Geometric and Material Modelling Aspects for Strength Prediction of Riveted Joints
Abstract
:1. Introduction
2. Experiments on Riveted Joints
2.1. Rivet Joint Configuration
2.2. Experimental Results
2.3. Plate and Rivet Material
3. Finite Element Modelling
3.1. Material Model
3.2. Contact Interaction and Boundary Conditions
3.3. Pre-Load in Rivets
4. Validation of FEA Modelling Framework
5. Application to Industrial Component
5.1. Results of Joining Methods
5.2. Re-Design of the Riveted Joint
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
c | Configuration of plates |
d | Rivet shank diameter |
dmat | Damage in material |
E | Young’s modulus |
E’ | Diminished Young’s modulus |
Fu | Ultimate strength |
Fe | Conventional elastic strength |
Fmax | Force equal to 80% of the ultimate strength after the peak load |
lb | Bottom rivet head height |
le | Characteristic length |
lg | Gauge length |
ls | Rivet shank length |
lt | Top rivet head height |
n | Number of rivets |
N | Hardening exponent |
p | Pitch between rivets |
r | Rivet distance from plate edge |
SN | Specimen number |
t | Plate thickness |
upl | Plastic equivalent displacement |
ufpl | Plastic equivalent displacement at fracture |
w | Plate width |
α | Rivet head angle |
δ | Displacement |
δu | Displacement corresponding to ultimate strength |
δe | Displacement corresponding to elastic strength |
δmax | Displacement corresponding to force equal to 80% of ultimate strength |
Δ | Displacement-controlled loading |
ε | Strain |
ε0 | Initial yield strain |
εN | Normalizing strain |
εS | Offset strain |
Strain rate | |
Equivalent plastic strain at onset of fracture | |
σ0 | Yield strength |
σFEA | Pressure applied on rivet heads |
σut | Ultimate strength |
Experimental true stress following softening response | |
ξ | Normalized length of rivet shank |
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Specimen Number | Specimen from [27] | c (-) | d (mm) | t (mm) | w (mm) | r (mm) | p (mm) | n (-) |
---|---|---|---|---|---|---|---|---|
SN-1 | S-16-10-1 | Symmetric | 16 | 10 | 70 | 35 | - | 1 |
SN-2 | U-16-10-1 | Unsymmetric | 16 | 10 | 70 | 35 | - | 1 |
SN-3 | S-19-10-1 | Symmetric | 19 | 10 | 90 | 45 | - | 1 |
SN-4 | U-19-10-1 | Unsymmetric | 19 | 10 | 90 | 45 | - | 1 |
SN-5 | U-19-12-1 | Unsymmetric | 19 | 12 | 90 | 45 | - | 1 |
SN-6 | S-22-12-1 | Symmetric | 22 | 12 | 70 | 35 | - | 1 |
SN-7 | S-19-10-2 | Symmetric | 19 | 10 | 90 | 45 | 120 | 2 |
SN-8 | U-22-12-2 | Unsymmetric | 22 | 12 | 70 | 35 | 90 | 2 |
SN-9 | S-22-12-4 | Symmetric | 22 | 12 | 70 | 35 | 90 | 4 |
Plate No. | (MPa) | (-) | (mm/mm) | (mm/mm) | (MPa) | (mm/mm) |
1 | 303 | 0.208 | 0.008 | 0.012 | 523 | 0.17 |
2 | 294 | 0.214 | 0.008 | 0.012 | 514 | 0.17 |
3 | 302 | 0.217 | 0.008 | 0.014 | 509 | 0.17 |
4 | 302 | 0.216 | 0.008 | 0.014 | 510 | 0.17 |
Average | 300 | 0.214 | 0.008 | 0.013 | 514 | 0.17 |
Std. Dev. (±) | 4 | 0.003 | 0 | 0.001 | 6 | 0 |
Rivet No. | (MPa) | (-) | (mm/mm) | (mm/mm) | (MPa) | (mm/mm) |
1 | 271 | 0.160 | 0.000 | 0.006 | 478 | 0.18 |
2 | 308 | 0.245 | 0.008 | 0.020 | 500 | 0.13 |
3 | 316 | 0.180 | 0.008 | 0.020 | 471 | 0.16 |
4 | 335 | 0.116 | 0.008 | 0.010 | 438 | 0.13 |
5 | 325 | 0.150 | 0.008 | 0.005 | 495 | 0.09 |
6 | 352 | 0.085 | 0.000 | 0.002 | 471 | 0.06 |
7 | 343 | 0.114 | 0.008 | 0.004 | 515 | 0.14 |
8 | 347 | 0.118 | 0.008 | 0.011 | 474 | 0.10 |
9 | 325 | 0.187 | 0.008 | 0.023 | 479 | 0.20 |
Average | 325 | 0.151 | 0.007 | 0.011 | 480 | 0.13 |
Std. Dev. (±) | 23 | 0.046 | 0.003 | 0.008 | 21 | 0.04 |
Case | Analysis (1) | Fe (kN) | δe (mm) | Fu (kN) | δu (mm) | δmax (mm) | Fmax (kN) | Failure Mode |
---|---|---|---|---|---|---|---|---|
SN-1 | Experiment A | 107.01 | 0.39 | 146.08 | 5.51 | 7.00 | 116.86 | Shear failure of rivet |
Experiment B | 109.22 | 0.43 | 147.99 | 6.26 | 7.59 | 118.39 | ||
Experiment C | 90.06 | 0.35 | 131.43 | 3.90 | 5.34 | 105.14 | ||
Simulation | 109.29 | 0.12 | 143.66 | 5.10 | 6.29 | 114.93 | Shear failure of rivet | |
SN-2 | Experiment A | 66.94 | 0.41 | 80.02 | 2.50 | 3.39 | 64.02 | Shear failure of rivet |
Experiment B | 64.41 | 0.42 | 83.95 | 3.83 | 4.36 | 67.16 | ||
Experiment C | 62.30 | 0.45 | 76.71 | 3.06 | 3.91 | 61.39 | ||
Simulation | 66.29 | 0.34 | 79.92 | 3.02 | 4.22 | 63.94 | Shear failure of rivet | |
SN-3 | Experiment A | 136.01 | 0.46 | 180.45 | 5.80 | 11.17 | 144.36 | Bearing of plate at rivet hole |
Experiment B | 141.70 | 0.46 | 232.35 | 12.08 | 14.80 | 185.88 | ||
Experiment C | 130.02 | 0.53 | 207.12 | 10.10 | 11.40 | 165.70 | ||
Simulation | 152.64 | 0.14 | 204.83 | 10.39 | 11.59 | 163.86 | Bearing of plate at rivet hole | |
SN-4 | Experiment A | 47.36 | 0.43 | 86.99 | 3.04 | 3.85 | 69.59 | Shear failure of rivet |
Experiment B | 95.34 | 0.46 | 108.93 | 2.85 | 3.68 | 87.14 | ||
Experiment C | 64.00 | 0.47 | 108.52 | 5.12 | 6.04 | 86.82 | ||
Simulation | 88.03 | 0.34 | 107.70 | 3.09 | 4.33 | 86.16 | Shear failure of rivet | |
SN-5 | Experiment A | 60.07 | 0.41 | 100.63 | 3.65 | 4.15 | 80.50 | Shear failure of rivet |
Experiment B | 87.37 | 0.61 | 145.28 | 5.55 | 6.57 | 116.22 | ||
Experiment C | 73.36 | 0.80 | 106.84 | 3.81 | 4.72 | 85.47 | ||
Simulation | 87.64 | 0.30 | 107.23 | 2.87 | 4.07 | 85.78 | Shear failure of rivet | |
SN-6 | Experiment A | 156.72 | 0.48 | 236.18 | 4.32 | 6.11 | 188.94 | Bearing of plate at rivet hole |
Experiment B | 153.36 | 0.56 | 238.23 | 6.02 | 10.05 | 190.58 | ||
Simulation | 155.64 | 0.18 | 207.66 | 8.10 | 9.97 | 166.13 | Bearing of plate at rivet hole | |
SN-7 | Experiment A | 236.69 | 0.84 | 336.63 | 14.24 | 16.80 | 269.30 | Tearing of plate net section |
Experiment B | 240.71 | 0.60 | 346.02 | 16.27 | 18.75 | 276.82 | ||
Experiment C | 230.69 | 0.63 | 332.60 | 10.46 | 13.45 | 266.08 | ||
Simulation | 268.47 | 0.38 | 371.89 | 12.66 | 14.56 | 297.51 | Tearing of plate net section | |
SN-8 | Experiment A | 170.02 | 1.60 | 279.05 | 10.46 | 11.63 | 223.24 | Tearing of plate net section |
Experiment B | 184.03 | 1.63 | 255.24 | 8.88 | 10.13 | 204.19 | ||
Experiment C | 170.72 | 1.64 | 280.77 | 11.60 | 13.49 | 224.62 | ||
Simulation | 236.87 | 2.82 | 285.03 | 12.43 | 12.63 | 228.02 | Tearing of plate net section | |
SN-9 | Experiment A | 249.26 | 0.75 | 308.94 | 9.76 | 12.17 | 247.15 | Tearing of plate net section |
Experiment B | 250.06 | 0.85 | 298.54 | 9.76 | 12.00 | 238.83 | ||
Experiment C | 247.68 | 0.66 | 303.50 | 7.24 | 8.95 | 242.80 | ||
Simulation | 296.25 | 1.59 | 306.35 | 6.96 | 8.72 | 245.08 | Tearing of plate net section |
Steel Grade | (MPa) | (-) | (mm/mm) |
---|---|---|---|
S600MC | 600 | 0.096 | 0.130 |
S900MC | 997 | 0.095 | 0.016 |
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Lundkvist, A.; Barsoum, I.; Barsoum, Z.; Khurshid, M. Geometric and Material Modelling Aspects for Strength Prediction of Riveted Joints. Metals 2023, 13, 500. https://doi.org/10.3390/met13030500
Lundkvist A, Barsoum I, Barsoum Z, Khurshid M. Geometric and Material Modelling Aspects for Strength Prediction of Riveted Joints. Metals. 2023; 13(3):500. https://doi.org/10.3390/met13030500
Chicago/Turabian StyleLundkvist, Axel, Imad Barsoum, Zuheir Barsoum, and Mansoor Khurshid. 2023. "Geometric and Material Modelling Aspects for Strength Prediction of Riveted Joints" Metals 13, no. 3: 500. https://doi.org/10.3390/met13030500