strain in Three-Row, Countersunk, Riveted Lap Joints. J. Aircr.
**2007**, 44, 1275–1285. [Google Scholar] [CrossRef] - Li, G.; Shi, G.; Bellinger, N.C. Studies of Residual Stress in Single-Row Countersunk Riveted Lap Joints. J. Aircr.
**2006**, 43, 592–599. [Google Scholar] [CrossRef] - Bedair, O. Stress Field Characteristics of Eccentrically Loaded Aircraft Spliced Joints. Appl. Math. Model.
**2012**, 36, 4543–4556. [Google Scholar] [CrossRef] - Skorupa, M.; Skorupa, A.; Machniewicz, T.; Korbel, A. Effect of Production Variables On the Fatigue Behaviour of Riveted Lap Joints. Int. J. Fatigue
**2010**, 32, 996–1003. [Google Scholar] [CrossRef] - Naarayan, S.S.; Kumar, D.M.G.P.; Chandra, S. Implication of Unequal Rivet Load Distribution in the Failures and Damage Tolerant Design of Metal and Composite Civil Aircraft Riveted Lap Joints. Eng. Fail. Anal.
**2009**, 16, 2255–2273. [Google Scholar] [CrossRef] - Huang, W.; Wang, T.; Garbatov, Y.; Guedes Soares, C. Fatigue Reliability Assessment of Riveted Lap Joint of Aircraft Structures. Int. J. Fatigue
**2012**, 43, 54–61. [Google Scholar] [CrossRef] - Liao, M.; Shi, G.; Xiong, Y. Analytical Methodology for Predicting Fatigue Life Distribution of Fuselage Splices. Int. J. Fatigue
**2001**, 23S, S177–S185. [Google Scholar] [CrossRef] - Aman, F.; Cheraghi, S.H.; Krishnan, K.K.; Lankarani, H. Study of the Impact of Riveting Sequence, Rivet Pitch, and Gap Between Sheets On the Quality of Riveted Lap Joints Using Finite Element Method. Int. J. Adv. Manuf. Tech.
**2013**, 67, 545–562. [Google Scholar] [CrossRef] - Atre, A.; Johnson, W.S. Effect of Interference On the Mechanics of Load Transfer in Aircraft Fuselage Lap Joints. J. Eng. Mater.-T. Asme
**2007**, 129, 356–366. [Google Scholar] [CrossRef] - Cheraghi, S.H. Effect of Variations in the Riveting Process On the Quality of Riveted Joints. Int. J. Adv. Manuf. Tech.
**2008**, 39, 1144–1155. [Google Scholar] [CrossRef] - Manes, A.; Giglio, M.; Vigano, F. Effect of Riveting Process Parameters On the Local Stress Field of a T-Joint. Int. J. Mech. Sci.
**2011**, 53, 1039–1049. [Google Scholar] [CrossRef] - Liu, J.; Li, H.; Bi, Y.; Dong, H.; Ke, Y. Influence of the Deformation of Riveting-Side Working Head On Riveting Quality. Int. J. Adv. Manuf. Tech.
**2019**, 102, 4137–4151. [Google Scholar] [CrossRef] - Liu, J.; Zhao, A.; Ke, Z.; Zhu, Z.; Bi, Y. Influence of Rivet Diameter and Pitch On the Fatigue Performance of Riveted Lap Joints Based On Stress Distribution Analysis. Materials
**2020**, 13, 3625. [Google Scholar] [CrossRef] [PubMed] - Nowell, D.; Hills, D.A. Crack Initiation Criteria in Fretting Fatigue. Wear
**1990**, 136, 329–343. [Google Scholar] [CrossRef] - Yuan, X.; Yue, Z.F.; Yan, W.Z.; Wen, S.F.; Li, L. Experimental and Analytical Investigation of Fatigue and Fracture Behaviors for Scarfed Lap Riveted Joints with Different Lap Angle. Eng. Fail. Anal.
**2013**, 33, 505–516. [Google Scholar] [CrossRef] - Szolwinski, M.P.; Farris, T.N. Linking Riveting Process Parameters to the Fatigue Performance of Riveted Aircraft Structures. J. Aircraft
**2000**, 37, 130–137. [Google Scholar] [CrossRef] - Urban, M.R. Analysis of the Fatigue Life of Riveted Sheet Metal Helicopter Airframe Joints. Int. J. Fatigue
**2003**, 25, 1013–1026. [Google Scholar] [CrossRef] - Szymczyk, E.; Jachimowicz, J.; Slawinski, G.; Derewonko, A. Influence of Technological Imperfections on Residual Stress Fields in Riveted Joints. In Procedia Engineering; Chapter’ MESOMECHANICS; Korsunsky, A.M., Dini, D., Sih, G.C., Eds.; Elsevier: Amsterdam, The Netherlands, 2009; pp. 59–62. [Google Scholar]
- Lei, C.; Bi, Y.; Li, J.; Ke, Y. Effect of Riveting Parameters On the Quality of Riveted Aircraft Structures with Slug Rivet. Adv. Mech. Eng.
**2017**, 9, 168781401773471. [Google Scholar] [CrossRef]

**Figure 1.**Riveting deformation process: (

**a**) stage 1 of riveting process; (

**b**) stage 2 of riveting process; (

**c**) stage 3 of riveting process; (

**d**) stage 4 of riveting process.

**Figure 2.**Schematic diagram of riveted lap joint structure and size: (

**a**) the structure and size of the joint plate; (

**b**) the structure and size of the countersunk rivet.

**Figure 9.**Riveting force–displacement comparison curve obtained by finite element simulation and experiment.

**Figure 11.**Schematic diagram of the finite element model of different riveting angles and directions: (

**a**) 0-3: a pressure riveting model with the punch deflected by 3° under the direction of 0°; (

**b**) 180-3: a pressure riveting model with the punch deflected by 3° under the direction of 180°.

**Figure 12.**Simulation results of riveted parts after pressing riveting at different angles in the same direction (0°) (unit: MPa): (

**a**) the reference deformation and stress result of the punch at 0° when the punch is not deflected; (

**b**) the deformation and stress result of the punch pressing down at an angle of 3° in the direction of 0°; (

**c**) the deformation and stress result of the punch pressing down at an angle of 3° in the direction of 180°.

**Figure 13.**Simulation results of riveted piece after transverse stretching: (

**a**) the reference deformation and stress result of the punch at 0° when the punch is not deflected (0-0); (

**b**) the deformation and stress result of the punch pressing down at an angle of 3° in the direction of 0° (0-3); (

**c**) the deformation and stress result of the punch pressing down at an angle of 3° in the direction of 180° (180-3).

**Figure 15.**High-cycle and low-cycle fatigue test results of riveted lap joints: (

**a**) plate fractures with high-cycle fatigue failure; (

**b**) rivet fracture with low-cycle fatigue failure.

**Figure 16.**Fatigue fracture section of riveted lap joint: (

**a**) fatigue fracture section of 0° standard part (0-0); (

**b**) fatigue fracture section of riveted lap joint with 1° in the 0° direction (0-1); (

**c**) fatigue fracture section of riveted lap joint with 1° in the 180° direction (180-1).

**Figure 17.**Distribution diagram of maximum principal stress around the hole of riveted parts (unit: MPa): (

**a**) distribution of maximum principal stress of 0° standard part (0-0); (

**b**) distribution of maximum principal stress of riveted parts of 1° in the 0° direction (0-1); (

**c**) distribution of maximum principal stress of riveted parts of 1° in the 180° direction (180-1).

**Figure 18.**Fatigue failure morphology of riveted lap joints at different riveting angles: (

**a**) fatigue failure morphology of 0° standard part (0-0); (

**b**) fatigue failure morphology of riveted joints of 1° in the 0° direction (0-1); (

**c**) fatigue failure morphology of riveted joints of 2° in the 0° direction (0-2).

**Figure 19.**Distribution diagram of maximum principal stress of riveted joints of different riveting angles (unit: MPa): (

**a**) distribution of maximum principal stress of 0° standard part (0-0); (

**b**) distribution of maximum principal stress of riveted parts of 1° in the 0° direction (0-1); (

**c**) distribution of maximum principal stress of 2° in the 0° direction (0-2).

**Figure 20.**Fatigue failure morphology of riveted lap joints in different riveting directions: (

**a**) fatigue failure morphology of riveted joints of 1° in the 0° direction (0-1); (

**b**) fatigue failure morphology of riveted joints of 1° in the 180° direction (180-1); (

**c**) fatigue failure morphology of riveted joints of 2° in the 0° direction (0-2); (

**d**) fatigue failure morphology of riveted joints of 2° in the 180° direction (180-2).

**Figure 21.**Distribution diagram of maximum principal stress of riveted joints in different riveting directions (unit: MPa): (

**a**) distribution of maximum principal stress of riveted joints of 1° in the 0° direction (0-1); (

**b**) distribution of maximum principal stress of riveted joints of 1° in the 180° direction (180-1); (

**c**) distribution of maximum principal stress of 2° in the 0° direction (0-2); (

**d**) distribution of maximum principal stress of 2° in the 180° direction (180-2).

**Figure 22.**High-cycle fatigue failure and low-cycle fatigue failure of riveted joints of different riveting angles: (

**a**) comparison of high-cycle fatigue and low-cycle fatigue failures of 0° standard part (0-0); (

**b**) comparison of high-cycle fatigue and low-cycle fatigue failures of riveted parts of 1° in the 0° direction (0-1); (

**c**) comparison of high-cycle fatigue and low-cycle fatigue failures of riveted parts of 2° in the 0° direction (0-2).

**Figure 23.**Stress distribution diagram of rivet under shearing force (unit: MPa): (

**a**) stress distribution of rivet of 0° standard part (0-0); (

**b**) stress distribution of rivet of joints of 1° in the 0° direction (0-1); (

**c**) stress distribution of rivet of joints of 2° in the 0° direction (0-2); (

**d**) stress distribution of rivet of joints of 1° in the 180° direction (180-1); (

**e**) stress distribution of rivet of joints of 2° in the 180° direction (180-2).

Material Parameter | 2117-T4 Aluminum Alloy Rivets |
---|---|

Density, ρ | 2830 Kg/m^{3} |

Young’s modulus, E | 74 GPa |

Poisson’s ratio, ν | 0.33 |

Yield stress, σ_{S} | 172 MPa |

Strength coefficient, C ^{1}(0.02 ≤ ε_{true} ≤ 0.10) | 544 MPa |

Strength coefficient, C ^{1}(0.10 ≤ ε_{true} ≤ 1.0) | 551 MPa |

Hardening exponent, m ^{1}(0.02 ≤ ε_{true} ≤ 0.10) | 0.23 |

Hardening exponent, m ^{1}(0.10 ≤ ε_{true} ≤ 1.0) | 0.15 |

^{1}The parameters C and m satisfy the above Formula (1).

Material Parameter | 7050 Aluminum Alloy Rivets |
---|---|

Density, ρ | 2690 Kg/m^{3} |

Young’s modulus, E | 71.7 GPa |

Poisson’s ratio, ν | 0.33 |

Yield stress, σ_{S} | 310 MPa |

Strength coefficient, C ^{1}(ε_{y} ≤ ε_{true} ≤ 0.02) | 676 MPa |

Strength coefficient, C ^{1}(0.02 ≤ ε_{true} ≤ 0.1) | 745 MPa |

Hardening exponent, m ^{1}(ε_{y} ≤ ε_{true} ≤ 0.02) | 0.14 |

Hardening exponent, m ^{1}(0.02 ≤ ε_{true} ≤ 0.1) | 0.164 |

^{1}The parameters C and m satisfy the above Formula (1).

Parameters | Data |
---|---|

Diameter of driven head from simulation | 7.843 mm |

Diameter of driven head from test | 8.021 mm |

Driven head diameter difference | 0.178 mm |

Deviation | 2.2% |

Riveting Angle | 0° | 1° | 2° |
---|---|---|---|

High-cycle fatigue life (cycle) | 163,793 | 212,862 | 144,572 |

Low-cycle fatigue life (cycle) | 11,212 | 13,039 | 14,161 |

Riveting Directions | 0° | 1° | 2° |
---|---|---|---|

High-cycle fatigue life of 0° direction (cycle) | 163,793 | 212,862 | 144,572 |

High-cycle fatigue life of 180° direction (cycle) | 131,878 | 87,141 |

Riveting Angles | 0° | 1° | 2° |
---|---|---|---|

Low-cycle fatigue life of 0° direction (cycle) | 11,212 | 13,039 | 14,161 |

Low-cycle fatigue life of 180° direction (cycle) | 10,469 | 13,453 |

Riveting Angles | 0° | 1° | 2° |
---|---|---|---|

Maximum shear stress of 0° direction (MPa) | 616.4 | 602.4 | 588.1 |

Maximum shear stress of 180° direction (MPa) | 625.3 | 631.4 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liang, Q.; Zhang, T.; Zhu, C.; Bi, Y.
Effect of Riveting Angle and Direction on Fatigue Performance of Riveted Lap Joints. *Coatings* **2021**, *11*, 236.
https://doi.org/10.3390/coatings11020236

**AMA Style**

Liang Q, Zhang T, Zhu C, Bi Y.
Effect of Riveting Angle and Direction on Fatigue Performance of Riveted Lap Joints. *Coatings*. 2021; 11(2):236.
https://doi.org/10.3390/coatings11020236

**Chicago/Turabian Style**

Liang, Qingxiao, Tianpeng Zhang, Chunrun Zhu, and Yunbo Bi.
2021. "Effect of Riveting Angle and Direction on Fatigue Performance of Riveted Lap Joints" *Coatings* 11, no. 2: 236.
https://doi.org/10.3390/coatings11020236