- Email: [email protected]
Simulating fretting contact in single lap splices
International Journal of Fatigue 31 (2009) 375–384
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Simulating fretting contact in single lap splices A.M. Brown *, P.V. Straznicky Department of Mechanical and Aerospace Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, Canada K1S 5B6
a r t i c l e
i n f o
Article history: Received 8 April 2008 Received in revised form 18 July 2008 Accepted 25 July 2008 Available online 5 August 2008 Keywords: Finite element Fretting Rivet forming Lap splice
a b s t r a c t Cracks in riveted lap splices commonly nucleate in regions of fretting damage around the fastener holes. The crack location is dependent upon the rivet squeeze force and the clamped faying surface area around the holes since fretting damage occurs at the edge of contact. Being able to predict the amount of faying surface clamping from rivet forming and the peaks in edge-of-contact stresses associated with fretting contact will help in the understanding of splice fatigue failure. This paper describes the development of a 3D finite element splice model that predicts the variation of contact area and edge-of-contact stresses in a loaded splice. The prediction is made for four rivet squeeze force levels and both universal and countersunk rivet styles. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction One of the most common structural joints in aircraft design is the riveted single lap splice. The joint is used, despite its drawbacks, because of its low cost and simplicity. When the single lap splice is used on modern commercial aircraft, it is subjected to loading from pressurization of the fuselage. Pressurization makes for more efficient and comfortable flights but every ground-airground pressurization cycle provides one major cycle of fatigue loading on the splices in the airframe. All other in-service fatigue loads are secondary to this. The presence of fasteners in fuselage lap splices introduces stress concentrations that eventually cause fatigue cracks to nucleate. A great deal of research has been performed to understand crack formation in riveted splices [1–3] but little work has been performed on the contribution of fretting to the nucleation of splice fatigue cracks. Fretting is the term used to describe a wear/corrosion phenomenon that takes place in clamped bodies undergoing oscillatory motion. It is theorized that asperities of two clamped surfaces in contact will cold-weld together under normal pressure. Upon the application of oscillatory tangential loading, the bond between the asperities will break leaving behind debris and local areas of yielding. The exposed debris and substrate material is left to corrode as the asperities stick once more on the next cycle. This process continues with each oscillation. Fretting damage can lead to the formation of micro-cracks in the surface that, in the presence of a tensile stress field, will propagate into the substrate. In aluminum, fretting damage is easily identified from the oxidized wear * Corresponding author. Tel.: +1 613 520 2600x1684; fax: +1 613 520 5715. E-mail address: [email protected] (A.M. Brown). 0142-1123/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2008.07.012
debris; a black powder surrounding or falling away from the clamped area. Some preliminary work has been performed on fretting in lap splices at Purdue University, Vanderbilt University, and at the National Research Council of Canada. In the case of each research group, strides were made in the understanding of fretting in lap splices; however, there has been no in-depth look at fretting damage on the faying sheet surface where cracks often nucleate in splices. The research performed at Purdue University [4–7] was limited to geometry consisting of universal (MS20470) rivets and relatively thick (1.8–2.3 mm) untreated 2024-T3 aluminum sheet. In joints of that thickness, with low rivet interference, it was found that the critical fretting region was the rivet/sheet interface and that cracks did not nucleate from the faying sheet surface. For thinner sheet thicknesses, such as the 1 mm sheet used in this study, with high rivet interference, the location of crack nucleation is on the faying sheet surface surrounding the hole [8–10]. This location corresponds to the edge-of-contact and the region of greatest fretting damage. Finite element models of fretting contact created at Purdue University utilized a variety of methods to simulate the riveted joints. These included 2D and 3D shell models as well as axi-symmetric rivet forming models. Szolwinski and Farris simulated rivet forming in 2.3 mm sheet and found the rivet clamping to be negligible [7]. Because of the low clamping, Harish and Farris later used a 2D model to simulate splice loading [5]. The 2D model from [5] included representative mid-plane residual stress fields obtained from the rivet forming step but did not include secondary bending stresses. A 2D model is not practical for this study as secondary bending effects are significant and it is necessary to know the
376
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
faying surface residual stress field when looking at edge-of-contact stresses. In addition, 2D models do not provide results for the contact distribution on the surface of the splice during sheet loading. Knowledge of the contact area is important for correlating the location of crack nucleation in the models to actual tested splices. A study by Iyer et al. [11] from Vanderbilt University examined fretting in pinned connections with coarse finite element models. The coarseness of the models did not allow for accurate determination of fretting contact stresses or faying surface clamping. Interference was included; however, the rivet forming step was not performed in the simulation. The interference was introduced by forcing conformity of an oversized rivet into the rivet hole. This provided a simplified estimation of uniform radial interference between the rivet and the hole. It has been shown in other studies that uniform rivet expansion does not occur with driven solid rivets [3]. Liao et al. of the National Research Council of Canada modelled a 3-row single lap splice that determined a relationship between rivet squeeze force, coefficient of friction, and residual stress in the splice [9]. The investigation did not, however, look at faying surface clamping area or stress concentrations at the edge-ofcontact. The goal of this work is to bring together the different facets of lap splice fretting into a single 3D finite element model. The simulation must therefore include: rivet forming steps to incorporate the residual stresses in the sheets and faying surface clamping associated with different rivet forming loads, and loading of the splice to observe any changes in the faying surface edge-of-contact stresses. Simulation of different rivet forming loads is performed because increasing the rivet squeeze force changes the residual stress field around the rivet hole and increases the clamping area between the sheets. These combined factors change the location of crack nucleation. This paper describes the development, verification and validation of a model to simulate fretting contact in a single lap splice for both countersunk and universal rivets and presents the results for four different rivet squeeze forces.
all geometry creation and meshing. Two single lap splice geometries were modelled with different rivet types inserted in the sheet. NAS1097AD-4-4 countersunk rivets and MS20470AD-4-4 universal rivets were both studied. To simulate the complex interactions and large deformations associated with rivet forming and splice loading, explicit simulations were used. The splices consisted of two rivet rows with a row pitch of 38.1 mm and a rivet pitch of 25.4 mm. One millimeter bare 2024-T3 aluminum was used for both the inner and outer sheets. Fig. 1 shows the overall dimensions of the models and illustrates how symmetry was used to model only half of the splice. Along with the inner sheet, outer sheet, and two rivets, four rigid platens were included in the models as the rivet forming tools. The 2024-T3 sheet material was modelled using Ramberg–Osgood parameters [15] and the material model for the 2117-T4 aluminum rivets was based on two power law curves [6]. The splice simulations were broken into four loading steps: rivet forming, rivet springback, splice loading, and splice unloading. In the first step, the portion of the splice outside 12.7 mm (0.500 ) of the rivets was constrained and the rivets were formed to a designated squeeze force (Fig. 2). In the second step, unloading of the rivets to 1% of the maximum forming load allowed for material springback while controlling oscillation that could be induced by completely releasing the load. At the same time, the portions of the sheets that were constrained during the rivet forming steps were released. Only the symmetry constraints and the constraints on the end of either sheet were maintained. The third step applied a stress of 100 MPa [16], a typical stress for narrow body aircraft, to one end of the splice while the other end remained fixed in the X and Y directions (Fig. 3). Finally, in the fourth step the splice was unloaded to 1% of the maximum splice load. Time scaling was used in the simulation with the rivet forming, rivet springback, splice loading, and splice springback steps taking
2. Development of 3D lap splice simulations 2.1. Modelling details The commercial code Abaqus v.6.6.1 was adopted to model fretting contact in a single lap splice as it is commonly used in fretting contact studies [12–14]. Hyperworks Hypermesh was chosen for
Fig. 2. Rivet forming step. 6.7 kN (1500 lbf).
240 mm 64 mm 12.7 mm 38.1 mm
Outer Sheet
Top Rivet Row
1.0 mm Bottom Rivet Row
Fig. 1. Splice coupon and FEM model geometry.
Inner Sheet
377
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
Fig. 3. Splice loading step.
place over 0.003, 0.003, 0.012, and 0.006 s, respectively. Pauses were included in the loading after each step to allow for damping of any oscillations in the system. Time scaling was appropriate in this situation because the loading is quasi-static and the kinetic energy of the system was well below 5% of the total internal energy during the simulation [17]. This indicated that dynamic effects were not significant. Penalty contact definitions were used for all contact surfaces with the exception of the faying surface of the sheets. Since the faying surface is the region known to experience fretting damage, kinematic contact was used to better enforce sticking of the contacting nodes. Friction was imposed using the basic Coulomb model. For all contact surfaces except the faying surface, a coefficient of friction (COF) of 0.178 [18] was used. For the faying surface contact, the coefficient of friction was changed after the rivet springback step from 0.178 to 0.65 [6]. The increase in COF was necessary to properly represent the increase in COF observed in fretting tests of 2024-T351 [6]. Initially, when the sheets are riveted together, no fretting damage exists and the COF has been measured to be 0.178. After a few thousand cycles, however, fretting damage begins and the COF increases. Measurements performed by Szolwinski [6] have shown that after a quick rise in COF, corresponding to the formation of fretting damage, the COF reaches a steady state value. If a COF of 0.65 had been used in all steps, the increased surface tractions, combined with non-uniform expansion of the rivet hole, would provide different residual stress results in the sheets. The meshes for the rivets and the sheets were generated using 8-node C3D8R solid elements whereas the meshes for the rigid tools were generated using 4-node S4R shell elements. The solid meshes in the splice were biased toward the rivet hole with an average element edge length of 0.1 mm (0.00400 ). Properly capturing the contact stresses in a finite element fretting contact problem normally requires fine meshes in conjunction with strict contact formulations. For the relatively large and complex problem of loading in a single lap splice, this could pose a problem. 2D simulations of fretting contact often have elements with edge lengths on the order of 6 lm in the contact region [12,19,20]. Expanding these meshes into 3D can quickly produce prohibitively large simulations. One solution, shown to be effective in 3D contact simulations by Kim and Shankar [21], is to use sub-modelling techniques. 2.2. Sub-modelling Sub-modelling requires that a global model be run with a set of driving elements defined in the area of interest (the contact region). A smaller sub-model is then created that includes only the elements from that area (Fig. 4). As this geometry is smaller, a finer mesh can be defined. The displacements from the driving elements in the global model are applied to the outer boundary of the submodel during the sub-model analysis. The sub-model can then be used as a global model for further refinement until sufficient convergence in the results is achieved [17].
Fig. 4. Illustration of sub-modelling technique applied to splice simulation.
In the splice simulations, the region around the rivet in the top row of the outer sheet was the area of interest (Fig. 4). This region is where secondary bending stresses will interact with fretting induced stress concentrations to nucleate a crack. In the countersunk rivet splice, the countersink will cause a greater stress concentration than for the universal riveted splice. It can be noted that it is not necessary to model the rivets in any of the sub-model simulations as long as the driving elements are defined along the hole edge. Removing the rivet from the sub-model saves on the computation cost as each rivet consists of over 70,000 elements. 3. Model verification and validation 3.1. Introduction Methods of verifying and validating the rivet forming step and the splice loading step are described in the following sections. Since the area of interest is under the rivet head around the holes, direct comparison or measurement becomes a problem. To overcome this difficulty, indirect methods have been used. These methods include stress convergence, indirect comparison to neutron diffraction data, and the use of pressure sensitive film. 3.2. Stress convergence Convergence of the stresses obtained from the sub-models was the first technique used for verification of the splice model. The maximum principal stresses at the edge of contact around the hole were compared in the 11.1 kN (2500 lbf) rivet forming case for the global model and two sub-models. The element size was reduced from 0.100 mm in the global model to 0.050 mm and 0.025 mm in the first and second sub-models respectively. Convergence results for the sub-model analyses are presented in Table 1. The percent difference from the previous model was calculated using Eq. (1) where rn+1 is the maximum stress in the current model and rn is the maximum stress in the previous model
Table 1 Convergence results for 3D splice model Model
Element edge length (mm)
Max principal stress MPa (psi)
Percentage of difference from previous
Global Sub-model 1 Sub-model 2
0.100 0.050 0.025
202.6 (29389) 263.2 (38171) 274.4 (39796)
– 23 4
378
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
nþ1 r rn 100 %Diff ¼ rnþ1
ð1Þ
Radial Strain (%)
Based on the convergence results, it was determined that only two sub-models would be required in future splice simulations. 3.3. Residual strains
3.4. Rivet forming step – pressure sensitive film The next method of validating that the simulated rivets match actual installed rivets was the use of pressure sensitive film. Pressure sensitive film changes colour with the application of an applied pressure. The intensity of the colour is related to the amount of the pressure that is applied. Different types of film are available from ‘‘Super low” to ‘‘Super high” with a pressure range
0.00 -0.05 -0.10 FEM - 2D axisymmetric FEM - 3D LSDyna FEM - 3D Abaqus Neutron Diffraction
-0.15 -0.20 5
10
15
44.5 kN Squeeze Force Outer Sheet z=1.1mm
0.20
0.10
0.00
FEM - 2D axisymmetric FEM - 3D LSDyna FEM - 3D Abaqus Neutron Diffraction
-0.10
-0.20 5
10
15
associated with each. For this study, the ‘‘Super high” film was chosen (141–300 MPa) and was placed between the sheets of both the countersunk and universal splice coupons (Fig. 10). The holes were then drilled, rivets inserted, and formed to the prescribed load. Drilling out of the rivets and removing the film from between the sheets then provided results for the maximum pressures experienced on the faying sheet surfaces during the rivet forming step. Checks were made to ensure that the initial hole drilling step did not generate pressures large enough to activate the film. The pressure distribution of each film was digitized and the intensity was analyzed using image software and calibration curves that are provided by the manufacturer. This allowed for greater resolution than simple visual comparisons. Fig. 11 shows a typical film pressure
z (mm)
Z
6 Y
8 15
25
Fig. 7. Hoop strain in the outer riveted sheet.
4
10
20
Distance to Rivet Centre (mm)
2
5
25
Fig. 6. Radial strain in the outer riveted sheet.
0
0
20
Distance to Rivet Centre (mm)
Hoop Strain (%)
As an indirect validation of the model’s ability to reproduce the correct residual stress state around the rivet holes, a simulation was performed for a slightly different configuration where neutron diffraction data exists for the residual strains. The rivet forming that was modelled was based on neutron diffraction measurements taken for a study on residual strains around rivets by the National Research Council of Canada (NRCC) [22]. For a comparison to be made to the measurements, the geometry of the riveted sheets had to be scaled up by a factor of approximately two. The rivet forming model that was developed for the neutron diffraction comparison consisted of two 2.0 mm sheets with a MS20426AD8-9 rivet. The material models, contact interactions and boundary conditions were all kept identical to those used in the splice loading simulations. By changing only the geometry, an indirect validation can be made of the modelling methodology for the residual strains around the rivets in the splice loading simulation. Two different rivet forming loads were compared, 44.5 kN and 53.4 kN. Although two rivet forming loads were compared, only the radial and hoop strains for the 44.5 kN case are presented here for brevity as the results for both rivet forming levels matched the experimental data equally well (see Fig. 5). The residual strain results for three different finite element models are presented: 2D axi-symmetric data from the NRCC using NASTRAN, 3D data from Rans [10] using LS-DYNA, and finally the 3D data from this study using Abaqus. Fig. 6–9 show the residual radial and hoop strains for different points along the sheet thickness. The residual strains obtained from the simulation agree well with the neutron diffraction data points and show the same trends as the other FE data. In several cases, such as Fig. 6, the 3D Abaqus data agreed better than the other FE data. The discrepancies that do exist between the finite element data and the neutron diffraction measurements may be due to the neutron diffraction measurements being taken over a gauge volume of 1 mm3. The resolution problems of the neutron diffraction technique are discussed in detail in a paper using the same data by Li et al. [22].
44.5 kN Squeeze Force Outer Sheetz=0.5mm
0.05
20 x (mm)
25
30
Fig. 5. Locations for neutron diffraction residual stress measurements.
X
35
379
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
0.00
Radial Strain (%)
-0.05
44.5 kN Squeeze Force Inner Sheet z=3.1mm
-0.10 -0.15 -0.20 -0.25 FEM - 2D axisymmetric FEM - 3D LSDyna FEM - 3D Abaqus Neutron Diffraction
-0.30 -0.35 -0.40 5
10
15
20
25
Fig. 11. Pressure film imprint from 13.3 kN (3000 lbf) rivet squeeze force case (top) and FEM result (bottom).
Distance to Rivet Centre (mm) Fig. 8. Radial strain in the inner riveted sheet. Max pressureat Maxp ressurea tffayingsheet ayings heetsurface surface during rivet Shrivet forming.Sheet: 1mm 2024-T3 during forming. eet: 1mm 2024-T3 Rivets:NAS1097 AD-4-4 Rivets: NAS1097AD-4-4
44.5 kN Squeeze Force Inner Sheet z=3.1mm
600
Pressure (MPa)
0.30
Hoop Strain (%)
0.20 0.10 0.00 -0.10 FEM - 2D axisymmetric FEM - 3D LSDyna FEM - 3D Abaqus Neutron Diffraction
-0.20 -0.30
11.1 kN
400
Hole Edge
10
15
20
25
Distancet o Rivet Centre (mm) Fig. 9. Hoop strain in the inner riveted sheet.
Outer Sheet
Outer Faying Surface
Pressure Film Inner Faying Surface
Inner Sheet
Fig. 10. Placement of pressure sensitive film during hole drilling and rivet forming.
distribution and a simulated pressure distribution around a countersunk hole formed to 13.3 kN (3000 lbf). Comparison of the film results to the simulated faying surface stresses is presented in Figs. 12 and 13 for the countersunk and the universal rivet cases, respectively. The plots show that although the highest available pressure range was used, the 6.7 kN case was the only one where the peaks in the forming pres-
8.9 kN 6.7 kN Film Range
200
0 1.5
5
FEM Film
13.3 kN
2
2.5
3
Distance from hole center (mm) Fig. 12. Comparison of max forming pressure predicted in FEM simulation and that recorded by pressure sensitive film for countersunk rivets.
sure was captured. For the higher rivet forming loads, only the outer periphery of the pressure could be captured. Despite the load limitation of the film, good agreement was found for the 6.7 kN case and for the clamping areas shown in the higher squeeze force cases. 3.5. Splice loading step – contact area As a final step in validating the splice loading model, a comparison was made between the simulated faying surface contact areas and the fretting scars associated with contact in fatigued coupons. Since the contact area changes during cycling, the FEM results for both the loaded and unloaded states are included. The test coupons were cycled using the same parameters modelled in the simulations (100 MPa, R = 0.1) until a 1 mm surface crack had initiated beyond the rivet head, ensuring that any fretting scar would be fully developed. The comparison is shown for the NAS1097AD-4-4 rivets in Figs. 14–17 and for the MS20470AD-4-4 rivets in Figs. 18–21. Four different rivet forming loads are presented for each rivet type (6.7 kN, 8.9 kN, 11.1 kN, and 13.3 kN). The images show typical fretting wear on the faying surface of a bare splice coupon with the predicted contact areas on the faying surface of the splice as a superimposed boundary. In the figures, three general regions of fretting contact can be identified: stick, stick-slip, and slip (identified in Fig. 15). These regions refer to the behaviour of the contacting asperities in that
380
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
Max pressure pressure at at faying fayingsheet sheetsurface surface Max duringrivet rivetforming. forming.Sheet: Sheet:1mm 1mm2024-T3 2024-T3 during Rivets: MS20470 AD-4-4 Rivets: NAS1097AD-4-4
Pressure (MPa)
600
13.3 kN
FEM Film
11.1 kN
400
Hole Edge
8.9 kN 6.7 kN Film Range
200
0 1.5
2
2.5
3
Distance from hole center (mm) Fig. 13. Comparison of max forming pressure predicted in FEM simulation and that recorded by pressure sensitive film for universal rivets.
Fig. 16. FEM predicted contact area outline superimposed onto countersunk fretted coupon hole (11.1 kN case).
Fig. 14. FEM predicted contact area outline superimposed onto countersunk fretted coupon hole (6.7 kN case).
Fig. 17. FEM predicted contact area outline superimposed onto countersunk fretted coupon hole (13.3 kN case).
Fig. 15. FEM predicted contact area outline superimposed onto countersunk fretted coupon hole (8.9 kN case).
Fig. 18. FEM predicted contact area outline superimposed onto universal fretted coupon hole (6.7 kN case).
region and are especially noticeable in the countersunk rivet figures. ‘‘Stick” occurs when the clamping force is sufficiently high
and no slip happens between the contacting asperities. This can be seen in the figures as the region inside the boundaries where the
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
Fig. 19. FEM predicted contact area outline superimposed onto universal fretted coupon hole (8.9 kN case).
Fig. 20. FEM predicted contact area outline superimposed onto universal fretted coupon hole (11.1 kN case).
381
and this area is known as ‘‘slip”. This region is outside the observable contact since it does not produce any type of scar or damage on the surface. The stick-slip region lies in-between the other two regions, at the edge-of-contact, and is where the most severe fretting damage will occur. This region is identified by the presence of black oxidized debris. The debris can be observed in the figures between the contact boundaries of the loaded splice state and the unloaded splice state. It is in the ‘‘stick-slip” region that micro-cracks will form and eventually propagate into fatigue cracks. It was observed in both the predicted contact area and the actual fretting scars that the contact area does not always return to the symmetrical distribution created by the rivet forming step. The skewed contact area plays an important role in where fretting cracks will nucleate. This means that any simulations of splice fretting in thin sheets cannot assume the annular pressure distribution that is present after rivet springback. In the lower rivet squeeze force cases (6.7 kN, 8.9 kN), the edgeof-contact coincides with the net section of the splice at the hole edge. For the high rivet squeeze force cases (11.1 kN, 13.3 kN), greater clamping is observed and the edge-of-contact is pushed away from the hole edge. The figures of the universal MS20470 rivets show that the predicted contact area does not generally increase until the 13.3 kN case. Although the predicted clamping area does not increase, the magnitude of the clamping pressure does. For the low rivet squeeze force cases (Figs. 18 and 19) the fretting damage in the universal rivet coupons is not as severe as the corresponding (Figs. 14 and 15) in the machine countersunk rivet coupons. This is because the universal rivet forming simulations show lower sheet clamping than the countersunk rivet forming simulations. With less clamping pressure on the surface, less fretting damage will occur. The above sections have shown that verification and validation of the splice models were performed using four different methods: stress convergence, residual strain comparison, pressure measurements, and comparison to test coupons. The stress convergence results showed that, through the use of sub-modelling, stress convergence could be obtained in a large model. The residual strain comparison indirectly validated the modelling technique by simulating similar splice geometry and achieving good results. The pressure sensitive film measurements were an indirect validation of the rivet forming step as measurements could only be taken for the pressures around the rivet holes at the maximum squeeze force and not the pressures after rivet springback. Good agreement was, however, produced for the maximum forming pressures. Finally, comparison of the predicted faying sheet surface contact area to the fretting wear scars on tested splice coupons showed good agreement with areas that would be expected to show signs of stick, stick-slip, and slip characteristics. With confidence in the splice FE models it was then possible to look at stress results and possibilities for using them in a life prediction tool.
4. Stress results and discussion
Fig. 21. FEM predicted contact area outline superimposed onto universal fretted coupon hole (13.3 kN case).
clamping area does not change during splice loading. On the other extreme, at very low clamping forces the asperities will freely slide
Figs. 22–29 show representative fretting wear scars around rivet holes in the top row of the outer splice sheet. Contour plots of the maximum principal stresses are superimposed on the images. In addition to the contour plots in the figures, the predicted contact area boundaries and representive initiated cracks are highlighted. Results for the machine countersunk coupons are presented in Figs. 22–25 whereas the results for the universal coupons are presented in Figs. 25–29. Each of the four figures in a set gives the results for a particular rivet squeeze force. The low rivet squeeze force cases (6.7 kN and 8.9 kN) of the countersunk rivet coupons (Figs. 22 and 23) show maximum
382
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
Fig. 22. Contour plot of maximum principal stress with superimposed fatigue crack for countersunk rivet (6.7 kN case).
Fig. 23. Contour plot of maximum principal stress with superimposed fatigue crack for countersunk rivet (8.9 kN case).
Fig. 24. Contour plot of maximum principal stress with superimposed fatigue crack for countersunk rivet (11.1 kN case).
principal stresses occurring near the net section with a lower peak stress in the 8.9 kN case. The peaks in stress correspond to the loaded state edge-of-contact. Crack nucleation is also found to originate from the edge-of-contact and the location of maximum
Fig. 25. Contour plot of maximum principal stress with superimposed fatigue crack for countersunk rivet (13.3 kN case).
Fig. 26. Contour plot of maximum principal stress with superimposed fatigue crack for universal rivet (6.7 kN case).
Fig. 27. Contour plot of maximum principal stress with superimposed fatigue crack for universal rivet. (8.9 kN case).
principal stress. The high rivet squeeze force cases (11.1 kN and 13.3 kN) of the countersunk rivet coupons (Figs. 24 and 25) show decreased peaks in stress at locations removed away from the hole edge. Crack nucleation is, again, observed to originate from the loaded splice edge of contact stress peaks.
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
383
the benefit of higher forming loads [2,3], being able to model the effect on fretting becomes important. As shown here, the magnitude of the rivet squeeze force will determine where the location of crack nucleation will occur from areas of fretting damage at the edge-of-contact. In thin sheet splices, nucleation of fretting fatigue cracks on the faying surface provides the opportunity to treat the surface with possible palliatives for further increases in fatigue life. The maximum principal stress results have provided interesting data on crack nucleation around rivet holes subject to fretting but they do not tell when the cracks will nucleate. Stress data from the splice models presented here should, however, enable the use of a critical plane life prediction model [20] such as the Fatemi–Socie model or the modified Smith–Watson–Topper model. It remains as the next step in this work to see how effective these methods are at predicting the fretting fatigue life of the splices and the location of crack nucleation. Fig. 28. Contour plot of maximum principal stress with superimposed fatigue crack for universal rivet (11.1 kN case).
5. Conclusions The following conclusions can be drawn from the work presented in this paper:
Fig. 29. Contour plot of maximum principal stress with superimposed fatigue crack for universal rivet (13.3 kN case).
3D explicit simulations can be used to capture edge of contact stresses in fretting contact situations for complex geometries. Multiple indirect validation methods showed that the 3D splice simulation was able to accurately model rivet forming in a splice. Faying surface contact areas agreed with fretted regions in tested splice coupons. The best agreement was found with the countersunk splices. It is not valid to assume an annular pressure distribution for rivet clamping in thin sheet splices subject to fatigue for any time beyond rivet springback. Peaks in maximum principal stress for surface contact plots corresponded well to locations of crack nucleation in the splices with the magnitudes of the stresses decreasing as the rivet forming load increased.
Acknowledgment The reduction in stress level at the edge-of-contact with increasing rivet squeeze force can be attributed to the formation of high compressive residual stresses in the sheets. This effect also tends to move the crack nucleation location away from the hole edge as witnessed by other researchers [10]. An indication of crack nucleation away from the hole edge in the high rivet squeeze force cases can be seen in Figs. 24 and 25 as a sharp kink in the crack path close to the hole. The kink suggests that the crack nucleated away from the hole edge, at the edge-of-contact, and then proceeded to grow outward from the hole as well as toward the hole edge. Similar trends are observed in the universal rivet coupon cases (Figs. 26–29) as those discussed for the countersunk rivet coupon set. Namely, an increase in rivet squeeze force tends to move crack nucleation from the net section (Fig. 26) to a location away from the hole edge (Fig. 29) corresponding to peaks in stress associated with the edge-of-contact in the loaded splice. The edge of contact stresses in the universal rivet coupons, most notably in Figs. 28 and 29, are more subtle than their counterparts in the countersunk rivet set because of decreased bending caused by the constraint of the universal rivet head. The lower stresses at the edge-of-contact lead to higher fatigue lives in the universal splice coupons over the machine countersunk splice coupons. As advances in manufacturing technology have allowed for close control of the rivet squeeze force and research has shown
This work was supported by research Grants from the Natural Sciences and Engineering Research Council (NSERC). References [1] de Rijck R. Stress analysis of fatigue cracks in mechanically fastened joints. In: Aerospace engineering. Delft, The Netherlands: Delft University of Technology; 2005. p. 302. [2] Müller RPG. An experimental and analytical investigation on the fatigue behaviour of fuselage riveted lap joints: the significance of the rivet squeeze force and a comparison of 2024-T3 and Glare 3. Delft, The Netherlands: Delft University of Technology; 1995. [3] Rans CD, Alderliesten RC, Straznicky PV. Riveting process induced residual stresses around solid rivets in mechanically fastened joints. J Aircraft 2007;44(1):323–9. [4] Harish GaTNF. Shell modeling of fretting in riveted lap joints. AIAA J 1998;36(6):1087–93. [5] Harish GaTNF. An integrated approach for prediction of fretting crack nucleation in riveted lap joints. In: AIAA/ASME/ASCE/AHS/ASC 40th structures, structural dynamics, and materials conference. St. Louis, MO: AIAA; 1999. [6] Szolwinski MP. The mechanics and tribology of fretting fatigue with application to riveted lap joints. West Layfayette, IN, USA: Purdue University; 1998. [7] Szolwinski MPaTNF. Linking riveting process parameters to the fatigue performance of riveted aircraft structures. J Aircraft 2000;37(1):130–7. [8] Brown AMaPVS. Modelling fretting contact stresses in a single lap splice. In: International symposium on fretting fatigue 5 Montreal, Canada; 2007. [9] Liao M, Shi G, Xiong Y. Analytical methodology for predicting fatigue life distribution of fuselage splices. Int J Fatigue 2001;23:S177–85.
384
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
[10] Rans CD. The Role of Rivet Installation on the Fatigue Performance of Riveted Lap Joints. In: Mechanical and aerospace engineering, vol. PhD. Ottawa: Carleton University; 2007. [11] Iyer K, Bastias PC, Rubin CA, Hahn GT. Influence of interference and clamping on fretting fatigue in single rivet-row lap joints. J Tribol 2001;123(4):686–98. [12] Sum WS, Williams Edward J, Leen Sean B. Finite element, critical-plane, fatigue life prediction of simple and complex contact configurations. Int J Fatigue 2005;27:403–16. [13] Tsai CT, Shankar Mall. Elasto-plastic finite element analysis of fretting stresses in pre-stressed strip in contact with cylindrical pad. Finite Elem Anal Des 2000;36:171–87. [14] Tur M, Fuenmayor J, Rodenas JJ, Giner E. 3D analysis of the influence of specimen dimensions on fretting stresses. Finite Elem Anal Des 2003;39:933–49. [15] MIL-HDBK-5H. Metallic materials and elements for aerospace vehicle structures. US Department of Defense; 1998.
[16] Eastaugh G. Multiple site fatigue damage in fuselage skin splices. In: Mechanical and aerospace engineering. Master of Engineering Ottawa: Carleton University; 1993. p. 207. [17] ABAQUS. User’s and theory manuals version 6.6. Pawtucket: Rhode Island: HKS; 2006. [18] Urban MR. Analysis of the fatigue life of riveted sheet metal helicopter airframe joints. Int J Fatigue 2003;25:1013–26. [19] Ding J, Leen SB, McColl IR. The effect of slip regime on fretting wear-induced stress evolution. Int J Fatigue 2004;26:521–31. [20] Lykins CD, Shankar Mall, Vinod Jain. An evaluation of parameters for predicting fretting fatigue crack initiation. Int J Fatigue 2000;22:703–16. [21] Kim HS, Shankar Mall. Investigation into three-dimensional effects of finite contact width on fretting fatigue. Finite Elem Anal Des 2005;41:1140–59. [22] Li G, George Shi, Nicholas Bellinger. Study of the residual strain in lap joints. J Aircraft 2006;43(4):1145–51.
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Simulating fretting contact in single lap splices A.M. Brown *, P.V. Straznicky Department of Mechanical and Aerospace Engineering, Carleton University, 1125 Colonel By Drive, Ottawa, Canada K1S 5B6
a r t i c l e
i n f o
Article history: Received 8 April 2008 Received in revised form 18 July 2008 Accepted 25 July 2008 Available online 5 August 2008 Keywords: Finite element Fretting Rivet forming Lap splice
a b s t r a c t Cracks in riveted lap splices commonly nucleate in regions of fretting damage around the fastener holes. The crack location is dependent upon the rivet squeeze force and the clamped faying surface area around the holes since fretting damage occurs at the edge of contact. Being able to predict the amount of faying surface clamping from rivet forming and the peaks in edge-of-contact stresses associated with fretting contact will help in the understanding of splice fatigue failure. This paper describes the development of a 3D finite element splice model that predicts the variation of contact area and edge-of-contact stresses in a loaded splice. The prediction is made for four rivet squeeze force levels and both universal and countersunk rivet styles. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction One of the most common structural joints in aircraft design is the riveted single lap splice. The joint is used, despite its drawbacks, because of its low cost and simplicity. When the single lap splice is used on modern commercial aircraft, it is subjected to loading from pressurization of the fuselage. Pressurization makes for more efficient and comfortable flights but every ground-airground pressurization cycle provides one major cycle of fatigue loading on the splices in the airframe. All other in-service fatigue loads are secondary to this. The presence of fasteners in fuselage lap splices introduces stress concentrations that eventually cause fatigue cracks to nucleate. A great deal of research has been performed to understand crack formation in riveted splices [1–3] but little work has been performed on the contribution of fretting to the nucleation of splice fatigue cracks. Fretting is the term used to describe a wear/corrosion phenomenon that takes place in clamped bodies undergoing oscillatory motion. It is theorized that asperities of two clamped surfaces in contact will cold-weld together under normal pressure. Upon the application of oscillatory tangential loading, the bond between the asperities will break leaving behind debris and local areas of yielding. The exposed debris and substrate material is left to corrode as the asperities stick once more on the next cycle. This process continues with each oscillation. Fretting damage can lead to the formation of micro-cracks in the surface that, in the presence of a tensile stress field, will propagate into the substrate. In aluminum, fretting damage is easily identified from the oxidized wear * Corresponding author. Tel.: +1 613 520 2600x1684; fax: +1 613 520 5715. E-mail address: [email protected] (A.M. Brown). 0142-1123/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijfatigue.2008.07.012
debris; a black powder surrounding or falling away from the clamped area. Some preliminary work has been performed on fretting in lap splices at Purdue University, Vanderbilt University, and at the National Research Council of Canada. In the case of each research group, strides were made in the understanding of fretting in lap splices; however, there has been no in-depth look at fretting damage on the faying sheet surface where cracks often nucleate in splices. The research performed at Purdue University [4–7] was limited to geometry consisting of universal (MS20470) rivets and relatively thick (1.8–2.3 mm) untreated 2024-T3 aluminum sheet. In joints of that thickness, with low rivet interference, it was found that the critical fretting region was the rivet/sheet interface and that cracks did not nucleate from the faying sheet surface. For thinner sheet thicknesses, such as the 1 mm sheet used in this study, with high rivet interference, the location of crack nucleation is on the faying sheet surface surrounding the hole [8–10]. This location corresponds to the edge-of-contact and the region of greatest fretting damage. Finite element models of fretting contact created at Purdue University utilized a variety of methods to simulate the riveted joints. These included 2D and 3D shell models as well as axi-symmetric rivet forming models. Szolwinski and Farris simulated rivet forming in 2.3 mm sheet and found the rivet clamping to be negligible [7]. Because of the low clamping, Harish and Farris later used a 2D model to simulate splice loading [5]. The 2D model from [5] included representative mid-plane residual stress fields obtained from the rivet forming step but did not include secondary bending stresses. A 2D model is not practical for this study as secondary bending effects are significant and it is necessary to know the
376
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
faying surface residual stress field when looking at edge-of-contact stresses. In addition, 2D models do not provide results for the contact distribution on the surface of the splice during sheet loading. Knowledge of the contact area is important for correlating the location of crack nucleation in the models to actual tested splices. A study by Iyer et al. [11] from Vanderbilt University examined fretting in pinned connections with coarse finite element models. The coarseness of the models did not allow for accurate determination of fretting contact stresses or faying surface clamping. Interference was included; however, the rivet forming step was not performed in the simulation. The interference was introduced by forcing conformity of an oversized rivet into the rivet hole. This provided a simplified estimation of uniform radial interference between the rivet and the hole. It has been shown in other studies that uniform rivet expansion does not occur with driven solid rivets [3]. Liao et al. of the National Research Council of Canada modelled a 3-row single lap splice that determined a relationship between rivet squeeze force, coefficient of friction, and residual stress in the splice [9]. The investigation did not, however, look at faying surface clamping area or stress concentrations at the edge-ofcontact. The goal of this work is to bring together the different facets of lap splice fretting into a single 3D finite element model. The simulation must therefore include: rivet forming steps to incorporate the residual stresses in the sheets and faying surface clamping associated with different rivet forming loads, and loading of the splice to observe any changes in the faying surface edge-of-contact stresses. Simulation of different rivet forming loads is performed because increasing the rivet squeeze force changes the residual stress field around the rivet hole and increases the clamping area between the sheets. These combined factors change the location of crack nucleation. This paper describes the development, verification and validation of a model to simulate fretting contact in a single lap splice for both countersunk and universal rivets and presents the results for four different rivet squeeze forces.
all geometry creation and meshing. Two single lap splice geometries were modelled with different rivet types inserted in the sheet. NAS1097AD-4-4 countersunk rivets and MS20470AD-4-4 universal rivets were both studied. To simulate the complex interactions and large deformations associated with rivet forming and splice loading, explicit simulations were used. The splices consisted of two rivet rows with a row pitch of 38.1 mm and a rivet pitch of 25.4 mm. One millimeter bare 2024-T3 aluminum was used for both the inner and outer sheets. Fig. 1 shows the overall dimensions of the models and illustrates how symmetry was used to model only half of the splice. Along with the inner sheet, outer sheet, and two rivets, four rigid platens were included in the models as the rivet forming tools. The 2024-T3 sheet material was modelled using Ramberg–Osgood parameters [15] and the material model for the 2117-T4 aluminum rivets was based on two power law curves [6]. The splice simulations were broken into four loading steps: rivet forming, rivet springback, splice loading, and splice unloading. In the first step, the portion of the splice outside 12.7 mm (0.500 ) of the rivets was constrained and the rivets were formed to a designated squeeze force (Fig. 2). In the second step, unloading of the rivets to 1% of the maximum forming load allowed for material springback while controlling oscillation that could be induced by completely releasing the load. At the same time, the portions of the sheets that were constrained during the rivet forming steps were released. Only the symmetry constraints and the constraints on the end of either sheet were maintained. The third step applied a stress of 100 MPa [16], a typical stress for narrow body aircraft, to one end of the splice while the other end remained fixed in the X and Y directions (Fig. 3). Finally, in the fourth step the splice was unloaded to 1% of the maximum splice load. Time scaling was used in the simulation with the rivet forming, rivet springback, splice loading, and splice springback steps taking
2. Development of 3D lap splice simulations 2.1. Modelling details The commercial code Abaqus v.6.6.1 was adopted to model fretting contact in a single lap splice as it is commonly used in fretting contact studies [12–14]. Hyperworks Hypermesh was chosen for
Fig. 2. Rivet forming step. 6.7 kN (1500 lbf).
240 mm 64 mm 12.7 mm 38.1 mm
Outer Sheet
Top Rivet Row
1.0 mm Bottom Rivet Row
Fig. 1. Splice coupon and FEM model geometry.
Inner Sheet
377
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
Fig. 3. Splice loading step.
place over 0.003, 0.003, 0.012, and 0.006 s, respectively. Pauses were included in the loading after each step to allow for damping of any oscillations in the system. Time scaling was appropriate in this situation because the loading is quasi-static and the kinetic energy of the system was well below 5% of the total internal energy during the simulation [17]. This indicated that dynamic effects were not significant. Penalty contact definitions were used for all contact surfaces with the exception of the faying surface of the sheets. Since the faying surface is the region known to experience fretting damage, kinematic contact was used to better enforce sticking of the contacting nodes. Friction was imposed using the basic Coulomb model. For all contact surfaces except the faying surface, a coefficient of friction (COF) of 0.178 [18] was used. For the faying surface contact, the coefficient of friction was changed after the rivet springback step from 0.178 to 0.65 [6]. The increase in COF was necessary to properly represent the increase in COF observed in fretting tests of 2024-T351 [6]. Initially, when the sheets are riveted together, no fretting damage exists and the COF has been measured to be 0.178. After a few thousand cycles, however, fretting damage begins and the COF increases. Measurements performed by Szolwinski [6] have shown that after a quick rise in COF, corresponding to the formation of fretting damage, the COF reaches a steady state value. If a COF of 0.65 had been used in all steps, the increased surface tractions, combined with non-uniform expansion of the rivet hole, would provide different residual stress results in the sheets. The meshes for the rivets and the sheets were generated using 8-node C3D8R solid elements whereas the meshes for the rigid tools were generated using 4-node S4R shell elements. The solid meshes in the splice were biased toward the rivet hole with an average element edge length of 0.1 mm (0.00400 ). Properly capturing the contact stresses in a finite element fretting contact problem normally requires fine meshes in conjunction with strict contact formulations. For the relatively large and complex problem of loading in a single lap splice, this could pose a problem. 2D simulations of fretting contact often have elements with edge lengths on the order of 6 lm in the contact region [12,19,20]. Expanding these meshes into 3D can quickly produce prohibitively large simulations. One solution, shown to be effective in 3D contact simulations by Kim and Shankar [21], is to use sub-modelling techniques. 2.2. Sub-modelling Sub-modelling requires that a global model be run with a set of driving elements defined in the area of interest (the contact region). A smaller sub-model is then created that includes only the elements from that area (Fig. 4). As this geometry is smaller, a finer mesh can be defined. The displacements from the driving elements in the global model are applied to the outer boundary of the submodel during the sub-model analysis. The sub-model can then be used as a global model for further refinement until sufficient convergence in the results is achieved [17].
Fig. 4. Illustration of sub-modelling technique applied to splice simulation.
In the splice simulations, the region around the rivet in the top row of the outer sheet was the area of interest (Fig. 4). This region is where secondary bending stresses will interact with fretting induced stress concentrations to nucleate a crack. In the countersunk rivet splice, the countersink will cause a greater stress concentration than for the universal riveted splice. It can be noted that it is not necessary to model the rivets in any of the sub-model simulations as long as the driving elements are defined along the hole edge. Removing the rivet from the sub-model saves on the computation cost as each rivet consists of over 70,000 elements. 3. Model verification and validation 3.1. Introduction Methods of verifying and validating the rivet forming step and the splice loading step are described in the following sections. Since the area of interest is under the rivet head around the holes, direct comparison or measurement becomes a problem. To overcome this difficulty, indirect methods have been used. These methods include stress convergence, indirect comparison to neutron diffraction data, and the use of pressure sensitive film. 3.2. Stress convergence Convergence of the stresses obtained from the sub-models was the first technique used for verification of the splice model. The maximum principal stresses at the edge of contact around the hole were compared in the 11.1 kN (2500 lbf) rivet forming case for the global model and two sub-models. The element size was reduced from 0.100 mm in the global model to 0.050 mm and 0.025 mm in the first and second sub-models respectively. Convergence results for the sub-model analyses are presented in Table 1. The percent difference from the previous model was calculated using Eq. (1) where rn+1 is the maximum stress in the current model and rn is the maximum stress in the previous model
Table 1 Convergence results for 3D splice model Model
Element edge length (mm)
Max principal stress MPa (psi)
Percentage of difference from previous
Global Sub-model 1 Sub-model 2
0.100 0.050 0.025
202.6 (29389) 263.2 (38171) 274.4 (39796)
– 23 4
378
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
nþ1 r rn 100 %Diff ¼ rnþ1
ð1Þ
Radial Strain (%)
Based on the convergence results, it was determined that only two sub-models would be required in future splice simulations. 3.3. Residual strains
3.4. Rivet forming step – pressure sensitive film The next method of validating that the simulated rivets match actual installed rivets was the use of pressure sensitive film. Pressure sensitive film changes colour with the application of an applied pressure. The intensity of the colour is related to the amount of the pressure that is applied. Different types of film are available from ‘‘Super low” to ‘‘Super high” with a pressure range
0.00 -0.05 -0.10 FEM - 2D axisymmetric FEM - 3D LSDyna FEM - 3D Abaqus Neutron Diffraction
-0.15 -0.20 5
10
15
44.5 kN Squeeze Force Outer Sheet z=1.1mm
0.20
0.10
0.00
FEM - 2D axisymmetric FEM - 3D LSDyna FEM - 3D Abaqus Neutron Diffraction
-0.10
-0.20 5
10
15
associated with each. For this study, the ‘‘Super high” film was chosen (141–300 MPa) and was placed between the sheets of both the countersunk and universal splice coupons (Fig. 10). The holes were then drilled, rivets inserted, and formed to the prescribed load. Drilling out of the rivets and removing the film from between the sheets then provided results for the maximum pressures experienced on the faying sheet surfaces during the rivet forming step. Checks were made to ensure that the initial hole drilling step did not generate pressures large enough to activate the film. The pressure distribution of each film was digitized and the intensity was analyzed using image software and calibration curves that are provided by the manufacturer. This allowed for greater resolution than simple visual comparisons. Fig. 11 shows a typical film pressure
z (mm)
Z
6 Y
8 15
25
Fig. 7. Hoop strain in the outer riveted sheet.
4
10
20
Distance to Rivet Centre (mm)
2
5
25
Fig. 6. Radial strain in the outer riveted sheet.
0
0
20
Distance to Rivet Centre (mm)
Hoop Strain (%)
As an indirect validation of the model’s ability to reproduce the correct residual stress state around the rivet holes, a simulation was performed for a slightly different configuration where neutron diffraction data exists for the residual strains. The rivet forming that was modelled was based on neutron diffraction measurements taken for a study on residual strains around rivets by the National Research Council of Canada (NRCC) [22]. For a comparison to be made to the measurements, the geometry of the riveted sheets had to be scaled up by a factor of approximately two. The rivet forming model that was developed for the neutron diffraction comparison consisted of two 2.0 mm sheets with a MS20426AD8-9 rivet. The material models, contact interactions and boundary conditions were all kept identical to those used in the splice loading simulations. By changing only the geometry, an indirect validation can be made of the modelling methodology for the residual strains around the rivets in the splice loading simulation. Two different rivet forming loads were compared, 44.5 kN and 53.4 kN. Although two rivet forming loads were compared, only the radial and hoop strains for the 44.5 kN case are presented here for brevity as the results for both rivet forming levels matched the experimental data equally well (see Fig. 5). The residual strain results for three different finite element models are presented: 2D axi-symmetric data from the NRCC using NASTRAN, 3D data from Rans [10] using LS-DYNA, and finally the 3D data from this study using Abaqus. Fig. 6–9 show the residual radial and hoop strains for different points along the sheet thickness. The residual strains obtained from the simulation agree well with the neutron diffraction data points and show the same trends as the other FE data. In several cases, such as Fig. 6, the 3D Abaqus data agreed better than the other FE data. The discrepancies that do exist between the finite element data and the neutron diffraction measurements may be due to the neutron diffraction measurements being taken over a gauge volume of 1 mm3. The resolution problems of the neutron diffraction technique are discussed in detail in a paper using the same data by Li et al. [22].
44.5 kN Squeeze Force Outer Sheetz=0.5mm
0.05
20 x (mm)
25
30
Fig. 5. Locations for neutron diffraction residual stress measurements.
X
35
379
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
0.00
Radial Strain (%)
-0.05
44.5 kN Squeeze Force Inner Sheet z=3.1mm
-0.10 -0.15 -0.20 -0.25 FEM - 2D axisymmetric FEM - 3D LSDyna FEM - 3D Abaqus Neutron Diffraction
-0.30 -0.35 -0.40 5
10
15
20
25
Fig. 11. Pressure film imprint from 13.3 kN (3000 lbf) rivet squeeze force case (top) and FEM result (bottom).
Distance to Rivet Centre (mm) Fig. 8. Radial strain in the inner riveted sheet. Max pressureat Maxp ressurea tffayingsheet ayings heetsurface surface during rivet Shrivet forming.Sheet: 1mm 2024-T3 during forming. eet: 1mm 2024-T3 Rivets:NAS1097 AD-4-4 Rivets: NAS1097AD-4-4
44.5 kN Squeeze Force Inner Sheet z=3.1mm
600
Pressure (MPa)
0.30
Hoop Strain (%)
0.20 0.10 0.00 -0.10 FEM - 2D axisymmetric FEM - 3D LSDyna FEM - 3D Abaqus Neutron Diffraction
-0.20 -0.30
11.1 kN
400
Hole Edge
10
15
20
25
Distancet o Rivet Centre (mm) Fig. 9. Hoop strain in the inner riveted sheet.
Outer Sheet
Outer Faying Surface
Pressure Film Inner Faying Surface
Inner Sheet
Fig. 10. Placement of pressure sensitive film during hole drilling and rivet forming.
distribution and a simulated pressure distribution around a countersunk hole formed to 13.3 kN (3000 lbf). Comparison of the film results to the simulated faying surface stresses is presented in Figs. 12 and 13 for the countersunk and the universal rivet cases, respectively. The plots show that although the highest available pressure range was used, the 6.7 kN case was the only one where the peaks in the forming pres-
8.9 kN 6.7 kN Film Range
200
0 1.5
5
FEM Film
13.3 kN
2
2.5
3
Distance from hole center (mm) Fig. 12. Comparison of max forming pressure predicted in FEM simulation and that recorded by pressure sensitive film for countersunk rivets.
sure was captured. For the higher rivet forming loads, only the outer periphery of the pressure could be captured. Despite the load limitation of the film, good agreement was found for the 6.7 kN case and for the clamping areas shown in the higher squeeze force cases. 3.5. Splice loading step – contact area As a final step in validating the splice loading model, a comparison was made between the simulated faying surface contact areas and the fretting scars associated with contact in fatigued coupons. Since the contact area changes during cycling, the FEM results for both the loaded and unloaded states are included. The test coupons were cycled using the same parameters modelled in the simulations (100 MPa, R = 0.1) until a 1 mm surface crack had initiated beyond the rivet head, ensuring that any fretting scar would be fully developed. The comparison is shown for the NAS1097AD-4-4 rivets in Figs. 14–17 and for the MS20470AD-4-4 rivets in Figs. 18–21. Four different rivet forming loads are presented for each rivet type (6.7 kN, 8.9 kN, 11.1 kN, and 13.3 kN). The images show typical fretting wear on the faying surface of a bare splice coupon with the predicted contact areas on the faying surface of the splice as a superimposed boundary. In the figures, three general regions of fretting contact can be identified: stick, stick-slip, and slip (identified in Fig. 15). These regions refer to the behaviour of the contacting asperities in that
380
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
Max pressure pressure at at faying fayingsheet sheetsurface surface Max duringrivet rivetforming. forming.Sheet: Sheet:1mm 1mm2024-T3 2024-T3 during Rivets: MS20470 AD-4-4 Rivets: NAS1097AD-4-4
Pressure (MPa)
600
13.3 kN
FEM Film
11.1 kN
400
Hole Edge
8.9 kN 6.7 kN Film Range
200
0 1.5
2
2.5
3
Distance from hole center (mm) Fig. 13. Comparison of max forming pressure predicted in FEM simulation and that recorded by pressure sensitive film for universal rivets.
Fig. 16. FEM predicted contact area outline superimposed onto countersunk fretted coupon hole (11.1 kN case).
Fig. 14. FEM predicted contact area outline superimposed onto countersunk fretted coupon hole (6.7 kN case).
Fig. 17. FEM predicted contact area outline superimposed onto countersunk fretted coupon hole (13.3 kN case).
Fig. 15. FEM predicted contact area outline superimposed onto countersunk fretted coupon hole (8.9 kN case).
Fig. 18. FEM predicted contact area outline superimposed onto universal fretted coupon hole (6.7 kN case).
region and are especially noticeable in the countersunk rivet figures. ‘‘Stick” occurs when the clamping force is sufficiently high
and no slip happens between the contacting asperities. This can be seen in the figures as the region inside the boundaries where the
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
Fig. 19. FEM predicted contact area outline superimposed onto universal fretted coupon hole (8.9 kN case).
Fig. 20. FEM predicted contact area outline superimposed onto universal fretted coupon hole (11.1 kN case).
381
and this area is known as ‘‘slip”. This region is outside the observable contact since it does not produce any type of scar or damage on the surface. The stick-slip region lies in-between the other two regions, at the edge-of-contact, and is where the most severe fretting damage will occur. This region is identified by the presence of black oxidized debris. The debris can be observed in the figures between the contact boundaries of the loaded splice state and the unloaded splice state. It is in the ‘‘stick-slip” region that micro-cracks will form and eventually propagate into fatigue cracks. It was observed in both the predicted contact area and the actual fretting scars that the contact area does not always return to the symmetrical distribution created by the rivet forming step. The skewed contact area plays an important role in where fretting cracks will nucleate. This means that any simulations of splice fretting in thin sheets cannot assume the annular pressure distribution that is present after rivet springback. In the lower rivet squeeze force cases (6.7 kN, 8.9 kN), the edgeof-contact coincides with the net section of the splice at the hole edge. For the high rivet squeeze force cases (11.1 kN, 13.3 kN), greater clamping is observed and the edge-of-contact is pushed away from the hole edge. The figures of the universal MS20470 rivets show that the predicted contact area does not generally increase until the 13.3 kN case. Although the predicted clamping area does not increase, the magnitude of the clamping pressure does. For the low rivet squeeze force cases (Figs. 18 and 19) the fretting damage in the universal rivet coupons is not as severe as the corresponding (Figs. 14 and 15) in the machine countersunk rivet coupons. This is because the universal rivet forming simulations show lower sheet clamping than the countersunk rivet forming simulations. With less clamping pressure on the surface, less fretting damage will occur. The above sections have shown that verification and validation of the splice models were performed using four different methods: stress convergence, residual strain comparison, pressure measurements, and comparison to test coupons. The stress convergence results showed that, through the use of sub-modelling, stress convergence could be obtained in a large model. The residual strain comparison indirectly validated the modelling technique by simulating similar splice geometry and achieving good results. The pressure sensitive film measurements were an indirect validation of the rivet forming step as measurements could only be taken for the pressures around the rivet holes at the maximum squeeze force and not the pressures after rivet springback. Good agreement was, however, produced for the maximum forming pressures. Finally, comparison of the predicted faying sheet surface contact area to the fretting wear scars on tested splice coupons showed good agreement with areas that would be expected to show signs of stick, stick-slip, and slip characteristics. With confidence in the splice FE models it was then possible to look at stress results and possibilities for using them in a life prediction tool.
4. Stress results and discussion
Fig. 21. FEM predicted contact area outline superimposed onto universal fretted coupon hole (13.3 kN case).
clamping area does not change during splice loading. On the other extreme, at very low clamping forces the asperities will freely slide
Figs. 22–29 show representative fretting wear scars around rivet holes in the top row of the outer splice sheet. Contour plots of the maximum principal stresses are superimposed on the images. In addition to the contour plots in the figures, the predicted contact area boundaries and representive initiated cracks are highlighted. Results for the machine countersunk coupons are presented in Figs. 22–25 whereas the results for the universal coupons are presented in Figs. 25–29. Each of the four figures in a set gives the results for a particular rivet squeeze force. The low rivet squeeze force cases (6.7 kN and 8.9 kN) of the countersunk rivet coupons (Figs. 22 and 23) show maximum
382
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
Fig. 22. Contour plot of maximum principal stress with superimposed fatigue crack for countersunk rivet (6.7 kN case).
Fig. 23. Contour plot of maximum principal stress with superimposed fatigue crack for countersunk rivet (8.9 kN case).
Fig. 24. Contour plot of maximum principal stress with superimposed fatigue crack for countersunk rivet (11.1 kN case).
principal stresses occurring near the net section with a lower peak stress in the 8.9 kN case. The peaks in stress correspond to the loaded state edge-of-contact. Crack nucleation is also found to originate from the edge-of-contact and the location of maximum
Fig. 25. Contour plot of maximum principal stress with superimposed fatigue crack for countersunk rivet (13.3 kN case).
Fig. 26. Contour plot of maximum principal stress with superimposed fatigue crack for universal rivet (6.7 kN case).
Fig. 27. Contour plot of maximum principal stress with superimposed fatigue crack for universal rivet. (8.9 kN case).
principal stress. The high rivet squeeze force cases (11.1 kN and 13.3 kN) of the countersunk rivet coupons (Figs. 24 and 25) show decreased peaks in stress at locations removed away from the hole edge. Crack nucleation is, again, observed to originate from the loaded splice edge of contact stress peaks.
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
383
the benefit of higher forming loads [2,3], being able to model the effect on fretting becomes important. As shown here, the magnitude of the rivet squeeze force will determine where the location of crack nucleation will occur from areas of fretting damage at the edge-of-contact. In thin sheet splices, nucleation of fretting fatigue cracks on the faying surface provides the opportunity to treat the surface with possible palliatives for further increases in fatigue life. The maximum principal stress results have provided interesting data on crack nucleation around rivet holes subject to fretting but they do not tell when the cracks will nucleate. Stress data from the splice models presented here should, however, enable the use of a critical plane life prediction model [20] such as the Fatemi–Socie model or the modified Smith–Watson–Topper model. It remains as the next step in this work to see how effective these methods are at predicting the fretting fatigue life of the splices and the location of crack nucleation. Fig. 28. Contour plot of maximum principal stress with superimposed fatigue crack for universal rivet (11.1 kN case).
5. Conclusions The following conclusions can be drawn from the work presented in this paper:
Fig. 29. Contour plot of maximum principal stress with superimposed fatigue crack for universal rivet (13.3 kN case).
3D explicit simulations can be used to capture edge of contact stresses in fretting contact situations for complex geometries. Multiple indirect validation methods showed that the 3D splice simulation was able to accurately model rivet forming in a splice. Faying surface contact areas agreed with fretted regions in tested splice coupons. The best agreement was found with the countersunk splices. It is not valid to assume an annular pressure distribution for rivet clamping in thin sheet splices subject to fatigue for any time beyond rivet springback. Peaks in maximum principal stress for surface contact plots corresponded well to locations of crack nucleation in the splices with the magnitudes of the stresses decreasing as the rivet forming load increased.
Acknowledgment The reduction in stress level at the edge-of-contact with increasing rivet squeeze force can be attributed to the formation of high compressive residual stresses in the sheets. This effect also tends to move the crack nucleation location away from the hole edge as witnessed by other researchers [10]. An indication of crack nucleation away from the hole edge in the high rivet squeeze force cases can be seen in Figs. 24 and 25 as a sharp kink in the crack path close to the hole. The kink suggests that the crack nucleated away from the hole edge, at the edge-of-contact, and then proceeded to grow outward from the hole as well as toward the hole edge. Similar trends are observed in the universal rivet coupon cases (Figs. 26–29) as those discussed for the countersunk rivet coupon set. Namely, an increase in rivet squeeze force tends to move crack nucleation from the net section (Fig. 26) to a location away from the hole edge (Fig. 29) corresponding to peaks in stress associated with the edge-of-contact in the loaded splice. The edge of contact stresses in the universal rivet coupons, most notably in Figs. 28 and 29, are more subtle than their counterparts in the countersunk rivet set because of decreased bending caused by the constraint of the universal rivet head. The lower stresses at the edge-of-contact lead to higher fatigue lives in the universal splice coupons over the machine countersunk splice coupons. As advances in manufacturing technology have allowed for close control of the rivet squeeze force and research has shown
This work was supported by research Grants from the Natural Sciences and Engineering Research Council (NSERC). References [1] de Rijck R. Stress analysis of fatigue cracks in mechanically fastened joints. In: Aerospace engineering. Delft, The Netherlands: Delft University of Technology; 2005. p. 302. [2] Müller RPG. An experimental and analytical investigation on the fatigue behaviour of fuselage riveted lap joints: the significance of the rivet squeeze force and a comparison of 2024-T3 and Glare 3. Delft, The Netherlands: Delft University of Technology; 1995. [3] Rans CD, Alderliesten RC, Straznicky PV. Riveting process induced residual stresses around solid rivets in mechanically fastened joints. J Aircraft 2007;44(1):323–9. [4] Harish GaTNF. Shell modeling of fretting in riveted lap joints. AIAA J 1998;36(6):1087–93. [5] Harish GaTNF. An integrated approach for prediction of fretting crack nucleation in riveted lap joints. In: AIAA/ASME/ASCE/AHS/ASC 40th structures, structural dynamics, and materials conference. St. Louis, MO: AIAA; 1999. [6] Szolwinski MP. The mechanics and tribology of fretting fatigue with application to riveted lap joints. West Layfayette, IN, USA: Purdue University; 1998. [7] Szolwinski MPaTNF. Linking riveting process parameters to the fatigue performance of riveted aircraft structures. J Aircraft 2000;37(1):130–7. [8] Brown AMaPVS. Modelling fretting contact stresses in a single lap splice. In: International symposium on fretting fatigue 5 Montreal, Canada; 2007. [9] Liao M, Shi G, Xiong Y. Analytical methodology for predicting fatigue life distribution of fuselage splices. Int J Fatigue 2001;23:S177–85.
384
A.M. Brown, P.V. Straznicky / International Journal of Fatigue 31 (2009) 375–384
[10] Rans CD. The Role of Rivet Installation on the Fatigue Performance of Riveted Lap Joints. In: Mechanical and aerospace engineering, vol. PhD. Ottawa: Carleton University; 2007. [11] Iyer K, Bastias PC, Rubin CA, Hahn GT. Influence of interference and clamping on fretting fatigue in single rivet-row lap joints. J Tribol 2001;123(4):686–98. [12] Sum WS, Williams Edward J, Leen Sean B. Finite element, critical-plane, fatigue life prediction of simple and complex contact configurations. Int J Fatigue 2005;27:403–16. [13] Tsai CT, Shankar Mall. Elasto-plastic finite element analysis of fretting stresses in pre-stressed strip in contact with cylindrical pad. Finite Elem Anal Des 2000;36:171–87. [14] Tur M, Fuenmayor J, Rodenas JJ, Giner E. 3D analysis of the influence of specimen dimensions on fretting stresses. Finite Elem Anal Des 2003;39:933–49. [15] MIL-HDBK-5H. Metallic materials and elements for aerospace vehicle structures. US Department of Defense; 1998.
[16] Eastaugh G. Multiple site fatigue damage in fuselage skin splices. In: Mechanical and aerospace engineering. Master of Engineering Ottawa: Carleton University; 1993. p. 207. [17] ABAQUS. User’s and theory manuals version 6.6. Pawtucket: Rhode Island: HKS; 2006. [18] Urban MR. Analysis of the fatigue life of riveted sheet metal helicopter airframe joints. Int J Fatigue 2003;25:1013–26. [19] Ding J, Leen SB, McColl IR. The effect of slip regime on fretting wear-induced stress evolution. Int J Fatigue 2004;26:521–31. [20] Lykins CD, Shankar Mall, Vinod Jain. An evaluation of parameters for predicting fretting fatigue crack initiation. Int J Fatigue 2000;22:703–16. [21] Kim HS, Shankar Mall. Investigation into three-dimensional effects of finite contact width on fretting fatigue. Finite Elem Anal Des 2005;41:1140–59. [22] Li G, George Shi, Nicholas Bellinger. Study of the residual strain in lap joints. J Aircraft 2006;43(4):1145–51.