Experimental and finite elements study of the behaviour of a double shear bolted joint submitted to tensile and bending forces

Transcription

1 Experimental and finite elements study of the behaviour of a double shear bolted joint submitted to tensile and bending forces K. Koffi', R. Chieragatti', J. Huef & E. Bouchef 1 Department of Mechanical Engineering, (ENSICA), 1 place Emile Blouin Toulouse cedex, France koffi@ensica.fr, chieragatti@ensica.fr ^Aerospatiale, 316 Rte de Bayonne Toulouse cedex 03 France eric. bouchet@avions. aerospatiale.fr, Jacques. huet@avions. aerospatiale.fr Abstract A great deal of work has been done since 1950 to improve the design of the bolted joint. In this paper a series of tests on a double shear bolted joint was performed both by finite elements methods and testing machine. The parameters of the study are the ratio R (tensile stress/bending stress) and the tightening torque Q. We notice that the maximum stress at the hole edge evolves according to R. The most loaded fasteners are located in the tensile part of the joint. The likeness of the distribution of stress obtained by numerical study and photostress analysis is remarkable. We also noticed a good correlation between the results proposed by finite elements analysis and strain gages measurements when the tightening torque is small. When the tightening force is great, there is a gap between the two results. The load transferred by the first and the last line becomes greater and greater when the tightening force increases. This increase of the tightening force gives rise to a bad distribution of the load per line of fastener and consequently a bad distribution of stress concentration around the fastener's hole.

2 362 Computational Methods and Experimental Measurements 1 Introduction Mechanical fastening is one of the common joining in aeronautical structures. The accurate analysis of fastened joints is very important in the correct design of aircraft structures. A bad design leads to a limited life of the aircraft and an excessive weight. Nowadays in aeronautical structural study, finite elements analysis is more and more used according to the quickness of computation of the new work stations. The results of this analysis must be compared to the experimental tests in order to validate the final solution. Several studies are made on aeronautical bolted joints, but most of the time the joint is submitted to tensile stress only. In this paper we show a numerical and experimental study of an aeronautical bolted joint submitted to tensile and bending forces. Our aim is the knowledge of the stress concentration at the hole edge under this type of load. This complex loading type represents the load subjected to a civil aircraft frame during the flight. A good knowledge of the by-passing and the bearing forces suggested by Huth [1] acting in the joint is essential to understand the behaviour of the whole structure. Figure 1 presents a single shear joint in which the total load FO is shown to be decomposed in Fbp and Fit, where: -FO : total load applied, -Fbp : by-passing force, -Fit : load transferred (bearing and friction), the influence of geometrical parameters on the load transferred has been studied by Koffi[2]. In order to make a qualitative comparison between experimental results and numerical ones, a polycarbonate plate is bounded to the test specimen, photostress techniques is then used to analyse the stress distribution. But to make a quantitative comparison strain gages are glued (to the main plate) at the interface of the plates to measure the strain at the hole edge. ^ O Figure 1: Forces in a single shear joint

3 Computational Methods and Experimental Measurements Experimental methods 2.1 Models for the representation of fasteners In order to study the load transfer with the finite element software SAMCEF, a model (figure 2) for the representation of fasteners is made. This model proposed by Santgerma[3] is used to study the stress concentration factor around the hole. The fasteners are represented by two disks linked to the plates by contact conditions. The disks are linked each other by springs. Each disk is divided in N finite elements. The finite element used for the plate is a twodimensional membrane element. Figure 2: Model for representation of fasteners 2.2 Test procedure The test is performed on a double lap-shear joint. The material of the plate are aluminium alloy 7075 T6 and the bolts (Hi-lite) arevin titanium alloy (Ta6V). The characteristics of plate and bolts are given in table 1, where: - E : Young modulus, v: Poisson ratio - Rm : Yield tensile strength - TR : Yield shear strength. L : total length of the plate - D : bolt diameter - W : total width of the plate - P : pitch of implantation of fasteners. - T : thickness of the plate The test specimen is represented on figure 3. The pretension load of the bolts is applied by a electronic dynamometric wrench with a precision of 1%. The clearance between the bolt and the plate is about 0.2%D. To have a qualitative comparison with the finite element analysis, a

4 364 Computational Methods and Experimental Measurements polycarbonate plate of 3mm thick is bounded on the plate. A photo-stress [4] device is then used to study stress distribution. Strain gages method is then used to make a quantitative study of the transfer of load and the stress concentration around the bolt hole. The strain gages are put near the bolt hole (see figure 3) at the interface of the plates on the main plate. This implantation is very difficult to be realised because of the thickness of the gages. A slot of 0.3mm depth is making on the secondary plate in order to avoid all electrical contact and prevent the gauges from friction damage. Secondary plate 32 hi-lite bolts Polycarbonate plate \ //j Main plate ^=0-0- JL Gauge for load transfer measurement 1 VpA-'VLA-V^/ /i\,/t\ j^tx,/tx '\J^f '. I I/-T\ vjj \i) /~K vp /i\ (4) /T\ tzm^q^t^i /^t^^tsxk-ii^vi 1 vp vp \P \\) !}($}<& <&~&~ /TVi^*V~tTTVifTVn \T5^\pr-\^y "\p7 ' I/t\ Vjy \L? /t\ /t\ xjt ft\ V/ / 1 1 Q_ ^ 3 Gauge for stress concentration measurement Figure 3: Test specimen and bolts distribution I ^ =_ **- F^ plate bolt E Mpa 72, ,000 V Rm Mpa %R Mpa L mm 160 D mm 9.52 W mm 160 P mm 4*D T mm 5 Table 1: Test specimen characteristics

5 Computational Methods and Experimental Measurements Testing machine The testing machine has been designed and constructed specially by the department of mechanical engineering (ENSICA) for this application. The machine must be able to apply both tensile and bending forces on the specimen. The bending moment is applied through a four point bending device. Two electrical jack are used for the test specimen loading. The loading sensors and the gauges are related to a computer for results analysis. The machine is represented on figure 4. Figure 4: Testing machine 3. Experimental results 3.1 Photo-stress analysis results The equal stress (MPa) curves obtained by finite element and photo-stress analysis are represented respectively on figure 5a and 5b. As we can see on these

6 366 Computational Methods and Experimental Measurements figures, the likeness of the stress distribution is remarkable. The torque value applied is 15Nm. We will show later the influence of the torque value. Figure 5a: Finite elements equal stress results Figure 5b: Photo-stress equal stress results

7 Computational Methods and Experimental Measurements Load transfer results Comparison of numerical and experimental load transfer rates To measure load transfer, the value of tightening torque applied to the bolts is the same as that used for photo-stress analysis. Figure 6 represents the rate of load transfer versus the joint line number for experimental measurements and numerical analysis. The rate of transfer is the same for both cases v v Q=15Nm - - numerical results line number 3 Figure 6: Comparison of numerical and experimental values of load transfer Influence of the tightening force on load transfer rate In order to study the effect of the tightening torque (Q) on load transfer, four values of torque are applied. Figure 7 gives the rate of transfer against the line number. When the torque value is lower (15Nm) the experimental result is the same that the result obtained by finite elements method. When the torque value becomes greater, the two results are different. The amount of load transferred by the first and last line becomes greater than that of the middle lines. This phenomenon can be explained by the fact that the finite element model (2D model) does not take into account the friction effect which according to Weissberg [5] and Atzori [6] increases with the torque applied to the bolt. According to these authors, When the tightening torque increases the apparent flexibility of the bolts also changes. Therefore the behaviour of the joint is not the same.

8 368 Computational Methods and Experimental Measurements Figure 7: Load transfer per line for different values of Q (tightening torque) 3.3 Stress concentration The result of the principal stress at the hole edge with the ratio of stress R(tensile/bending) is represented on figure 9. The value of the torque applied to the bolt is 30Nm (usual value). As we can see on figure 8 and 9, the gauge 4 which is in the tensile part of the specimen has a greater value of stress than the gauge 1 located on the compression part. The gap between the two curves of stress decreases when R increases (when the bending load is more and more lower). Bolt 1 Bolt 2 o o o o O 0 O 0 o o o o o o o o o o o cv/ BoltS O O O Ou 0 00 O^ Bolt 4 o o o o Figure 8: bolts implantation and specimen loading forces

9 Computational Methods and Experimental Measurements 369 gauge 4 gauge 3 gauge 2 gauge 1 Figure 9: Principal stress versus stress ratio R. In order to study the influence of the torque value applied to the bolts on the stress concentration at the hole edge, two values are used (Q=15Nm and 30Nm). Figure 10 shows the stress concentration (Von-Mises value) around the most loaded bolt (stress measured by gauge 4). For Q=15Nm, the test result and the finite element analysis (F.E.A) result are closer. There is a good correlation between numerical results and experimental ones when the friction effect is lower. I _ Q=30Nm -- F.E.A Q=15Nm Figure 10: Von-mises stress around bolt 4 versus stress ratio R. 4 Discussion We noticed in this study that the model proposed for the representation of bolts is not valid when the tightening force increases (when the contact friction

10 370 Computational Methods and Experimental Measurements increases). The model can be improved by using springs with dampers instead of springs only. Another way to improve the joint behaviour is to make a 3D model, but this one is too arduous to manage. In fact in aeronautical industries, a layer of mastic is inserted at the interface of the plates to reduce the friction effect in order to prevent the joint from fatigue corrosion. Therefore it is not necessary to take into account the friction effect in the numerical model. The load is supposed to be transferred from one plate to another only by bearing. 5 Conclusion A two-dimensional plane stress analysis is developed for the case of bending and tensile forces in a double shear bolted joint. A numerical model for the representation of fasteners is proposed. The experimental test shows that the load transfer per line of fastener evolves according to the torque applied to the bolt (Q) and to the stress ratio R. When the torque value increases the load distribution becomes more and more worst. The use of photo-stress analysis and strain gauges measurement give a large knowledge of the behaviour of the joint. Therefore this type of joint can be studied by the finite element model proposed without the fastidious and costly experimental test. A fatigue study is developing to analyse the fracture process of the joint. References 1. Heimo Huth, H., Influence of fasteners flexibility on the prediction of load transfer and fatigue life for multi-row joints, Poc. of ASTM STP 927, Fatigue in Mechanically fastened composite and metallic joints, John M. potter Ed., Philadelphia, pp , K. Koffi, R. Chieragatti, J. Guillot, Y. Caumel, Optimisation of load transfer in aeronautical joints : influence of geometrical parameters, Proc. of the 2^ Int. Conf. on Integrated Designed and Manufacturing in Mechanical Engineering, Compiegne, pp , A. Santgerma, Modelisation numerique d'une fixation, DEA de Genie Mecanique, Universite Paul Sabatier Toulouse, R. Hetwood, B., Photoelasticity for engineers, Pergamon Press, New- York, V. Weissberg, K. Wander, R. Itzhakov, A new approach to load transfer in bolted joints, ICAS, pp , B. Artozi, P.Lazzarin, M. Quaresimin, A re-analysis on fatigue data of aluminium alloy bolted joints, Int. J. fatigue, 7, pp , 1997.