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2001-41

Initial Multi-Bolt Joint Results from BOLJAT, a Tool for Semi-Automated Three-Dimensional Modelling of

Composite Aircraft Bolted Joints

Reference No. 2001-41

Authors: M.A. McCarthy, C.T. McCarthy*, G.S. Padhi

Composites Research Centre Mechanical & Aeronautical Engineering Department

University of Limerick, Limerick Rep. of Ireland

Tel: +353 061 202544

E-mail: michael.mccarthy@ul.ie conor.mccarthy@ul.ie

gouri.padhi@ul.ie Abstract Three dimensional finite element models of multi–bolt composite aircraft joints were generated using a semi-automatic analysis tool developed in the MSC.Patran Command Language (PCL). A parametric study was carried out where clearance between the bolt and bolt-hole was varied, and the resultant transfer of load to other holes quantified. The models generated were analysed in MSC.Marc, and results indicate clearance has a significant effect on load distribution within the joint, which should be taken into account in composite joint design. Key words: Bolted Joints, Composites, Clearance, Contact, Multi Bolt Joints. *-Presenting Author

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Nomenclature Symbol Description Unit

3,2,1, =iEii Young’s Moduli 2/ mN

jijiGij ≠= ,3,2,1,, Shear Moduli 2/ mN

jijiij ≠= ,3,2,1,,ν Poisson Ratios - 1. Introduction The use of composite materials in aircraft structural components has grown steadily with each generation of aircraft. From initial applications in non-structural parts and secondary structures, composites have increasingly found use in primary aircraft structures, particularly in light aircraft, commuter planes, military fighters and helicopters. To date, their use in the primary structure of commercial aircraft has been relatively limited. However intensive efforts are currently taking place on future composite wing and fuselage structures, and the use of composites in primary structures is likely to increase substantially over the coming decade. Such developments are being driven by the potential benefits of composites, chiefly in relation to reduced weight and operating cost. However realising the full value of this potential still involves many technical challenges. The knowledge base of composite structures behaviour still needs to be extended and advanced design tools need to be developed. An EU research project, BOJCAS addresses a critical aspect of this challenge, namely composite bolted joints. Because joints represent potential weak points in the structure, the design of the overall structure tends to follow from, and be significantly limited by, the design of the joint. Non-optimal design of joints can lead to overweight structures, in-service structural problems and high life-cycle costs. This is even more pronounced in composite structures, since maximum joint efficiencies are at best 40-50%, and at worst considerably less. This compares with 70-80% for metals and thus detracts from the weight advantage of composites over metals. Hence optimising joint efficiency is crucial to realising the maximum potential benefits of composites. Within this project, the University of Limerick is developing a tool for semi-automated, three-dimensional, finite element analysis of composite bolted joints. The tool (BOLJAT – Bolted Joint Analysis Tool), utilises the MSC.Patran Command Language (PCL) and the MSC.Marc finite element code. This paper presents initial results from using the tool to generate multi-bolt joint models, and draws comparisons with models generated manually in an earlier paper [1]. Models with varying bolt hole clearance are presented, and the effects on load transfer and distribution are given. 2. Model Development The single lap, multi bolt joint geometry being tested and modelled is shown in Figure 1. Four different clearances are being tested in a comprehensive test matrix, however only the case

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where all holes have a neat fit (coded “C1_C1_C1”), and the case where two holes have a neat fit with the third hole having a large clearance (coded “C4_C1_C1”) are presented herein. The bolt numbering scheme is shown in Figure 1 and clearances used in each model are presented in Table 1.

Figure 1 Joint geometry with bolt-hole clearance numbering scheme Table 1 Bolt-hole clearances in multi-bolt models Code Hole 1 Clearance Hole 2 Clearance Hole 3 Clearance C1_C1_C1 C1 (10 microns) C1 (10 microns) C1 (10 microns) C4_C1_C1 C4 (240 microns) C1 (10 microns) C1 (10 microns)

2.1 Model Generation Using BOLJAT The models were generated semi-automatically in BOLJAT (Bolted Joint Analysis Tool). BOLJAT is a suite of MSC.Patran Command Language (PCL) functions [2] which automate the process of generating finite element models for the joint-plate, bolt and washer in a bolted joint, from their basic joint configurations. Currently BOLJAT can create finite element models for bolted joints with one or three bolts. Figure 2 shows the main MSC.Patran menu with BOLJAT installed. As shown in this figure, BOLJAT has six modules, however only those that address the joint-plate are presented herein.

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Figure 2 MSC.Patran main menu with BOLJAT

The first step for creating a finite element model for a bolted joint is to create a solid model and a finite element model for the joint plate. The first selection under BOLJAT, “Plate Solid Model (Three Bolts)”, is designed for creating a solid model of a joint plate from its basic geometric parameters such as length, width, diameter and so on. For convenience in meshing, and defining contact, BOLJAT divides the plate into two zones: overlap zone and non-overlap zone. The overlap zone is further divided into three zones (three-bolt case). These three zones are further divided into washer contact zones and outer zones (figure 4). The former are meant for defining contact between the plate and the washer.

Each contact zone is made up of eight sector solids. Each outer zone consists of eight solids. The non-overlap zone consists of two solids. Thus, the total number of solids in the joint plate is fifty. Upon selection of the first item in the BOLJAT menu (Figure 2), the graphical user interface (GUI) shown in Figure 3 is displayed. This GUI has nine databoxes: one each for length, width, thickness, hole-1 radius, hole-2 radius, hole-3 radius, edge distance, pitch, and contact zone radius. Upon selecting the “Apply” button, this form creates the solid model shown in Figure 4.

Figure 3 GUI for three bolt joint plate solid model

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Figure 4 Typical solid model for the three bolt joint-plate

If the “Cancel” button is selected, the user goes back to the MSC.Patran main session. All the required input parameters have associated defaults. The user may override these defaults by typing in the new values into the databoxes. After a solid model has been created using the above form, the user is ready to develop a finite element mesh for the joint plate. The GUI shown in Figure 5 is designed for this and appears when the user selects the second item from the main BOLJAT menu (figure 2). This GUI has six databoxes, one “Apply” button and one “Cancel” button. Efficient control on the finite element mesh is obtained by defining the number of seeds in the contact zone, the outer zone, and the non-overlap zone. In the contact zone, two seeds, radial and sector (circumferential), are defined with the first and second databoxes. The thickness seed in the third databox remains the same for all the solids in the joint plate. These three seed definitions create a uniform finite element mesh in the contact zone as shown in Figure 6. For the outer zone, only one seed needs to be defined. This is the outer zone radial seed. However, since it is required to create a biased mesh in the outer zone, a bias factor also needs to be defined. In this zone, the elements are created with an increasing element edge length. The non-uniform seed spacing is calculated through a geometric progression based on the given bias factor. For the non-overlap zone, only one mesh seed needs to be defined. This creates a uniform finite element mesh in the non-overlap zone as shown in Figure 6.

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Figure 5 GUI for three bolt joint-plate F.E. model

Figure 6 Typical F.E. mesh for the joint-plate

2.2 Complete Finite Element Model Solid model and mesh generation of the bolt and washers is similar to the composite plate generation described in Section 2.1. The complete finite element model of the joint generated in BOLJAT is shown in Figure 7. For comparison, the mesh seed and bias factors were chosen so the resulting mesh would match the mesh developed manually by McCarthy et al [1]. In order to keep the model to a manageable size only five elements were used through the thickness of the

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laminates. Eight-noded isoparametric hexahedral elements with a full integration scheme were used in the analysis. Wedge elements exist in the centre of the bolts.

Figure 7 F.E. Model with Boundary Conditions

2.3 Boundary Conditions and Loading Boundary conditions for the multi-bolt model were applied automatically by BOLJAT and are identical to that used in [1] where the gripped areas in Figure 1 were not modelled. Instead the ends of the top and bottom laminate were given prescribed displacement boundary conditions, as shown in Figure 7. Additionally, light springs were applied to the components which were not fully constrained, i.e. the bottom laminate and the three bolts, in order to avoid potential rigid body modes. In this analysis, the washers were attached to the bolts using a glued contact definition and therefore required no boundary conditions or springs. 2.4 Material Properties The laminate material used was made from HTA/6376 (high tensile strength carbon fibre, toughened epoxy). Material properties used in the analysis were developed in [3]. They are “equivalent” homogeneous, orthotropic properties, representative of a quasi-isotropic lay-up [45/0/-45/90]5s and are presented in Table 2. The bolts were titanium alloy 6Al-4V, the nuts were steel, and steel washers were used on nut and head side of each bolt. Table 2: “Equivalent” laminate material properties for quasi-isotropic layup * - verified by laminate theory

11E

(GPa) 22E

(GPa) 33E

(GPa) 12G

(Gpa) 13G

(GPa) 23G

(GPa) 12ν 13ν 23ν

Equivalent Properties

54.25* 54.25* 12.59 20.72* 4.55 4.55 0.309* 0.332 0.332

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3. Results Figure 8 shows the deformed shape of the two joints at a displacement magnification factor of two. Model C1_C1_C1 shows an anti-symmetric deformation, but as would be expected anti-symmetry is lost in the C4_C1_C1 model. The bolts are numbered from right to left (figure 8a) and the clearance at each hole corresponds to Table 1. In the C1_C1_C1 model all three bolts are tilted by approximately the same degree of rotation. The situation is different in the C4_C1_C1 joint, where Bolt 1 has not rotated as much as Bolts 2 and 3. The reason for this is that Bolt 1 is not contacted and hence, not rotated by the laminate, until the clearance at that hole is taken up. This has a significant effect on the load distribution among the other two fasteners as will be shown in Section 3.1.

(a) C1_C1_C1 deformed shape, showing anti-symmetric deformation

(b) C4_C1_C1 deformed shape, anti-symmetry is lost

Figure 8 Deformed shape of the multi-bolt models ( 2× magnification) Figure 9 shows the deformed shape of a section through the mid-plane of the joint. The yellow regions indicate where contact is detected. There are seventeen contact bodies in the model which leads to long computing times, however model generation time using BOLJAT is short. As computing power increases, runtimes for detailed finite element models such as the bolted joint model analysed here will decrease substantially, rendering BOLJAT a useful design tool in the near future.

1 2 3 Prescribed Displacement Fixed End

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Figure 9 Sectional view (mid-plane) of deformed join.

3.1 Load Distribution Analysis The method used to determine bolt-load distribution in the FE models was to sum the x-components of the contact forces at each bolt-hole (figure 10). Most of these forces were due to contact by the bolt on the inside of the hole, while components due to contact of the laminate surface with the washer were very small because the model was frictionless. It was confirmed (figure 11) that summing the three “bolt forces” obtained in this way equaled the total applied force which indicates that the composite laminate was in static equilibrium at each solution step.

Figure 10 Vector plot of contact forces at each bolt hole

Figure 11 Equilibrium is confirmed as slope of graph equals one

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Figure 12 shows the load-deflection curve for the C1_C1_C1 and C4_C1_C1 joints. The C1_C1_C1 joint has an essentially linear load-deflection curve, however the C4_C1_C1 joint is only piecewise linear. The reason for this lies in the load distribution among the bolts in the presence of variable bolt-hole clearances. The load in the C1_C1_C1 joint is taken up by all three bolts after the first few increments. In contrast, the load in the C4_C1_C1 joint is only taken up by Bolts 2 and 3 until the clearance is taken up in Hole 1, which is why the stiffness of the C4_C1_C1 joint is initially lower.

Figure 12 Load-deflection curve for the C1_C1_C1 and C4_C1_C1 joints

Although the load-displacement curve for the C1_C1_C1 joint is linear, the load transferred through the joint is not distributed equally among each bolt as is illustrated in Figure 13a. The load taken at Hole 1 and 3 is approximately the same due to the anti-symmetric nature of the joint. Considerably less load is taken at Hole 2, so Hole 2 is therefore not a critical area in the joint to be considered in a failure analysis. However, when clearance is introduced into Hole 1 (in the C4_C1_C1 model), Hole 2 becomes the most highly loaded hole until the clearance is taken up in Hole 1 as illustrated in Figure 13b. As the load is increased further, the load taken by each bolt starts to level off and would theoretically approach that of the control case (C1_C1_C1 model) eventually. However the joint would fail long before this would happen. This suggests that all three holes are of equal importance when considering a failure analysis since it is highly unlikely that a joint could be manufactured to have all perfect-fit bolt holes as in the control case analysed here.

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(a) C1_C1_C1 joint (b) C4_C1_C1 joint

Figure 13 Load taken at each bolt hole 4. Discussion and Conclusion Comparing results from models generated by BOLJAT in MSC.Patran and analysed in MSC.Marc with models generated manually in MSC.Marc [1] it was found that they were identical suggesting that BOLJAT was working correctly. Although the analysis time for both methods of model generation was the same, the actual user intervention and time spent preparing the models with BOLJAT was a fraction of that when prepared manually. As computing power increases analysis time will inevitably decrease so it is important that model generation time follows suit. With reference to load transfer in multi-bolt composite joints, it was found that it is a complex problem which is highly dependent on joint parameters such a bolt-hole clearance. In order to fully understand the mechanics of load transfer, a large amount of modeling where joint parameters are varied is needed. It was found that BOLJAT is an ideal tool to do this because of its parametric nature. As well as load transfer, the stiffness and anti-symmetry properties of single lap joints are also affected by varying clearances. In the case of a failure analysis, three dimensional finite element models are needed to give valuable information on the load transfer, and stress and strain distributions in multi bolt joints. 5. Acknowledgments BOJCAS - Bolted Joints in Composite Aircraft Structures is a RTD project partially funded by the European Union under the European Commission GROWTH programme, Key Action: New Perspectives in Aeronautics, Contract No. G4RD-CT99-00036.

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6. References 1. McCarthy, M.A., McCarthy,.C.T., and Padhi, G.S., “Three-dimensional Modelling of Multi-Bolt Composite Joints,” Proceedings, of the 9th ACME conference, University of Birmingham, U.K., 8-10 April 2001, pp 123-126. 2. MSC.Patran PCL Reference Manual, Version 9. 3. McCarthy, C.T., McCarthy, M.A. and Padhi, G.S., “Three Dimensional Modelling of Single-Bolt Composite Joints,” Proceedings, of the 9th ACME conference, University of Birmingham, U.K., 8-10 April 2001, pp 111-114.