- Email: [email protected]
Fatigue strength evaluation of self-piercing riveted Al-5052 joints under different specimen configurations
International Journal of Fatigue 80 (2015) 58–68
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue strength evaluation of self-piercing riveted Al-5052 joints under different specimen configurations Se-Hyung Kang a, Ho-Kyung Kim b,⇑ a b
Graduate School, Seoul National University of Science and Technology, Seoul 139-743, Republic of Korea Dept. of Mechanical and Automotive Engineering, Seoul National University of Science and Technology, Seoul 139-743, Republic of Korea
a r t i c l e
i n f o
Article history: Received 21 January 2015 Received in revised form 7 May 2015 Accepted 10 May 2015
Keywords: SPR joints Fatigue lifetime Coach-peel Tensile–shear Equivalent stress intensity factor
a b s t r a c t In this study, static and fatigue tests were conducted using coach-peel, cross-tension and tensile–shear specimens with Al-5052 plates for evaluation of the fatigue strength of the SPR joints. For the coach-peel, cross-tension and tensile–shear geometries, the ratios of the fatigue endurance limit to static strength were 11%, 14% and 34%, respectively, assuming fatigue cycles of 106 for an infinite lifetime. The equivalent stress intensity factor range can properly predict the current experimental fatigue lifetime. Fatigue crack initiation occurred due to fretting damage between the upper and lower sheets and between the rivet and these sheets. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction One of the main objectives in the automotive industry currently is to reduce the weights of automobiles. To achieve this goal, a new joining technology as a replacement for spot welding in lightweight metals, such as aluminum and magnesium alloys, is required in the automotive industry. Riveting methods are often considered as substitutes for spot welding. Among the several types of riveting methods available, the self-piercing riveting (henceforth SPR) process is gaining in popularity due to its many advantages. SPR does not require a pre-drilled hole, and this method can be used to join a wide range of materials, including combinations of similar or dissimilar materials. SPR is essentially a cold-forming joining process. During the SPR process, a semi-tubular rivet is pressed by a punch into the sheets. The rivet pierces the upper sheet and flares into the bottom sheet under the influence of an upset die. A mechanical interlock is formed between the two sheets, which is key to the structural strength of the joints. The fatigue strength of the SPR joints has been investigated by a number of authors for a number of materials [1–6]. For example, Mori et al. [2] examined the static and fatigue strengths of spot-welded and self-piercing rivet joints in aluminum alloy sheets
⇑ Corresponding author. Tel.: +82 02 970 6348; fax: +82 02 979 7032. E-mail address: [email protected] (H.-K. Kim). http://dx.doi.org/10.1016/j.ijfatigue.2015.05.003 0142-1123/Ó 2015 Elsevier Ltd. All rights reserved.
under tensile–shear and cross-tension configurations. They observed that while the static strength of the self-piercing rivet joint was about 1.5 times as large as that of the spot-welded joints, the fatigue strength was increased by about three times in the tensile–shear configuration. He et al. [3] investigated the strength, stiffness, impact resistance, failure modes and failure mechanisms of SPR joints with similar and dissimilar metal sheets consisting of an aluminum alloy and a copper alloy. They reported that the fatigue strength of SPR joints was largely affected by the properties of the sheets and that both the static and fatigue strength of SPR joints increased with an enhancement of the joint stiffness. Xing et al. [4] investigated the static and fatigue strength of multiple-rivet SPR joints. They reported that these levels are influenced by the rivet number and rivet distribution pattern. Franco et al. [5] investigated the possibility of joining aluminum alloys and carbon fiber composites using SPR. They reported large values of the fatigue resistance of SPR joints, even for load amplitudes close to the maximum static resistance of the joint and a fairly large range of fatigue strengths. Su et al. [6] investigated the fatigue behavior of SPR and clinch joints in tensile–shear specimens of aluminum sheets. They reported that the experimental fatigue lives of these joints can be estimated using structural stress solutions. However, fatigue lifetime data of a SPR joint is normally reported as a function of the applied load range [7–9]. The reported fatigue strength data are not high enough to apply the other types of specimens due to the obscurity of the various factors that govern
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
59
Fig. 1. Stress–strain curves of the Al5052-H32 alloy.
Table 1 Mechanical properties of the Al5052-H32. Material
ru (MPa)
ry (MPa)
E (GPa)
Elong. (%)
Al5052-H32
251.7
186.7
78.3
10
their fatigue strengths. The fatigue lifetime of a SPR joint specimen is generally dependent on the load magnitude, the loading type, the dimensions and configuration of the specimen, the sheet material, and other factors. Even with the same rivet diameter, sheet material, and sheet thickness, the load range amplitude representing the fatigue strength can differ from one specimen type to another due to different loading types. Therefore, the fatigue strength data for the SPR joints under several types of loading are needed in order to design a structure with SPR joints. To solve this problem, it is desirable to adopt general structural parameters, such as the stress, strain, and multiaxial fatigue criteria, to assess the fatigue lifetimes of these joints. Thus far, there has not been any report on appropriate fatigue strength parameters to correlate the fatigue lifetimes of SPR joints with different specimen configurations. Therefore, in this study, fatigue tests under constant amplitude loads are conducted using coach-peel, cross-tension and tensile– shear specimens of Al-5052 aluminum alloy sheets to evaluate the fatigue strength of SPR joints under different specimen configurations. The experimental fatigue lifetimes of SPR joint specimens are also estimated using fatigue strength parameters. Finally, appropriate parameters for evaluating the fatigue lifetimes of three types of specimens are proposed.
Fig. 2. Geometries of three types of SPR specimens: (a) coach-peel, (b) crosstension and (c) tensile–shear.
2. Experimental procedure 2.1. Specimen preparation and fatigue test Al5052-H32 aluminum alloy sheets with a thickness of 1.5 mm were joined by SPR. Tensile tests on the sheet material were conducted in order to obtain the tensile stress–strain curve for a FEM structural analysis. The tensile specimen was machined to a uniform gage length and width of 70 mm and 12.5 mm,
Fig. 3. Cross-section of the SPR joint after riveting.
respectively. Fig. 1 shows the engineering stress–strain curve for the Al5052-H32 alloy. The mechanical properties of the material are summarized in Table 1.
60
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
Fig. 4. 2-D mesh about cross section from the center of the SPR joint.
Fig. 6. Punching force against the maximum tensile–shear force for the SPR specimens.
Fig. 7. Comparison of the applied load versus the displacement curves for the three specimen types.
Fig. 5. 3-D FEA models of SPR joints: (a) coach-peel, (b) cross-tension and (c) tensile–shear specimens.
Coach-peel, cross-tension and tensile–shear specimens, as shown in Fig. 2, were utilized to evaluate the static and fatigue strengths of the SPR joint. Steel rivets of 0.35 wt.% carbon steel with an aluminum surface coating (Almac) were used. Rivets with a diameter of 5.0 mm and a length of 5.0 mm were supplied by Henrob Ltd. A servo-hydraulic universal testing machine (Instron 8516) with a capacity of 100 kN was used for the SPR joining, static and fatigue tests. A special fixture was used for the SPR joining process. The fixture consists of a punch, a die and a blank holder. The fixture is mounted into a universal testing machine by fixing the die and punch with hydraulic grips. During the SPR process, the punch pushes the rivet through the hole in the blank holder, while, the die moves toward the blank holder to clamp the upper and lower sheets which are positioned between the die and the blank
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
holder. Fatigue tests were conducted at a load ratio R = (Pmin/Pmax) of 0.1 at a frequency of 12 Hz for the tensile–shear specimen and 2 Hz for the coach-peel and cross-tension specimens.
2.2. Structural analysis of the SPR joint specimen A three-dimensional finite element analysis (FEA) of a single self-piercing rivet was performed. The SPR joint, as shown in Fig. 3, is not perfectly axisymmetrical. Therefore, the shape and dimensions of the rivet after SPR joining were determined, as shown in Fig. 4, after averaging the dimensions of the rivet from its center. Finally, FEA models with a single SPR joint were completed for the coach-peel, cross-tension and tensile–shear specimen geometries, as shown in Fig. 5. FEA analyses were carried out using ABAQUS (version 6.6) for the solver and HyperMesh (version 7.0) as the pre- and post-processor.
Table 2 Summarized fatigue testing results for the (a) coach-peel, (b) cross-tension and (c) tensile–shear specimens. Note: 1 and 2 depict cracking failure in the upper and lower sheet, respectively. Pamp (N)
Nf (cycles)
Failure type
(a) 166.1 135.9 117.8 99.6 90.6 87.6 81.5 75.5 69.4
14,646 28,393 40,836 71,030 121,321 429,880 732,905 399,278 1,785,200
1 1 1 1 1 1 1 1 1
(b) 340.7 327.6 288.2 275.1 262.0 248.9 235.8 222.7 216.2 203.1 209.6
51,232 71,473 97,449 191,206 299,691 334,617 617,116 673,989 662,414 973,297 1,061,163
1 1 1 1 1 1 1 1 1 1 Non
(c) 1389.6 1327.8 1312.4 1296.9 1281.5 1273.8 1266.0 1250.6 1242.9 1235.2 1219.7 1212.0 1204.3 1204.3 1188.8 1173.4 1158.0 1158.0 1142.5 1142.5 1127.1 1080.8 1065.3 1034.4 1003.6 972.7
139,714 239,369 199,629 340,824 474,155 554,891 110,889 463,045 542,731 432,344 364,706 744,908 495,545 1,177,302 1,317,694 912,297 774,896 640,458 1,580,590 984,742 2,004,214 1,909,862 1,467,037 1,944,137 2,208,391 3,575,872
1 1 1 1 2 1 1 1,2 1,2 2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2 Non
61
A joint specimen was modeled using solid elements of C3D6 and C3D8. The models for the coach-peel, cross-tension and tensile–shear specimen were composed of 53,522 nodes with 44,480 elements, 57,176 nodes with 47,376 elements, 57,161 nodes with 47,576 elements, respectively. Contact between the rivet and sheet and between the upper and lower sheet faces was introduced by means of the master–slave technique. The friction coefficients between the rivet and sheet and between the upper and lower sheet faces were assumed to be 0.2 and 0.15, respectively [10]. True stress–strain curve data with a non-linear kinematic hardening elastic–plastic material model, as shown in Fig. 1, was adopted in the structural analysis. 3. Experimental results and discussion 3.1. Optimal punching force for SPR joining For SPR specimens, the joint strength is dependent on the sheet thickness, rivet diameter, die geometry, joining force, and other factors. In this study, a series of monotonic tensile tests was conducted on tensile–shear specimens with different amounts of punching force in an effort to determine the optimal punching force. Fig. 6 shows the punching force against the maximum tensile– shear force for the SPR specimens in this study. Each data point is the average value from two specimens. As the punching force increases, the maximum tensile–shear force increases continuously. The peak value is reached at a punching force of 21 kN with subsequent fluctuation, as shown in Fig. 6. Therefore, the optimal punching force was determined to be 21 kN for the current SPR joining condition. All of the coach-peel, cross-tension and tensile–shear SPR joint fatigue specimens were manufactured at the optimal punching force of 21 kN. 3.2. Evaluation of the monotonic strength of SPR joints Fig. 7 shows the monotonic test results after testing the force against the displacement for the coach-peel, cross-tension and tensile–shear SPR specimens produced with punching force of 21 kN. The coach-peel, cross-tension and tensile–shear specimens exhibit
Fig. 8. Load amplitude against the number of failure cycles for the three types of specimens.
62
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
maximum forces of approximately 700 N, 1650 N and 3450 N, respectively. The upper and lower sheet partially separated and failed after they reached the peak amount of force. The magnitudes of displacement for the coach-peel and cross-tension specimens were greater than that for the tensile–shear specimen under the same applied load. This implies that SPR joints are vulnerable to coach-peel and cross-tension loading as compared to tensile–shear loading. This also occurs in spot-welded and mechanical pressed joints [11]. 3.3. Evaluation of the fatigue lifetimes of SPR joints Fatigue tests were conducted on SPR joint specimens, with three types of geometries under a controlled cyclic load. The
fatigue lifetimes and failure modes are summarized in Table 2. Fig. 8 shows the applied load amplitude against the fatigue lifetimes for the coach-peel, cross-tension and tensile–shear specimens. The fatigue failure time was defined as a visible failure of the specimen. The fatigue strength of the tensile–shear specimens was found to be much higher than those of the coach-peel and cross-tension specimens. The difference is primarily due to the loading conditions on the SPR joint. The load amplitudes, corresponding to the fatigue strength at 106 cycles for the coach-peel, cross-tension and tensile–shear specimens, are 71 N, 210 N and 1150 N, respectively. These values are approximately 11%, 14% and 34% of the corresponding static strengths. The coach-peel and cross-tension specimen geometries have very low fatigue ratios, compared to that of the tensile–shear geometry, similar to
Fig. 9. Maximum principal stress distribution of SPR joints for fatigue lifetimes of 1.0 106: (a) coach-peel, (b) cross-tension and (c) tensile–shear.
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
63
Fig. 10. Fatigue failure specimens: (a) coach-peel, (b) cross-tension, (c) tensile–shear in the high-loading range and (d) tensile–shear in the low-loading range.
Fig. 11. Fatigue-fractured surface of the coach-peel experiment specimen in the low-loading condition (Pmax = 154.3 N); (a) fracture surface of the front view, (b) enlarged local area marked in (a), (c) enlarged local area of the crack initiation location, (d) enlarged local view of the area around the rivet, and (e) enlarged local area of the flat fracture surface.
the behavior of spot-welded and clinched joints [11]. The load amplitude as a function of the number of failure cycles can be expressed as: Pamp ¼ 715:5 N 0:166 , Pamp ¼ 1967:3 N 0:162 and P amp ¼ 3395:5 N 0:078 for the coach-peel, cross-tension and tensile–shear specimens, respectively. 3.4. Structural analysis results The fatigue crack initiation sites observed in the experiments are close to the locations with the maximum principal stresses
from the FE analyses. The von Mises stress was found to be not as good as the maximum principal stress for identifying potential crack initiation positions. Fig. 9 shows the maximum principal stress distribution around the rivet at fatigue lifetimes of 106 for the three specimen geometries. Fig. 9(a) shows the stress distribution of the coach-peel specimen at P = 129 N with a maximum stress of approximately 203 MPa. Fig. 9(b) shows the stress distribution of the cross-tension specimen at P = 408 N with the maximum stress of approximately 217 MPa. These maximum stresses for the coach-peel and cross-tension specimens are located at faying (bottom) surface of the upper sheet near the rivet shank,
64
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
Fig. 12. Fatigue-fractured surface of a cross-tension specimen under a low-loading condition (Pmax = 582.3 N): (a) fracture surface of the front view and (b) enlarged local area indicated in (a), (c) enlarged local area of the crack initiation location, (d) enlarged local view of the area around the rivet, and (e) enlarged local view of the flat fracture surface.
Fig. 13. Fracture surfaces of the upper sheet of the tensile–shear specimen in a high-loading condition (Pmax = 2882 N).
identical to the crack initiation site. Fig. 9(c) shows the stress distribution of the tensile–shear specimen at P = 2653 N. The maximum stress of approximately 312 MPa is located at the rivet tail, which is in contact with the lower sheet, close to the crack initiation site. The value of 312 MPa is much higher than ultimate tensile strength of the Al5052 H32 sheet (=252 MPa). The excessive stress level is partially caused from the FEA, which did not account for the residual stress produced during SPR joining. Furthermore,
adopting cyclic stress–strain curve data may produce better results than the true stress–strain curve for a structural analysis of a joint under repeated loading. 3.5. Fatigue failure mode The fatigue-fractured surfaces and wear scars at the interfaces between the aluminum sheet and rivet were investigated by a
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
65
Fig. 14. Fracture surfaces of the lower sheet for the tensile–shear specimen in the low-loading condition (Pmax = 2230 N).
Table 3 EDX analysis on the fretting region for tensile–shear specimens under the lowloading condition (Pmax = 2230.2 N) (wt.%). Element
Rivet
Bare surface of Al-5052
Fretted surface of Al-5052
C N O Mg Al Si Cl Fe Zn Sn Total
9.61 1.31 16.48 – 4.02 1.03 0.43 0.34 32.55 34.02 100
3.04 – 6.64 3.08 87.24 – – – – – 100
1.40 – 47.08 0.35 20.35 0.33 – 0.76 21.60 8.13 100
scanning electron microscope (SEM, Model JSM 6400) in an energy dispersive X-ray (EDX) analysis. In monotonic tests, a rivet was pulled out of the lower sheet with large plastic deformation near the rivet. However, the failure modes of the fatigue test differed from those of the monotonic tests. Fig. 10(a) and (b) shows the fatigue failure type for the coach-peel and cross-tension specimens, respectively, where fatigue crack initiation generally occurred near the rivet on the upper sheet and propagated across the upper sheet. Fig. 10(c) shows the fatigue-failed tensile–shear specimen in a high-loading (low fatigue lifetimes) region (P = 1273.8 < Pamp < P = 1420.4 N). This type is typically an eyebrow failure. A fatigue crack generally initiated on the faying (bottom) surface of the upper sheet slightly away from the rivet shank due to fretting damage. It then propagated through the upper sheet thickness perpendicular to the loading direction. Therefore, the tensile–shear specimens mainly failed due to fatigue with crack growth in the upper sheet, as shown in Table 1. Fig. 10(d) shows the fatiguefailed tensile–shear specimen in the low-loading (high fatigue lifetimes) region (P = 1003.6 < Pamp < P = 1188.8 N). Fatigue crack initiation generally occurred near the rivet tail on the lower sheet due to fretting damage. The crack then propagated across the lower sheet perpendicular to the loading direction. Fig. 11(b) is an enlarged figure of the ‘‘1’’ location Fig. 11(a), showing the fatigue-fractured upper sheet of the coach-peel
specimen at Pmax = 154.3 N. Fig. 11(c), (d), and (e) are enlarged figures of locations (2), (3), and (4) in Fig. 11(b), respectively. Fatigue crack initiated at (2) and propagated into (3) and (4) in Fig. 11(b). As shown Fig. 11(c), fatigue crack initiated at the location corresponding to the left edge of the sheet at location ‘‘1’’ in Fig. 11(a), coming into contact with the rivet and then propagating in the direction indicated by the arrow, as shown in Fig. 11(d) and (e). Fig. 12 shows the fatigue-fractured upper sheet of the cross-tension specimen at Pmax = 582.3 N. Fig. 12(b) is an enlarged view of the ‘‘1’’ location in Fig. 12(a). Fig. 12(c), (d), and (e) are enlarged views of locations (2), (3), and (4) in Fig. 12(b), respectively. Fatigue crack initiated at location (2) and propagated into locations (3) and (4) in Fig. 12(b). As shown in Fig. 12(c), fatigue crack initiated at the location corresponding to the left edge of the sheet in location ‘‘1’’ in Fig. 12(a), coming into contact with the rivet and propagating in the direction indicated by the arrow, as shown in Fig. 12(d) and (e). Oxidized (black) wear was observed due to rubbing between the rivet shank and the upper sheet. Bolt generally causes fretting damage during fatigue due to very small relative displacement of the contacting surfaces of between the upper and lower sheets and between the bolt and these sheets [12]. The condition of the SPR joints is similar. Fig. 13 shows the fatigue-fractured surfaces of the upper sheet of the tensile–shear specimen under a high-loading condition (Pmax = 2882 N). Oxidized black wear debris was observed on the upper sheet caused by it rubbing against the lower sheet. Several micro-cracks (as denoted by the square in Fig. 13) are visible in the fretting region. The fatigue crack initiated on the faying (bottom) surface of the upper sheet due to fretting. A crack grew through the upper sheet thickness and propagated perpendicular to the loading direction, finally resulting in a fracture with excessive plastic deformation. Fig. 14 shows the fretting region of the SPR joint with the tensile–shear specimen geometry under a low-loading condition (Pmax = 2230 N). Fretting wear patterns and multiple crack initiation sites are visible at the interface between the lower sheet and the rivet skirt. For this specimen, it can be judged that crack initiation occurred due to fretting at the interface between the rivet
66
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
shank and the lower sheet, after which the crack propagated along the sheet thickness. The chemical compositions of the fretting zone of the lower sheet in Fig. 14, the bare Al-5052 sheet and the rivet were analyzed using an EDX system and compared, as shown in Table 3. Additional elements of Si, Fe, Zn, Sn, Cl and N were detected in the fretting zone, compared to the chemical compositions of the bare Al-5052 sheet surface without fretting, suggesting that these elements stemmed from contamination due to rubbing by the rivet during fatigue cycling. Specifically much more oxygen exists in the fretting zone, indicating that this fretting zone is oxidized. In summary, Fig. 15 shows the fretting region of the tensile–shear specimen with a SPR joint under the high and low load conditions.
engineering components. In this study, the von Mises stress, maximum principal stress and SWT (Smith–Watson–Topper) fatigue parameter [13] are selected to predict the fatigue lifetimes for the three types specimen geometries. The von Mises effective stress is generally used to predict the fatigue failure lifetimes of components with complicated geometries. The maximum principal stress was chosen because FEA results reveal that the locations with the maximum principal stress coincide with the crack initiation sites of the three specimen geometries. The SWT fatigue parameter is frequently correlated fatigue lifetimes of components under multiaxial loading [13]. Therefore, the SWT relationship was utilized to evaluate the fatigue life of the SPR joints. SWT relationship is expressed as shown below [13], 0 2
De1 ðrf Þ ¼ ð2Nf Þ2b þ r0f e0f ð2N f Þbþc ¼ f ðNf Þ 2 E
3.6. Application of multiaxial stress fatigue criterion to fatigue lifetimes
rmax 1
SPR joints that undergo fatigue loading generally experience multiaxial stresses. Several multiaxial fatigue criterions [13–16] have been proposed to predict fatigue lifetimes of many
where, De1 =2 is the maximum principal strain amplitude and rmax 1 is the maximum stress on the De1 plane. Thus, the SWT FP (fatigue parameter) of the term on the left in Eq. (1) was selected to evaluate
Fig. 15. Fretting region of the tensile–shear specimen with a SPR joint under (a) high-loading and (b) low-loading conditions.
ð1Þ
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
67
Fig. 16(a), (b), and (c), the effective stress, the maximum principal stress, and SWT fatigue parameter are not sufficient to correlate the fatigue lifetimes for the coach-peel, cross-tension and tensile– shear specimen geometries of SPR joints. For spot welds, crack tips or notch tips arise due to the geometry along the nugget circumference. Stress intensity factor (SIF) solutions for spot welds at critical locations have been developed to investigate the fatigue lifetimes of spot welds [17]. For SPR joints, their faying surface of SPR joints, i.e., where two sheets are joined, can be considered as a crack or notch. Cracking initiates from faying surfaces partially due to fretting, meaning that SPR joints, similar to spot-welded joints, can be evaluated by fracture mechanics to investigate the fatigue lifetimes of SPR joints in various types of specimens. Therefore, the SIF can be used to correlate the fatigue data of the three types SPR specimens. In this study, the SPR joints in the test specimens are considered to be identical to spot-welded joints. Thus, the SIFs of spot-welded joints were directly adopted to calculate the SIFs of the SPR joint specimens. The equivalent SIFs at the spot weld in various geometries of specimens are known [17]. The equivalent SIF at a spot weld are shown below,
K cp eq ¼ 1:103
eF pffiffi dt t
ð2Þ
K ct eq ¼ 0:108
cF pffiffi dt t
ð3Þ
F K tseq ¼ 0:694 pffiffi d t
ð4Þ
for the coach-peel, cross-tension and tensile–shear spot welds specimen geometries, which have the corresponding superscript notation of cp, ct and ts. Here, F is the applied load range, d (=5 mm) is the rivet diameter, t (=1.5 mm) denotes the specimen thickness, c (=50 mm) is the load spacing, and e (=15 mm) represents the eccentricity, as shown in Fig. 2. The test data in terms of the load range were converted with the aid of formulas into the equivalent SIF range. As shown in Fig. 17, the equivalent stress intensity factor range (R 0.90) shows a good correlation with experimental fatigue
Fig. 16. The experimented fatigue lifetimes for SPR joints as a function of (a) the maximum von Mises stress, (b) the maximum principal stress and (c) the SWT multiaxial fatigue criteria.
the fatigue lifetimes of the SPR joints. The stress and strain distribution obtained from the FE models was used as a parameter to determine the fatigue lifetime of each specimen’s geometry. As shown in
Fig. 17. The experimental fatigue lifetimes as a function of the effective stress intensity factor range for SPR joints.
68
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
describes the experimental fatigue lifetime data under various loading conditions, compared to the effective, maximum principal stress and the SWT fatigue parameter, such that the fatigue lifetimes for SPR joints can be predicted quantitatively for any type of specimen through the equivalent stress intensity factor range. Failure modes of the fatigue test differed from those of monotonic tests. For the coach-peel and cross-tension specimens, fatigue crack initiation generally occurred near the rivet on the upper sheet and propagated across the upper sheet. However, for the tensile–shear specimen, fatigue cracking generally initiated on the faying surface of the upper sheet slightly away from the rivet shank due to fretting damage. It then propagated through the upper sheet thickness perpendicular to the loading direction in the high-loading test region. Fatigue crack initiation generally occurred near the rivet tail on the lower sheet due to fretting damage. The crack then propagated across the lower sheet in the low-loading test region. Acknowledgements
Fig. 18. Estimated fatigue lifetimes using the equivalent stress intensity factor range versus the experimental fatigue lifetimes for the three types specimens.
lifetime data, compared to data based on the effective, maximum principal stress and SWT fatigue parameter. This fact indicates that the crack initiation and growth near the SPR joint circumference are controlled by the stress intensity factors of the cracks near the joints. The results of the comparison of the calculated and experimental fatigue lifetimes using the equivalent stress intensity factor range are shown in Fig. 18. It can be seen in this plot that most of the data points fall within a factor of three. Thus, it is possible to achieve a good correlation between the experimental and calculated fatigue lifetimes with the stress intensity factor for SPR joint. Therefore, in the engineering field, for fatigue analysis of automotive body structure with SPR joints, the joint can be simply modeled, instead being modeled in detail, as connection elements which transfer forces and moments similarly to spot-welded joint. Finally, the fatigue strength of SPR joint can be determined simply with geometrical dimensions and applied loads under various loading conditions. 4. Conclusion In this study, static strength and fatigue tests were conducted with coach-peel, cross-tension and tensile-shear specimens with Al-5052 plates for an evaluation of the fatigue strength of SPR joints. A structural analysis of the three types of specimens was carried out using the finite element code ABAQUS. For the tensile–shear specimen with Al-5052 plates, the optimal applied punching force for the SPR joining process was found to be 21 kN using the current sheet thickness of 1.5 mm and the geometrical dimensions of the rivet. For the coach-peel, cross-tension and tensile–shear geometries, the fatigue endurance limits were determined to be 71 N, 1460 N, and 1150 N, respectively, assuming fatigue cycles of 106 for an infinite lifetime. The corresponding ratios of the fatigue endurance limit to the static strength were 11%, 14% and 34%. This indicates that the SPR joints are vulnerable to coach-peel and cross-tension loading, compared to tensile– shear loading. The equivalent stress intensity factor range suitably
This study was financially supported by Seoul National University of Science & Technology. The authors would like to acknowledge Monotec Korea for providing the rivets and the fixture for the SPR process. References [1] Fu M, Mallick PK. Fatigue of self-piercing riveted joints in aluminum alloy 6111. Int J Fatigue 2003;25:183–9. [2] Mori K, Abe Y, Kato T. Mechanism of superiority of fatigue strength for aluminum alloy sheets joined by mechanical clinching and self-pierce riveting. J Mater Process Technol 2012;212:1900–5. [3] He X, Zhao L, Deng C, Xing B, Gu F, Ball A. Self-piercing riveting of similar and dissimilar metal sheets of aluminum alloy and copper alloy. Mater Des 2015;65:923–33. [4] Xing B, He X, Zeng K, Wang Y. Mechanical properties of self-piercing riveted joints in aluminum alloy 5052. Int J Adv Manuf Technol 2014;75:351–61. [5] Franco GD, Fratini L, Pasta A, Ruisi VF. On the self-piercing riveting of aluminum blanks and carbon fiber composite panels. Int J Mater Form 2013;6:137–44. [6] Su Z, Lin P, Lai W, Pan J. Fatigue analyses of self-piercing rivets and clinch joints in lap-shear specimens of aluminum sheets. Int J Fatigue 2015;72:53–65. [7] Han L, Chrysanthou A, Sullivan JMO. Fretting behavior of self-piercing riveted aluminium alloy joints under different interfacial conditions. Mater Des 2006;27:200–8. [8] Huang Z, Zhou Z, Huang W. Mechanical behaviors of self-piercing riveting joining dissimilar sheets. Adv Mater Res 2010;97–101:3932–5. [9] Miyashita Y, Teow YCJ, Karasawa T, Aoyagi N, Otsuka Y, Mutoh Y. Strength of adhesive aided SPR joint for AM50 magnesium alloy sheets. Proc Eng 2011;10:2532–7. [10] Porcaro R, Hanssen AG, Langseth M, Aalberg A. The behaviour of a self-piercing riveted connection under quasi-static loading conditions. Int J Solids Struct 2006;43:5110–31. [11] Krause AR, Chernenkoff RA. A comparative study of the fatigue behavior of spot welded and mechanically fastened aluminum joints. SAE technical paper series 950710; 1995. [12] Zografos A, Dini D, Olver AV. Fretting fatigue and wear in bolted connections: a multi-level formulation for the computation of local contact stresses. Tribol Int 2009;42:1663–75. [13] Smith RN, Watson P, Topper TH. A stress strain function for the fatigue of metal. J Mater 1970;5:767–78. [14] Fatemi A, Socie DF. A critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fatigue Fract Eng Mater Struct 1988;11:149–65. [15] Li J, Zhang ZP, Sun Q, Li CW, Qiao YJ. A new multiaxial fatigue damage model for various metallic materials under the combination of tension and torsion loadings. Int J Fatigue 2009;31:776–81. [16] Glinka G, Shen G, Plumtree A. A multiaxial fatigue strain energy density parameter related to the critical plane. Fatigue Fract Eng Mater Struct 1995;18:37–46. [17] Zhang S. Stress intensities at spot welds. Int J Fract 1997;88:167–85.
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Fatigue strength evaluation of self-piercing riveted Al-5052 joints under different specimen configurations Se-Hyung Kang a, Ho-Kyung Kim b,⇑ a b
Graduate School, Seoul National University of Science and Technology, Seoul 139-743, Republic of Korea Dept. of Mechanical and Automotive Engineering, Seoul National University of Science and Technology, Seoul 139-743, Republic of Korea
a r t i c l e
i n f o
Article history: Received 21 January 2015 Received in revised form 7 May 2015 Accepted 10 May 2015
Keywords: SPR joints Fatigue lifetime Coach-peel Tensile–shear Equivalent stress intensity factor
a b s t r a c t In this study, static and fatigue tests were conducted using coach-peel, cross-tension and tensile–shear specimens with Al-5052 plates for evaluation of the fatigue strength of the SPR joints. For the coach-peel, cross-tension and tensile–shear geometries, the ratios of the fatigue endurance limit to static strength were 11%, 14% and 34%, respectively, assuming fatigue cycles of 106 for an infinite lifetime. The equivalent stress intensity factor range can properly predict the current experimental fatigue lifetime. Fatigue crack initiation occurred due to fretting damage between the upper and lower sheets and between the rivet and these sheets. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction One of the main objectives in the automotive industry currently is to reduce the weights of automobiles. To achieve this goal, a new joining technology as a replacement for spot welding in lightweight metals, such as aluminum and magnesium alloys, is required in the automotive industry. Riveting methods are often considered as substitutes for spot welding. Among the several types of riveting methods available, the self-piercing riveting (henceforth SPR) process is gaining in popularity due to its many advantages. SPR does not require a pre-drilled hole, and this method can be used to join a wide range of materials, including combinations of similar or dissimilar materials. SPR is essentially a cold-forming joining process. During the SPR process, a semi-tubular rivet is pressed by a punch into the sheets. The rivet pierces the upper sheet and flares into the bottom sheet under the influence of an upset die. A mechanical interlock is formed between the two sheets, which is key to the structural strength of the joints. The fatigue strength of the SPR joints has been investigated by a number of authors for a number of materials [1–6]. For example, Mori et al. [2] examined the static and fatigue strengths of spot-welded and self-piercing rivet joints in aluminum alloy sheets
⇑ Corresponding author. Tel.: +82 02 970 6348; fax: +82 02 979 7032. E-mail address: [email protected] (H.-K. Kim). http://dx.doi.org/10.1016/j.ijfatigue.2015.05.003 0142-1123/Ó 2015 Elsevier Ltd. All rights reserved.
under tensile–shear and cross-tension configurations. They observed that while the static strength of the self-piercing rivet joint was about 1.5 times as large as that of the spot-welded joints, the fatigue strength was increased by about three times in the tensile–shear configuration. He et al. [3] investigated the strength, stiffness, impact resistance, failure modes and failure mechanisms of SPR joints with similar and dissimilar metal sheets consisting of an aluminum alloy and a copper alloy. They reported that the fatigue strength of SPR joints was largely affected by the properties of the sheets and that both the static and fatigue strength of SPR joints increased with an enhancement of the joint stiffness. Xing et al. [4] investigated the static and fatigue strength of multiple-rivet SPR joints. They reported that these levels are influenced by the rivet number and rivet distribution pattern. Franco et al. [5] investigated the possibility of joining aluminum alloys and carbon fiber composites using SPR. They reported large values of the fatigue resistance of SPR joints, even for load amplitudes close to the maximum static resistance of the joint and a fairly large range of fatigue strengths. Su et al. [6] investigated the fatigue behavior of SPR and clinch joints in tensile–shear specimens of aluminum sheets. They reported that the experimental fatigue lives of these joints can be estimated using structural stress solutions. However, fatigue lifetime data of a SPR joint is normally reported as a function of the applied load range [7–9]. The reported fatigue strength data are not high enough to apply the other types of specimens due to the obscurity of the various factors that govern
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
59
Fig. 1. Stress–strain curves of the Al5052-H32 alloy.
Table 1 Mechanical properties of the Al5052-H32. Material
ru (MPa)
ry (MPa)
E (GPa)
Elong. (%)
Al5052-H32
251.7
186.7
78.3
10
their fatigue strengths. The fatigue lifetime of a SPR joint specimen is generally dependent on the load magnitude, the loading type, the dimensions and configuration of the specimen, the sheet material, and other factors. Even with the same rivet diameter, sheet material, and sheet thickness, the load range amplitude representing the fatigue strength can differ from one specimen type to another due to different loading types. Therefore, the fatigue strength data for the SPR joints under several types of loading are needed in order to design a structure with SPR joints. To solve this problem, it is desirable to adopt general structural parameters, such as the stress, strain, and multiaxial fatigue criteria, to assess the fatigue lifetimes of these joints. Thus far, there has not been any report on appropriate fatigue strength parameters to correlate the fatigue lifetimes of SPR joints with different specimen configurations. Therefore, in this study, fatigue tests under constant amplitude loads are conducted using coach-peel, cross-tension and tensile– shear specimens of Al-5052 aluminum alloy sheets to evaluate the fatigue strength of SPR joints under different specimen configurations. The experimental fatigue lifetimes of SPR joint specimens are also estimated using fatigue strength parameters. Finally, appropriate parameters for evaluating the fatigue lifetimes of three types of specimens are proposed.
Fig. 2. Geometries of three types of SPR specimens: (a) coach-peel, (b) crosstension and (c) tensile–shear.
2. Experimental procedure 2.1. Specimen preparation and fatigue test Al5052-H32 aluminum alloy sheets with a thickness of 1.5 mm were joined by SPR. Tensile tests on the sheet material were conducted in order to obtain the tensile stress–strain curve for a FEM structural analysis. The tensile specimen was machined to a uniform gage length and width of 70 mm and 12.5 mm,
Fig. 3. Cross-section of the SPR joint after riveting.
respectively. Fig. 1 shows the engineering stress–strain curve for the Al5052-H32 alloy. The mechanical properties of the material are summarized in Table 1.
60
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
Fig. 4. 2-D mesh about cross section from the center of the SPR joint.
Fig. 6. Punching force against the maximum tensile–shear force for the SPR specimens.
Fig. 7. Comparison of the applied load versus the displacement curves for the three specimen types.
Fig. 5. 3-D FEA models of SPR joints: (a) coach-peel, (b) cross-tension and (c) tensile–shear specimens.
Coach-peel, cross-tension and tensile–shear specimens, as shown in Fig. 2, were utilized to evaluate the static and fatigue strengths of the SPR joint. Steel rivets of 0.35 wt.% carbon steel with an aluminum surface coating (Almac) were used. Rivets with a diameter of 5.0 mm and a length of 5.0 mm were supplied by Henrob Ltd. A servo-hydraulic universal testing machine (Instron 8516) with a capacity of 100 kN was used for the SPR joining, static and fatigue tests. A special fixture was used for the SPR joining process. The fixture consists of a punch, a die and a blank holder. The fixture is mounted into a universal testing machine by fixing the die and punch with hydraulic grips. During the SPR process, the punch pushes the rivet through the hole in the blank holder, while, the die moves toward the blank holder to clamp the upper and lower sheets which are positioned between the die and the blank
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
holder. Fatigue tests were conducted at a load ratio R = (Pmin/Pmax) of 0.1 at a frequency of 12 Hz for the tensile–shear specimen and 2 Hz for the coach-peel and cross-tension specimens.
2.2. Structural analysis of the SPR joint specimen A three-dimensional finite element analysis (FEA) of a single self-piercing rivet was performed. The SPR joint, as shown in Fig. 3, is not perfectly axisymmetrical. Therefore, the shape and dimensions of the rivet after SPR joining were determined, as shown in Fig. 4, after averaging the dimensions of the rivet from its center. Finally, FEA models with a single SPR joint were completed for the coach-peel, cross-tension and tensile–shear specimen geometries, as shown in Fig. 5. FEA analyses were carried out using ABAQUS (version 6.6) for the solver and HyperMesh (version 7.0) as the pre- and post-processor.
Table 2 Summarized fatigue testing results for the (a) coach-peel, (b) cross-tension and (c) tensile–shear specimens. Note: 1 and 2 depict cracking failure in the upper and lower sheet, respectively. Pamp (N)
Nf (cycles)
Failure type
(a) 166.1 135.9 117.8 99.6 90.6 87.6 81.5 75.5 69.4
14,646 28,393 40,836 71,030 121,321 429,880 732,905 399,278 1,785,200
1 1 1 1 1 1 1 1 1
(b) 340.7 327.6 288.2 275.1 262.0 248.9 235.8 222.7 216.2 203.1 209.6
51,232 71,473 97,449 191,206 299,691 334,617 617,116 673,989 662,414 973,297 1,061,163
1 1 1 1 1 1 1 1 1 1 Non
(c) 1389.6 1327.8 1312.4 1296.9 1281.5 1273.8 1266.0 1250.6 1242.9 1235.2 1219.7 1212.0 1204.3 1204.3 1188.8 1173.4 1158.0 1158.0 1142.5 1142.5 1127.1 1080.8 1065.3 1034.4 1003.6 972.7
139,714 239,369 199,629 340,824 474,155 554,891 110,889 463,045 542,731 432,344 364,706 744,908 495,545 1,177,302 1,317,694 912,297 774,896 640,458 1,580,590 984,742 2,004,214 1,909,862 1,467,037 1,944,137 2,208,391 3,575,872
1 1 1 1 2 1 1 1,2 1,2 2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 2 Non
61
A joint specimen was modeled using solid elements of C3D6 and C3D8. The models for the coach-peel, cross-tension and tensile–shear specimen were composed of 53,522 nodes with 44,480 elements, 57,176 nodes with 47,376 elements, 57,161 nodes with 47,576 elements, respectively. Contact between the rivet and sheet and between the upper and lower sheet faces was introduced by means of the master–slave technique. The friction coefficients between the rivet and sheet and between the upper and lower sheet faces were assumed to be 0.2 and 0.15, respectively [10]. True stress–strain curve data with a non-linear kinematic hardening elastic–plastic material model, as shown in Fig. 1, was adopted in the structural analysis. 3. Experimental results and discussion 3.1. Optimal punching force for SPR joining For SPR specimens, the joint strength is dependent on the sheet thickness, rivet diameter, die geometry, joining force, and other factors. In this study, a series of monotonic tensile tests was conducted on tensile–shear specimens with different amounts of punching force in an effort to determine the optimal punching force. Fig. 6 shows the punching force against the maximum tensile– shear force for the SPR specimens in this study. Each data point is the average value from two specimens. As the punching force increases, the maximum tensile–shear force increases continuously. The peak value is reached at a punching force of 21 kN with subsequent fluctuation, as shown in Fig. 6. Therefore, the optimal punching force was determined to be 21 kN for the current SPR joining condition. All of the coach-peel, cross-tension and tensile–shear SPR joint fatigue specimens were manufactured at the optimal punching force of 21 kN. 3.2. Evaluation of the monotonic strength of SPR joints Fig. 7 shows the monotonic test results after testing the force against the displacement for the coach-peel, cross-tension and tensile–shear SPR specimens produced with punching force of 21 kN. The coach-peel, cross-tension and tensile–shear specimens exhibit
Fig. 8. Load amplitude against the number of failure cycles for the three types of specimens.
62
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
maximum forces of approximately 700 N, 1650 N and 3450 N, respectively. The upper and lower sheet partially separated and failed after they reached the peak amount of force. The magnitudes of displacement for the coach-peel and cross-tension specimens were greater than that for the tensile–shear specimen under the same applied load. This implies that SPR joints are vulnerable to coach-peel and cross-tension loading as compared to tensile–shear loading. This also occurs in spot-welded and mechanical pressed joints [11]. 3.3. Evaluation of the fatigue lifetimes of SPR joints Fatigue tests were conducted on SPR joint specimens, with three types of geometries under a controlled cyclic load. The
fatigue lifetimes and failure modes are summarized in Table 2. Fig. 8 shows the applied load amplitude against the fatigue lifetimes for the coach-peel, cross-tension and tensile–shear specimens. The fatigue failure time was defined as a visible failure of the specimen. The fatigue strength of the tensile–shear specimens was found to be much higher than those of the coach-peel and cross-tension specimens. The difference is primarily due to the loading conditions on the SPR joint. The load amplitudes, corresponding to the fatigue strength at 106 cycles for the coach-peel, cross-tension and tensile–shear specimens, are 71 N, 210 N and 1150 N, respectively. These values are approximately 11%, 14% and 34% of the corresponding static strengths. The coach-peel and cross-tension specimen geometries have very low fatigue ratios, compared to that of the tensile–shear geometry, similar to
Fig. 9. Maximum principal stress distribution of SPR joints for fatigue lifetimes of 1.0 106: (a) coach-peel, (b) cross-tension and (c) tensile–shear.
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
63
Fig. 10. Fatigue failure specimens: (a) coach-peel, (b) cross-tension, (c) tensile–shear in the high-loading range and (d) tensile–shear in the low-loading range.
Fig. 11. Fatigue-fractured surface of the coach-peel experiment specimen in the low-loading condition (Pmax = 154.3 N); (a) fracture surface of the front view, (b) enlarged local area marked in (a), (c) enlarged local area of the crack initiation location, (d) enlarged local view of the area around the rivet, and (e) enlarged local area of the flat fracture surface.
the behavior of spot-welded and clinched joints [11]. The load amplitude as a function of the number of failure cycles can be expressed as: Pamp ¼ 715:5 N 0:166 , Pamp ¼ 1967:3 N 0:162 and P amp ¼ 3395:5 N 0:078 for the coach-peel, cross-tension and tensile–shear specimens, respectively. 3.4. Structural analysis results The fatigue crack initiation sites observed in the experiments are close to the locations with the maximum principal stresses
from the FE analyses. The von Mises stress was found to be not as good as the maximum principal stress for identifying potential crack initiation positions. Fig. 9 shows the maximum principal stress distribution around the rivet at fatigue lifetimes of 106 for the three specimen geometries. Fig. 9(a) shows the stress distribution of the coach-peel specimen at P = 129 N with a maximum stress of approximately 203 MPa. Fig. 9(b) shows the stress distribution of the cross-tension specimen at P = 408 N with the maximum stress of approximately 217 MPa. These maximum stresses for the coach-peel and cross-tension specimens are located at faying (bottom) surface of the upper sheet near the rivet shank,
64
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
Fig. 12. Fatigue-fractured surface of a cross-tension specimen under a low-loading condition (Pmax = 582.3 N): (a) fracture surface of the front view and (b) enlarged local area indicated in (a), (c) enlarged local area of the crack initiation location, (d) enlarged local view of the area around the rivet, and (e) enlarged local view of the flat fracture surface.
Fig. 13. Fracture surfaces of the upper sheet of the tensile–shear specimen in a high-loading condition (Pmax = 2882 N).
identical to the crack initiation site. Fig. 9(c) shows the stress distribution of the tensile–shear specimen at P = 2653 N. The maximum stress of approximately 312 MPa is located at the rivet tail, which is in contact with the lower sheet, close to the crack initiation site. The value of 312 MPa is much higher than ultimate tensile strength of the Al5052 H32 sheet (=252 MPa). The excessive stress level is partially caused from the FEA, which did not account for the residual stress produced during SPR joining. Furthermore,
adopting cyclic stress–strain curve data may produce better results than the true stress–strain curve for a structural analysis of a joint under repeated loading. 3.5. Fatigue failure mode The fatigue-fractured surfaces and wear scars at the interfaces between the aluminum sheet and rivet were investigated by a
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
65
Fig. 14. Fracture surfaces of the lower sheet for the tensile–shear specimen in the low-loading condition (Pmax = 2230 N).
Table 3 EDX analysis on the fretting region for tensile–shear specimens under the lowloading condition (Pmax = 2230.2 N) (wt.%). Element
Rivet
Bare surface of Al-5052
Fretted surface of Al-5052
C N O Mg Al Si Cl Fe Zn Sn Total
9.61 1.31 16.48 – 4.02 1.03 0.43 0.34 32.55 34.02 100
3.04 – 6.64 3.08 87.24 – – – – – 100
1.40 – 47.08 0.35 20.35 0.33 – 0.76 21.60 8.13 100
scanning electron microscope (SEM, Model JSM 6400) in an energy dispersive X-ray (EDX) analysis. In monotonic tests, a rivet was pulled out of the lower sheet with large plastic deformation near the rivet. However, the failure modes of the fatigue test differed from those of the monotonic tests. Fig. 10(a) and (b) shows the fatigue failure type for the coach-peel and cross-tension specimens, respectively, where fatigue crack initiation generally occurred near the rivet on the upper sheet and propagated across the upper sheet. Fig. 10(c) shows the fatigue-failed tensile–shear specimen in a high-loading (low fatigue lifetimes) region (P = 1273.8 < Pamp < P = 1420.4 N). This type is typically an eyebrow failure. A fatigue crack generally initiated on the faying (bottom) surface of the upper sheet slightly away from the rivet shank due to fretting damage. It then propagated through the upper sheet thickness perpendicular to the loading direction. Therefore, the tensile–shear specimens mainly failed due to fatigue with crack growth in the upper sheet, as shown in Table 1. Fig. 10(d) shows the fatiguefailed tensile–shear specimen in the low-loading (high fatigue lifetimes) region (P = 1003.6 < Pamp < P = 1188.8 N). Fatigue crack initiation generally occurred near the rivet tail on the lower sheet due to fretting damage. The crack then propagated across the lower sheet perpendicular to the loading direction. Fig. 11(b) is an enlarged figure of the ‘‘1’’ location Fig. 11(a), showing the fatigue-fractured upper sheet of the coach-peel
specimen at Pmax = 154.3 N. Fig. 11(c), (d), and (e) are enlarged figures of locations (2), (3), and (4) in Fig. 11(b), respectively. Fatigue crack initiated at (2) and propagated into (3) and (4) in Fig. 11(b). As shown Fig. 11(c), fatigue crack initiated at the location corresponding to the left edge of the sheet at location ‘‘1’’ in Fig. 11(a), coming into contact with the rivet and then propagating in the direction indicated by the arrow, as shown in Fig. 11(d) and (e). Fig. 12 shows the fatigue-fractured upper sheet of the cross-tension specimen at Pmax = 582.3 N. Fig. 12(b) is an enlarged view of the ‘‘1’’ location in Fig. 12(a). Fig. 12(c), (d), and (e) are enlarged views of locations (2), (3), and (4) in Fig. 12(b), respectively. Fatigue crack initiated at location (2) and propagated into locations (3) and (4) in Fig. 12(b). As shown in Fig. 12(c), fatigue crack initiated at the location corresponding to the left edge of the sheet in location ‘‘1’’ in Fig. 12(a), coming into contact with the rivet and propagating in the direction indicated by the arrow, as shown in Fig. 12(d) and (e). Oxidized (black) wear was observed due to rubbing between the rivet shank and the upper sheet. Bolt generally causes fretting damage during fatigue due to very small relative displacement of the contacting surfaces of between the upper and lower sheets and between the bolt and these sheets [12]. The condition of the SPR joints is similar. Fig. 13 shows the fatigue-fractured surfaces of the upper sheet of the tensile–shear specimen under a high-loading condition (Pmax = 2882 N). Oxidized black wear debris was observed on the upper sheet caused by it rubbing against the lower sheet. Several micro-cracks (as denoted by the square in Fig. 13) are visible in the fretting region. The fatigue crack initiated on the faying (bottom) surface of the upper sheet due to fretting. A crack grew through the upper sheet thickness and propagated perpendicular to the loading direction, finally resulting in a fracture with excessive plastic deformation. Fig. 14 shows the fretting region of the SPR joint with the tensile–shear specimen geometry under a low-loading condition (Pmax = 2230 N). Fretting wear patterns and multiple crack initiation sites are visible at the interface between the lower sheet and the rivet skirt. For this specimen, it can be judged that crack initiation occurred due to fretting at the interface between the rivet
66
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
shank and the lower sheet, after which the crack propagated along the sheet thickness. The chemical compositions of the fretting zone of the lower sheet in Fig. 14, the bare Al-5052 sheet and the rivet were analyzed using an EDX system and compared, as shown in Table 3. Additional elements of Si, Fe, Zn, Sn, Cl and N were detected in the fretting zone, compared to the chemical compositions of the bare Al-5052 sheet surface without fretting, suggesting that these elements stemmed from contamination due to rubbing by the rivet during fatigue cycling. Specifically much more oxygen exists in the fretting zone, indicating that this fretting zone is oxidized. In summary, Fig. 15 shows the fretting region of the tensile–shear specimen with a SPR joint under the high and low load conditions.
engineering components. In this study, the von Mises stress, maximum principal stress and SWT (Smith–Watson–Topper) fatigue parameter [13] are selected to predict the fatigue lifetimes for the three types specimen geometries. The von Mises effective stress is generally used to predict the fatigue failure lifetimes of components with complicated geometries. The maximum principal stress was chosen because FEA results reveal that the locations with the maximum principal stress coincide with the crack initiation sites of the three specimen geometries. The SWT fatigue parameter is frequently correlated fatigue lifetimes of components under multiaxial loading [13]. Therefore, the SWT relationship was utilized to evaluate the fatigue life of the SPR joints. SWT relationship is expressed as shown below [13], 0 2
De1 ðrf Þ ¼ ð2Nf Þ2b þ r0f e0f ð2N f Þbþc ¼ f ðNf Þ 2 E
3.6. Application of multiaxial stress fatigue criterion to fatigue lifetimes
rmax 1
SPR joints that undergo fatigue loading generally experience multiaxial stresses. Several multiaxial fatigue criterions [13–16] have been proposed to predict fatigue lifetimes of many
where, De1 =2 is the maximum principal strain amplitude and rmax 1 is the maximum stress on the De1 plane. Thus, the SWT FP (fatigue parameter) of the term on the left in Eq. (1) was selected to evaluate
Fig. 15. Fretting region of the tensile–shear specimen with a SPR joint under (a) high-loading and (b) low-loading conditions.
ð1Þ
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
67
Fig. 16(a), (b), and (c), the effective stress, the maximum principal stress, and SWT fatigue parameter are not sufficient to correlate the fatigue lifetimes for the coach-peel, cross-tension and tensile– shear specimen geometries of SPR joints. For spot welds, crack tips or notch tips arise due to the geometry along the nugget circumference. Stress intensity factor (SIF) solutions for spot welds at critical locations have been developed to investigate the fatigue lifetimes of spot welds [17]. For SPR joints, their faying surface of SPR joints, i.e., where two sheets are joined, can be considered as a crack or notch. Cracking initiates from faying surfaces partially due to fretting, meaning that SPR joints, similar to spot-welded joints, can be evaluated by fracture mechanics to investigate the fatigue lifetimes of SPR joints in various types of specimens. Therefore, the SIF can be used to correlate the fatigue data of the three types SPR specimens. In this study, the SPR joints in the test specimens are considered to be identical to spot-welded joints. Thus, the SIFs of spot-welded joints were directly adopted to calculate the SIFs of the SPR joint specimens. The equivalent SIFs at the spot weld in various geometries of specimens are known [17]. The equivalent SIF at a spot weld are shown below,
K cp eq ¼ 1:103
eF pffiffi dt t
ð2Þ
K ct eq ¼ 0:108
cF pffiffi dt t
ð3Þ
F K tseq ¼ 0:694 pffiffi d t
ð4Þ
for the coach-peel, cross-tension and tensile–shear spot welds specimen geometries, which have the corresponding superscript notation of cp, ct and ts. Here, F is the applied load range, d (=5 mm) is the rivet diameter, t (=1.5 mm) denotes the specimen thickness, c (=50 mm) is the load spacing, and e (=15 mm) represents the eccentricity, as shown in Fig. 2. The test data in terms of the load range were converted with the aid of formulas into the equivalent SIF range. As shown in Fig. 17, the equivalent stress intensity factor range (R 0.90) shows a good correlation with experimental fatigue
Fig. 16. The experimented fatigue lifetimes for SPR joints as a function of (a) the maximum von Mises stress, (b) the maximum principal stress and (c) the SWT multiaxial fatigue criteria.
the fatigue lifetimes of the SPR joints. The stress and strain distribution obtained from the FE models was used as a parameter to determine the fatigue lifetime of each specimen’s geometry. As shown in
Fig. 17. The experimental fatigue lifetimes as a function of the effective stress intensity factor range for SPR joints.
68
S.-H. Kang, H.-K. Kim / International Journal of Fatigue 80 (2015) 58–68
describes the experimental fatigue lifetime data under various loading conditions, compared to the effective, maximum principal stress and the SWT fatigue parameter, such that the fatigue lifetimes for SPR joints can be predicted quantitatively for any type of specimen through the equivalent stress intensity factor range. Failure modes of the fatigue test differed from those of monotonic tests. For the coach-peel and cross-tension specimens, fatigue crack initiation generally occurred near the rivet on the upper sheet and propagated across the upper sheet. However, for the tensile–shear specimen, fatigue cracking generally initiated on the faying surface of the upper sheet slightly away from the rivet shank due to fretting damage. It then propagated through the upper sheet thickness perpendicular to the loading direction in the high-loading test region. Fatigue crack initiation generally occurred near the rivet tail on the lower sheet due to fretting damage. The crack then propagated across the lower sheet in the low-loading test region. Acknowledgements
Fig. 18. Estimated fatigue lifetimes using the equivalent stress intensity factor range versus the experimental fatigue lifetimes for the three types specimens.
lifetime data, compared to data based on the effective, maximum principal stress and SWT fatigue parameter. This fact indicates that the crack initiation and growth near the SPR joint circumference are controlled by the stress intensity factors of the cracks near the joints. The results of the comparison of the calculated and experimental fatigue lifetimes using the equivalent stress intensity factor range are shown in Fig. 18. It can be seen in this plot that most of the data points fall within a factor of three. Thus, it is possible to achieve a good correlation between the experimental and calculated fatigue lifetimes with the stress intensity factor for SPR joint. Therefore, in the engineering field, for fatigue analysis of automotive body structure with SPR joints, the joint can be simply modeled, instead being modeled in detail, as connection elements which transfer forces and moments similarly to spot-welded joint. Finally, the fatigue strength of SPR joint can be determined simply with geometrical dimensions and applied loads under various loading conditions. 4. Conclusion In this study, static strength and fatigue tests were conducted with coach-peel, cross-tension and tensile-shear specimens with Al-5052 plates for an evaluation of the fatigue strength of SPR joints. A structural analysis of the three types of specimens was carried out using the finite element code ABAQUS. For the tensile–shear specimen with Al-5052 plates, the optimal applied punching force for the SPR joining process was found to be 21 kN using the current sheet thickness of 1.5 mm and the geometrical dimensions of the rivet. For the coach-peel, cross-tension and tensile–shear geometries, the fatigue endurance limits were determined to be 71 N, 1460 N, and 1150 N, respectively, assuming fatigue cycles of 106 for an infinite lifetime. The corresponding ratios of the fatigue endurance limit to the static strength were 11%, 14% and 34%. This indicates that the SPR joints are vulnerable to coach-peel and cross-tension loading, compared to tensile– shear loading. The equivalent stress intensity factor range suitably
This study was financially supported by Seoul National University of Science & Technology. The authors would like to acknowledge Monotec Korea for providing the rivets and the fixture for the SPR process. References [1] Fu M, Mallick PK. Fatigue of self-piercing riveted joints in aluminum alloy 6111. Int J Fatigue 2003;25:183–9. [2] Mori K, Abe Y, Kato T. Mechanism of superiority of fatigue strength for aluminum alloy sheets joined by mechanical clinching and self-pierce riveting. J Mater Process Technol 2012;212:1900–5. [3] He X, Zhao L, Deng C, Xing B, Gu F, Ball A. Self-piercing riveting of similar and dissimilar metal sheets of aluminum alloy and copper alloy. Mater Des 2015;65:923–33. [4] Xing B, He X, Zeng K, Wang Y. Mechanical properties of self-piercing riveted joints in aluminum alloy 5052. Int J Adv Manuf Technol 2014;75:351–61. [5] Franco GD, Fratini L, Pasta A, Ruisi VF. On the self-piercing riveting of aluminum blanks and carbon fiber composite panels. Int J Mater Form 2013;6:137–44. [6] Su Z, Lin P, Lai W, Pan J. Fatigue analyses of self-piercing rivets and clinch joints in lap-shear specimens of aluminum sheets. Int J Fatigue 2015;72:53–65. [7] Han L, Chrysanthou A, Sullivan JMO. Fretting behavior of self-piercing riveted aluminium alloy joints under different interfacial conditions. Mater Des 2006;27:200–8. [8] Huang Z, Zhou Z, Huang W. Mechanical behaviors of self-piercing riveting joining dissimilar sheets. Adv Mater Res 2010;97–101:3932–5. [9] Miyashita Y, Teow YCJ, Karasawa T, Aoyagi N, Otsuka Y, Mutoh Y. Strength of adhesive aided SPR joint for AM50 magnesium alloy sheets. Proc Eng 2011;10:2532–7. [10] Porcaro R, Hanssen AG, Langseth M, Aalberg A. The behaviour of a self-piercing riveted connection under quasi-static loading conditions. Int J Solids Struct 2006;43:5110–31. [11] Krause AR, Chernenkoff RA. A comparative study of the fatigue behavior of spot welded and mechanically fastened aluminum joints. SAE technical paper series 950710; 1995. [12] Zografos A, Dini D, Olver AV. Fretting fatigue and wear in bolted connections: a multi-level formulation for the computation of local contact stresses. Tribol Int 2009;42:1663–75. [13] Smith RN, Watson P, Topper TH. A stress strain function for the fatigue of metal. J Mater 1970;5:767–78. [14] Fatemi A, Socie DF. A critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fatigue Fract Eng Mater Struct 1988;11:149–65. [15] Li J, Zhang ZP, Sun Q, Li CW, Qiao YJ. A new multiaxial fatigue damage model for various metallic materials under the combination of tension and torsion loadings. Int J Fatigue 2009;31:776–81. [16] Glinka G, Shen G, Plumtree A. A multiaxial fatigue strain energy density parameter related to the critical plane. Fatigue Fract Eng Mater Struct 1995;18:37–46. [17] Zhang S. Stress intensities at spot welds. Int J Fract 1997;88:167–85.