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2001-40

Automated Three-Dimensional Finite Element Modelling of Composite Aircraft Bolted Joints – Modelling Issues

Reference No. 2001-40

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

Composites Research Centre Mechanical & Aeronautical Engineering Department

University of Limerick, Limerick Rep. of Ireland

Tel: +353 061 202544

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

Abstract The development of three dimensional finite element models of composite bolted joints is a time consuming task. In order to reduce development time, a tool for semi-automated three-dimensional analysis of composite bolted joints is being developed using the MSC.Patran Command Language (PCL) and the non-linear finite element code, MSC.Marc. As part of the development process, models of single lap, single bolt joints have first been developed manually in MSC.Marc, and the lessons learned from this are being incorporated into the tool. This paper describes these issues, with particular emphasis on correct and efficient contact definition, as well as material properties. To illustrate the use of these models, results are presented for joints with different bolt-hole clearance. It has been found that clearance between the bolt and hole causes a delay in load take-up, as expected. Additionally clearance causes a reduction in stiffness after load take-up and increased non-linearity in the load-deflection curve. Key words: Bolted Joints, Composites, Clearance, Contact, Single 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

rε Radial Strain - jijiij ≠= ,3,2,1,,ν Poisson Ratios -

1. Introduction Intensive efforts are currently taking place in Europe on future composite wing and fuselage structures, and the use of composites in the primary structure of commercial aircraft 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. An EU research project, “BOJCAS - Bolted Joints in Composite Aircraft Structures” is addressing a crucial aspect of this challenge, namely composite bolted joints. Bolted joints are critical to safety and overall structural performance. Non-optimal design of joints can lead to overweight structures, in-service structural problems and high life-cycle costs. BOJCAS is focused on the development of improved design methods based on finite element analysis, including global methods for preliminary design, and local methods for detailed design of critical joints. The local methods will be capable of accounting for three-dimensional effects such as non-uniform through-thickness stress distributions. The design methods will be validated against a number of experimental tests on complex “benchmark” joints as well as simpler “specimen” joints. Within this project, the University of Limerick is developing a tool (BOLJAT – Bolted Joint Analysis Tool) for semi-automated, three-dimensional, finite element analysis of composite bolted joints using the MSC.Patran Command Language (PCL) and the MSC.Marc finite element code. As part of the development process, models have first been developed manually in MSC.Marc, and the lessons learned from this (to be incorporated into BOLJAT) are described herein. Particular emphasis is placed on correct and efficient contact definition, and comparisons are made between using the new layered continuum, composite element, available in MSC.Marc 2000, and “equivalent”, homogeneous, orthotropic properties. To test out the models, comparisons are made between models with different degrees of bolt-hole clearance. 2. Model Development The single lap, single bolt joint geometry being tested and modelled is shown in Figure 1. Four different clearances are being tested. Clearance is between the bolt and the hole, and is obtained

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by reaming the laminates with different size reamers. Clearances range from neat fit (0 to 10 microns) which is coded “C1”, to slightly larger than those found in aerospace primary structures (240 microns) which is coded “C4”. In this paper, only the smallest (C1) and the largest (C4) clearance models are presented. 2.1 Finite Element Mesh A typical finite element model used is shown in Figure 2. The meshing of the laminates is similar to that used by Ireman [1] with relatively high radial mesh density near the hole and under the washer, where high strain gradients exist. However, differently from Ireman, the washer was modelled separately. Eight-noded isoparametric hexahedral elements with a full integration scheme were used in the analysis. Wedge elements exist in the centre of the bolt.

48

75

155

24

32

5.2

8

Grip Area

Grip Area

Figure 1 Joint Geometry Figure 2 F.E. model 2.2 Boundary Conditions and Loading Comparing Figures 1 and 2, it can be seen that the gripped areas have not been modelled. Instead the ends of the top and bottom laminate were given prescribed displacement boundary conditions (Figure 3). Additionally, light springs were applied to the components which were not fully constrained, i.e. the bottom laminate and the bolt, in order to avoid potential rigid body modes. The “glued” contact option in MSC.Marc was used to attach the washers to the bolt head and nut. Finally to induce bolt pre-load due to applied bolt torque, orthotropic thermal expansion coefficients (allowing thermal expansion/contraction only in the bolt’s longitudinal axis) were

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applied in the bolt-washer system. The system was then subjected to a temperature differential prior to mechanical loading.

Figure 3 Boundary conditions and light springs (shown red) to avoid rigid body modes 2.3 Material Properties The laminates were made from HTA/6376 (high tensile strength carbon fibre, toughened epoxy) and the material properties are listed in Table 1. The stacking sequence was quasi-isotropic, [45/0/-45/90]5s, with 40 plies in each laminate, giving a total laminate thickness of 5.2mm. The bolt was titanium alloy 6Al-4V, the nut was steel, and steel washers were used on nut and head side. The laminates were modeled with a layered continuum element available in MSC.Marc. This element is an eight-noded three-dimensional arbitrarily distorted brick which allows modelling of a minimum of two and a maximum of five orthotropic layers per element. Each layer contains four integration points in-plane. Thus far, the laminates have been modeled with ten elements through the thickness, allowing each element to model four layers of the composite material. To allow easier understanding of the model results and hence clearer determination as to whether contact was working correctly, “equivalent” homogeneous, orthotropic material properties for the laminates were developed. This was done by performing a series of tensile and shear numerical experiments on a block of layered material and where possible validated against classic laminate theory. The equivalent material properties are also listed in Table 1.

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Table 1: Lamina and Equivalent laminate material properties for quasi-isotropic layup * - verified by laminate theory

2.4 Contact Definition Contact in MSC.Marc requires the definition of “contact bodies”, i.e. bodies which potentially may come in contact with each other. Contact bodies can be the physical bodies themselves (e.g. the two laminates, the bolt, and the washers). However it is more efficient to select subsets of the physical bodies which are likely to be involved in contact (see Figure 4) since less checking for contact is required at each solution step. Efficiency can also be improved by the use of “contact tables”. Contact tables define which contact bodies are likely to contact each other. For example, it is known a-priori that the two washers will never come into contact, so the contact table can be set up to eliminate checking for this possibility. Figure 5 shows the contact table for the single bolt joint case. It can be seen that the contact table is quite sparse indicating an efficient contact definition. The leading diagonal has no entries which eliminates any checking for self contact and the lower left area of the contact table is deactivated by selecting a single sided contact definition.

Figure 4 Contact bodies in model, which are defined by possible contacting elements only

11E

(GPa) 22E

(GPa) 33E

(GPa) 12G

(GPa) 13G

(GPa) 23G

(GPa) 12ν 13ν 23ν

Lamina Properties

140 10 10 5.2 5.2 3.9 0.3 0.3 0.5

“Equivalent” Properties for

QI Lay-up

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

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Figure 5 A contact table defined in MSC.Mentat for the bolted joint model ‘T’ indicates touching contact between two bodies

‘G’ indicates glued contact between two bodies

Detection of contact is done by checking if potential contact nodes are “in contact” with potential contact segments. In 3D deformable contact, contact segments are the faces of contact bodies. A tolerance is used to decide if a node is “in contact” – see Figure 6(a). If the trial position of the node is within the contact tolerance zone, it is considered to be in contact. If it lies beyond the contact zone (as in Figure 6(a)), it is considered to have penetrated and the increment is split and a new trial position found. Too small a tolerance leads to a lot of increment splitting (and hence high computational cost), but too large a tolerance leads to premature contact detection. Because a primary goal of this work is to examine differences between e.g. clearance of 10 microns on the diameter and 80 microns on the diameter (i.e. a difference of just 35 microns on the radius), smaller than usual contact tolerances have been used. A contact tolerance of 10 microns has been used, but with a “Bias Factor” of 0.9. This biases the contact zone into the contacted body – thus the contact zone ranges from (1-Bias)*tolerance (1 micron) “above” the body to (1+Bias)*tolerance (19 microns) “into” the body (Figure 6(b)).

(a) (b)

Figure 6 (a) Contact tolerance showing penetration (which leads to increment splitting) (b) Contact tolerance with Bias factor used here Once a node is detected to be in contact with a segment, the node is placed on that segment by means of a multi-point constraint (a so-called “tying” constraint). For 3D contact, 5 nodes in total (the contacting node and four nodes from the contacted segment) are retained in a constrained set. The contacting node remains on the segment (free to move on the segment according to any friction laws that are imposed) unless a separation force above a user-defined threshold is detected. This method is known as the “Direct Constraint” method [2] and differs

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from methods such as Lagrange multipliers, Penalty methods and special contact/gap element methods found in other finite element codes. In MSC.Marc, both “single-sided” and “double-sided” contact is available. In single-sided contact, when two contact bodies come into contact, the contact body which is defined first is the contacting body, while the other body is the contacted body. The first body thus supplies the contacting nodes, and the second body provides the contacted segments, so the order in which contact bodies are defined is important. In double-sided contact, the check is done both ways, i.e. the nodes of the first body are checked for contact with the segments of the second body, and then the nodes of the second body are checked for contact with the segments of the first body. This is obviously computationally more expensive, but might be thought to be more accurate. In fact, this is often not the case and certainly was not here. The problem is that once a node becomes a contacting node, then any face attached to it cannot become a contacted segment because that node has been transformed and moved into a constrained set. The opposite also applies. This can lead to “holes” in the contact as illustrated in Figure 7.

Switch in bodyconsidered to becontact ing

Pass-thru

(a) (b)

(c) (d) Figure 7 Problems with Double -Sided Contact

(a) Contact Status – yellow indicates contacting nodes (b) Pass-through of node which is not considered a contacting node (c) Another view of contacting nodes (d) Resulting anomaly in rε distribution

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Figure 7(a) shows a view of the “Contact Status”. Yellow indicates contacting nodes, and a switch in the body considered to be contacting (from laminate to bolt) is seen at the indicated location. The node (on the laminate) highlighted in Figure 7(b) is NOT a contacting node because it is attached to a contacted segment; while the segment which it interfaces with on the bolt is NOT a contacted segment since one of its nodes is a contacting node. The result is the node can pass through the segment. Another view of the contact status is shown in Figure 7(c) and the resulting radial strain is shown in Figure 7(d) where an anomaly clearly exists in the problem area. Single-sided contact has thus been found to give the best results. However, this places restrictions on the mesh. The recommendation in the MSC.Marc documentation [2] is that the body with the finer mesh should be defined first, i.e. should be the contacting body. Thus far, this rule has been followed. The only exception is the contact between the top and bottom composite laps which have the same mesh density. It would not make sense to give these bodies different mesh densities since it would require complicated meshing schemes to be automated when generating the model automatically in MSC.Patran. Changes to parts of the mesh (e.g. refinement of the bolt) must take into account this consideration. It is also recommended in a NAFEMS publication [3] that the contacting body should have the lowest stiffness. The biggest stiffness mismatch in the model is that between the steel washer (210GPa) and the stiffness in the z-direction of the laminate (12.6GPa). However, defining the washer as the contacting body has not been found to be a problem. Finally, a problem not mentioned in [2] or [3] is that which arises when a contacting body “overhangs” a contacted body. This arises between the top and bottom composite lap contact bodies, as illustrated in Figure 8. The upper laminate, top lap, is defined first and therefore is the contacting body, while the bottom lap is the contacted body. The “overhanging” contacting node on top lap in Figure 8(a) does not interface with a contacted segment and so meets no resistance. This allows penetration as shown. Reversing the order of definition of top lap and bottom lap would only shift the problem to the other side of the joint. The problem cannot be fully eliminated but can be reduced to a negligible level by radial refinement of the mesh (Figure 8(b)).

(a) (b) Figure 8 (a) Penetration due to overhanging contacting body (b) Reduced by refined radial mesh in this area

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The final issue that had a major influence on the contact results, was the use of so-called “analytical” rather than “discrete” contact. The tying constraint that is applied when a node contacts a segment, uses information regarding the segment’s outward normal. In “discrete” contact, the finite element piecewise linear representation of the surface is used for calculating this normal, which leads to a discontinuity in the normal as a contacting node slides from one face to another (Figure 9). This has an adverse effect on the results. When “analytical” contact is used, MSC.Marc fits a smooth Coons surface through the finite elements, which gives a much more accurate representation of the physical geometry and removes the problem with discontinuity in normals. Clearly for the curved geometry in the bolted joint problem, analytical contact is essential.

Figure 9 Piecewise linear geometry description in deformable contact A key point is that when MSC.Marc fits a Coons surface to an object, it must be told in advance where the discontinuities in the object’s geometry are. Otherwise it will attempt to fit a single smooth surface to the object and will obviously fail (e.g. corners will be rounded etc.). To do this, the discontinuous edges of the contact body (not the physical body) must be picked and placed into a set. The MSC.Marc pre-processor, MSC.Mentat allows selection of nodes and/or element edges for this purpose; only edges should be used for 3D problems. MSC.Mentat does not display the edges which have been picked which makes the process slow and fraught with the possibility of error, however this can be overcome. For example, the top lap contact body is displayed in Figure 10(a). Picking all the edges of this body by hand is very laborious, but there is an option in MSC.Mentat to display the “outline” of the body as shown in Figure 10(b) – “box-picking” the result gives the desired edges. A comparison between discrete and analytical contact is shown in Figure 11. The homogeneous “equivalent” material properties from Section 2.3 were used here. The discrete contact model is seriously flawed in that peaks in rε occur not just at the °0 position in the hole (i.e. the bearing plane), but also at other locations; the rε distribution is also not symmetric which it should be with these material properties. These problems do not exist with the analytical contact model.

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(a) (b)

Figure 10 (a) The top lap contact body, and (b) selection of its discontinuities by the “outline” display option in MSC.Mentat

(a) (b)

Figure 11 Radial strain distribution, rε , with (a) discrete and (b) analytical contact 3. Results Figure 12 shows the deformed shape of the joint at a displacement magnification factor of two. Secondary bending of the laminates and bolt rotation is clearly evident.

Figure 12 Deformed shape of C1 joint ( 2× magnification)

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Figure 13 shows the load deflection curve for two C1 (10 micron clearance) joints, one analysed using the equivalent material properties developed in section 2.3, the other using layered continuum elements. It can be seen (figure 13) that the layered model is slightly less stiff. This is because, in the numerical experiments used to determine the equivalent properties, the elements were forced to behave in a homogeneous manner using constraint equations. Figure 14 shows the load-deflection curve for C1 and C4 clearance joints. The C4 curve shows a delay in load take-up approximately equal to the clearance. Neither curve is totally linear, however the C4 curve exhibits a higher degree of non-linearity. The explanation for these stiffness variations lies in the development of the contact area between the bolt and the laminate. Figure 15 shows the growth of the contact area between the bolt and the bottom (moving) laminate in the lower (C1) clearance joint. It can be seen that the contact area gets up to its final value quite quickly, with a contact angle of °160 - °170 , which is fairly constant through the thickness. In contrast in the C4 joint, shown in Figure 16, significant contact is not made until clearance is taken up (0.276mm deflection). Initial contact is over a very small contact arc. By increment 28, the bolt has tilted, and the contact area has grown – however it is still much less than in the C1 joint, which explains the lower stiffness of the C4 curve. Thereafter, unlike the C1 joint where the contact area is relatively constant after the first few increments, the contact area in the C4 joint continues to grow which explains the continuing stiffening of the C4 curve.

Figure 13 Load Deflection curve for C1 joints

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Figure 14 Load-deflection curve for the C1 and C4 joints

(a) Inc 8 (0.046mm) (b) Inc 14 (0.184mm) (c) Inc 28 (0.506mm)

Figure 15 Development of the contact area in the C1 joint

(a) Inc18 (0.276mm) (b) Inc 28 (0.506mm) (c) Inc 38 (0.736 mm)

Figure 16 Development of the contact area in the C4 joint

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4. Discussion and Conclusion One aim of this study was to develop a three dimensional finite element model of a composite bolted joint in a way that it could be automated in MSC.Patran. It was found that MSC.Marc is a suitable analysis code because it supports layered continuum elements and has a powerful contact algorithm which is essential to solve problems of this type. In addition, MSC.Patran supports MSC.Marc which is ideal because models can be generated semi-automatically in MSC.Partan and analysed in MSC.Marc. Another aspect of this work was to examine the effect that clearance has on the performance of composite joints. It was found that clearance causes a delay in load take-up, as expected. However, additionally clearance causes a reduction in stiffness after load take-up and increased non-linearity in the load-deflection curve. This reason for this phenomenon lies in the development of the contact area between the bolt and the hole in joints that exhibit some degree of clearance. Essentially, as clearance increases, contact area decreases and the joint becomes less stiff. 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. The authors would like to thank the people at MSC.Marc Support Group. 6. References 1. Ireman, T., “Three-dimensional Stress Analysis of Bolted Single-lap Composite Joints,”

Composite Structures, Vol. 43, 1998, pp. 195-216. 2. MSC.Marc User’s Manual “Volume A: Theory and User Information”, MSC.Software

Corporation, March 2000. 3. Konter, A., How to undertake a contact and friction analysis, NAFEMS Ltd., 2000.