MODELLING OF THE RIVET FORMING PROCESS IN ALUMINUM AND GLARE FOR DESIGN AGAINST FATIGUE

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MODELLING OF THE RIVET FORMING PROCESS IN ALUMINUM AND GLARE FOR DESIGN AGAINST FATIGUE Calvin D. Rans 1, René C. Alderliesten 2, Paul V. Straznicky 1 1 Department of Mechanical and Aerospace Engineering, Carleton University, 1125 Colonel By Drive, K1S 5B6, Ottawa, Canada 2 Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS, Delft, the Netherlands Keywords: rivet forming, finite element, GLARE, residual stresses. Abstract. The residual stress field induced around a rivet hole during the riveting process has been shown to improve the fatigue life of riveted structures. The rivet installation force or squeeze force has been identified as critical variable in determining this effect and has been the focus of several finite element studies. These studies, however, have been limited in scope to single rivet-sheet combinations. In order to further understand the influence of rivet type and sheet material on the formation of residual stresses during riveting, a 3-dimensional finite element model of a force-controlled riveting process has been developed. The formation of residual stresses in monolithic 224-T3 and GLARE sheets with universal and countersunk rivets has been studied. Contrary to expectations, countersunk rivets were found to provide similar or greater expansion levels in the outer (or countersunk) sheet compared to universal rivets, depending on the rivet squeeze force and flushness of the countersunk rivet. Riveting was also found to produce larger and more compressive regions of residual compressive tangential stress in GLARE compared to 224-T3 due to the apparent strain hardening behaviour of the fibre layer. 1 INTRODUCTION Mechanical fastening is one of the major methods for joining airframe structural components and its use will continue in the foreseeable future despite a number of disadvantages. Localized load transfer at discrete fastener locations causes stress concentrations which increase susceptibility to fatigue. Current practices for design against fatigue rely heavily on simplified analytical models, design rules-of-thumb, and verification testing. Fatigue of riveted joints and the rivet installation process will be the focus of this paper. Rivet installation is typically governed by design rules-of-thumb and is generally not considered a design variable. Developments in riveting technology and the advent of force-controlled and fully automated riveting machines, however, have improved the consistency of rivet installation, providing the opportunity to include its influence on fatigue at the design stage. This influence is well understood on a qualitative level. Expansion of the rivet shank during installation produces an interference that results in a residual stress field around the rivet hole. The nature of this residual stress field plays an important role in the nucleation and growth of cracks in the vicinity of the rivet hole. Furthermore, the final geometry of an installed rivet influences the clamping and bending constraints provided by the rivet. Fretting damage and the potential for fretting-induced 1

crack initiation at faying joint surfaces are highly dependent on the materials, clamping force and the constraint provided by the installed rivet. The geometry of the manufactured and driven rivet heads also influences the location of peak bending stress due to rivet rotation; a prime location for crack initiation. A quantitative understanding of these factors is essential for design optimization of riveted joints. The emergence of glass reinforced aluminum laminates (GLARE) 1,2 as a damage tolerant alternative to aluminum 224-T3 in aircraft fuselage applications provides further motivation for expanding the current understanding of rivet installation on fatigue. The alternating layers of aluminum and pre-impregnated glass-epoxy (prepreg) which make up GLARE laminates interact with each other to provide a unique set of material properties. Most notably, the forming 3,4 and fatigue crack initiation/growth 1,5 behaviour in GLARE differs from that of monolithic aluminum and fibre reinforced composites. Despite this, existing splice designs and limits on rivet installation based on experience with monolithic aluminum sheet are currently applied directly to GLARE. A detailed investigation into the influence of rivet installation force (squeeze force) completed by Müller demonstrated that the fatigue life of riveted joints could be increased tenfold by increasing the squeeze force. 5 Since these findings, several finite element studies have been undertaken in an attempt to further understand this relationship. 62 These studies, however, have been limited to investigating the influence of the rivet squeeze force in the context of single combinations of rivet type and sheet material. The influence of rivet type and sheet material, in conjunction with the rivet squeeze force, on residual stress distribution is still largely unknown. Motivated by the need for greater understanding of the rivet installation process, a 3- dimensional finite element model was developed to study the installation process of universal and countersunk rivets in monolithic 224-T3 aluminum and GLARE sheets. This paper details the model used and summarizes the results in relation to the relative performance of the various rivet and sheet material combinations. 2 FINITE ELEMENT MODEL The influence of rivet type and installation on the residual stress distribution and related fatigue performance of riveted joints was investigated using a 3-dimensional finite element model of force-controlled rivet installation. The basic configuration of the model consisted of two 25.4 mm square sheets joined at their centres by a single 3.2 mm diameter 2117-T4 aluminum rivet (Figure 1). Rivet installation was simulated in 1. mm thick 224-T3 and.86 mm thick GLARE3/1-.3 sheets using universal and countersunk head rivets (MS247AD4-4 and NAS197AD4-4 respectively 13 ). The models were created using the pre-processor ETA/FEMB v28 and solved using the explicit finite element code LS-DYNA v97. Eight-node single-point integration brick elements (ELFORM 1) were used to define the rivet and sheets while rigid surface meshes were used to define the rivet set and bucking bar. Type 6 stiffness based hourglass control was applied to resist the zero-energy or hourglass deformation modes possible with the single-point integration brick elements. Quarter-symmetry was utilized 2

with symmetry boundary conditions applied along the two symmetry planes and along the periphery of the sheets. Nodes on the free surfaces along the sheet periphery were additionally constrained along the rivet axis direction to prevent rigid body deformation. Contact interfaces were defined between the rivet and sheets, rivet and riveting tools, and along the interface between the two sheets. A segment-based (SOFT = 2) contact method employing LS-DYNA s automatic contact treatment was used. Frictional effects were included by prescribing a coefficient of friction of.18 for all contact surfaces, based on data obtained by other researchers. 9 In simulations containing GLARE sheets, tiedcontact interfaces were used to fix the relative position of nodes on opposite faces of the interfaces between adjacent layers in the laminate. Installation of the rivet was simulated by applying the squeeze force to the rivet bucking bar. Load was linearly increased until the desired squeeze force was reached, held at the maximum squeeze force until the simulation came to rest, and then reduced to 2 N. The small residual squeeze force was included to prevent oscillations in the simulation from forming due to a break in contact between the rivet and riveting tools. Five squeeze forces were considered in this study: 1, 15, 2, 25, and 3 lbf (4.4, 6.8, 8.9, 11.1, and 13.3 kn respectively). Quasi-static assumptions were applied and simulation time was scaled to minimize processing time. The non-linear material behaviour of the 2117-T4 aluminum rivets, 224-T3 aluminum sheets and 224-T3 GLARE layers was taken into account using power-law plasticity model with isotropic hardening (MAT 18). An orthotropic elastic material model (MAT 2) was used for the prepreg layers in the GLARE sheets. A summary of the material 1, 11, 13, 14 properties required by these models is given in Table 1. 2.1 Model verification Verification of the finite element model was not a trivial task. The residual stress results of interest are hidden beneath the manufactured and driven rivet heads, making most experimental stress analysis techniques unfeasible. Stresses and strains beyond the rivet head can easily be determined experimentally; however, this is not an adequate measure for verifying the performance of the model underneath the rivet head where stresses and strains can be greater by an order of magnitude or more. In order to verify the performance of the finite element model in the critical region beneath the rivet head, the model was adapted to simulate the cold expansion process. The mechanisms for forming residual stress during riveting and cold expansion are analogous; however cold expansion is a simpler process for which analytical models are available. The finite element results were found to agree well with such analytical models, improving confidence in the present model. Further details of the cold expansion simulations can be found in another paper by the present authors. 15 Another common benchmark that has been used in previous rivet forming studies is the load-deflection behaviour of the driven rivet head. 81 The load-deflection behaviour of the rivet from the current model is given in Figure 3. Good agreement is observed with 3

experimentally obtained curves with less than a 5% error, verifying the stiffness and plasticity of the rivet material model. 3 RESULTS AND DISCUSSION This discussion focuses on presenting the relative effects of the installation of universal and countersunk rivets in 224-T3 and GLARE3/1-.3 sheet. As a result, only a small subset of the results obtained from the described finite element model are presented. For simplicity of presentation, general trends and results observed in this study will first be discussed in context of the 224-T3 simulations. Differences observed for GLARE3/1-.3 sheet material are discussed in Section 3.4. 3.1 Influence of protruding countersunk rivet head In practice, appropriate countersunk depths are produced such that the countersunk rivet head protrudes above the sheet surface within the range of.1 to.2 mm. 5 Experience has shown that the presence of this small protrusion is beneficial to fatigue performance, likely due to improved hole filling of the conical recess of the countersunk sheet. Müller also found a correlation between the amount of rivet head protrusion and the incidence of fatigue cracking in the non-countersunk sheet along the bottom row of 3-row riveted lap splices. 5 He attributed this effect to a permanent curvature (or imperfection as it was called) resulting from bending of the inner and outer sheets around the protruding countersunk rivet head at high squeeze forces. Presence of an imperfection was shown to reduce the secondary bending moment along the top rivet row and increase it along the bottom rivet row (Figure 4). Most FE studies carried out by other researchers have neglected the influence of the rivet head protrusion, opting for simulating a perfectly flush rivet. 5,7,9 To investigate the effects of this simplification, models containing countersunk rivets that were perfectly flush and that protruded.7 mm above the sheet surface were simulated. Rather than varying the countersink depth, this protrusion was generated by adding a.7 mm extension to the countersunk rivet head. Results between the two variations agreed up until a squeeze force of 2 lbf (8.9 kn), above which significantly larger amounts of expansion were observed for the protruding rivet case (Figure 5). This squeeze force also corresponds to the point at which the driven rivet head diameter exceeds that of the countersunk rivet head. At these higher squeeze forces, frictional slip occurs causing the outer sheet to slide up the countersunk rivet head and expand through a wedging action. This expansion mechanism improves the residual compressive tangential stress state in the outer sheet and results in larger compressive radial stresses as the wedging action is reversed upon removal of the squeeze force (Figure 7 and Figure 8). Increased expansion of the inner sheet was also observed, indicating that the influence of the wedging expansion was transmitted from the outer sheet through friction (Figure 5); however, improvements in residual stresses were less pronounced in the inner sheet due to the smaller relative increase in total expansion. This large improvement in residual tangential stress generated in the outer sheet compared to the inner sheet could be a contributing factor to the incidence of fatigue cracking in the inner sheet as examined by Müller. 5 4

Li and Shi also investigated the residual stress state resulting from the installation of a countersunk rivet that protruded.7 mm above the sheet surface; however, there was no evidence of the wedging expansion described above. 8 Several key differences in their model could have contributed to this. First, Li and Shi considered a MS2426 style countersunk rivet, which has a larger countersunk head than the NAS197 style considered in the current investigation. As a result, the driven rivet head diameter did not exceed the countersunk rivet head diameter in their simulations. Bending in the outer sheet associated with this event could be critical in initiating frictional slip between the outer sheet and countersunk rivet head. Second, the depth of the countersink was equal to the thickness of the outer sheet in Li and Shi s model. The absence of a cylindrical hole surface in the outer sheet removes the contribution of radial pressure along this surface to frictional slip. 3.2 Countersunk vs. universal rivets Generally, the use of universal rivets results in an improvement in fatigue performance over a similar joint with countersunk rivets. A portion of this improved fatigue performance is often attributed to the likelihood of lower levels of expansion within the countersunk portion of the outer sheet in countersunk rivet joints. Results from this study, however, do not support this hypothesis. Expansion values in the outer and inner sheets for universal rivets were similar to those observed for a flush countersunk rivet and lower than those observed for the protruding countersunk rivet (Figure 6). Similarly, nearly identical residual stress distributions were observed for the universal and flush countersunk rivets, while the wedge expansion mechanism in the protruding countersunk rivet resulted in an improved residual stress distribution (Figure 7, Figure 8, and Figure 9). These results suggest that other factors including stress concentrations in the outer sheet due to the presence of the countersink and variations in load transfer and secondary bending account for the reduced fatigue performance of countersunk rivet joints. 3.3 Faying surface residual stress distribution Knowledge of residual stress distributions along the faying joint surfaces is important as they are most adversely affected by fretting and tensile secondary bending stresses under joint loading conditions, making them a likely location for crack initiation. Figure 11 compares the residual tangential stress distribution along these surfaces for countersunk and universal rivets installed in 224-T3 sheet under various squeeze forces. For discussion purposes, these distributions will be divided into four zones illustrated in Figure 1. Zones 1, 2, and 3 correspond to the region of plastic deformation in the sheets. Zone 1 contains large through-thickness stresses due to pressure from the driven rivet head during and after rivet installation. Zone 2 develops large through-thickness stresses due to pressure from the driven rivet head during rivet installation; however these stresses are relieved during unloading due to elastic springback of the rivet. Zone 3 lies beyond the driven rivet head, but experiences sufficient radial stress during rivet installation for plastic deformation to occur. Zone 4 corresponds to the elastic region of the sheet. The importance of through-thickness stress in the sheets due to transmission of the rivet squeeze force through the driven rivet head during installation is often overlooked in discussions on riveting. Within the current study, through-thickness stresses beneath the 5

driven rivet head (Zone 1) were found to exceed radial stresses by up to a factor of two during rivet installation, highlighting their contribution to yielding and the formation of compressive tangential stresses. Within the outer sheet, through-thickness stresses are reduced due to the larger footprint of the manufactured (universal or countersunk) rivet head reacting against the squeeze force. Radial expansion levels, however, are also reduced in the outer sheet resulting in the merger of Zones 1-3 as shown in Figures 11 (a) and (b). For the case of the protruding countersunk rivet, radial expansion levels increase and Zones 2 and 3 reappear as a result of the wedge expansion mechanism at high squeeze forces (Balloon A in Figure 11b). Evidence of regions of reduced hole-filling by the rivet are also evident in the residual tangential stress distributions in Figure 11. Differences in the amount of radial expansion of the outer and inner sheet create a small step in radial displacement at the faying joint surfaces. The larger radial displacement of the inner sheet reduces the hole-filling near the as the rivet is unable to completely conform to the displacement step, locally reducing the residual compressive tangential stress at the hole edge. A similar effect is observed in the outer sheet for the protruding countersunk rivet case when the wedging expansion mechanism reduces hole-filling of the cylindrical portion of the hole at high squeeze forces. In both cases, the reduction in residual tangential stress is highly localized; however, due to its location along the faying joint surface near the hole edge, its role in fatigue crack initiation cannot be discounted. 3.4 Influence of sheet material Overall, GLARE3/1-.3 exhibited similar trends as described above for 224-T3 with respect to rivet protrusion, rivet type, and squeeze force. Additionally, no significant differences in radial expansion levels were observed between GLARE and 224-T3. Effects of the prepreg layers, however, are evident when directly comparing results from the two sheet materials. Figure 11 and Figure 12 compare the residual tangential stress distributions along the faying joint surfaces for GLARE3/1-.3 and 224-T3 sheet. These results show that riveting in GLARE resulted in larger regions of plasticity (indicated by the location of peak tensile stress) and smaller gradients in residual stress, particularly towards the edge of the plastic region. This behaviour can be attributed to the apparent strain hardening behaviour caused by the fibre layers. As the aluminum layers begin to yield, their stiffness drops and load is redistributed through the elastic fibre layers, producing a stiffer yield response than monolithic aluminum. Plastic strains are thus distributed over a larger region, resulting in the larger plastic regions and smaller stress gradients. This dependence on strain hardening is also predicted by analytical cold-expansion models and has been observed in a previous study on cold expansion of GLARE laminates. 15,16 Larger magnitudes of residual compressive tangential stresses are also evident near the hole edge for GLARE (Figure 12). Despite the lower stiffness of the prepreg layers, lack of plasticity allows them to store more elastic energy during riveting compared to the aluminum layers. As a result, the larger springback response of the prepreg layers is resisted by the aluminum layers resulting in larger compressive hoop stresses at the hole 6

edge. Similarly, the elasticity of the prepreg layers produces a larger clamping force between the outer and inner sheet (Figure 13) as the rivet resists the through-thickness springback of the sheets. This larger clamping force could have significant consequences related to frictional load transfer and fretting fatigue in GLARE joints. Anisotropy of the prepreg layers had a minimal influence on residual stresses in the aluminum layers near the rivet hole. This is illustrated in Figure 14 for the case of a 3 lbf installed universal rivet in GLARE. Further from the rivet hole, residual tangential stresses in the aluminum layers along the θ = 45 direction become slightly more tensile due to the reduced combined stiffness (and springback response) of the two prepreg layers in this direction. Similar trends were also observed for the countersunk rivet case. One factor not considered in this study is the potential for delamination when riveting GLARE. The formation of small delaminations has been observed in cold-expansion experiments in GLARE, indicating a potential for their occurrence during riveting. 17 Although delamination damage is often regarded as undesirable, it plays a critical role in preserving the integrity of the prepreg layers and determining the damage tolerant behaviour of GLARE. Further discussion on delamination damage and its effect on fastener holes in GLARE can be found in a previous study carried out by the current authors. 15 4 CONCLUSIONS A 3D finite element analysis has been carried out to investigate the influence of rivet installation on residual stresses in the context of universal and countersunk rivets installed in 224-T3 and GLARE3/1-.3. Based on the results of the finite element simulations, the following conclusions can be made: Limited protrusion of the countersunk rivet head above the outer joint surface results in expansion of the outer sheet through a wedging action of the countersunk rivet head under high squeeze forces. Increased expansion of the inner sheet is also observed under these conditions, indicating that the effect is transmitted through the joint thickness by friction between the inner and outer sheets. Universal rivets do not provide a significant increase in expansion of the outer sheet over countersunk rivets. If the wedging expansion mechanism is present, countersunk rivets provide improved expansion and residual tangential stress distribution in the outer sheet compared to universal rivets. Through-thickness stresses during rivet installation play a dominant role in yielding and the resulting residual stress distribution. The apparent strain hardening behaviour of the prepreg layers results in larger regions of plastic flow (and compressive residual tangential stresses) in GLARE compared to 224-T3. 7

Elastic springback of the prepreg layers is resisted by the less resilient aluminum layers/rivet, resulting in larger residual compressive tangential stresses and larger rivet clamping forces than riveting in 224-T3. Anisotropy of the prepreg layers in GLARE has a minimal effect on the residual tangential stress distribution, particularly close to the rivet hole. REFERENCES [1] R.C. Alderliesten, M. Hagenbeek, J.J. Homan, P.A. Hooijmeijer, T.J. De Vries, and C.A.J.R. Vermeeren, "Fatigue and damage tolerance of Glare," Applied Composite Materials, vol. 1, pp. 22342, 23. [2] G.H.J.J. Roebroeks, "Glare features," in Fibre Metal Laminates an Introduction, A. Vlot and J.W. Gunnink, Eds. Dordrecht: Kluwer Academic Publishers, 21, pp. 238. [3] T. de Jong, "Forming of Laminates," Ph.D. dissertation, Delft University of Technology, Delft, the Netherlands, 24. [4] T.W. de Jong, E. Kroon, and J. Sinke, "Formability," in Fibre Metal Laminates an Introduction, A. Vlot and J.W. Gunnink, Eds. Dordrecht: Kluwer Academic Publishers, 21, pp. 337-353. [5] R.P.G. Müller, "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 224-T3 and Glare 3," Ph.D. dissertation, Delft University of Technology, Delft, The Netherlands, 1995. [6] X. Deng and J.W. Hutchinson, "The clamping stress in a cold-driven rivet," International Journal of Mechanical Science, vol. 4, pp. 683-694, 1998. [7] B. Langrand, E. Deletombe, E. Markiewicz, and P. Drazetic, "Riveted joint modeling for numerical analysis of airframe crashworthiness," Finite Elements in Analysis and Design, vol. 38, pp. 21-44, 21. [8] G. Li and G. Shi, "Effect of the riveting process on the residual stress in fuselage lap joints," CASI, vol. 5, pp. 915, 24. [9] L. Ryan and J. Monaghan, "Failure mechanism of riveted joint in fibre metal laminates," Journal of Materials Processing Technology, vol. 13, pp. 36-43, 2. [1] M.P. Szolwinski, "The mechanics and tribology of fretting fatigue with application to riveted lap joints," Ph.D. dissertation, Purdue University, West Lafayette, IN, U.S.A., 1998. [11] M.P. Szolwinski and T.N. Farris, "Linking riveting process parameters to the fatigue performance of riveted aircraft structures," Journal of Aircraft, vol. 37, pp. 1337, 2. 8

[12] M.R. Urban, "Analysis of the fatigue life of riveted sheet metal helicopter airframe joints," International Journal of Fatigue, vol. 25, pp. 11326, 23. [13] DND, "MIL-HDBK-5H," 1998. [14] M. Hagenbeek, "Thermal and mechanical properties of UD glass-fibre epoxy," Report B2V-4 (restricted), Delft, the Netherlands, June 24. [15] C.D. Rans, R.C. Alderliesten, and P.V. Straznicky, "Residual stresses in GLARE laminates due to the cold expansion process," in CANCOM. Vancouver, Canada, 25. [16] D.L. Ball, "Elastic-plastic stress analysis of cold expanded fastener holes," Fatigue and Fracture of Engineering Materials and Structures, vol. 18, pp. 47-63, 1994. [17] E.M.A.H. van der Kuip, "Fatigue crack initiation and crack growth in GLARE with coldworked holes," M.Sc. Thesis, Delft University of Technology, Delft, the Netherlands, 22. 9

TABLES Material Model Parameter Value 1, 11 2117-T4 (Power Law Plasticity) Elastic modulus, E 71.7 GPa Strength coefficient, k 544 MPa Hardening exponent, n.23 Poisson ratio, ν.33 224-T3 (Power Law Plasticity) 13 Elastic modulus, E 72.4 GPa Strength coefficient, k 53 MPa Hardening exponent, n.1 Poisson ratio, ν.33 Unidirectional Prepreg (Orthotropic Elastic) 14 Local 11 elastic modulus, E11 5.6 GPa Local 22 elastic modulus, E22 9.9 GPa Local 33 elastic modulus, E33 9.9 GPa Local 12 shear modulus, G12 3.7 GPa Local 23 shear modulus, G23 3.7 GPa Local 31 shear modulus, G31 3.7 GPa Local 21 Poisson ratio, ν21.63 Local 31 Poisson ratio, ν31.63 Local 32 Poisson ratio, ν32.32 Table 1: Summary of material properties. FIGURES 12.7 mm 12.7 mm z y x Rigid Rivet Set Outer Sheet Inner Sheet Rigid Bucking Bar Outer Sheet layup 24-T3 - prepreg* -9 prepreg* 24-T3 Inner Sheet layup 24-T3 - prepreg* -9 prepreg* 24-T3 *angle of fibres w.r.t. x-axis Figure 1: Schematic of FE model showing coordinate system and GLARE3/1-.3 lay-up orientation. 1

(a) (b) Figure 2: Cross-section of deformed 3D model showing typical mesh density in the radial direction: (a) 224-T3 sheet with countersunk rivet (F sq = 3 lbf) (b) GLARE3/1-.3 with universal rivet (F sq = 3 lbf). -5-4 (kn) -6-8 2 FE model experimental 5 5-3 4.5 1 1.5 2 2.5 3 3.5 bucking bar displacement (mm) (lbf) Figure 3: Comparison between experimental and finite element force-deflection response of the rivet bucking bar during installation of a NAS197AD4-4 rivet in 224-T3 sheet with a 3lbf squeeze force. outer sheet bottom rivet row P P top rivet row inner sheet Figure 4: Schematic of a 3-row riveted lap joint. 11

224-T3 with flush NAS197AD4-4 t =.4" (1.mm), R =.64" (1.6mm) 224-T3 with protruding NAS197AD4-4 t =.4" (1.mm), R =.64" (1.6mm).7mm normalized vertical position (z/t) -.5.5 z 1lbf 15lbf 2lbf 25lbf 3lbf normalized vertical position (z/t) -.5.5 z 1lbf 15lbf 2lbf 25lbf 3lbf 1% 2% 3% 4% 5% 6% 7% 8% radial expansion of hole edge (%R) (a) 1% 2% 3% 4% 5% 6% 7% 8% radial expansion of hole edge (%R) Figure 5: Variations in radial expansion in 224-T3 sheet with a countersunk rivet for various squeeze forces: (a) a perfectly flush countersunk rivet and (b) a countersunk rivet with.7 mm protruding head. (b) 224-T3 with MS247AD4-4 t =.4" (1.mm), R =.64"(1.6mm) normalized vertical position (z/t) -.5.5 z 1lbf 15lbf 2lbf 25lbf 3lbf 1% 2% 3% 4% 5% 6% 7% 8% radial expansion of hole edge (%R) Figure 6: Variations in radial expansion in 224-T3 sheet with a universal rivet for various squeeze forces. 12

1 1.8.5.2 -.9 -.6 -.3.3.6.9 1.2 σ r.4.2 -.8 -.6 -.4 -.2.2.4.6 vertical position (mm) vertical position (mm) -3 = 3lbf (13.3kN) σ y = 42ksi (29MPa) -3 = 3lbf (13.3kN) σ y = 42ksi (29MPa) -4 1 2 3 4 5 6 distance from rivet/hole centreline (mm) (a) -4 1 2 3 4 5 6 distance from rivet/hole centreline (mm) Figure 7: Residual stresses for a perfectly flush countersunk rivet in 224-T3 sheet (F sq = 3 lbf): (a) residual tangential stress; (b) residual radial stress. (b) 1 1.8.5.2 -.9 -.6 -.3.3.6.9 1.2 σ r.4.2 -.8 -.6 -.4 -.2.2.4.6 vertical position (mm) vertical position (mm) -3 = 3lbf (13.3kN) σ y = 42ksi (29MPa) -3 = 3lbf (13.3kN) σ y = 42ksi (29MPa) -4 (a) 1 2 3 4 5 6 distance from rivet/hole centreline (mm) -4 (b) 1 2 3 4 5 6 distance from rivet/hole centreline (mm) Figure 8: Residual stresses for a.7 mm protruding countersunk rivet in 224-T3 sheet (F sq = 3 lbf): (a) residual tangential stress; (b) residual radial stress. 13

.8.5.2 -.9 -.6 -.3.3.6.9 1.2 σ r.4.2 -.8 -.6 -.4 -.2.2.4.6 1 1 vertical position (mm) vertical position (mm) -3 = 3lbf (13.3kN) σ y = 42ksi (29MPa) -3 = 3lbf (13.3kN) σ y = 42ksi (29MPa) (a) 1 2 3 4 5 6 distance from rivet/hole centreline (mm) Figure 9: Residual stresses for a universal rivet in 224-T3 (F sq = 3 lbf): (a) residual tangential stress; (b) residual radial stress. (b) 1 2 3 4 5 6 distance from rivet/hole centreline (mm) 1 2 3 4 plastic region elastic region reduction in rivet clamping area due to rivet springback 1 2 3 4 5 radial position, r / R Figure 1: Schematic of residual tangential stress distribution. 14

.5.5 -.5 MS247AD4-4 outer sheet 1lbf 15lbf 2lbf 25lbf 3lbf -.5 NAS197AD4-4 A outer sheet 1lbf 15lbf 2lbf 25lbf 3lbf.5 224-T3, t =.4"(1.mm), R =.64" (1.6mm), σ y = 42ksi (29MPa).5 224-T3, t =.4" (1.mm), R =.64" (1.6mm), σ y = 42ksi (29MPa) (a) 1 1.5 2 2.5 3 3.5 4 4.5 5 radial position, r / R 1 1.5 2 2.5 3 3.5 4 4.5 5 radial position, r / R (b).5 224-T3, t =.4"(1.mm), R =.64" (1.6mm), σ y = 42ksi (29MPa).5 224-T3, t =.4"(1.mm), R =.64" (1.6mm), σ y = 42ksi (29MPa) -.5.5 MS247AD4-4 inner sheet 1lbf 15lbf 2lbf 25lbf 3lbf -.5.5 NAS197AD4-4 inner sheet 1lbf 15lbf 2lbf 25lbf 3lbf 1 1.5 2 2.5 3 3.5 4 4.5 5 radial position, r / R (c) 1 1.5 2 2.5 3 3.5 4 4.5 5 radial position, r / R Figure 11: Influence of rivet squeeze force on residual tangential stress in 224-T3 sheet: (a) outer sheet with universal rivet; (b) outer sheet with.7 mm protruding countersunk rivet; (c) inner sheet with universal rivet; (d) inner sheet with.7 mm protruding countersunk rivet. (d) 15

.5.5 -.5 MS247AD4-4 outer sheet 1lbf 15lbf 2lbf 25lbf 3lbf -.5 NAS197AD4-4 outer sheet 1lbf 15lbf 2lbf 25lbf 3lbf.5 (a) GLARE3/1-.3, t =.34"(.86mm), R =.64"(1.6mm), σ y = 42ksi (29MPa) 1 1.5 2 2.5 3 3.5 4 4.5 5 radial position, x / R.5 GLARE3/1-.3, t =.34"(.86mm), R =.64"(1.6mm), σ y = 42ksi (29MPa) 1 1.5 2 2.5 3 3.5 4 4.5 5 radial position, x / R (b).5 GLARE3/1-.3, t =.34"(.86mm), R =.64"(1.6mm), σ y = 42ksi (29MPa).5 GLARE3/1-.3, t =.34"(.86mm), R =.64"(1.6mm), σ y = 42ksi (29MPa) -.5 1lbf 15lbf 2lbf 25lbf 3lbf -.5 1lbf 15lbf 2lbf 25lbf 3lbf.5 (c) MS247AD4-4 inner sheet 1 1.5 2 2.5 3 3.5 4 4.5 5 radial position, x / R 1 1.5 2 2.5 3 3.5 4 4.5 5 radial position, x / R Figure 12: Influence of rivet squeeze force on residual tangential stress in GLARE3/1-.3 sheet: (a) outer sheet with universal rivet; (b) outer sheet with.7 mm protruding countersunk rivet; (c) inner sheet with universal rivet; (d) inner sheet with.7 mm protruding countersunk rivet..5 (d) NAS197AD4-4 inner sheet 5 universal rivet countersunk rivet 4 rivet clamping force (N) 3 2 1 GLARE3/1-.3 224-T3 2 4 6 8 1 12 14 16 (kn) 5 1 15 2 25 3 35 (lbf) Figure 13: Comparison of residual rivet clamping force in 224-T3 and GLARE3/1-.3 sheet. 16

1.5 θ =45 o GLARE3/1-.3, = 3lbf (13.3kN) σ y = 42ksi (29MPa), R =.64" (1.6mm) 1.5 GLARE3/1-.3, = 3lbf (13.3kN) σ y = 42ksi (29MPa), R =.64" (1.6mm) -.5 θ = o θ =9 o -.5 θ =45 o θ =9 o θ = o.5 MS247AD4-4 outer sheet y θ x.5 MS247AD4-4 inner sheet (a) 1 2 3 4 5 r/r 1 2 3 4 5 r/r Figure 14: Angular variation of residual tangential stress distribution in GLARE3/1-.3 with a universal rivet (F sq = 3 lbf): (a) outer sheet (b) inner sheet. (b) 17