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Fatigue response of electromagnetic riveted joints with different rivet dies subjected to pull-out loading
International Journal of Fatigue 129 (2019) 105238
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue response of electromagnetic riveted joints with different rivet dies subjected to pull-out loading Hao Jianga, Yanjun Conga, Jinsheng Zhangb, Xianhe Wub, Guangyao Lia, Junjia Cuia, a b
T
⁎
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China Chongqing Changan Automobile Co. Ltd, Chongqing 401120, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Electromagnetic riveting Rivet die Fatigue behavior Pull-out loading
Electromagnetic riveting (EMR) as a green manufacturing and efficient process has extensive application prospect in engineering fields. In this study, the fatigue properties of electromagnetic riveted joints with different rivet dies under pull-out loading were studied. The results showed that rivet dies had a significant effect on the pull-out fatigue performance. The pull-out fatigue life of the electromagnetic riveted joints with special dies was higher than that with the flat die. The reason was that the special rivet dies restricted the radial flow of the material in driven head. More material flowed into the riveted hole and rivet shaft became larger. The joints were reinforced by larger interference fit. Particularly, the joints with 80° rivet die had the best pull-out fatigue properties due to more uniform and moderate interference fit. Fracture analysis showed that there were two typical failure modes for the joints under pull-out loading: rivet manufactured head and upper sheet fracture. Due to the effect of cyclic impact and fretting wear damage, the joints with a flat die at high stress levels (194.8 MPa and 173.2 MPa) failed in rivet manufactured head, while the joints with special dies at all stress levels and with a flat die at low stress levels (151.5 MPa and 129.87 MPa) failed in upper sheet.
1. Introduction Using lightweight material is one of the most effective ways to realize energy conservation and emission reduction of automobile and airplane [1–4]. Aluminum (Al) alloy has been becoming a primary choice of lightweight material due to its good characteristics. Usually, the auto body and fuselage consist of many aluminum parts. However, traditional joining technologies (e.g. bolting, riveting and bonding) are hard to connect them well. The bolt joint loosens easily. The adhesive joint is liable to brittle fracture. The regular riveted joint has non-uniform interference and is easy to produce stress concentration. Electromagnetic riveting (EMR) as an advanced manufacturing process, can assembly Al alloy structures efficiently, and produces firm joints [5–7]. Compared with conventional riveting, EMR technique has the characteristics of large riveting force, fast riveting speed, no pollution and high efficiency [8]. Moreover, Cao et al. [9] found that the EMR joints had more uniform interference fit due to the effect of stress wave. Li et al. [10] further proved that the mechanical properties of EMR joints usually performed better than conventional riveted joints. Due to its great advantages and application prospect, many researchers were further studied the effects of EMR process parameter and rivet die on the joints performance [11–16]. Jiang et al. [11] found
⁎
that the discharge energies directly affected the rivet driven heads’ deformation, which further influenced joints’ mechanical properties and fatigue properties. Specifically, the results showed that the driven head with larger deformation has a tighter interference fit, and a proper interference could effectively improve the shear fatigue properties. As for fatigue properties on the shear direction, the fatigue life of the joints increased first and then decreased with the increase of the driven heads’ deformation. In addition, adiabatic shearing deformation usually occurred in the driven head during EMR, and adiabatic shear bands (ASBs) were formed along the diagonal direction of the driven head [12]. As a crucial feature of EMR, ASBs could affect not only the microstructure of the driven head, but also the joints strength. Deng et al. [13] reported that the ASBs deformed more seriously with the increase of discharge energy. Higher discharge energy generated higher strain rate, and the high strain rate would induce the precipitation hardening in ASBs, which easily led to cracks in the driven head [14]. Accordingly, Reinhall et al. [15] designed a special rivet die with an angle to control the formation of the cracks. The results showed that the joints with a special rivet die could effectively reduce the maximum shear stress and impede the crack expansion. Recently, Cui et al. [16] comprehensively investigated the influence of the rivet die constructions on the mechanical and microscopic properties using the experimental and
Corresponding author. E-mail address: [email protected] (J. Cui).
https://doi.org/10.1016/j.ijfatigue.2019.105238 Received 11 April 2019; Received in revised form 11 August 2019; Accepted 19 August 2019 Available online 20 August 2019 0142-1123/ © 2019 Elsevier Ltd. All rights reserved.
International Journal of Fatigue 129 (2019) 105238
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2.2. Electromagnetic riveting process
numerical methods. They also found that the special rivet dies could obviously enhance the pull-out properties of the EMR joints and inhibit the formation of ASBs. Abovementioned studies mainly focused on mechanical properties, fatigue performance in shear direction and microscopic properties of EMR joints. However, in practical application, the joints are not only subjected to the shear loading, but also to the pull-out loading [17–19]. Especially in the actual service of automobile and aircraft, the joints were affected by different working conditions for a long time. So the fatigue performance of the joint in pull out direction was particularly significant [20]. Moreover, in literatures, Nguyen et al. [21] and Choi et al. [22] respectively found that when the pin and riveted joints were subjected to loads in different directions, theirs failure behaviors performed different. While previous studies on the fatigue behaviors of EMR joints in the pull-out direction are not systematic, especially the pull-out fatigue performance with a special rivet die. It is of great significance for the using of special rivet dies in automotive and aircraft manufacturing and assembly. This paper is aimed to investigate the pull-out fatigue properties of the electromagnetic riveted joints with different rivet dies. Firstly, EMR experiments with different rivet dies were carried out to obtain the test specimens. Subsequently, the interference sizes measurements, joint cross-section observations and hardness measurements were conducted to analyze the joint strength. Meanwhile, the pull-out fatigue tests were performed with designed fixture to obtain the fatigue performance. Finally, the fatigue failure modes were analyzed.
Fig. 2 shows the schematic of the EMR process. It mainly consists of a magnetic pulse generator and riveting mold. The magnetic pulse generator is in the charge of providing the energy, and the discharge energy saves in the capacitors. Specifically, when the power switch is closed, the capacitance completes charging quickly. Then, closing the discharge switch, alternating current is flowing into the coil, and a strong magnetic field is produced around it. The strong magnetic field makes driver plate generate an induced current, which generates a reversed magnetic field. The eddy current repulsive force generated by the two magnetic fields drives the amplifier strike the rivet, which leads to plastic deformation of the rivet in a short time. In the riveting process, the rivet die has a significant effect on the deformation of the driven head, which would further affect the joint performance [23]. After referring to previous studies [14–15,24], three special rivet dies (sidewall intersection angles of 40°, 60° and 80°) and one universal flat die were designed. The specific geometry dimensions and physical maps of different rivet dies are described in Fig. 3. In addition, based on the previous study [11], the discharge energy of 5.0 kJ for flat die could obtain better joint quality. Therefore, to avoid the effect of discharge energy on joint performance, all EMR experiments were performed with discharge energy of 5.0 kJ. Fig. 4 shows the typical pull-out fatigue test specimens with different rivet dies after EMR. 2.3. Mechanical property test and micro-structure observations
2. Experimental materials and methods
The pull-out fatigue tests employed with Instron 8801 servo hydraulic fatigue test machine as shown in Fig. 5. The cyclic stress in the fatigue tests was a sine curve. The frequency was 20 Hz/s and the stress ratio was 0.1. Based on the pull-out quasi-static tests, maximum cyclic stresses selected in the paper were 194.8 MPa, 173.2 MPa, 151.5 MPa and 129.8 MPa, respectively. Besides, three replicate tests were performed at each stress levels for each rivet die to ensure the credibility of the results. After the EMR, the samples were firstly cut with a metallographic cutter. Then samples were prepared in an epoxy mount and polished with an automatic polishing machine, and finally corroded with Keller corrosion fluid. The relative interference of four different pier heads were obtained and hardness values were got with a Tukon-1102 micro hardness tester, whose pressing load was set to 0.3 kg and pressure was maintained for 15 s. The pull-out fatigue fracture were observed by FEI QuANTA200 scanning electron microscope.
2.1. Sample preparation In this study, 6082 T6 Al sheets and 2A10 Al rivets were employed. As depicted in Fig. 1, the diameter of Al rivets and the thickness of Al sheets were 5 mm and 4 mm, respectively. According to the QJ-782A2005 riveting standard, the diameter of prefabricated hole in the Al sheets and the length of rivet shaft was set to 5.1 mm and 14.0 mm, respectively. In order to obtain the precise dimensions, the riveted sheets were manufactured by wire cutting. Besides, the surfaces of Al rivet were treated with chemical conversion, and Al sheets were cold rolled to increase the hardness and strength. Specifically, material properties of Al 6082 T6 and Al 2A10 are presented in Table 1.
3. Results and discussions 3.1. Interference analysis According to the previous studies [25,26], interference size of the riveted joints had significant influence on fatigue properties. So the diameters of rivet shaft after EMR were measured by vernier caliper with an accuracy of 0.01 mm. In order to reduce the measurement deviations, each position was measured three times at intervals of 120°. The relative interference (I) was calculated by following Eq. (1):
I = [(D − D0)/ D0] × 100%
(1)
where D and D0 are the diameters of deformed rivet shaft and original hole. Table 2 and Fig. 6 show the measured results and the interference sizes of the electromagnetic riveted joints for different rivet dies. It could be seen that the interference values reduced from position 1 to position 3 for all samples. Compared with the interferences of special head, the interference of flat head was minimal at all positions. Especially the 40° deformed head had the largest interference at position 1, with up to 5.431%. While the flat deformed head at the position 3 had the smallest interference value, which was only 0.784%. At the position
Fig. 1. Specimen geometry for pull-out fatigue tests (dimension in mm). 2
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Table 1 Material properties of Al 6082 T6 and Al 2A10. Properties 3
Density (g/cm ) Poisson ratio Tensile modulus (GPa) Yield strength (MPa) Tensile strength (MPa) Chemical composition (%)
Al 6082 T6 sheet
Al 2A10 rivet
2.7 0.32 67.2 240 325 Zn = 0.03, Si = 0.97, Fe = 0.37, Mn = 0.67, Mg = 1.02, Ti = 0.01, Cu = 0.07, Al = balance
2.7 0.33 73.8 250 400 Si = 0.25, Fe = 0.2, Cu = 3.9–4.5, Mn = 0.3–0.5, Mg = 0.15–0.30, Zn = 0.1, Ti = 0.15, Al = balance
1, it could be found that the interference value substantially decreased as the angle of the riveting die increased. This was due to the constant volume principle. The special rivet dies could limit the rivet material flow and squeeze more material into the riveted hole. Moreover, as the angle of the rivet dies decreased, the volume of the rivet cavity decreased, causing more material will be squeezed into the hole, so as to make the joints with small angle rivet die have higher interference.
3.2. Metallographic structure and hardness analysis Fig. 7 presents the micro-structures of the riveted joints in the driven head with different rivet dies, which are composed of a number of metallographic photographs. It could be seen that no cracks were found in the driven head for all types of joints. However, for the joints with flat die, grains were highly deformed after EMR and the adiabatic shear bands (ASBs) were more obvious than other rivet dies. This indicated that the rivet die with sidewall intersection angles could suppress the forming of ASBs, which could further prevent inducing cracks. Fig. 8 shows the hardness distribution of the driven head with different rivet dies. Note that the original hardness value of the rivets was around 113 HV. In Fig. 8(a), the peak of the curve appeared at position 3 (about 1–1.5 mm from the upper surface of the head) for the flat head. While for the 40°, 60° and 80° formed heads, with the constraint of the rivet die, the material deformation in the cavity were not as strong as the corresponding position in the flat head. Therefore, the peaks of the curves appeared at position 6 (about 2–2.5 mm from the upper surface of the heads). It showed that the serious microstructure deformation in
Fig. 2. The schematic of EMR: (a) electromagnetic setup; (b) riveting process.
Fig. 3. Geometry dimensions and physical maps of different dies. 3
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Fig. 4. The typical pull-out fatigue test specimens with different rivet dies.
different rivet dies. The fatigue data were fitted by the following power function [27]:
the driven heads made the material strengthening effect, resulting in an increase in hardness. The hardness distribution depicted in Fig. 8(a) and metallographic structure depicted in Fig. 7 in the formed heads were basically coincident. In Fig. 8(b), it could be seen that there were two hardness peaks (position 3 and 12) on the path for the flat head. The hardness values reached 175 HV and 162 HV, respectively. The positions of two peaks coincided with the two ASBs. This was due to the hardness peaks were induced by the strain hardening effect in the ASBs. In addition, there was only one peak in the 60° or 80° formed heads, which was consistent with the lower shear band. Moreover, due to the fine-grain strengthening effect, the hardness of the area above the lower shear band was also higher than that of the original material. For the 40° head, there was also only one peak with a large width on the hardness curve. The reason was that the distance between the two ASBs was relatively close. The material between the two ASBs was subjected to the radial compressive stress and circumferential tensile stress simultaneously, so that the hardness value increased to some extent. Besides, as the 40° rivet die had the smallest cavity volume, the material in the cavity was relatively difficult to deform. So the grain over ASBs deformed slightly, and the hardness values of the position 6–13 were relatively low.
SM = a (Nf )b
(2)
where SM and Nf represent the maximum cyclic stress and fatigue life, respectively. Fig. 9 shows the fitted curves of the fatigue results for the joints with different rivet dies. It could be clearly found that pull-out fatigue life of the joints with special rivet dies were almost higher than that of the flat die. Only at the low stress level (129.8 MPa), the fatigue life of the joints with 40° and flat dies were approximate. Besides, it could be seen that the joints with 80° rivet die have the best fatigue properties. Especially, the fatigue life of the joints with 80° rivet head were almost 2 times longer than that of other joints. This demonstrated that using special rivet dies in EMR could effectively improve the pullout fatigue life of joints. In particular, the 80° rivet die was the optimal. The reason was that the joints with special rivet dies had relatively higher interference fit comparing to the flat die. High interference on the one hand could make joint tighter. On the other hand, if the interference fit was excessive, the sheet extrusion deformation would be serious, which could easily lead to stress concentration [28]. According to the above interference measured results, the joints with 80° rivet die had more uniform and moderate interference fit (average value of 3.5%). It also proved that this interference value had better pull-out fatigue performance for riveted joints.
3.3. Pull-out fatigue life Table 3 presents the fatigue test data of the riveted joints with
Fig. 5. The fixture of pull-out fatigue tests. 4
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Table 2 Rivet diameters and interference of the joints for different rivet dies. Type
Position
Diameter 1 (mm)
Diameter 2 (mm)
Diameter 3 (mm)
Average value (mm)
Relative interference (%)
Flat head
1 2 3
5.21 5.17 5.13
5.18 5.17 5.14
5.20 5.19 5.15
5.197 5.177 5.140
1.902 1.510 0.784
40° head
1 2 3
5.40 5.24 5.20
5.36 5.24 5.20
5.37 5.25 5.19
5.377 5.243 5.197
5.431 2.804 1.902
60° head
1 2 3
5.33 5.26 5.19
5.31 5.26 5.20
5.32 5.27 5.21
5.320 5.263 5.200
4.314 3.196 1.961
80° head
1 2 3
5.26 5.22 5.17
5.27 5.22 5.18
5.27 5.22 5.18
5.267 5.220 5.177
3.275 2.353 1.510
40° head 60° head 80° head Flat head
Relative interference (%)
5 4 3
flat head suffered larger stresses and deformed more easily. Besides, the stress value gradually decreased from the riveted hole to the edge, and the stress around the rivet hole was much higher than other locations. This indicated that the stress concentration was most severe around position 1. Combined with the results of the interference fit, the position near the driven head had the largest interference amount, so the fretting wear degree would be the most serious in this position [31]. To compare the stress concentration degree of the joints with different dies in detail, the nominal stress was calculated from the average stress of the points in the Fig. 12. After calculation, the Kt value for pull out loading on the upper sheets with 40°, 60°, 80° and flat dies were obtained, which were respectively 2.75, 2.25, 1.90 and 1.96. The results showed that the Kt value of the joint with 80° die was smaller than that with other dies. It indicated that the use of 80° rivet die could reduce the stress concentration level of the sheet under pull out loading. This was also one of the reasons that the joints with 80° die had better fatigue properties. Fig. 13(a) shows the stress maps of the rivets with different formed heads under pull-out loading. It could be clearly seen that the stress near the driven head was greater than that of the manufacturing head. This was because the driven head occurred serious plastic deformation in the riveting process, while the manufacturing head was restricted by the die and had little deformation. This also proved that the driven head was enhanced to some extent compared with the manufacturing head. So the manufacturing head was more likely to break than the driven head [10]. Besides, to avoid the influence of riveting process on the stress analysis of rivets under pull-out loading, the stress values near the manufacturing head were obtained as shown in Fig. 13(b). It could be seen that the average stress of the joints with flat head near the manufacturing head was higher than that of other joints with special heads, indicating that the rivet with flat head suffered larger force when it was subjected to pull-out loading. So the rivet of the joints with flat head were prone to fracture compared to the joints with special heads.
1 mm Position 1 Position 2 Position 3
1 mm
2 1 0
1
2
3
Measured position Fig. 6. Comparison of interference sizes of electromagnet riveted joints for different rivet dies.
In addition, the predictive life was obtained by the above S-N curves. The relationship between predictive life and fatigue test life was showed in Fig. 10. It could be seen that the scatter points were all within 2 times distribution band. This indicated that the fitted curves in Fig. 9 could predict fatigue life of the joints accurately. In addition, in order to further assess the pull out fatigue properties, the stress concentration factors of the joints were analyzed [29,30]. The stress concentration factor (Kt) is defined as Eq. (3):
Kt =
σm σ0
(3)
where σm and σ0 are the maximum and nominal stresses, respectively. In this study, Kt values of the joints with different rivet dies were obtained by numerical simulation method. The simulation model was established in LS-DYNA commercial software. Fig. 11(a) and (b) show the numerical simulation model of EMR and loading case, respectively. Constant stress solid element and Automatic Surface to Surface contact law were employed. The material models of the sheets and rivet were the same as in Ref. [16]. The load state on the specimen was applied according to the actual conditions. The pull out force applied in this case was 3328 N. Fig. 12(a) and (b) show the stress maps of the sheets and the stress values at the specific positions under pull-out loading, respectively. It could be seen from the upper sheets that the maximum stress was found around the rivet hole, implying that this position was the most vulnerable in the upper sheets for all specimens. So the fatigue cracks were prone to initiate from the riveted holes. Furthermore, as shown in Fig. 12(b), the stress of the joint with flat head was much higher than that of the joint with special heads. This indicated that when the specimen was subjected to the pull-out loading, the sheets in joints with
3.4. Statistical analysis In order to obtain the fatigue life of the joints with high reliability, the statistical analysis were conducted using two-parameter Weibull distribution [32]. The probability density function f(t), corresponding cumulative distribution function F(t) and the reliability function R(t) were respectively defined as Eq. (4), Eq. (5) and Eq. (6):
f (t ) =
β⎛t ⎞ ⎜ ⎟ η ⎝η⎠
β−1
β
⎡ t ⎤ exp ⎢−⎛⎜ ⎞⎟ ⎥ η ⎣ ⎝ ⎠ ⎦
(4)
β
⎡ t ⎤ F (t ) = 1 − exp ⎢−⎜⎛ ⎟⎞ ⎥ η ⎣ ⎝ ⎠ ⎦ 5
(5)
International Journal of Fatigue 129 (2019) 105238
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Fig. 7. The micro-structures of the riveted joints in the driven head with different rivet dies. β
⎡ t ⎤ R (t ) = exp ⎢−⎛⎜ ⎞⎟ ⎥ η ⎣ ⎝ ⎠ ⎦
standard deviation (SD) were derived by following Eq. (8) and Eq. (9), respectively.
(6)
where β is the shape parameter, η is the scale parameter, and t is the random variable value. Based on the Eq. (6), the following Eq. (7) was derived as:
lnln
1 = βln (t ) − βlnη R (t )
E (T ) =
170
Vickers hardness (HV0.3)
Vickers hardness (HV)
(b)
160 150 140 130 Flat 40° 60° 80°
110 100 90
1
2
3
4
5
head head head head
6
7
8
1 tf (t ) dt = ηΓ ⎜⎛1 + ⎞⎟ β⎠ ⎝
(8)
(9)
Table 4 shows the calculated results of Weibull parameters. Based on the results, the fatigue life of various reliability (10%, 36.8%, 50% and 90%) were calculated as following Eq. (10):
180
120
+∞
2 1 η2 ⎡Γ ⎛⎜1 + ⎟⎞ − Γ 2 ⎜⎛1 + ⎟⎞ ⎤ ⎢ β⎠ β ⎠⎥ ⎝ ⎣ ⎝ ⎦
SD (T ) = (7)
lnln[1/R(t)] and ln(t) have a linear relation. To obtain the shape parameter β and scale parameter η, the Weibull probability maps were plotted as shown in Fig. 14. Correspondingly, mean fatigue life (E) and
(a)
∫0
180 170 160 150 140 130
9
Measured position of route 1
Flat head 40° head 60° head 80° head
1
2
3
4
5
6
7
8
9 10 11 12 13
Measured position of route 2
Fig. 8. The hardness distribution of the driven head with different rivet dies: (a) route 1; (b) route 2. 6
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manufactured head fell off and Al sheets were barely damaged. For the failure mode 2, the upper sheet ruptured into two sections along the rivet hole, and the rivet stayed in the lower sheet. Moreover, it could be also found that there were two sub-cracks on both sides of the upper sheet, which resulted from the bending of upper sheet and limiting of clamp fixing block. In general, the leading crack in the middle was the main reason for the failure of the specimens. Besides, the black residue was found in the riveted hole, which inferred that the surface of rivet shaft and hole was subjected to low amplitude oscillations. So it was determined that the fretting wear between rivet and sheets occurred under both failure modes. Fig. 17 summarizes the specific failure modes of the riveted joints with different dies. Specifically, for the joints with the flat rivet die, it was a hybrid failure mode. At high stress levels (194.8 MPa and 173.2 MPa), almost all specimens failed in mode 1. At low stress levels (151.5 MPa and 129.87 MPa), almost all specimens failed in mode 2. This phenomenon was caused by the effects of fretting wear and cyclic impact. According to the previous study [33], the fretting wear degree was related to the friction and cyclic stress, and the friction coefficient was significantly affected by interference fit. When the interference fit of the joint was inadequate, the friction coefficient between the sheets and rivet was small, and the joint was prone to loosen. Therefore, when the joint with flat die which had less interference fit (see Fig. 6) was subjected to fatigue cyclic loading, fretting wear occurred. At higher stress levels, fretting wear degree was more serious and it was easier to induce a clearance between the rivet and sheets. As the number of fatigue cycles increased, the clearance became larger and severe cyclic impact damage occurred, which made the manufactured head of the joints could not suffer and finally fractured. At lower stress levels, degree of fretting wear was relatively mild and it was difficult to induce the clearance between the rivet and sheets. So the cyclic impact damage on manufactured head was insufficient. After long time loading, the cracks initiated from the riveted hole and the Al sheets eventually broke. For the joints with special rivet dies, at each stress level, almost all specimens failed in Al sheets (mode 2). This was because the joints with special dies had higher interference fit. On the one hand it could produce a strengthening effect around the rivet manufactured head, on the other hand the larger interference fit made it more difficult to produce a clearance between the sheets and the rivet. So under the action of fretting wear for a long time, the Al sheet broke. Fig. 18 presents the typical pull-out fatigue fracture morphology for failure mode 1. It could be seen that the fracture were obviously divided into three typical zones. From the high magnification images of zone I, it could be found that there were several micro-cracks at the edge of the fracture. Moreover, on the opposite side (zone 3), there were plenty of equiaxial dimples, indicating that the region developed ductile fractures. So it could be confirmed that cracks were initiated from zone I, and final rupture occurred at zone III. A large number of small flat facets and striations were found in the zone II. Since aluminum alloy was a face-centered cubic material, the microscopic feature could be considered as a quasi-cleavage fracture facet, which was a significant feature of the fatigue crack stability propagation stage. Besides, the existence of striations further proved that this zone was fatigue propagation zone. The fatigue striations were the microscopic plastic deformation trace of the local instantaneous front line in the fatigue crack, the vertical direction of fatigue striations were consistent with the expansion direction of the fatigue crack [34,35]. Each fatigue striation represented a stress cycle. Therefore, it could be concluded that the fatigue cracks extended from one side of manufactured head to the other (from zone I to zone III), not from both sides to the middle. Fig. 19 presents the typical pull-out fatigue fracture morphology for failure mode 2. The fracture could be also divided into three typical areas. In the zone I, the radial streaks (area 1) were observed around bottom of the hole. It was the typical characteristics of fatigue initiation, which demonstrated that the cracks initiated from bottom of the riveted hole. The reason was that the upper sheet was subjected to
Table 3 The fatigue test data of the riveted joints with different rivet dies. Flat die
40° die
60° die
80° die
194.8
102,903 154,012 100,146
232,020 149,802 151,103
181,434 140,758 148,202
373,812 364,580 385,064
173.2
197,554 157,201 231,078
295,393 326,901 253,572
506,848 367,926 515,578
707,834 423,025 792,003
151.5
558,790 532,780 683,340
487,293 592,740 512,560
906,297 558,159 883,902
1,578,030 1,150,188 1,463,552
129.87
1,092,721 1,230,710 955,790
1,090,118 1,273,108 1,302,213
1,412,378 1,349,011 1,595,520
2,227,127 3,094,327 3200000+
Maximum circulation stress (MPa)
Maximum cyclic stress (MPa)
200 190
80° head 60° head 40° head Flat head
180 170 160
SM=1547.09(Nf)-0.17163
150
SM=2545.35(Nf)-0.21314
140
SM=1402.49(Nf)-0.1697
130 120
SM=2411.18(Nf)-0.19629
105
Fatigue life
106
Fig. 9. S-N curve of electromagnetic riveted joints with different rivet dies.
Life expectancy
107
106
40° head 60° head 80° head Flat head
105
104 4 10
105
106
Experimental life
107
Fig. 10. Relationship between predictive life and fatigue test life.
NRx = η [−ln (Rx )]−1/ β
(10)
where NRx represents the fatigue life with x% reliability. Fig. 15 presents the S-N curves of the joints with different dies under various reliability levels. These S-N curves could be used to predict the fatigue life of electromagnetic riveted joint with different dies under different reliability. Moreover, high reliability of 90% was recommended as a reference for designing the auto body and fuselage structures. 3.5. Pull-out fatigue fracture Fig. 16 shows the typical failure modes of the joints under pull-out fatigue loading. There were two typical failure modes for the riveted joints under pull-out loading: (1) rivet manufactured head fracture and (2) sheet fracture. For the failure mode 1, it could be seen that the rivet 7
International Journal of Fatigue 129 (2019) 105238
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Fig. 11. Schematic diagram of numerical simulation: (a) EMR; (b) loading case.
(b)
600 40° head 60° head 80° head Flat head
Nominal stress (MPa)
500 400 300 200 100 1
2
3
4
5
6
7
8
9
10
Position Fig. 12. The stress results of the sheets in the specimens under pull-out loading: (a) stress maps; and (b) the stress values at the specific positions.
(b) 160 40° head 60° head 80° head Flat head
Stress (MPa)
150 140 130 120 110 100
0
2
4
6
8
10
12
Position Fig. 13. The stress results of the rivets in the specimens under pull-out loading: (a) stress maps; and (b) the stress values at the specific positions.
which was about 45° of horizontal direction. In the zone III, smooth and flat surfaces (area 4) were observed on the upside of the sheet, which was a typical transient slip surface and brittle fracture feature. This illustrated that the region broke instantaneously until the strength of the sheet was insufficient to withstand the fatigue load. Therefore, it
bending load and the bottom surface suffered tensile stress under pullout loading, which caused this position to initiate cracks easily. In the zone II, arc-shaped fatigue lines (area 2) and trench lines (area 3) were found. It was the typical characteristics of fatigue growth. The fatigue crack propagation direction was along the normal of the fatigue lines, 8
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(a)
0.5
0.0
ln ln [R(t)]
0.0
ln ln [R(t)]
(b)
194.8 MPa 173.2 MPa 151.5 MPa 129.8 MPa
0.5
-0.5
-0.5
-1.0
-1.0
-1.5
-1.5
11.0
11.5
12.0
12.5
13.0
13.5
194.8 MPa 173.2 MPa 151.5 MPa 129.8 MPa
14.0
11.5
12.0
ln (t)
(c)
(d) 194.8 MPa 173.2 MPa 151.5 MPa 129.8 MPa
ln ln [R(t)]
ln ln [R(t)]
14.5
-0.5
-1.0
-1.5
-1.5 12.5
14.0
0.5
-1.0
12.0
13.5
0.0
-0.5
11.5
13.0
ln (t)
0.5
0.0
12.5
13.0
13.5
14.0
14.5
ln (t)
194.8 MPa 173.2 MPa 151.5 MPa 129.8 MPa 13.0
13.5
14.0
14.5
15.0
15.5
ln (t)
Fig. 14. The Weibull probability maps of the riveted joints with different dies: (a) flat die; (b) 40° die; (c) 60° die; (d) 80° die.
dies were all failure in mode 2. It could be seen that there were several macroscopic cracks inside the hole wall for the joints with 40° and 60° rivet dies, extending upward from the bottom to upside of the sheet. While little obvious cracks were observed in the hole wall of joints with 80° rivet die. This was due to the joints with 40° and 60° rivet dies had larger interference, resulting in serious extrusion deformation of the riveted hole. Besides, the phenomenon was consistent with the stress concentration analysis in simulation. The Kt values of the upper sheets with 40° and 60° dies were higher than that with 80° die. It was more prone to induce micro-cracks under pull-out loading. This further proved that fatigue life of the joints with 80° rivet die were higher than that of the joints with 40° and 60° rivet dies. In summary, this illustrated that the interference size of electromagnetic riveted joints produced by 80° rivet die was the most appropriate for pull-out cyclic loading. In order to better understand the two fatigue failure modes, the schematic of the electromagnetic riveted joints under pull-out loading was drawn as shown in Figs. 21 and 22. The schematic diagram of failure mode 1 is shown in Fig. 21. Note that the joints with flat die at high cyclic stresses failed in this mode. When the riveted specimen was under the cyclic pull-out loading, the manufactured head and driven head suffered a downward and an upward reaction stress, respectively. Subsequently, near the manufactured head, the cracks initiated, propagated and eventually broke. The reasons for failure in mode 1 were described as follows. Firstly, the interference value around the manufactured head was minimal, which caused an inadequate interference reinforcement. Moreover, compared with the side of driven head, the
Table 4 Weibull parameters of the riveted joints with different dies. Type
Maximum cyclic stress (MPa)
Shape parameter β
Scale parameter η
Mean fatigue life (cycles)
Flat die
194.8 173.2 151.5 129.8
3.36 5.06 6.45 7.62
132,935 211,340 638,861 1,147,109
119,352 194,183 595,035 1,077,740
40° die
194.8 173.2 159.0 129.8
3.17 7.36 9.21 9.23
197,289 306,971 558,741 1,284,768
176,621 287,899 529,664 1,218,022
60° die
194.8 173.2 151.5 129.8
6.58 4.71 3.26 10.84
167,168 506,589 871,450 1,511,755
155,870 463,531 781,236 1,443,086
80° die
194.8 173.2 151.5 129.8
37.63 2.81 5.79 4.52
379,218 733,320 1,510,542 3,121,765
373,662 653,077 1,398,635 2,849,651
could be concluded that the cracks initiated from riveted hole, and then propagated along the thickness and width direction of the sheets. Finally, it ruptured on the upside of the sheet. To further clarify the failure behavior of the joints with special dies, the microscopic morphology of the hole wall for the riveted joints with special dies were observed as shown in Fig. 20. These joints with special 9
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220 R=10% R=36.8% R=50% R=90%
200
180
(b)
-0.1842
SM=1762Nf -0.1737 SM=1494Nf -0.1693 SM=1396Nf -0.1495 SM=1026Nf
160
140
120 5
200
-0.2385
SM=3712Nf -0.2192 SM=2791Nf -0.2108 SM=2471Nf -0.1726 SM=1426Nf
180 160 140
5
Fatigue life
200
(d)
-0.1665
SM=1504Nf -0.1707 SM=1548Nf -0.1722 SM=1561Nf -0.1759 SM=1536Nf
160 140 120 10
Fatigue life
240 R=10% R=36.8% R=50% R=90%
220
180
5
10
Fatigue life
Maximum cyclic stress (MPa)
R=10% R=36.8% R=50% R=90%
6
10
6
10
240 220
Maximum cyclic stress (MPa)
R=10% R=36.8% R=50% R=90%
120
10
(c)
240 220
Maximum cyclic stress (MPa)
Maximum cyclic stress (MPa)
(a)
200 180 160 140 120 100 5 10
6
10
-0.1757
SM=1894Nf -0.1901 SM=2249Nf -0.1952 SM=2379Nf -0.1924 SM=2136Nf
6
10
Fatigue life
Fig. 15. The S-N curves of the rivet joints with different dies under various reliability levels: (a) flat die; (b) 40° die; (c) 60° die; (d) 80° die.
Fig. 16. Typical failure modes of pull-out fatigue: (a) ruptured at rivet; (b) ruptured at sheet.
sheet near the clamping area. Finally, the main crack in the middle further extended until it ruptured. The reasons for failure mode 2 were described as follows. For the joints with special dies, it was due to the special rivet die restricted the radial flow of the material in driven head, and more material flowed into the riveted hole. The rivet shaft was strengthened. So the rivet was difficult to occur breakage. Besides, the joints with special dies usually had larger interference, which could make the joints become tighter and also cause serious deformation of the sheets. When the joints were subjected to pull out loading, the stress concentration factors of upper sheets were relatively high, and cracks were induced in the hole wall of the sheets more easily. Moreover,
strengthening effect of plastic deformation around manufactured head was relatively weaker. When subjected to the higher cyclic stresses, a small clearance between the rivet and the sheets was induced by fretting wear, which further resulted in the manufactured head suffering cyclic impact. So the manufactured head eventually failed. The schematic diagram of failure mode 2 is shown in Fig. 22. Note that the joints with a flat die at low cyclic stresses and special dies at all cyclic stresses failed in this mode. According to the fracture morphology analysis, it could be known that the cracks firstly initiated from riveted hole and extended to both sides. Subsequently, the upper sheet was bent, and two sub-cracks were generated on both sides of the upper 10
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Maximum cyclic stress (MPa)
Ruptured at sheet
strength of rivets, thus improving the pull-out fatigue performance of the joints. Moreover, it could effectively prevent the rivets (fasteners) from breaking under pull-out loading, which was more safe and reliable in practical application.
Ruptured at rivet
194.8
4. Conclusions
173.2
In this paper, the pull-out fatigue properties of electromagnetic riveted joints with different rivet dies were investigated. The primary conclusions were drawn as follows:
151.5
(1) The electromagnetic riveted joints with special dies could improve the interference fit. Moreover, the interference value was increased with decreasing of the sidewall intersection angles. This was due to the constant volume principle, the special rivet dies restricted the radial flow of the material in driven head, and more material flowed into the riveted hole. (2) Compared with the electromagnetic riveted joints with a flat die, the joints with special dies could retard the forming of ASBs at a certain degree. No cracks were found in the driven head for all joints. Besides, the hardness distribution law was basically consistent with grain deformation degree. (3) The pull-out fatigue life of the electromagnetic riveted joints with special dies was higher than that with the flat die. Especially, the joints with 80° rivet die had the best pull-out fatigue properties. This was due to the joints with 80° rivet die had more uniform and moderate interference fit.
129.87 40° die
60° die
80° die
Flat die
Rivet die Fig. 17. The failure modes of the riveted joints with different rivet dies.
when upper sheet suffered the upward tensile loading, bending of the sheet made the bottom surface bear tensile stress. So the cracks initiated from the bottom surface of the sheets. For the joints with a flat die under low stresses, the fretting wear between the rivet and sheets was weakened at low stress levels, which made it hard to induce the clearances between them. So the cyclic impact damage on manufactured head was insufficient, and under the effect of fretting wear for a long time, the upper sheet finally failed. In general, the EMR technique with special dies could enhance the
Fig. 18. The typical pull-out fatigue fracture morphology of the joint with flat die under maximum cyclic stress of 194.8 MPa. 11
International Journal of Fatigue 129 (2019) 105238
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Fig. 19. The typical fatigue fracture morphology of the joint with 60° die under maximum cyclic stress of 194.8 MPa.
Fig. 20. Microscopic topography of the riveted hole wall under maximum cyclic stress of 173.2 MPa: (a) 40° rivet die; (b) 60° rivet die; (c) 80° rivet die.
Fig. 21. Schematic of pull-out fatigue failure mode 1: (a) crack initiation; (b) crack propagation; (c) final fracture.
phenomenon was caused by both effects of cyclic impact damage and fretting wear.
(4) The joints under pull-out fatigue loading were ruptured in two modes: rivet manufactured head and upper sheet fracture. The joints with a flat die at high stress levels failed in rivet manufactured head, while the joints with a flat die at low stress levels and special dies at all stress levels failed in upper sheet. This 12
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Fig. 22. Schematic of pull-out fatigue failure mode 2: (a) crack initiation; (b) crack propagation; (c) final fracture.
Acknowledgement
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This project is supported by the Natural Science Foundation of Hunan Province (2019JJ30005), the National Key Research and Development Program of Hunan Province (2017GK2090) and Hunan Provincial Innovation Foundation for Postgraduate (CX2017B077). Declaration of Competing Interest None. Data availability The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijfatigue.2019.105238. References [1] Nascimento M, Voorwald H, Payão Filho J. Fatigue strength of tungsten inert gasrepaired weld joints in airplane critical structures. J Mater Process Technol 2011;211:1126–35. [2] Kaluza A, Kleemann S, Frohlich T, Herrmann C, Vietor T. Concurrent design & life cycle engineering in automotive lightweight component development. Procedia CIRP 2017;66:16–21. [3] Geng HH, Sun LQ, Li GY, Cui JJ, Huang L, Xu ZD. Fatigue fracture properties of magnetic pulse welded dissimilar Al-Fe lap joints. Int J Fatigue 2019;121:146–54. [4] Kleiner M, Chatti S, Klaus A. Metal forming techniques for lightweight construction. J Mater Process Technol 2006;177:2–7. [5] Repetto EA, Radovitzky R, Ortiz M, Lundquist RC, Sandstrom DR. A finite element study of electromagnetic riveting. ASME, J Manuf Sci Eng 1999;121:61–8. [6] Jiang H, Cong YJ, Zhang X, Li GY, Cui JJ. Fatigue degradation after salt spray ageing of electromagnetically riveted joints for CFRP/Al hybrid structure. Mater Des 2018;142:297–307. [7] Zhang X, Zhang MY, Sun LQ, Li CF. Numerical simulation and experimental investigations on TA1 titanium alloy rivet in electromagnetic riveting. Arch Civil Mech Eng 2018;18:887–901. [8] Hartmann J, Brown T. Integration and qualification of the HH500 hand operated electromagnetic riveting system on the 747 Section 11. In: SAE Aerofast Conference, Wichita; September, 1993. [9] Cao ZQ, Cardew-Hall M. Interference-fit riveting technique in fiber composite laminates. Aerosp Sci Technol 2006;10:327–30. [10] Li GY, Jiang H, Zhang X, Cui JJ. Mechanical properties and fatigue behavior of electromagnetic riveted lap joints influenced by shear loading. J Manuf Processes 2017;26:226–39. [11] Jiang H, Li GY, Zhang X, Cui JJ. Fatigue and failure mechanism in carbon fiber reinforced plastics/aluminum alloy single lap joint produced by electromagnetic
13
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue response of electromagnetic riveted joints with different rivet dies subjected to pull-out loading Hao Jianga, Yanjun Conga, Jinsheng Zhangb, Xianhe Wub, Guangyao Lia, Junjia Cuia, a b
T
⁎
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China Chongqing Changan Automobile Co. Ltd, Chongqing 401120, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Electromagnetic riveting Rivet die Fatigue behavior Pull-out loading
Electromagnetic riveting (EMR) as a green manufacturing and efficient process has extensive application prospect in engineering fields. In this study, the fatigue properties of electromagnetic riveted joints with different rivet dies under pull-out loading were studied. The results showed that rivet dies had a significant effect on the pull-out fatigue performance. The pull-out fatigue life of the electromagnetic riveted joints with special dies was higher than that with the flat die. The reason was that the special rivet dies restricted the radial flow of the material in driven head. More material flowed into the riveted hole and rivet shaft became larger. The joints were reinforced by larger interference fit. Particularly, the joints with 80° rivet die had the best pull-out fatigue properties due to more uniform and moderate interference fit. Fracture analysis showed that there were two typical failure modes for the joints under pull-out loading: rivet manufactured head and upper sheet fracture. Due to the effect of cyclic impact and fretting wear damage, the joints with a flat die at high stress levels (194.8 MPa and 173.2 MPa) failed in rivet manufactured head, while the joints with special dies at all stress levels and with a flat die at low stress levels (151.5 MPa and 129.87 MPa) failed in upper sheet.
1. Introduction Using lightweight material is one of the most effective ways to realize energy conservation and emission reduction of automobile and airplane [1–4]. Aluminum (Al) alloy has been becoming a primary choice of lightweight material due to its good characteristics. Usually, the auto body and fuselage consist of many aluminum parts. However, traditional joining technologies (e.g. bolting, riveting and bonding) are hard to connect them well. The bolt joint loosens easily. The adhesive joint is liable to brittle fracture. The regular riveted joint has non-uniform interference and is easy to produce stress concentration. Electromagnetic riveting (EMR) as an advanced manufacturing process, can assembly Al alloy structures efficiently, and produces firm joints [5–7]. Compared with conventional riveting, EMR technique has the characteristics of large riveting force, fast riveting speed, no pollution and high efficiency [8]. Moreover, Cao et al. [9] found that the EMR joints had more uniform interference fit due to the effect of stress wave. Li et al. [10] further proved that the mechanical properties of EMR joints usually performed better than conventional riveted joints. Due to its great advantages and application prospect, many researchers were further studied the effects of EMR process parameter and rivet die on the joints performance [11–16]. Jiang et al. [11] found
⁎
that the discharge energies directly affected the rivet driven heads’ deformation, which further influenced joints’ mechanical properties and fatigue properties. Specifically, the results showed that the driven head with larger deformation has a tighter interference fit, and a proper interference could effectively improve the shear fatigue properties. As for fatigue properties on the shear direction, the fatigue life of the joints increased first and then decreased with the increase of the driven heads’ deformation. In addition, adiabatic shearing deformation usually occurred in the driven head during EMR, and adiabatic shear bands (ASBs) were formed along the diagonal direction of the driven head [12]. As a crucial feature of EMR, ASBs could affect not only the microstructure of the driven head, but also the joints strength. Deng et al. [13] reported that the ASBs deformed more seriously with the increase of discharge energy. Higher discharge energy generated higher strain rate, and the high strain rate would induce the precipitation hardening in ASBs, which easily led to cracks in the driven head [14]. Accordingly, Reinhall et al. [15] designed a special rivet die with an angle to control the formation of the cracks. The results showed that the joints with a special rivet die could effectively reduce the maximum shear stress and impede the crack expansion. Recently, Cui et al. [16] comprehensively investigated the influence of the rivet die constructions on the mechanical and microscopic properties using the experimental and
Corresponding author. E-mail address: [email protected] (J. Cui).
https://doi.org/10.1016/j.ijfatigue.2019.105238 Received 11 April 2019; Received in revised form 11 August 2019; Accepted 19 August 2019 Available online 20 August 2019 0142-1123/ © 2019 Elsevier Ltd. All rights reserved.
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2.2. Electromagnetic riveting process
numerical methods. They also found that the special rivet dies could obviously enhance the pull-out properties of the EMR joints and inhibit the formation of ASBs. Abovementioned studies mainly focused on mechanical properties, fatigue performance in shear direction and microscopic properties of EMR joints. However, in practical application, the joints are not only subjected to the shear loading, but also to the pull-out loading [17–19]. Especially in the actual service of automobile and aircraft, the joints were affected by different working conditions for a long time. So the fatigue performance of the joint in pull out direction was particularly significant [20]. Moreover, in literatures, Nguyen et al. [21] and Choi et al. [22] respectively found that when the pin and riveted joints were subjected to loads in different directions, theirs failure behaviors performed different. While previous studies on the fatigue behaviors of EMR joints in the pull-out direction are not systematic, especially the pull-out fatigue performance with a special rivet die. It is of great significance for the using of special rivet dies in automotive and aircraft manufacturing and assembly. This paper is aimed to investigate the pull-out fatigue properties of the electromagnetic riveted joints with different rivet dies. Firstly, EMR experiments with different rivet dies were carried out to obtain the test specimens. Subsequently, the interference sizes measurements, joint cross-section observations and hardness measurements were conducted to analyze the joint strength. Meanwhile, the pull-out fatigue tests were performed with designed fixture to obtain the fatigue performance. Finally, the fatigue failure modes were analyzed.
Fig. 2 shows the schematic of the EMR process. It mainly consists of a magnetic pulse generator and riveting mold. The magnetic pulse generator is in the charge of providing the energy, and the discharge energy saves in the capacitors. Specifically, when the power switch is closed, the capacitance completes charging quickly. Then, closing the discharge switch, alternating current is flowing into the coil, and a strong magnetic field is produced around it. The strong magnetic field makes driver plate generate an induced current, which generates a reversed magnetic field. The eddy current repulsive force generated by the two magnetic fields drives the amplifier strike the rivet, which leads to plastic deformation of the rivet in a short time. In the riveting process, the rivet die has a significant effect on the deformation of the driven head, which would further affect the joint performance [23]. After referring to previous studies [14–15,24], three special rivet dies (sidewall intersection angles of 40°, 60° and 80°) and one universal flat die were designed. The specific geometry dimensions and physical maps of different rivet dies are described in Fig. 3. In addition, based on the previous study [11], the discharge energy of 5.0 kJ for flat die could obtain better joint quality. Therefore, to avoid the effect of discharge energy on joint performance, all EMR experiments were performed with discharge energy of 5.0 kJ. Fig. 4 shows the typical pull-out fatigue test specimens with different rivet dies after EMR. 2.3. Mechanical property test and micro-structure observations
2. Experimental materials and methods
The pull-out fatigue tests employed with Instron 8801 servo hydraulic fatigue test machine as shown in Fig. 5. The cyclic stress in the fatigue tests was a sine curve. The frequency was 20 Hz/s and the stress ratio was 0.1. Based on the pull-out quasi-static tests, maximum cyclic stresses selected in the paper were 194.8 MPa, 173.2 MPa, 151.5 MPa and 129.8 MPa, respectively. Besides, three replicate tests were performed at each stress levels for each rivet die to ensure the credibility of the results. After the EMR, the samples were firstly cut with a metallographic cutter. Then samples were prepared in an epoxy mount and polished with an automatic polishing machine, and finally corroded with Keller corrosion fluid. The relative interference of four different pier heads were obtained and hardness values were got with a Tukon-1102 micro hardness tester, whose pressing load was set to 0.3 kg and pressure was maintained for 15 s. The pull-out fatigue fracture were observed by FEI QuANTA200 scanning electron microscope.
2.1. Sample preparation In this study, 6082 T6 Al sheets and 2A10 Al rivets were employed. As depicted in Fig. 1, the diameter of Al rivets and the thickness of Al sheets were 5 mm and 4 mm, respectively. According to the QJ-782A2005 riveting standard, the diameter of prefabricated hole in the Al sheets and the length of rivet shaft was set to 5.1 mm and 14.0 mm, respectively. In order to obtain the precise dimensions, the riveted sheets were manufactured by wire cutting. Besides, the surfaces of Al rivet were treated with chemical conversion, and Al sheets were cold rolled to increase the hardness and strength. Specifically, material properties of Al 6082 T6 and Al 2A10 are presented in Table 1.
3. Results and discussions 3.1. Interference analysis According to the previous studies [25,26], interference size of the riveted joints had significant influence on fatigue properties. So the diameters of rivet shaft after EMR were measured by vernier caliper with an accuracy of 0.01 mm. In order to reduce the measurement deviations, each position was measured three times at intervals of 120°. The relative interference (I) was calculated by following Eq. (1):
I = [(D − D0)/ D0] × 100%
(1)
where D and D0 are the diameters of deformed rivet shaft and original hole. Table 2 and Fig. 6 show the measured results and the interference sizes of the electromagnetic riveted joints for different rivet dies. It could be seen that the interference values reduced from position 1 to position 3 for all samples. Compared with the interferences of special head, the interference of flat head was minimal at all positions. Especially the 40° deformed head had the largest interference at position 1, with up to 5.431%. While the flat deformed head at the position 3 had the smallest interference value, which was only 0.784%. At the position
Fig. 1. Specimen geometry for pull-out fatigue tests (dimension in mm). 2
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Table 1 Material properties of Al 6082 T6 and Al 2A10. Properties 3
Density (g/cm ) Poisson ratio Tensile modulus (GPa) Yield strength (MPa) Tensile strength (MPa) Chemical composition (%)
Al 6082 T6 sheet
Al 2A10 rivet
2.7 0.32 67.2 240 325 Zn = 0.03, Si = 0.97, Fe = 0.37, Mn = 0.67, Mg = 1.02, Ti = 0.01, Cu = 0.07, Al = balance
2.7 0.33 73.8 250 400 Si = 0.25, Fe = 0.2, Cu = 3.9–4.5, Mn = 0.3–0.5, Mg = 0.15–0.30, Zn = 0.1, Ti = 0.15, Al = balance
1, it could be found that the interference value substantially decreased as the angle of the riveting die increased. This was due to the constant volume principle. The special rivet dies could limit the rivet material flow and squeeze more material into the riveted hole. Moreover, as the angle of the rivet dies decreased, the volume of the rivet cavity decreased, causing more material will be squeezed into the hole, so as to make the joints with small angle rivet die have higher interference.
3.2. Metallographic structure and hardness analysis Fig. 7 presents the micro-structures of the riveted joints in the driven head with different rivet dies, which are composed of a number of metallographic photographs. It could be seen that no cracks were found in the driven head for all types of joints. However, for the joints with flat die, grains were highly deformed after EMR and the adiabatic shear bands (ASBs) were more obvious than other rivet dies. This indicated that the rivet die with sidewall intersection angles could suppress the forming of ASBs, which could further prevent inducing cracks. Fig. 8 shows the hardness distribution of the driven head with different rivet dies. Note that the original hardness value of the rivets was around 113 HV. In Fig. 8(a), the peak of the curve appeared at position 3 (about 1–1.5 mm from the upper surface of the head) for the flat head. While for the 40°, 60° and 80° formed heads, with the constraint of the rivet die, the material deformation in the cavity were not as strong as the corresponding position in the flat head. Therefore, the peaks of the curves appeared at position 6 (about 2–2.5 mm from the upper surface of the heads). It showed that the serious microstructure deformation in
Fig. 2. The schematic of EMR: (a) electromagnetic setup; (b) riveting process.
Fig. 3. Geometry dimensions and physical maps of different dies. 3
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Fig. 4. The typical pull-out fatigue test specimens with different rivet dies.
different rivet dies. The fatigue data were fitted by the following power function [27]:
the driven heads made the material strengthening effect, resulting in an increase in hardness. The hardness distribution depicted in Fig. 8(a) and metallographic structure depicted in Fig. 7 in the formed heads were basically coincident. In Fig. 8(b), it could be seen that there were two hardness peaks (position 3 and 12) on the path for the flat head. The hardness values reached 175 HV and 162 HV, respectively. The positions of two peaks coincided with the two ASBs. This was due to the hardness peaks were induced by the strain hardening effect in the ASBs. In addition, there was only one peak in the 60° or 80° formed heads, which was consistent with the lower shear band. Moreover, due to the fine-grain strengthening effect, the hardness of the area above the lower shear band was also higher than that of the original material. For the 40° head, there was also only one peak with a large width on the hardness curve. The reason was that the distance between the two ASBs was relatively close. The material between the two ASBs was subjected to the radial compressive stress and circumferential tensile stress simultaneously, so that the hardness value increased to some extent. Besides, as the 40° rivet die had the smallest cavity volume, the material in the cavity was relatively difficult to deform. So the grain over ASBs deformed slightly, and the hardness values of the position 6–13 were relatively low.
SM = a (Nf )b
(2)
where SM and Nf represent the maximum cyclic stress and fatigue life, respectively. Fig. 9 shows the fitted curves of the fatigue results for the joints with different rivet dies. It could be clearly found that pull-out fatigue life of the joints with special rivet dies were almost higher than that of the flat die. Only at the low stress level (129.8 MPa), the fatigue life of the joints with 40° and flat dies were approximate. Besides, it could be seen that the joints with 80° rivet die have the best fatigue properties. Especially, the fatigue life of the joints with 80° rivet head were almost 2 times longer than that of other joints. This demonstrated that using special rivet dies in EMR could effectively improve the pullout fatigue life of joints. In particular, the 80° rivet die was the optimal. The reason was that the joints with special rivet dies had relatively higher interference fit comparing to the flat die. High interference on the one hand could make joint tighter. On the other hand, if the interference fit was excessive, the sheet extrusion deformation would be serious, which could easily lead to stress concentration [28]. According to the above interference measured results, the joints with 80° rivet die had more uniform and moderate interference fit (average value of 3.5%). It also proved that this interference value had better pull-out fatigue performance for riveted joints.
3.3. Pull-out fatigue life Table 3 presents the fatigue test data of the riveted joints with
Fig. 5. The fixture of pull-out fatigue tests. 4
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Table 2 Rivet diameters and interference of the joints for different rivet dies. Type
Position
Diameter 1 (mm)
Diameter 2 (mm)
Diameter 3 (mm)
Average value (mm)
Relative interference (%)
Flat head
1 2 3
5.21 5.17 5.13
5.18 5.17 5.14
5.20 5.19 5.15
5.197 5.177 5.140
1.902 1.510 0.784
40° head
1 2 3
5.40 5.24 5.20
5.36 5.24 5.20
5.37 5.25 5.19
5.377 5.243 5.197
5.431 2.804 1.902
60° head
1 2 3
5.33 5.26 5.19
5.31 5.26 5.20
5.32 5.27 5.21
5.320 5.263 5.200
4.314 3.196 1.961
80° head
1 2 3
5.26 5.22 5.17
5.27 5.22 5.18
5.27 5.22 5.18
5.267 5.220 5.177
3.275 2.353 1.510
40° head 60° head 80° head Flat head
Relative interference (%)
5 4 3
flat head suffered larger stresses and deformed more easily. Besides, the stress value gradually decreased from the riveted hole to the edge, and the stress around the rivet hole was much higher than other locations. This indicated that the stress concentration was most severe around position 1. Combined with the results of the interference fit, the position near the driven head had the largest interference amount, so the fretting wear degree would be the most serious in this position [31]. To compare the stress concentration degree of the joints with different dies in detail, the nominal stress was calculated from the average stress of the points in the Fig. 12. After calculation, the Kt value for pull out loading on the upper sheets with 40°, 60°, 80° and flat dies were obtained, which were respectively 2.75, 2.25, 1.90 and 1.96. The results showed that the Kt value of the joint with 80° die was smaller than that with other dies. It indicated that the use of 80° rivet die could reduce the stress concentration level of the sheet under pull out loading. This was also one of the reasons that the joints with 80° die had better fatigue properties. Fig. 13(a) shows the stress maps of the rivets with different formed heads under pull-out loading. It could be clearly seen that the stress near the driven head was greater than that of the manufacturing head. This was because the driven head occurred serious plastic deformation in the riveting process, while the manufacturing head was restricted by the die and had little deformation. This also proved that the driven head was enhanced to some extent compared with the manufacturing head. So the manufacturing head was more likely to break than the driven head [10]. Besides, to avoid the influence of riveting process on the stress analysis of rivets under pull-out loading, the stress values near the manufacturing head were obtained as shown in Fig. 13(b). It could be seen that the average stress of the joints with flat head near the manufacturing head was higher than that of other joints with special heads, indicating that the rivet with flat head suffered larger force when it was subjected to pull-out loading. So the rivet of the joints with flat head were prone to fracture compared to the joints with special heads.
1 mm Position 1 Position 2 Position 3
1 mm
2 1 0
1
2
3
Measured position Fig. 6. Comparison of interference sizes of electromagnet riveted joints for different rivet dies.
In addition, the predictive life was obtained by the above S-N curves. The relationship between predictive life and fatigue test life was showed in Fig. 10. It could be seen that the scatter points were all within 2 times distribution band. This indicated that the fitted curves in Fig. 9 could predict fatigue life of the joints accurately. In addition, in order to further assess the pull out fatigue properties, the stress concentration factors of the joints were analyzed [29,30]. The stress concentration factor (Kt) is defined as Eq. (3):
Kt =
σm σ0
(3)
where σm and σ0 are the maximum and nominal stresses, respectively. In this study, Kt values of the joints with different rivet dies were obtained by numerical simulation method. The simulation model was established in LS-DYNA commercial software. Fig. 11(a) and (b) show the numerical simulation model of EMR and loading case, respectively. Constant stress solid element and Automatic Surface to Surface contact law were employed. The material models of the sheets and rivet were the same as in Ref. [16]. The load state on the specimen was applied according to the actual conditions. The pull out force applied in this case was 3328 N. Fig. 12(a) and (b) show the stress maps of the sheets and the stress values at the specific positions under pull-out loading, respectively. It could be seen from the upper sheets that the maximum stress was found around the rivet hole, implying that this position was the most vulnerable in the upper sheets for all specimens. So the fatigue cracks were prone to initiate from the riveted holes. Furthermore, as shown in Fig. 12(b), the stress of the joint with flat head was much higher than that of the joint with special heads. This indicated that when the specimen was subjected to the pull-out loading, the sheets in joints with
3.4. Statistical analysis In order to obtain the fatigue life of the joints with high reliability, the statistical analysis were conducted using two-parameter Weibull distribution [32]. The probability density function f(t), corresponding cumulative distribution function F(t) and the reliability function R(t) were respectively defined as Eq. (4), Eq. (5) and Eq. (6):
f (t ) =
β⎛t ⎞ ⎜ ⎟ η ⎝η⎠
β−1
β
⎡ t ⎤ exp ⎢−⎛⎜ ⎞⎟ ⎥ η ⎣ ⎝ ⎠ ⎦
(4)
β
⎡ t ⎤ F (t ) = 1 − exp ⎢−⎜⎛ ⎟⎞ ⎥ η ⎣ ⎝ ⎠ ⎦ 5
(5)
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Fig. 7. The micro-structures of the riveted joints in the driven head with different rivet dies. β
⎡ t ⎤ R (t ) = exp ⎢−⎛⎜ ⎞⎟ ⎥ η ⎣ ⎝ ⎠ ⎦
standard deviation (SD) were derived by following Eq. (8) and Eq. (9), respectively.
(6)
where β is the shape parameter, η is the scale parameter, and t is the random variable value. Based on the Eq. (6), the following Eq. (7) was derived as:
lnln
1 = βln (t ) − βlnη R (t )
E (T ) =
170
Vickers hardness (HV0.3)
Vickers hardness (HV)
(b)
160 150 140 130 Flat 40° 60° 80°
110 100 90
1
2
3
4
5
head head head head
6
7
8
1 tf (t ) dt = ηΓ ⎜⎛1 + ⎞⎟ β⎠ ⎝
(8)
(9)
Table 4 shows the calculated results of Weibull parameters. Based on the results, the fatigue life of various reliability (10%, 36.8%, 50% and 90%) were calculated as following Eq. (10):
180
120
+∞
2 1 η2 ⎡Γ ⎛⎜1 + ⎟⎞ − Γ 2 ⎜⎛1 + ⎟⎞ ⎤ ⎢ β⎠ β ⎠⎥ ⎝ ⎣ ⎝ ⎦
SD (T ) = (7)
lnln[1/R(t)] and ln(t) have a linear relation. To obtain the shape parameter β and scale parameter η, the Weibull probability maps were plotted as shown in Fig. 14. Correspondingly, mean fatigue life (E) and
(a)
∫0
180 170 160 150 140 130
9
Measured position of route 1
Flat head 40° head 60° head 80° head
1
2
3
4
5
6
7
8
9 10 11 12 13
Measured position of route 2
Fig. 8. The hardness distribution of the driven head with different rivet dies: (a) route 1; (b) route 2. 6
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manufactured head fell off and Al sheets were barely damaged. For the failure mode 2, the upper sheet ruptured into two sections along the rivet hole, and the rivet stayed in the lower sheet. Moreover, it could be also found that there were two sub-cracks on both sides of the upper sheet, which resulted from the bending of upper sheet and limiting of clamp fixing block. In general, the leading crack in the middle was the main reason for the failure of the specimens. Besides, the black residue was found in the riveted hole, which inferred that the surface of rivet shaft and hole was subjected to low amplitude oscillations. So it was determined that the fretting wear between rivet and sheets occurred under both failure modes. Fig. 17 summarizes the specific failure modes of the riveted joints with different dies. Specifically, for the joints with the flat rivet die, it was a hybrid failure mode. At high stress levels (194.8 MPa and 173.2 MPa), almost all specimens failed in mode 1. At low stress levels (151.5 MPa and 129.87 MPa), almost all specimens failed in mode 2. This phenomenon was caused by the effects of fretting wear and cyclic impact. According to the previous study [33], the fretting wear degree was related to the friction and cyclic stress, and the friction coefficient was significantly affected by interference fit. When the interference fit of the joint was inadequate, the friction coefficient between the sheets and rivet was small, and the joint was prone to loosen. Therefore, when the joint with flat die which had less interference fit (see Fig. 6) was subjected to fatigue cyclic loading, fretting wear occurred. At higher stress levels, fretting wear degree was more serious and it was easier to induce a clearance between the rivet and sheets. As the number of fatigue cycles increased, the clearance became larger and severe cyclic impact damage occurred, which made the manufactured head of the joints could not suffer and finally fractured. At lower stress levels, degree of fretting wear was relatively mild and it was difficult to induce the clearance between the rivet and sheets. So the cyclic impact damage on manufactured head was insufficient. After long time loading, the cracks initiated from the riveted hole and the Al sheets eventually broke. For the joints with special rivet dies, at each stress level, almost all specimens failed in Al sheets (mode 2). This was because the joints with special dies had higher interference fit. On the one hand it could produce a strengthening effect around the rivet manufactured head, on the other hand the larger interference fit made it more difficult to produce a clearance between the sheets and the rivet. So under the action of fretting wear for a long time, the Al sheet broke. Fig. 18 presents the typical pull-out fatigue fracture morphology for failure mode 1. It could be seen that the fracture were obviously divided into three typical zones. From the high magnification images of zone I, it could be found that there were several micro-cracks at the edge of the fracture. Moreover, on the opposite side (zone 3), there were plenty of equiaxial dimples, indicating that the region developed ductile fractures. So it could be confirmed that cracks were initiated from zone I, and final rupture occurred at zone III. A large number of small flat facets and striations were found in the zone II. Since aluminum alloy was a face-centered cubic material, the microscopic feature could be considered as a quasi-cleavage fracture facet, which was a significant feature of the fatigue crack stability propagation stage. Besides, the existence of striations further proved that this zone was fatigue propagation zone. The fatigue striations were the microscopic plastic deformation trace of the local instantaneous front line in the fatigue crack, the vertical direction of fatigue striations were consistent with the expansion direction of the fatigue crack [34,35]. Each fatigue striation represented a stress cycle. Therefore, it could be concluded that the fatigue cracks extended from one side of manufactured head to the other (from zone I to zone III), not from both sides to the middle. Fig. 19 presents the typical pull-out fatigue fracture morphology for failure mode 2. The fracture could be also divided into three typical areas. In the zone I, the radial streaks (area 1) were observed around bottom of the hole. It was the typical characteristics of fatigue initiation, which demonstrated that the cracks initiated from bottom of the riveted hole. The reason was that the upper sheet was subjected to
Table 3 The fatigue test data of the riveted joints with different rivet dies. Flat die
40° die
60° die
80° die
194.8
102,903 154,012 100,146
232,020 149,802 151,103
181,434 140,758 148,202
373,812 364,580 385,064
173.2
197,554 157,201 231,078
295,393 326,901 253,572
506,848 367,926 515,578
707,834 423,025 792,003
151.5
558,790 532,780 683,340
487,293 592,740 512,560
906,297 558,159 883,902
1,578,030 1,150,188 1,463,552
129.87
1,092,721 1,230,710 955,790
1,090,118 1,273,108 1,302,213
1,412,378 1,349,011 1,595,520
2,227,127 3,094,327 3200000+
Maximum circulation stress (MPa)
Maximum cyclic stress (MPa)
200 190
80° head 60° head 40° head Flat head
180 170 160
SM=1547.09(Nf)-0.17163
150
SM=2545.35(Nf)-0.21314
140
SM=1402.49(Nf)-0.1697
130 120
SM=2411.18(Nf)-0.19629
105
Fatigue life
106
Fig. 9. S-N curve of electromagnetic riveted joints with different rivet dies.
Life expectancy
107
106
40° head 60° head 80° head Flat head
105
104 4 10
105
106
Experimental life
107
Fig. 10. Relationship between predictive life and fatigue test life.
NRx = η [−ln (Rx )]−1/ β
(10)
where NRx represents the fatigue life with x% reliability. Fig. 15 presents the S-N curves of the joints with different dies under various reliability levels. These S-N curves could be used to predict the fatigue life of electromagnetic riveted joint with different dies under different reliability. Moreover, high reliability of 90% was recommended as a reference for designing the auto body and fuselage structures. 3.5. Pull-out fatigue fracture Fig. 16 shows the typical failure modes of the joints under pull-out fatigue loading. There were two typical failure modes for the riveted joints under pull-out loading: (1) rivet manufactured head fracture and (2) sheet fracture. For the failure mode 1, it could be seen that the rivet 7
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Fig. 11. Schematic diagram of numerical simulation: (a) EMR; (b) loading case.
(b)
600 40° head 60° head 80° head Flat head
Nominal stress (MPa)
500 400 300 200 100 1
2
3
4
5
6
7
8
9
10
Position Fig. 12. The stress results of the sheets in the specimens under pull-out loading: (a) stress maps; and (b) the stress values at the specific positions.
(b) 160 40° head 60° head 80° head Flat head
Stress (MPa)
150 140 130 120 110 100
0
2
4
6
8
10
12
Position Fig. 13. The stress results of the rivets in the specimens under pull-out loading: (a) stress maps; and (b) the stress values at the specific positions.
which was about 45° of horizontal direction. In the zone III, smooth and flat surfaces (area 4) were observed on the upside of the sheet, which was a typical transient slip surface and brittle fracture feature. This illustrated that the region broke instantaneously until the strength of the sheet was insufficient to withstand the fatigue load. Therefore, it
bending load and the bottom surface suffered tensile stress under pullout loading, which caused this position to initiate cracks easily. In the zone II, arc-shaped fatigue lines (area 2) and trench lines (area 3) were found. It was the typical characteristics of fatigue growth. The fatigue crack propagation direction was along the normal of the fatigue lines, 8
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(a)
0.5
0.0
ln ln [R(t)]
0.0
ln ln [R(t)]
(b)
194.8 MPa 173.2 MPa 151.5 MPa 129.8 MPa
0.5
-0.5
-0.5
-1.0
-1.0
-1.5
-1.5
11.0
11.5
12.0
12.5
13.0
13.5
194.8 MPa 173.2 MPa 151.5 MPa 129.8 MPa
14.0
11.5
12.0
ln (t)
(c)
(d) 194.8 MPa 173.2 MPa 151.5 MPa 129.8 MPa
ln ln [R(t)]
ln ln [R(t)]
14.5
-0.5
-1.0
-1.5
-1.5 12.5
14.0
0.5
-1.0
12.0
13.5
0.0
-0.5
11.5
13.0
ln (t)
0.5
0.0
12.5
13.0
13.5
14.0
14.5
ln (t)
194.8 MPa 173.2 MPa 151.5 MPa 129.8 MPa 13.0
13.5
14.0
14.5
15.0
15.5
ln (t)
Fig. 14. The Weibull probability maps of the riveted joints with different dies: (a) flat die; (b) 40° die; (c) 60° die; (d) 80° die.
dies were all failure in mode 2. It could be seen that there were several macroscopic cracks inside the hole wall for the joints with 40° and 60° rivet dies, extending upward from the bottom to upside of the sheet. While little obvious cracks were observed in the hole wall of joints with 80° rivet die. This was due to the joints with 40° and 60° rivet dies had larger interference, resulting in serious extrusion deformation of the riveted hole. Besides, the phenomenon was consistent with the stress concentration analysis in simulation. The Kt values of the upper sheets with 40° and 60° dies were higher than that with 80° die. It was more prone to induce micro-cracks under pull-out loading. This further proved that fatigue life of the joints with 80° rivet die were higher than that of the joints with 40° and 60° rivet dies. In summary, this illustrated that the interference size of electromagnetic riveted joints produced by 80° rivet die was the most appropriate for pull-out cyclic loading. In order to better understand the two fatigue failure modes, the schematic of the electromagnetic riveted joints under pull-out loading was drawn as shown in Figs. 21 and 22. The schematic diagram of failure mode 1 is shown in Fig. 21. Note that the joints with flat die at high cyclic stresses failed in this mode. When the riveted specimen was under the cyclic pull-out loading, the manufactured head and driven head suffered a downward and an upward reaction stress, respectively. Subsequently, near the manufactured head, the cracks initiated, propagated and eventually broke. The reasons for failure in mode 1 were described as follows. Firstly, the interference value around the manufactured head was minimal, which caused an inadequate interference reinforcement. Moreover, compared with the side of driven head, the
Table 4 Weibull parameters of the riveted joints with different dies. Type
Maximum cyclic stress (MPa)
Shape parameter β
Scale parameter η
Mean fatigue life (cycles)
Flat die
194.8 173.2 151.5 129.8
3.36 5.06 6.45 7.62
132,935 211,340 638,861 1,147,109
119,352 194,183 595,035 1,077,740
40° die
194.8 173.2 159.0 129.8
3.17 7.36 9.21 9.23
197,289 306,971 558,741 1,284,768
176,621 287,899 529,664 1,218,022
60° die
194.8 173.2 151.5 129.8
6.58 4.71 3.26 10.84
167,168 506,589 871,450 1,511,755
155,870 463,531 781,236 1,443,086
80° die
194.8 173.2 151.5 129.8
37.63 2.81 5.79 4.52
379,218 733,320 1,510,542 3,121,765
373,662 653,077 1,398,635 2,849,651
could be concluded that the cracks initiated from riveted hole, and then propagated along the thickness and width direction of the sheets. Finally, it ruptured on the upside of the sheet. To further clarify the failure behavior of the joints with special dies, the microscopic morphology of the hole wall for the riveted joints with special dies were observed as shown in Fig. 20. These joints with special 9
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220 R=10% R=36.8% R=50% R=90%
200
180
(b)
-0.1842
SM=1762Nf -0.1737 SM=1494Nf -0.1693 SM=1396Nf -0.1495 SM=1026Nf
160
140
120 5
200
-0.2385
SM=3712Nf -0.2192 SM=2791Nf -0.2108 SM=2471Nf -0.1726 SM=1426Nf
180 160 140
5
Fatigue life
200
(d)
-0.1665
SM=1504Nf -0.1707 SM=1548Nf -0.1722 SM=1561Nf -0.1759 SM=1536Nf
160 140 120 10
Fatigue life
240 R=10% R=36.8% R=50% R=90%
220
180
5
10
Fatigue life
Maximum cyclic stress (MPa)
R=10% R=36.8% R=50% R=90%
6
10
6
10
240 220
Maximum cyclic stress (MPa)
R=10% R=36.8% R=50% R=90%
120
10
(c)
240 220
Maximum cyclic stress (MPa)
Maximum cyclic stress (MPa)
(a)
200 180 160 140 120 100 5 10
6
10
-0.1757
SM=1894Nf -0.1901 SM=2249Nf -0.1952 SM=2379Nf -0.1924 SM=2136Nf
6
10
Fatigue life
Fig. 15. The S-N curves of the rivet joints with different dies under various reliability levels: (a) flat die; (b) 40° die; (c) 60° die; (d) 80° die.
Fig. 16. Typical failure modes of pull-out fatigue: (a) ruptured at rivet; (b) ruptured at sheet.
sheet near the clamping area. Finally, the main crack in the middle further extended until it ruptured. The reasons for failure mode 2 were described as follows. For the joints with special dies, it was due to the special rivet die restricted the radial flow of the material in driven head, and more material flowed into the riveted hole. The rivet shaft was strengthened. So the rivet was difficult to occur breakage. Besides, the joints with special dies usually had larger interference, which could make the joints become tighter and also cause serious deformation of the sheets. When the joints were subjected to pull out loading, the stress concentration factors of upper sheets were relatively high, and cracks were induced in the hole wall of the sheets more easily. Moreover,
strengthening effect of plastic deformation around manufactured head was relatively weaker. When subjected to the higher cyclic stresses, a small clearance between the rivet and the sheets was induced by fretting wear, which further resulted in the manufactured head suffering cyclic impact. So the manufactured head eventually failed. The schematic diagram of failure mode 2 is shown in Fig. 22. Note that the joints with a flat die at low cyclic stresses and special dies at all cyclic stresses failed in this mode. According to the fracture morphology analysis, it could be known that the cracks firstly initiated from riveted hole and extended to both sides. Subsequently, the upper sheet was bent, and two sub-cracks were generated on both sides of the upper 10
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Maximum cyclic stress (MPa)
Ruptured at sheet
strength of rivets, thus improving the pull-out fatigue performance of the joints. Moreover, it could effectively prevent the rivets (fasteners) from breaking under pull-out loading, which was more safe and reliable in practical application.
Ruptured at rivet
194.8
4. Conclusions
173.2
In this paper, the pull-out fatigue properties of electromagnetic riveted joints with different rivet dies were investigated. The primary conclusions were drawn as follows:
151.5
(1) The electromagnetic riveted joints with special dies could improve the interference fit. Moreover, the interference value was increased with decreasing of the sidewall intersection angles. This was due to the constant volume principle, the special rivet dies restricted the radial flow of the material in driven head, and more material flowed into the riveted hole. (2) Compared with the electromagnetic riveted joints with a flat die, the joints with special dies could retard the forming of ASBs at a certain degree. No cracks were found in the driven head for all joints. Besides, the hardness distribution law was basically consistent with grain deformation degree. (3) The pull-out fatigue life of the electromagnetic riveted joints with special dies was higher than that with the flat die. Especially, the joints with 80° rivet die had the best pull-out fatigue properties. This was due to the joints with 80° rivet die had more uniform and moderate interference fit.
129.87 40° die
60° die
80° die
Flat die
Rivet die Fig. 17. The failure modes of the riveted joints with different rivet dies.
when upper sheet suffered the upward tensile loading, bending of the sheet made the bottom surface bear tensile stress. So the cracks initiated from the bottom surface of the sheets. For the joints with a flat die under low stresses, the fretting wear between the rivet and sheets was weakened at low stress levels, which made it hard to induce the clearances between them. So the cyclic impact damage on manufactured head was insufficient, and under the effect of fretting wear for a long time, the upper sheet finally failed. In general, the EMR technique with special dies could enhance the
Fig. 18. The typical pull-out fatigue fracture morphology of the joint with flat die under maximum cyclic stress of 194.8 MPa. 11
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Fig. 19. The typical fatigue fracture morphology of the joint with 60° die under maximum cyclic stress of 194.8 MPa.
Fig. 20. Microscopic topography of the riveted hole wall under maximum cyclic stress of 173.2 MPa: (a) 40° rivet die; (b) 60° rivet die; (c) 80° rivet die.
Fig. 21. Schematic of pull-out fatigue failure mode 1: (a) crack initiation; (b) crack propagation; (c) final fracture.
phenomenon was caused by both effects of cyclic impact damage and fretting wear.
(4) The joints under pull-out fatigue loading were ruptured in two modes: rivet manufactured head and upper sheet fracture. The joints with a flat die at high stress levels failed in rivet manufactured head, while the joints with a flat die at low stress levels and special dies at all stress levels failed in upper sheet. This 12
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Fig. 22. Schematic of pull-out fatigue failure mode 2: (a) crack initiation; (b) crack propagation; (c) final fracture.
Acknowledgement
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