A finite element stress analysis of aircraft bolted joints loaded in tension

Transcription

1 THE AERONAUTICAL JOURNAL JUNE 2010 VOLUME 114 NO 1156 A finite element stress analysis of aircraft bolted joints loaded in tension R.H. Oskouei reza.oskouei@eng.monash.edu.au Department of Mechanical and Aerospace Engineering Monash University Melbourne, Australia M. Keikhosravy m.keikhosravy@gmail.com Department of Mechanical Engineering, Islamic Azad University Firuzkooh Branch Firuzkooh, Iran C. Soutis c.soutis@sheffield.ac.uk Aerospace Engineering, The University of Sheffield Sheffield, UK ABSTRACT Accurate stress and strain analysis in bolted joints is of considerable interest in order to design more efficient and safer aerospace structural elements. In this paper, a finite element modelling of aluminium alloy 7075-T6 bolted plates, which are extensively used in aircraft structures, is discussed. The ANSYS Finite Element (FE) package was used for modelling the joint and estimating the stresses and strains created in the joint due to initial clamping forces and subsequent longitudinal tensile loadings. A double-lap bolted joint with a single bolt and nut was considered in the study. A three-dimensional (3D) finite element model of the joint was generated, and then subjected to three different simulated clamping forces followed by different levels of longitudinal tensile load. 3D surface-to-surface contact elements were employed to model the contact between the various components of the bolted joint. Friction effects were considered in the numerical analysis; and moreover, the clearance between the bolt and the plates was simulated in the model. FE results revealed beneficial compressive stresses near the hole edge as a result of applying the clamping. It was found that a higher clamping force can significantly decrease the magnitude of the resultant tensile stress at the hole edge and also bearing stress in the joint when subjected to the longitudinal tensile load. 1.0 INTRODUCTION Mechanically fastened joints are the most common method of connecting structural components in aerospace structures. The skinto-spar/rib connections in a wing structure and the wing-to-fuselage connection are typical examples of bolted joints in aircraft primary structures. It is well-recognised that bolt fasteners can clamp joint parts together well and show a good load carrying capability. In this respect, a number of authors (1-4) have detailed the design methods for bolted joints mostly under static loading conditions. However, drilling fastener holes in members inherently introduces a stress concentration near the hole and reduces the load carrying cross sectional area. A drilling process may also cause a rough surface finish in the bore of the fastener hole which is prone to fatigue crack initiations under cyclic loads. Aircraft structures are primarily constructed from high strength light alloys and composites as their low density provides optimum strength-to-weight ratio aerospace materials. Since safety is of paramount importance in aerospace vehicles, several investigations have been conducted with the aim to optimise the design of structural bolted joints (metallic and composites) so that catastrophic failure during the flight can be prevented (5-11). A bolted joint is most commonly preloaded through an initial torque. When the torque is applied to the nut, the bolt is axially Paper No Manuscript received 10 July 2009, revised version received 27 January 2010, accepted 4 February 2010.

2 NUMBER THE AERONAUTICAL JOURNAL JUNE 2010 stretched. As the bolt head and nut clamp the joint members together, the bolt is left in tension (called a preload) and the mechanical members are compressed together (1). Past research confirmed that the bolt clamping effect can decrease the stress concentration at the bolted hole region when the joint is subjected to a longitudinal tensile load, and thus increases the fracture and fatigue strengths of the joint (12-16). Based on FE Analysis (FEA) results, it was found that a clamping force can introduce favourable compressive stresses around the bolted hole of a single clamped plate. The higher applied clamping force the higher magnitude of the compressive stress at the hole region (12,13). Such negative stresses can reduce the magnitude of the resultant stress in the plate under the applied tensile loads. Although the stress state was determined in the single clamped plate (in the absence of other joint plates), obtained experimental results of fatigue life and experimental observations of initial cracks location verified the FEA results well (13). Furthermore, it was also found that a great increase in the clamping force magnitude may cause the phenomenon of fretting on the surfaces of mating bolted plates under cyclic loading conditions (16,17). The determination of the local stress distribution in a bolted joint is generally a 3D problem due to the clamping of the fastener (9). Some methods are available in order to estimate the stiffness of the joint members based on the conventional assumptions of pressure distribution within the clamped zone (1,9,18,19). Rötscher (18) proposed that the stresses are contained within two conical frusta symmetric about the mid-plane of the joint, each having a vertex angle of 2α. Then a half-apex angle of α = 45 was selected to compute the stiffness. FE stress results of a double-lap aluminium bolted joint discussed by the authors in previous study (9) showed an overall crock-shaped pressure distribution at the clamped plates including a pair of frustum hollow cones developed at the outer plates and a hollow cylinder shape at the middle plate uniformly distributed along the thickness. It is reported that the finite element method is a convenient and efficient way to determine and analyse the stresses and strains in bolted joints (9). However, a literature review confirmed that 3D stress analysis of bolted joints due to both the clamping and tensile loading is complex and has still not been thoroughly investigated. The main purpose of the present study is to determine the stress and strain distributions in an aircraft aluminium double-lap bolted joint loaded in tension with the aim to predict the ultimate failure of such joints. Appropriate 3D finite element models were generated and developed to simulate the bolt clamping force and subsequent tensile load applied remotely at the plates end. Stress and strain results developed in the hole region are reported and discussed with the aim of improving the bolted joints design in metallic and composite aircraft structures. 2.0 FINITE ELEMENT MODELLING PROCEDURE A double-lap bolted joint was designed to model and analyse using the ANSYS finite element package. The joint geometry and dimensions are shown in Fig. 1. The joint includes three identical aluminium alloy 7075-T6 plates with a thickness of 3mm and a 5mm-diameter hole. An appropriate standard aerospace bolt fastener (AN3-6A) with a diameter of 3/16in was selected to clamp the plates. As the joint geometry and loading conditions are completely symmetric with respect to two Cartesian planes, only one-fourth of the full model should be numerically analysed (Fig. 2). Symmetric displacement boundary conditions were defined for the nodes on these planes of symmetry. For the bolt geometry, a circular shape was assumed for the bolt head rather than its hexagonal shape. Because the bolt and its washer have approximately the same elastic modulus and Poisson s ratio, the washer geometric model with an outside diameter of 10mm and a thickness of 1mm was merged with the bolt head in order to minimise the contact element use (with ignoring the contact elements between the bolt head and washer). It is well-known that the grip length of the bolt shank at shear joints should be approximately equal to the total thickness of the fastened members (20). For the bolt selected to be modelled, this grip length is 3/8in, according to the aerospace AN bolt standard dimensions. Therefore, there is no need to consider the bolt threads in this model. A radial clearance of 0 1mm is assumed between the bolt shank and the fastener hole, as shown in Fig. 3. The 3D structural brick elements, as called SOLID45 in ANSYS, were used for the 3D modelling of the bolt and plate sections. This cubic-shaped element has eight nodes, and each having three degrees of freedom (translations in the x, y, and z directions). The use of these elements provides the same accuracy in plasticity (2 2 2 integration points) as the higher-order elements (20-node element), but requires much less computational power to converge the numerical solutions especially in nonlinear problems such as a contact analysis (21). To achieve an optimal mesh density, size of the dummy divisions of the plates and bolt, and then the elements were modified several times in order to achieve element-size-independent results. Figure 4 (next page) shows the final meshed model of the joint. Table 1 Data points of stress-strain curve for 7075-T6 Strain Stress (MPa) Figure 1. Joint geometry and dimensions (in mm). Figure 2. Geometric modelling: full model and model of one-fourth for FE analysis.

3 OSKOUEI EL AL A FINITE ELEMENT STRESS ANALYSIS OF AIRCRAFT BOLTED JOINTS LOADED IN TENSION NUMBER Since the joint was intentionally considered to be subjected to different levels of longitudinal load (low, moderate and high), an elastic-plastic multilinear kinematic hardening material model was used to represent the aluminium alloy 7075-T6 stress-strain behaviour. This material model was selected to calculate stresses and strains in the plastic region of the material particularly around the hole of the middle plate. Thin aluminium sheets show an orthotropic behaviour due to rolling process (different yield stress in the rolling and transverse directions). In some cases, this difference can be up to 10%, but in this study, in the material modelling of the aluminium plates, this orthotropic effect was neglected. A true stress-strain diagram for the aluminium alloy 7075-T6 was obtained from a simple tensile test in the rolling direction (Fig. 5), and then, seven data points from this diagram were used as input data for the material model, as given in Table 1. Furthermore, the elastic modulus and Poisson s ratio were measured to be E = 71 0GPa and ν = 0 33, respectively. However, for the steel bolt and its steel washer, a linear elastic material relationship was assumed with a Young s modulus of 210GPa and a Poisson s ratio of This is based on the tested fact that the bolt material remained in the elastic region (without any plastic deformation) when it was subjected to the maximum selected wrenching torque (5 5Nm) (9). The friction effect between all potential contacting surfaces was included in the model using the elastic Coulomb friction model with a friction coefficient of 0 33 between the steel bolt (head and shank) and the aluminium plates (9), and 0 32 between the top and middle plates (16). A 3D 4-node surface-to-surface contact element CONTA173 was used to represent the contact between contacting surfaces in the joint model. This element was preferred to the 8-node element CONTA174 (with midside nodes) because the use of structural SOLID45 elements for the solid model of the joint which have no midside nodes (9,22). Contact occurs when the contact element surface penetrates one of the target segment elements on a specified target surface. A 3D target segment element TARGE170 was used to associate with CONTA173 via a shared real constant set to create four different contact pairs between all contacting surfaces in the model, as listed in Table 2. Figure. 3. Developed solid bolt model where clamping force is represented by an axial displacement at bottom surface of bolt shank. Table 2 Contact pairs and their contact and target surfaces Contact pair No Contact surface Target surface 1 Bottom surface of bolt head Top surface of top plate 2 Bottom surface of top plate Top surface of middle plate 3 Bolt shank surface Bore of the hole of top plate 4 Bolt shank surface Bore of the hole of middle plate Two different load steps were defined for the joint model in order to apply a clamping force and a longitudinal tensile load subsequently. It is reported that the solid bolt model is the most realistic finite element model in order to model the bolt fastener in the structures with the best Table 3 Percent reduction (average) in maximum magnitude of tensile and bearing stresses due to the increase in clamping force Tensile stress Bearing stress F cl (kn) from 1 to 3 from 1 to 6 from 3 to 6 from 1 to 3 from 1 to 6 from 3 to 6 Reduction(%) Figure 4. Optimised FE meshed model.

4 NUMBER THE AERONAUTICAL JOURNAL JUNE Compressive stresses Stress (MPa) MN MX Strain F cl (kn) σ x,min (MPa) Figure 5. True stress-strain curve for Al-alloy 7075-T6. Figure 6. Distribution of longitudinal stress (σ x ) in middle plate with maximum magnitudes due to different clamping forces. Bearing Crack initiation Bearing Stresses Maximum tensile stress Figure 7. Distribution of resultant longitudinal stress (σ x ) in MPa in middle plate due to 1kN clamping force and 150MPa applied longitudinal stress. Figure 8. Fatigue failure in middle plate of a specimen with clamping force of 1 15kN and applied maximum remote longitudinal stress of 144MPa (16). Figure 9. Maximum magnitude of: (a) tensile stress; and (b) bearing stress, at hole edge of middle plate due to different magnitudes of clamping force and applied longitudinal stress. simulation approach for accuracy in which tensile, bending and thermal loads can be transferred through the bolt (9,23). In the previous work (9), the solid bolt modelling approach was developed for simulating the clamping force in the joint by directly applying an axial displacement at the bottom surface of the bolt shank in the solid bolt model. To conduct the first load step, which is applying the only clamping force, the problem was numerically solved by applying an initial negative displacement at the bottom surface of the bolt shank in the Y direction (Fig. 3). Then the corresponding clamping force due to the axial displacement was quantified by obtaining the total reaction force in the solid bolt model. This approach was repeated several times to accurately achieve three previously selected clamping forces of 1,000N, 3,000N and 6,000N. Afterwards, for each solved model with its particular clamping force, a longitudinal remote tensile load of 11 25kN was applied to the joint. Therefore, a corresponding remote stress of 150MPa was statically applied in the X direction to the far end of the middle plate (i.e. away from the hole) in the second load step. This stress was incrementally increased in 15 sub-steps with the aim of obtaining numerical results for all 10, 20, 30,, 150MPa applied stress magnitudes. In addition to the symmetric displacement boundary conditions, the end of the top plate was constrained against all degrees of freedom as well.

5 OSKOUEI EL AL A FINITE ELEMENT STRESS ANALYSIS OF AIRCRAFT BOLTED JOINTS LOADED IN TENSION NUMBER 3.0 FE STRESS RESULTS AND DISCUSSION The finite element results of transverse normal stresses within the clamped zone showed an overall crock-shaped pressure distribution at the joint considering all the plates. These results were discussed in previous work by the authors (9). It was observed that the magnitude of the clamping has an effect on the tensile strength of the joint, and is represented by the longitudinal normal stress (σ x ) component developed in the middle plate. The contours of stress σ x in the middle plate with maximum magnitudes (at the hole edge) due to different clamping forces are shown in Fig. 6. Although the magnitude of the compressive stresses even for the highest clamping force is not considerable, this stress component can potentially play a key role to control the resultant stress when the joint is subjected to a remotely applied longitudinal tensile load. Resultant stresses and strains as a function of the combined clamping and longitudinal loading were numerically estimated at the joint after applying a longitudinal tensile stress of 150MPa in 15 sub-steps to each differently clamped model. Figure 7 shows the distribution of the resultant longitudinal stress (σ x ) in the middle plate for the case with a clamping force of 1kN under a longitudinal stress of 150MPa. As the stress contours indicate, maximum tensile stresses are located at the critical edge of the hole particularly at the middle of the plate thickness where there is a localised stress concentration due to the notch presence. This obviously clarifies why failure occurs at the net section of the middle plate in a metallic double-lap bolted joint. In addition, the most compressive stresses exist at the bearing region where the bolt shank and the plate hole touch each other in order to transfer the applied load in the joint (bearing load transfer). In orthotropic composite plates, the stress results are influenced also by the fibre orientation and laminate stacking sequence of the middle plate (5,10). It was reported by Shankar and Dhamari (16) that the final fracture in similar double-lap bolted plates (with the same geometry and materials as the FE model) subjected to longitudinal cyclic loadings occurs in the middle plate at or in the vicinity of the net section at the fastener hole. Figure 8 shows a fatigue failure in the middle plate of a specimen clamped with 1 15kN failed under a cyclic load with a maximum stress of 144MPa and a load ratio of 0 1. Fractography of the failed specimen indicated that the fatigue initiates at the bore of the hole where there is a localised magnification of stress and the fracture line passes through the centre line of the fastener hole (16). The comparison between the experiments and the obtained finite element simulation results shows a good agreement and validates the FE modelling of the joint reasonably well. Comparing the obtained σ x stress results for all 45 models revealed how a higher clamping force can considerably decrease the stress concentration and bearing stress at the hole edge. These beneficial effects can be clearly seen in Figs 9(a) and 9(b), respectively. For example, for the clamped model with 1kN when the joint is subjected to a 100MPa longitudinal stress, maximum tensile stress (σ x,max ) at the hole edge is 530MPa; however, this stress was significantly reduced to 288MPa when the clamping force was increased to 6kN. For these cases, the maximum bearing stress (σ x,min ) at the hole edge decreased from 693 to 375MPa. It should be noted that in some loading cases, the stress magnitude in the aluminium plate exceeded the ultimate value in the stress-strain relation of the material model; however, ANSYS simply extrapolates the curve to analyse these large stresses and strains accordingly. In order to numerically find out by how much an increase in the amount of clamping force may reduce the resultant local stress, percent reductions in the maximum magnitude of the both tensile and bearing stresses were averaged and presented in Table 3 for two differently clamped models subjected to different levels of an applied longitudinal stress. One can see that increasing the clamping force from 1 to 6kN would generally decrease the maximum tensile and bearing stresses in the middle plate by 44% and 55%, respectively. (a) (b) Figure 10. Reduction in plastic zone around hole of middle plate by increasing clamping force from 1 to 6kN under longitudinal stress.of 150MPa. Figure 11. Distribution of resultant longitudinal stress (σ x ) in MPa in middle plate and location of maximum tensile stress due to 6kN clamping and 20MPa applied longitudinal stress. As previously mentioned, the joint was intentionally subjected to high level longitudinal loads as well as low and moderate levels with the aim of investigating the clamping effects for a locally yielded 7075-T6 plate of the joint. The contours of resultant von Mises plastic strain for the models with 1 and 6kN clamping force subjected to 150MPa longitudinal stress are shown in Figs 10(a) and 10(b), respectively. The strain contours show that by applying a high clamping force, the material around the hole is less stressed, and thus less plastically deformed even when the longitudinal tensile load applied remotely to the joint is relatively high. It reduced the maximum magnitude of von Mises plastic strain from to 2 2 x 10 3 which is a twelve-fold reduction. Furthermore, for the models with the highest clamping force (6kN) under low longitudinal stresses, less than 30MPa, the maximum tensile stress (σ x, max ) occurred further away from the hole edge, as shown in Fig. 11. However, the difference between the stress magnitude at the hole edge (18MPa) and the maximum (27MPa) is not significant. In these cases, it is believed that the compressive stresses created by a high clamping force can successfully overcome the small local stress due to the low level applied loads. Consequently, the maximum tensile stress may not necessarily occur at the hole edge. In fact, tightening the joint by a high torque

6 NUMBER THE AERONAUTICAL JOURNAL JUNE 2010 provides a high normal force to compress the joint plates, and thus a high friction between the mating surfaces. Since the applied longitudinal load is low, the plates are kept very firmly particularly in the hole region. Therefore, a significant portion of the load is transferred by friction rather than the bearing between the bolt shank and material at the hole edge. 4.0 CONCLUSIONS In this paper, a three-dimensional stress and strain analysis was performed for a typical aircraft structural double-lap bolted joint using the commercially available ANSYS FE package. A solid bolt model was developed as a finite element modelling technique to simulate the applied clamping force in bolted joints. The clamping simulation method had been successfully validated against the experimental results in earlier studies. The effects of the fastener clamping force were examined and the concluding remarks are summarised as following: A bolt clamping force can introduce beneficial longitudinal compressive stresses around the fastener hole with localised maximum magnitudes at the critical edge of the hole. These stresses are more compressive in firm bolted joints and can considerably reduce damage when a longitudinal tensile load is remotely applied in the joint. The numerical results indicated the beneficial effect of a high clamping force to decrease the stress concentration at the edge of the fastener hole up to 44% (average value) for the bolted plates longitudinally loaded in a wide range of applied loads. In general, these reductions can improve the tensile strength and fatigue life of the joint considerably. This work has confirmed that tightening the fasteners to hold (clamp) the joint firmly with a high preload (not more than maximum allowable value) can advantageously reduce damaging effects of the bearing stress at the fastener hole by altering the load transfer mechanism from Bearing to Friction even under high level longitudinal tensile loads. This may successfully prevent the bearing failure in highly loaded structural bolted joints, especially in composite structures where the critical failure mechanism is that of fibre microbuckling. It will be of interest to perform the above analysis to laminated composite plates where through-the-thickness stresses are also expected to play a significant role in damage evolution (24) and hence ultimate strength. REFERENCES 1. BUDYNAS, R.G. and NISBETT, J.K. Shigley s Mechanical Engineering Design, 8th ed, 2008, McGraw-Hill, Boston, USA. 2. BICKFORD, J.H. An introduction to the design and behaviour of bolted joints, 4th ed, 2008, CRC Press. 3. 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