- Email: [email protected]
Load transfer in multirow, single shear, composite-to-aluminium lap joints
COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 66 (2006) 875–885 www.elsevier.com/locate/compscitech
Load transfer in multirow, single shear, composite-to-aluminium lap joints Johan Ekh a
a,*
, Joakim Scho¨n
b
Division of Lightweight Structures, Department of Aeronautical and Vehicle Engineering, The Royal Institute of Technology, SE-100 44 Stockholm, Sweden b Swedish Defence Research Agency, FOI SE-172 90 Stockholm, Sweden Received 26 May 2005; received in revised form 26 August 2005; accepted 28 August 2005 Available online 2 November 2005
Abstract A three-dimensional finite element model has been developed in order to determine the load transfer in multifastener single shear joints. The model is based on continuum elements and accounts for all important mechanisms involved in load transfer, such as bolthole clearances, bolt clamp-up and friction. In particular, member plates can be of different thickness and stiffness and with different coefficient of thermal expansion. An experimental programme was conducted in order to validate the finite element model through measurements of fastener loads, by means of instrumented fasteners. Good agreement between simulations and experiments was achieved and it was found that bolt-hole clearance is the most important factor in terms of load distribution between the fasteners. Any variation in clearance between the different holes implies that load is shifted to the fastener where the smallest clearance occurs. Sensitivity to this variation in clearance was found to be large, so that temperature changes could significantly affect the load distribution if member plates with different thermal expansion properties are used. It was found that good accuracy in load transfer predictions requires that all aforementioned factors are taken into consideration and that nonlinear kinematics is accounted for in the solution process. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Bolted joint; Load transfer; Finite element method; Instrumented fastener
1. Introduction 1.1. Background Designing effective multifastener composite joints requires predictive capability regarding joint strength. Joint failure occurs in one or several macroscopic failure modes [9], such as bearing, net-section, shear-out and cleavage failure and is affected by several parameters. Shear-out and cleavage are generally considered premature in aircraft structures, caused by improper selection of materials and joint configuration, which renders the bearing and net-section modes more important. The different nature of the two
*
Corresponding author. Present address: ABB AB Corporate Research, SE-721 78 Va¨stera˚s, Sweden. Tel.: +46 21 323227; fax: +46 21 323212. E-mail address: [email protected] (J. Ekh). 0266-3538/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.08.015
modes, bearing mode is ductile whereas net-section mode is brittle, implies that it is important to take into account not only the failure load but also the mode of failure in the design process. Failure in composite joints is related to the local stress field in the vicinity of fastener holes. Stresses at a particular hole are affected by several factors such as the amount of load reacted by the fastener and the amount of load running through the plate cross-section which is reacted elsewhere in the joint. These two loads are referred to as bearing load, Pb, and bypass load, Pbp, respectively, and are illustrated in Fig. 1. In addition, properties of the contact between the fastener shank and the hole surface, such as the contact area and friction, may have significant effect on the local stress field. This is of particular relevance in single shear lap joints due to the nonuniform distribution of contact stress in the thickness direction caused by the eccentric load path.
876
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
Fig. 1. Loads acting on the plate.
Previous work [9,16] shows that initiation of failure is depending on the combined bearing stress, Sb, and bypass stress, Sbp, with definitions according to Pb ; dt P bp ; ¼ ðw dÞt
ð1Þ
Sb ¼ S bp
ð2Þ
where d is the hole diameter, w is the plate width and t is the thickness of the plate. Maximum strength is achieved for a hole without bearing stresses, i.e. when the applied load, PA, is totally reacted by other fasteners [10]. It appears that net-section failure occurs for small values of the bearing bypass ratio, b ¼ SSbpb , and that the strength decreases linearly when b is increased. At a certain value, b = bshift, the failure mode is shifted from net-section to bearing and additional increase of b has little effect. This implies that the critical fastener may not be the one that reacts the most load and there may be situations where an uneven load distribution results in higher overall joint strength [13] compared to an even load distribution. Thus, accurate strength predictions require that the load distribution between the fasteners is obtained first such that both the bearing load and the bypass load are known for critical fasteners. The load distribution can be estimated with experimental techniques or by using analytical or numerical methods. Bolt loads can be approximately calculated from measurements of bypass strains with strain gauges. Two similar procedures [6,15] have been used; the calibration method and the integration method. The calibration method involves measurements of strain in the vicinity of each fastener for a set of known load distributions, i.e. utilizing only one fastener or a small number of symmetrically positioned fasteners. This implies that a relation between strain at fastener i, i, and the load reacted by fastener j, Pj, can be established according to i ¼
N X oi Pi oP j j¼1
i ¼ 1; . . . ; N ;
ð3Þ
where N is the number of fasteners in the joint. Thus, the individual bolt loads, Pi, are obtained by solving the linear equation system (3). The other technique is more commonly used and is based on direct calculation of the bolt loads rather than using the calibration process described above. Strain gauges are mounted between the bolts, along transverse lines over the joint cross-section, on both sides of the plate.
By assuming some strain variation (usually linear) between the top and bottom surfaces of the plate it is possible to integrate the stress field over the cross-sectional area of the plate and obtain the bypass load. Both methods suffer from not being able to distinguish between fastener reacted load and load transferred by friction between the plates. An additional disadvantage is the extensive instrumentation required on each joint. A more attractive method is to use instrumented fasteners [15,22,26] to measure the fastener loads. Strain gauges can be mounted internally in the bolt in an axial rectangular hole through the fastener, or externally in shallow slots machined in the shank surface. The fasteners can be calibrated to measure axial or shear force in the fastener. Fastener reacted load is separated from frictional load and no instrumentation of the member plates is required. Thus, once the instrumented fasteners are calibrated and the testing procedure is developed, it is fairly easy to conduct systematic testing of a large number of joints. Experimental techniques are reliable and can be used on large, realistic aircraft structures or on simple idealized specimens. However, they are time consuming and expensive, and more important, they are of a validating nature rather than predictive. An efficient design process requires predictive capabilities that can only be offered by theoretical models. The dominant approach is to use the finite element method (FEM) to predict strength of composite joints. Most analyses have been oriented towards the study of failure mechanisms in the composite material and the objective is usually to establish predictive capability, both in terms of failure mode and failure load. Idealized single fastener structures that are suitable for numerical analysis and for experimental studies have been used extensively [1–4,12,8, 17,18,23]. Some workers [25,14,21,19] have investigated the behavior of single shear lap joints where the presence of stress singularities at the faying surface makes the problem more complex. Regarding multifastener joints, several analyses have been conducted where structural finite elements are used, rather than continuum elements, or where 2D continuum elements are utilized. Using structural elements usually implies that contact is not treated, or treated in a simplistic way, whereas a 2D model can not be used to accurately describe a single shear lap joint due to their 3D stress field. Eriksson et al. [7] proposed a methodology in which a two dimensional analysis was used to identify the most heavily loaded fastener, followed by a three dimensional stress analysis to predict failure. McCarthy and McCarthy [20] investigated the effect of clearance in a single shear, three fastener composite-to-composite joint by means of a 3D FE model based on continuum elements. Member plates were identical and finger tightened fasteners were assumed which implies that friction between the plates had little effect on the load transfer. The analysis was conducted in parallel with an experimental programme [26] and good
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
agreement between simulations and experiments regarding load distribution was achieved. However, modern aircraft structures that utilize composite materials still also partly consist of other materials, such as aluminium. This means that joints with member plates of different materials are necessary which introduces further difficulties. Holes in the two materials may be of different size due to shrinkage effects during the drilling process, the plates may have different stiffness and may react differently to temperature changes. This may influence the load distribution. The present study aims at developing a 3D FE model based on continuum elements that accounts for these factors. 1.2. Problem statement and objectives Consider a single shear, composite-to-aluminium, lap joint with 4 fasteners arranged in one column, subjected to quasi-static loading in tension. The objectives in the present study are: (1) Develop a 3D continuum FE-model that predicts the individual bolt loads, taking into account all mechanisms that are important with respect to load transfer. (2) Measure the bolt loads in the joint by means of instrumented fasteners in order to validate the accuracy of the FE-model. (3) Identify what mechanisms must be accounted for in accurate predictions of load distribution.
2. Joint configuration The joint is illustrated in Fig. 2. Member plate thicknesses are 4.16 (composite) and 8.0 (aluminium) mm and
a
877
tabs are glued at both ends to compensate for the geometrical asymmetry in single shear lap joints. Protruding head titanium bolts with a nominal diameter of 6 mm were used and a torque level of 6 Nm was applied. The bolts were anodized and treated with a solid film lubricant. Composite parts were manufactured from the carbonepoxy pre-preg material system AS4/8552 with nominal fiber volume fraction 63.5%. The elastic properties of the material constituents, the uni-directional lamina and the quasi-isotropic lay-up [±45/0/90]4s using 0.13 mm thick uni-directional laminae are given in Table 1. Aluminium parts were manufactured from AA7475-T76 and the fastener system consisted of titanium bolts, alloy steel nuts and stainless steel washers. All elastic properties are tabulated in Table 1. A total of 4 identical joints were used in the programme. 3. Finite element modeling The model has been described in previous work [5] and is briefly reviewed below to assist the reader. All physical entities in the joint, i.e. plates, bolts, nuts and washers were taken into account in the model and surface based contact, with Coulomb friction, was defined for all potential contact surfaces. The coefficient of friction, l, was set to 0.235 [24] between the plates and to 0.05 at all other contact surfaces. Plate materials were assumed to be homogenous, either isotropic or orthotropic, which implies that the model was symmetric with respect to the 1–3 plane in Fig. 3. Thus, only half the geometry was modeled and symmetry conditions were specified on the 1–3 plane. Tab regions indicated in Fig. 2(b) were excluded from the model. Nodes on the left end of the aluminium plate (lower plate in Fig. 3) were clamped whereas the nodes on the right end of the composite plate were prevented from moving in the 2- and 3-directions,
b
Fig. 2. Reference joint geometry.
Table 1 Elastic properties of materials and their constituents Material
E11 (GPa)
E22 (GPa)
E33 (GPa)
G12 (GPa)
G13 (GPa)
G23 (GPa)
m12
m13
m32
Fiber Matrix Lamina Laminate Aluminium Titanium Steel
238 3.3 140 54.25 71 110 210
– – 10 54.25 – – –
– – 10 10 – – –
22 1.2 5.2 20.72 – – –
– – 5.2 4.55 – – –
– – 3.9 4.55 – – –
0.2 0.35 0.3 0.309 0.31 0.29 0.30
– – 0.3 0.332 – – –
– – 0.5 0.332 – – –
878
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
Fig. 3. Finite element mesh of joint.
but free to move in the 1-direction. Fasteners were torqued (finger tight or highly torqued) using the ‘‘pre-tension’’ option in Abaqus. This was done in a separate analysis step, prior to applying the longitudinal load on the right end nodes, which is in accordance with the experimental procedure. Plates were discretisized using linear 8-node solid elements (C3D8I) with improved bending properties through the addition of incompatible deformation modes [11]. Bolts were defined as masters in the contact which implies that nodes belonging to washers and plates could not penetrate the element segments of the bolts. In order to ensure that the bolts were accurately described as circular with well defined radius they were modeled with quadratic solid elements (C3D20R) with reduced integration. Washers were modeled with linear elements with reduced integration (C3D8R). All analyses were static with nonlinear kinematics. 4. Experimental programme 4.1. Bolt-hole clearance During the manufacturing process, the specimen plates were drilled separately. As a result the holes were not perfectly lined up. Detailed comparisons between the FEmodel and the experiments required that the geometry of the specimens were modeled as accurately as possibly, in particular the sizes and the relative positions of the fastener holes. Measurements with a coordinate measurement machine were conducted on two specimens in order to establish hole diameters and positions. The coordinate measurement system utilizes a probe that is inserted approximately at the center of the hole. The probe is translated in radial direction until it hits the hole edge at which point the system is saving the coordinates of the probe. This was repeated for 32 points along the circumference and for a number of levels in the plate thickness direction. A Cartesian coordinate system is used which enables, under the assumption that the hole is circular, the calculation of hole center location and radius through minimizing qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 X 2 2 2 ¼ r ðxn x0 Þ þ ðy n y 0 Þ ; ð4Þ n
where xn, yn are the measured points and, x0,y0 and r are the solved for coordinates of the origin and the radius, respectively. It was found that the holes in the aluminium plates were larger than the holes in the composite plates and that the variation between holes in one material was small. Mean radii in the composite and in the aluminium were 3.003 and 3.021 mm, respectively. Furthermore, it was found that the holes were not concentric, i.e. the row spacing was different in the composite compared to the aluminium. Mean values of row spacing are presented in Table 2 where rsi denotes the distance between fastener i and i + 1 using the bolt numbers in Fig. 2(a). The actual clearances resulting from the measurements were estimated by making a number of assumptions and solving a linear equation system. Hole diameters in the composite and aluminium plates, dc and da, respectively (see Fig. 4), and the distances between adjacent hole edges, lci and laj where i, j = 1. . .3, are assumed to take the mean values presented in Table 2. Diameters of the fastener shanks were measured to 5.985 mm with small variations. The load submitted to the joint is tensional so that the composite plate is translated to the right and the aluminium plate to the left in Fig. 4 which implies that one of the clearances dci1 and one of dai2 , where i = 1. . .4, eventually will become zero as the first fastener starts to carry load. Assuming further that the fasteners are located at the center of each ‘‘effective’’ hole through both plates, i.e. that dci1 ¼ dai2 and that all clearances are non-negative, makes it possible to solve for the unknown clearances. Estimation of the clearances with this method yields that the clearances at the inner fasteners are zero whereas the clearance is maximum (22 lm) at the outer fasteners, i.e. the clearances are such that for the given hole sizes, maximum load is shifted from the outer fasteners to the inner fasteners. This will be accounted for in the FE-model. All calculated clearances are presented in Table 3.
Table 2 Mean values of measured row spacing Material
rs1 (mm)
rs2 (mm)
rs3 (mm)
Composite Aluminium
32.077 31.998
32.043 32.013
31.941 32.011
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
879
Fig. 4. Bolt hole clearances.
Table 3 Bolt-hole clearances (mm) Plate
d11
d12
d21
d22
d31
d32
d41
d42
Composite Aluminium
0.022 0.036
0 0.022
0 0.058
0.022 0
0 0.058
0.022 0
0.022 0.036
0 0.022
4.2. Measurement of bolt loads 4.2.1. Instrumented fastener Load carried by each bolt in the joint was measured with a fastener instrumented in such a way that its output signal is only affected by shear deformation of the fastener in the vicinity of the joint shear plane. This is achieved by machining slots in a regular titanium fastener and installing four strain gauges in a 45° angle to the bolt axis direction, two on either side of the fastener as illustrated in Fig. 5. The two gauges on each side of the fastener were mounted equidistant to, and on opposite sides of the joint shear plane. This type of instrumented fastener was previously used by Palmberg [22]. The load submitted to a fastener in a single shear joint is a combination of shear, torsion, bending and axial forces. Torquing the nut in assembling the joint submits torsional and axial forces. Tension or compression loading of the joint results in shear forces and bending of the fastener over the transverse direction (BT) of the joint. Secondary bending could imply twisting of the joint, depending on the stacking sequence used in the composite laminate, which
would cause the fastener to bend over the longitudinal direction (BL). In order to make the fastener output signal insensitive to all forces except the shear force, the four gauges were connected into a full Wheatstone bridge. Mapping the cylindrical surface of the bolt shank on a Cartesian coordinate system implies that the strain gauges are located according to Fig. 6(a). The electric potential in points a,. . .,d in Fig. 6(b) can be written as, a ¼ V in
b ¼ V in ;
c ¼ V in
G4 ; G3 þ G4
d ¼ 0; ð5Þ
where Gi is the resistance of gauge i, under the assumption that the potential in point d is zero. Output voltage, Vout, can be written as the potential in point c subtracted from the potential in point a which yields
a
Fig. 5. Machined slots and installed strain gauges in instrumented fastener.
G1 ; G1 þ G2
b
Fig. 6. (a) Strain gauges on the instrumented bolt are located equidistant from the joint shear plane and on either side of the bolt shank. (b) Strain gauges connected into a full Wheatstone bridge. Strain gauge configuration in instrumented bolt.
880
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
V out ¼ a c ¼ V in
G1 G4 V in . G1 þ G2 G3 þ G4
ð6Þ
Each of the forces subjected to the fastener will introduce strains in the gauges that could be tensional or compressive, which results in changed electrical resistance by DG and DG, respectively, as tabulated in Table 4. Introducing the contributions to the resistance from Table 4 into Eq. (6) for each type of load implies that the output voltage (Vout) is affected according to Eq. (7). Thus, Vout is only affected by the shear load subjected to the fastener. G þ DG G DG DG V in ¼ V in ; 2G 2G G G þ DG G þ DG V in ¼ 0; V torsion ¼ V in out 2G 2G G þ DG G þ DG V in ¼ 0; V bt out ¼ V in 2G þ 2DG 2G þ 2DG G þ DG G þ DG V in ¼ 0; V axial out ¼ V in 2G þ 2DG 2G þ 2DG G þ DG G DG V in ¼ 0. V bl out ¼ V in 2G þ 2DG 2G 2DG
V shear out ¼ V in
ð7Þ
The bolt was calibrated in a finger tightened, single fastener, single shear lap joint in order to establish a relation between output voltage and load carried by the fastener. This relation could then be used to calculate the approximate bolt load for any bolt for which the output signal had been recorded. 4.3. Testing procedure All plates were cleaned individually with ultrasonic technique in order to remove any grease from handling the plates, and loose particles from the drilling process. This cleaning process is in accordance with the process used when measuring the coefficient of friction [24] which was used in the finite element modeling. The level of torque was either 6 Nm or finger tight for all fasteners within the same joint. As only one instrumented fastener was available, each joint utilized three regular fasteners and the test was repeated four times with the instrumented fastener shifting position. The joint was completely disassembled between each test in order to remove all frictional forces built up during the test. The joints were mounted in an hydraulic test machine and subjected to displacement controlled, quasi-static (loading rate = 0.1 mm/min, max load = 18 kN) tension loading. Table 4 Change in electrical resistance at each gauge due to loading
Shear Torsion BT Axial BL
G1
G2
G3
G4
DG DG DG DG DG
DG DG DG DG DG
DG DG DG DG DG
DG DG DG DG DG
5. Results and discussion 5.1. Load transfer in single shear lap joints Results obtained with the continuum FE-model described in Section 3 are presented below in order to illustrate some fundamental characteristics of multifastener single shear lap joints. A four fastener composite-to-composite (equal thickness) joint with perfect fit, torqued fasteners was selected as an example. The coefficient of friction was set to be larger between the plates compared to all other contact surfaces. An external longitudinal tension load is transferred from one plate to the other through a number of contact surfaces, each of which contributes to fulfill the force equilibrium. Contact forces could be either normal, tangential (friction) or both and are presented in Fig. 7(a) in terms of their longitudinal components summed over all four fasteners. Individual normal bolt loads are shown in Fig. 7(b). Large frictional forces develop between the plates in the vicinity of the holes due to the clamping force generated by the fasteners and the load transfer is dominated by this friction when the level of applied load is low. At some point, when the load is increased, friction is fully developed and the plates start to slide relative to each other, which causes the load to be picked up by the fasteners through contact between the bolt shanks and the hole edges. Once sliding has started, the load transferred by friction between the plates remains essentially constant during further increase of the applied load. Deviations from this constant value can be explained by local changes in contact pressure between the plates. The compressive stresses in the plates close to the bolt-hole contact implies that the thickness of the plates is increased locally, due to the Poisson effect, which could increase the contact pressure between the plates. In other regions, the tensional bypass loads leads to a decreased thickness of the plates. The separation of the plates at the ends of the overlap region also affects the contact pressure between the plates. It appears that the net effect of these mechanisms leads to a reduced contact pressure between the plates for the joint presented in Fig. 7(a) which is reflected in the slightly decreased frictional load when the applied load is increased. Since the two member plates are identical, the joint is almost anti-symmetric with respect to a vertical line between bolts 2 and 3 in Fig. 2(a). The only deviation from antisymmetry is that the nuts are thicker than the bolt heads. Perfect anti-symmetry would imply that the two outer bolts would carry equal load as would the two inner bolts. Therefor, result from only one outer and one inner fastener is presented in Fig. 7(b). It can be seen that the outer fastener carries significantly more load than the inner fastener. The load is picked up earlier and is increasing at a higher rate as the applied load increases. This behavior is well known and is mainly attributed to the relative displacements of the hole centers. The outer fastener hole is displaced more from the anti-symmetry plane due to its
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
a
881
b
Fig. 7. Typical load transfer characteristics of a four fastener, antisymmetric single shear lap joint. (a) Longitudinal components of total normal bolt loads, total tangential bolt loads, total friction between washers and one plate and friction between the plates. (b) Longitudinal components of the normal contact load for one outer and one inner bolt.
larger distance from the plane, compared to that of the inner fastener, which is reflected in the distribution of load between the fasteners. 5.2. Comparison between experiments and FE-model In order to validate the FE-model, detailed comparisons with experiments were made regarding individual bolt loads. The experimental curves are mean values of results from all tested specimens and are assumed to represent the average behavior of the joint. Variations between the joints were found to be small. Output signal from the instrumented fastener is affected by shear strains in the fastener according to the previous discussion. Thus, all longitudinal load contributions that affects the shear
deformation in the fastener are taken into account in the FE-model, including normal and tangential bolt-hole contact forces and friction between washers and bolt heads. All results regarding hole sizes and positions, and the resulting clearances presented in Section 4.1, were used in the FE-model in order to describe the real test specimens as accurately as possible. The coefficient of friction between the plates was set to 0.235 according to measurements by Scho¨n [24] and to 0.05 at all other contact surfaces due to the solid film lubricant coating on the fasteners. Results for finger tightened fasteners (200 N axial load in FE-models) are presented in Fig. 8. Load pick-up is delayed at the outer bolts, and more load is carried by the inner bolts, due to the bolt-hole clearances at the outer bolts.
a
b
c
d
Fig. 8. Comparison between FE-models and experiments with finger tightened fasteners. (a) Bolt 1, (b) Bolt 2, (c) Bolt 3 and (d) Bolt 4.
882
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
The total amount of load transferred by the fasteners is 17.5 kN for the FE-model and 16.5 kN for the experiments which indicates that a small portion of the applied load is transferred by friction between the plates despite the lack of clamping pressure. The discrepancy between the model and the experiments can be attributed to small differences in clamping force, coefficient of friction and fastener compliance. According to Section 4.2.1, small slots were machined in the instrumented fastener to accommodate the installation of the strain gauges. This resulted in a reduction of the cross-sectional area of the fastener, at the shear plane of the joint, of approximately 7% which would make the fastener less stiff and possibly shift some load to the other fasteners. Since the only available instrumented fastener was used in different positions, in conjunction with three regular fasteners, it could imply that it consistently carried less load due to its reduced stiffness. However, it appeared that this effect was small as the agreement with the FE-model was good. Results for joints with torqued fasteners (6 Nm in experiments, 3740 N axial force in FE-models [5]) are presented in Fig. 9. Again, the FE-model generates results in good agreement with the experiments. Load pick-up is delayed at all bolts due to the friction between the plates but once load is picked up by the fasteners, the load distribution is similar to that of the finger tight case. Experimental load pick-up is more smooth compared to the FE-models which could indicate that the coefficient of friction at all surfaces except the faying surface, was set too low (0.05) in the FEmodel. Small amounts of load is picked up in a smooth
process for the FE-model and an increased coefficient of friction would cause the FE-curve to approach the experimental curve in Fig. 9(a) and (d). However, explicit, non-physics related fine tuning of the FE-models have consistently been avoided in the present work and the first assumption that the lubricant on the fasteners would generate a low coefficient of friction is maintained. It was concluded that the FE-model accurately accounts for the mechanisms affecting the load transfer and that it is capable of predicting individual bolt loads with good accuracy. 5.3. Influence of various mechanisms on load transfer Results presented in Figs. 8, 9 show that a detailed 3D continuum FE-model is capable of predicting individual fastener loads in complex multifastener joints. However, in developing the FE-model, detailed information regarding hole diameters, hole positions, surface conditions and fastener clamp-up force was taken into account. This information was obtained by means of several test programmes and it can be assumed that this information is in general not available in a regular design process of an aircraft structure. It is therefore of interest to investigate the relative importance of the different pieces of information in order to establish what needs to be accounted for and what can be neglected in accurate predictions of fastener loads using a continuum FE-model. The investigation was conducted by means of a series of analyses using the FE-model described in Section 3. A
a
b
c
d
Fig. 9. Comparison between FE-models and experiments with torqued fasteners. (a) Bolt 1, (b) Bolt 2, (c) Bolt 3 and (d) Bolt 4.
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
number of modifications were applied to the model in such a way that in each analysis, only one modification of the original model was in effect. The original FE-model is referred to as the ‘‘baseline’’ model in the remainder of this text. Modified FE-models are listed in Table 5. Results are presented in Fig. 10 in terms of fastener load fractions and absolute fastener loads. Fastener load fracf tion is defined as Fbbi where fbi is the load carried by fastener i and Fb is the total amount of load carried by all fasteners, i.e. the frictional load between the plates subtracted from the applied load. Regarding the load fractions (see Fig. 10(a)) it can be seen that hole eccentricity between the member plates has a large impact. The analyses with perfect fit fasteners and with clearance with concentric holes, differs significantly from the baseline model in the sense that load is shifted from the inner fasteners (2 and 3) to the outer fasteners (1 and 4). However, load fractions are almost identical for the two cases which implies that the parameter of importance is the difference in clearance between the holes rather than the magnitude. It appears that friction, torque and kinematical formulation (linear or non-linear) have a smaller influence on the load fractions compared to the bolt-hole clearance. However, in all cases, neglecting one of these parameters leads to a more even distribution of load fractions compared to the baseline model. Absolute fastener loads are presented in Fig. 10(b) and the effect of friction between member plates and fastener torque is illustrated. Neglecting either of these two parameters will cause the fasteners to carry more load compared to the baseline model. Table 5 Identification tag and description of conducted analyses ID
Modification
No clearance No ecc. No friction No torque Small disp.
No bolt hole clearance Concentric holes No friction between plates Finger tightened fasteners Linear kinematics
883
Thus, neglecting bolt clamp-up force or member plate friction would essentially preserve the relations between individual fastener loads compared to the baseline model but increase the amount of load carried by each fastener. Using linear kinematics generates a more even load distribution and in particular predicts a lower load carried by the most heavily loaded fastener compared to the baseline model, i.e. it may be unconservative to use linear kinematics. Neglecting any differences between the holes in effective bolt-hole clearances affects the results drastically which implies that meaningful evaluation of the results may be prevented. 5.4. Influence of temperature The strong influence on the load distribution of having different clearances at the holes caused by eccentricity of the holes opens a discussion about the influence of temperature. Thermal expansion in a composite laminate is depending on the thermal properties of the material constituents, their relative proportions and the laminate stacking sequence. In composite laminates used in aircraft structures, the thermal expansion coefficient can be assumed to be smaller than that of aluminium which implies that hole eccentricity could change if the temperature changes. In order to illustrate the effect of having member plates with different coefficient of expansion, an analysis was conducted with coefficients according to Table 6. The joint with concentric holes and different hole sizes in the two materials according to Section 4.1 was used. Effective
Table 6 Coefficients of thermal expansion Material
a (106/°C)
Aluminium Composite Titanium Steel
23 10 8.8 15
Fig. 10. Influence of various mechanisms on fastener load distribution. (a) Fractions of total fastener reacted load. Fastener numbers according to Fig. 2. (b) Individual fastener loads. Fastener numbers according to Fig. 2.
884
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
Table 7 Bolt-hole clearances (mm) Temperature (°C)
Clearance
d1
d2
d3
d4
20 20 20 50 50 50
Composite Aluminium Effective Composite Aluminium Effective
0.011 0.029 0.040 0.021 0.043 0.064
0.011 0.029 0.040 0.012 0.032 0.044
0.011 0.029 0.040 0.010 0.025 0.035
0.011 0.029 0.040 0.003 0.012 0.015
Fig. 11. Influence of temperature on fastener load fractions.
clearance at fastener i, di, denotes the relative displacement of the member plates required before the fastener starts to pick up load, i.e. it is the sum of the clearance in the composite and the aluminium plate. An additional load step was defined where a temperature load of DT = 70 °C was applied after torquing the fasteners but before applying the tensional load. Boundary conditions specified in the first load step were maintained in the added load step. This would approximately correspond to a situation where the joint was manufactured and assembled in room temperature and the aircraft was operating in a temperature of 50 °C. The main effect of the applied temperature load is that the aluminium plate contracts more than the composite plate which result in changed clearances according to Table 7. At 20 °C the effective clearance was 0.040 mm at all fasteners, but at 50 °C the effective clearance varies from 0.064 mm at bolt 1 down to 0.015 mm at bolt 4. This is clearly reflected in load transfer, which is illustrated in Fig. 11. The fastener load fraction is reduced for bolts 1 and 2 where the effective clearances were increased, and increased for bolts 3 and 4 where the clearances were decreased. The effect is more significant at the outermost fasteners where the change in clearance is larger compared to the innermost fasteners. 6. Summary and conclusions A detailed 3D, continuum finite element model was developed for a single shear, multifastener, composite-tometal lap joint in order to predict the joint load transfer. The model accounted for all mechanisms that were ex-
pected to affect the load transfer including fastener clamp-up force, member plate friction, bolt-hole clearance and nonlinear kinematics. In particular, the exact geometry regarding hole sizes and positions in the composite and in the aluminium plates was established by means of a coordinate measurement machine. Predicted results were found to agree well with experimental results obtained with instrumented fasteners. The developed FE-model proved to be accurate in terms of load transfer but it was also found to be numerically expensive and thus not suitable for systematic parametric studies in a design process. A parametric study was conducted to investigate whether any of the accounted for mechanisms could be neglected in order to simplify the model. Bolt-hole clearance was found to be the most important parameter. Any difference in clearance between the holes drastically shifted load towards the fasteners where the smallest clearances occurred. An important consequence of this is that changes in temperature could have a strong impact on the load distribution if member plates with different thermal expansion coefficient are used. Clearance appeared to have no effect as long as identical clearance was present at each fastener. Member plate friction and bolt clamp-up force had only small effects on the fastener load fractions but the absence of either friction or clamp-up significantly increased the load carried by each fastener. Assuming linear kinematics generated a more even load distribution and may thus be an unconservative assumption. It can be concluded that accurate predictions of load transfer requires that all the discussed mechanisms are accounted for. This implies that any significant reduction in computation time would require a different modeling approach, possibly involving structural finite elements rather than continuum elements.
Acknowledgements ‘‘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’’. ABB AB, Corporate Research is acknowledged for financial support and for providing computer resources. References [1] Marshall IH, Arnold WS, Wood J, Mousley RF. Observations on bolted connections in composite structures. Composites 1989;13(1): 133–51. [2] Camanho PP, Matthews FL. Delamination onset prediction in mechanically fastened joints in composite laminates. J Compos Mater 1999;33:906–27. [3] Chang F-K, Scott RA, Springer GS. Strength of mechanically fastened composite joints. J Compos Mater 1982;16(November): 470–94.
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885 [4] DiNicola AJ, Fantle SC. Bearing strength behavior of clearance-fit fastener holes in toughened graphite/epoxy laminates. Compos Mater: Testing Des 1993;11:220–37E.T. Camponeschi, Jr., (Ed.), ASTM STP 1206, American Society for Testing and Materials, Philadelphia. [5] Ekh J, Scho¨n J, Melin LG. Secondary bending in multi fastener, composite-to-aluminium single shear lap joints. Composites Part B: Engineering 2005;36(3):195–208. [6] P. Ericsson, Besta¨mning av sekunda¨rbo¨jning och lasto¨verfo¨ringsfo¨rdelningar hos enska¨rigt bultfo¨rband. Technical report, The Aeronautical Research Institute of Sweden, 1983. FFA TN 1983-17 [in Swedish]. [7] Eriksson I, Ba¨cklund J, Mo¨ller P. Design of multiple-row bolted composite joints under general in-plane loading. Compos Eng 1995;8(5):1051–68. [8] Hamada H, Maekawa Z-I, Haruna K. Strength prediction of mechanically fastened quasi-isotropic carbon/epoxy joints. J Compos Mater 1996;30(14):1596–612. [9] Hart-Smith LJ. Bolted joints in graphite-epoxy composites. Technical Report NASA CR-144899, Douglas Aircraft Company, June 1976. [10] Hart-Smith LJ. The design of efficient bolted and riveted fibrous composite structures. Technical Report Douglas Paper 8335, Douglas Aircraft Company, USA, July 1989. [11] Hibbit, Karlsson & Sorensen, Inc. ABAQUS/Standard UserÕs Manual, 6.4 ed., 2003. [12] Hollman K. Failure analysis of bolted composite joints exhibiting inplane failure modes. J Compos Mater 1996;30(3):358–83. [13] Hyer MW, Chastain PA. Effect of bolt load proportioning on the capacity of multiple-bolt composite joints. J Aircraft 1987;25:184–9. [14] Ireman T. Three-dimensional stress analysis of bolted single-lap composite joints. Compos Struct 1998;43:195–216. [15] Jarfall L. Shear loaded fastener installations. Int J Vehicle Des 1986;7:337–80.
885
[16] Crews Jr JH, Naik RA. Combined bearing and bypass loading on a graphite/epoxy laminate. Compos Struct 1986;6:21–40. [17] Jurf RA, Vinston JR. Failure analysis of bolted joints in composite laminates. In: Garbo SP, editor. Composite materials: testing and design (Ninth Volume), ASTM STP 1059. Philadelphia: American Society for Testing and Materials; 1990. p. 165–90. [18] Lessard LB, Shokrieh MM. Two-dimensional modeling of composite pinned-joint failure. J Compos Mater 1995;29:671–97. [19] McCarthy MA, McCarthy CT. Three-dimensional finite element analysis of single-bolt, single-lap composite bolted joints: part 2effects of bolt-hole clearance. Compos Struct 2005; in press. Available online 10 November 2004. [20] McCarthy MA, McCarthy CT. Finite element analysis of the effects of clearance on single-shear, composite bolted joints. J Plastics, Rubber Compos 2002;32(2):1–11. [21] McCarthy MA, McCarthy CT, Lawlor VP, Stanley WF. Threedimensional finite element analysis of single-bolt, single-lap composite bolted joints: part 1-model development and validation. Compos Struct 2005; in press. Available online 5 November 2004. [22] Palmberg B. Instrumented bolts for measurements of their shear load transfer in single and double shear joints. Technical report, The Aeronautical Research Institute of Sweden, 1991. FFA TN 1991-09. [23] Park H-J. Bearing failure analysis of mechanically fastened joints in composite laminates. Compos Struct 2001;53:199–211. [24] Scho¨n J. Coefficient of friction for Aluminium in contact with a carbon fiber epoxy composite. Tribol Int 2004;37(5): 395–404. [25] Smith PA, Pascoe KJ, Polak C, Stroud DO. The behavior of singlelap bolted joints in CFRP laminates. Compos Struct 1986;6: 41–55. [26] Stanley WF, McCarthy MA, Lawlor VP. Measurement of load distribution in multi-bolt, composite joints, in the presence of varying clearance. J Plastics, Rubber Compos 2002;31(9):412–8.
Load transfer in multirow, single shear, composite-to-aluminium lap joints Johan Ekh a
a,*
, Joakim Scho¨n
b
Division of Lightweight Structures, Department of Aeronautical and Vehicle Engineering, The Royal Institute of Technology, SE-100 44 Stockholm, Sweden b Swedish Defence Research Agency, FOI SE-172 90 Stockholm, Sweden Received 26 May 2005; received in revised form 26 August 2005; accepted 28 August 2005 Available online 2 November 2005
Abstract A three-dimensional finite element model has been developed in order to determine the load transfer in multifastener single shear joints. The model is based on continuum elements and accounts for all important mechanisms involved in load transfer, such as bolthole clearances, bolt clamp-up and friction. In particular, member plates can be of different thickness and stiffness and with different coefficient of thermal expansion. An experimental programme was conducted in order to validate the finite element model through measurements of fastener loads, by means of instrumented fasteners. Good agreement between simulations and experiments was achieved and it was found that bolt-hole clearance is the most important factor in terms of load distribution between the fasteners. Any variation in clearance between the different holes implies that load is shifted to the fastener where the smallest clearance occurs. Sensitivity to this variation in clearance was found to be large, so that temperature changes could significantly affect the load distribution if member plates with different thermal expansion properties are used. It was found that good accuracy in load transfer predictions requires that all aforementioned factors are taken into consideration and that nonlinear kinematics is accounted for in the solution process. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Bolted joint; Load transfer; Finite element method; Instrumented fastener
1. Introduction 1.1. Background Designing effective multifastener composite joints requires predictive capability regarding joint strength. Joint failure occurs in one or several macroscopic failure modes [9], such as bearing, net-section, shear-out and cleavage failure and is affected by several parameters. Shear-out and cleavage are generally considered premature in aircraft structures, caused by improper selection of materials and joint configuration, which renders the bearing and net-section modes more important. The different nature of the two
*
Corresponding author. Present address: ABB AB Corporate Research, SE-721 78 Va¨stera˚s, Sweden. Tel.: +46 21 323227; fax: +46 21 323212. E-mail address: [email protected] (J. Ekh). 0266-3538/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2005.08.015
modes, bearing mode is ductile whereas net-section mode is brittle, implies that it is important to take into account not only the failure load but also the mode of failure in the design process. Failure in composite joints is related to the local stress field in the vicinity of fastener holes. Stresses at a particular hole are affected by several factors such as the amount of load reacted by the fastener and the amount of load running through the plate cross-section which is reacted elsewhere in the joint. These two loads are referred to as bearing load, Pb, and bypass load, Pbp, respectively, and are illustrated in Fig. 1. In addition, properties of the contact between the fastener shank and the hole surface, such as the contact area and friction, may have significant effect on the local stress field. This is of particular relevance in single shear lap joints due to the nonuniform distribution of contact stress in the thickness direction caused by the eccentric load path.
876
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
Fig. 1. Loads acting on the plate.
Previous work [9,16] shows that initiation of failure is depending on the combined bearing stress, Sb, and bypass stress, Sbp, with definitions according to Pb ; dt P bp ; ¼ ðw dÞt
ð1Þ
Sb ¼ S bp
ð2Þ
where d is the hole diameter, w is the plate width and t is the thickness of the plate. Maximum strength is achieved for a hole without bearing stresses, i.e. when the applied load, PA, is totally reacted by other fasteners [10]. It appears that net-section failure occurs for small values of the bearing bypass ratio, b ¼ SSbpb , and that the strength decreases linearly when b is increased. At a certain value, b = bshift, the failure mode is shifted from net-section to bearing and additional increase of b has little effect. This implies that the critical fastener may not be the one that reacts the most load and there may be situations where an uneven load distribution results in higher overall joint strength [13] compared to an even load distribution. Thus, accurate strength predictions require that the load distribution between the fasteners is obtained first such that both the bearing load and the bypass load are known for critical fasteners. The load distribution can be estimated with experimental techniques or by using analytical or numerical methods. Bolt loads can be approximately calculated from measurements of bypass strains with strain gauges. Two similar procedures [6,15] have been used; the calibration method and the integration method. The calibration method involves measurements of strain in the vicinity of each fastener for a set of known load distributions, i.e. utilizing only one fastener or a small number of symmetrically positioned fasteners. This implies that a relation between strain at fastener i, i, and the load reacted by fastener j, Pj, can be established according to i ¼
N X oi Pi oP j j¼1
i ¼ 1; . . . ; N ;
ð3Þ
where N is the number of fasteners in the joint. Thus, the individual bolt loads, Pi, are obtained by solving the linear equation system (3). The other technique is more commonly used and is based on direct calculation of the bolt loads rather than using the calibration process described above. Strain gauges are mounted between the bolts, along transverse lines over the joint cross-section, on both sides of the plate.
By assuming some strain variation (usually linear) between the top and bottom surfaces of the plate it is possible to integrate the stress field over the cross-sectional area of the plate and obtain the bypass load. Both methods suffer from not being able to distinguish between fastener reacted load and load transferred by friction between the plates. An additional disadvantage is the extensive instrumentation required on each joint. A more attractive method is to use instrumented fasteners [15,22,26] to measure the fastener loads. Strain gauges can be mounted internally in the bolt in an axial rectangular hole through the fastener, or externally in shallow slots machined in the shank surface. The fasteners can be calibrated to measure axial or shear force in the fastener. Fastener reacted load is separated from frictional load and no instrumentation of the member plates is required. Thus, once the instrumented fasteners are calibrated and the testing procedure is developed, it is fairly easy to conduct systematic testing of a large number of joints. Experimental techniques are reliable and can be used on large, realistic aircraft structures or on simple idealized specimens. However, they are time consuming and expensive, and more important, they are of a validating nature rather than predictive. An efficient design process requires predictive capabilities that can only be offered by theoretical models. The dominant approach is to use the finite element method (FEM) to predict strength of composite joints. Most analyses have been oriented towards the study of failure mechanisms in the composite material and the objective is usually to establish predictive capability, both in terms of failure mode and failure load. Idealized single fastener structures that are suitable for numerical analysis and for experimental studies have been used extensively [1–4,12,8, 17,18,23]. Some workers [25,14,21,19] have investigated the behavior of single shear lap joints where the presence of stress singularities at the faying surface makes the problem more complex. Regarding multifastener joints, several analyses have been conducted where structural finite elements are used, rather than continuum elements, or where 2D continuum elements are utilized. Using structural elements usually implies that contact is not treated, or treated in a simplistic way, whereas a 2D model can not be used to accurately describe a single shear lap joint due to their 3D stress field. Eriksson et al. [7] proposed a methodology in which a two dimensional analysis was used to identify the most heavily loaded fastener, followed by a three dimensional stress analysis to predict failure. McCarthy and McCarthy [20] investigated the effect of clearance in a single shear, three fastener composite-to-composite joint by means of a 3D FE model based on continuum elements. Member plates were identical and finger tightened fasteners were assumed which implies that friction between the plates had little effect on the load transfer. The analysis was conducted in parallel with an experimental programme [26] and good
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
agreement between simulations and experiments regarding load distribution was achieved. However, modern aircraft structures that utilize composite materials still also partly consist of other materials, such as aluminium. This means that joints with member plates of different materials are necessary which introduces further difficulties. Holes in the two materials may be of different size due to shrinkage effects during the drilling process, the plates may have different stiffness and may react differently to temperature changes. This may influence the load distribution. The present study aims at developing a 3D FE model based on continuum elements that accounts for these factors. 1.2. Problem statement and objectives Consider a single shear, composite-to-aluminium, lap joint with 4 fasteners arranged in one column, subjected to quasi-static loading in tension. The objectives in the present study are: (1) Develop a 3D continuum FE-model that predicts the individual bolt loads, taking into account all mechanisms that are important with respect to load transfer. (2) Measure the bolt loads in the joint by means of instrumented fasteners in order to validate the accuracy of the FE-model. (3) Identify what mechanisms must be accounted for in accurate predictions of load distribution.
2. Joint configuration The joint is illustrated in Fig. 2. Member plate thicknesses are 4.16 (composite) and 8.0 (aluminium) mm and
a
877
tabs are glued at both ends to compensate for the geometrical asymmetry in single shear lap joints. Protruding head titanium bolts with a nominal diameter of 6 mm were used and a torque level of 6 Nm was applied. The bolts were anodized and treated with a solid film lubricant. Composite parts were manufactured from the carbonepoxy pre-preg material system AS4/8552 with nominal fiber volume fraction 63.5%. The elastic properties of the material constituents, the uni-directional lamina and the quasi-isotropic lay-up [±45/0/90]4s using 0.13 mm thick uni-directional laminae are given in Table 1. Aluminium parts were manufactured from AA7475-T76 and the fastener system consisted of titanium bolts, alloy steel nuts and stainless steel washers. All elastic properties are tabulated in Table 1. A total of 4 identical joints were used in the programme. 3. Finite element modeling The model has been described in previous work [5] and is briefly reviewed below to assist the reader. All physical entities in the joint, i.e. plates, bolts, nuts and washers were taken into account in the model and surface based contact, with Coulomb friction, was defined for all potential contact surfaces. The coefficient of friction, l, was set to 0.235 [24] between the plates and to 0.05 at all other contact surfaces. Plate materials were assumed to be homogenous, either isotropic or orthotropic, which implies that the model was symmetric with respect to the 1–3 plane in Fig. 3. Thus, only half the geometry was modeled and symmetry conditions were specified on the 1–3 plane. Tab regions indicated in Fig. 2(b) were excluded from the model. Nodes on the left end of the aluminium plate (lower plate in Fig. 3) were clamped whereas the nodes on the right end of the composite plate were prevented from moving in the 2- and 3-directions,
b
Fig. 2. Reference joint geometry.
Table 1 Elastic properties of materials and their constituents Material
E11 (GPa)
E22 (GPa)
E33 (GPa)
G12 (GPa)
G13 (GPa)
G23 (GPa)
m12
m13
m32
Fiber Matrix Lamina Laminate Aluminium Titanium Steel
238 3.3 140 54.25 71 110 210
– – 10 54.25 – – –
– – 10 10 – – –
22 1.2 5.2 20.72 – – –
– – 5.2 4.55 – – –
– – 3.9 4.55 – – –
0.2 0.35 0.3 0.309 0.31 0.29 0.30
– – 0.3 0.332 – – –
– – 0.5 0.332 – – –
878
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
Fig. 3. Finite element mesh of joint.
but free to move in the 1-direction. Fasteners were torqued (finger tight or highly torqued) using the ‘‘pre-tension’’ option in Abaqus. This was done in a separate analysis step, prior to applying the longitudinal load on the right end nodes, which is in accordance with the experimental procedure. Plates were discretisized using linear 8-node solid elements (C3D8I) with improved bending properties through the addition of incompatible deformation modes [11]. Bolts were defined as masters in the contact which implies that nodes belonging to washers and plates could not penetrate the element segments of the bolts. In order to ensure that the bolts were accurately described as circular with well defined radius they were modeled with quadratic solid elements (C3D20R) with reduced integration. Washers were modeled with linear elements with reduced integration (C3D8R). All analyses were static with nonlinear kinematics. 4. Experimental programme 4.1. Bolt-hole clearance During the manufacturing process, the specimen plates were drilled separately. As a result the holes were not perfectly lined up. Detailed comparisons between the FEmodel and the experiments required that the geometry of the specimens were modeled as accurately as possibly, in particular the sizes and the relative positions of the fastener holes. Measurements with a coordinate measurement machine were conducted on two specimens in order to establish hole diameters and positions. The coordinate measurement system utilizes a probe that is inserted approximately at the center of the hole. The probe is translated in radial direction until it hits the hole edge at which point the system is saving the coordinates of the probe. This was repeated for 32 points along the circumference and for a number of levels in the plate thickness direction. A Cartesian coordinate system is used which enables, under the assumption that the hole is circular, the calculation of hole center location and radius through minimizing qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 X 2 2 2 ¼ r ðxn x0 Þ þ ðy n y 0 Þ ; ð4Þ n
where xn, yn are the measured points and, x0,y0 and r are the solved for coordinates of the origin and the radius, respectively. It was found that the holes in the aluminium plates were larger than the holes in the composite plates and that the variation between holes in one material was small. Mean radii in the composite and in the aluminium were 3.003 and 3.021 mm, respectively. Furthermore, it was found that the holes were not concentric, i.e. the row spacing was different in the composite compared to the aluminium. Mean values of row spacing are presented in Table 2 where rsi denotes the distance between fastener i and i + 1 using the bolt numbers in Fig. 2(a). The actual clearances resulting from the measurements were estimated by making a number of assumptions and solving a linear equation system. Hole diameters in the composite and aluminium plates, dc and da, respectively (see Fig. 4), and the distances between adjacent hole edges, lci and laj where i, j = 1. . .3, are assumed to take the mean values presented in Table 2. Diameters of the fastener shanks were measured to 5.985 mm with small variations. The load submitted to the joint is tensional so that the composite plate is translated to the right and the aluminium plate to the left in Fig. 4 which implies that one of the clearances dci1 and one of dai2 , where i = 1. . .4, eventually will become zero as the first fastener starts to carry load. Assuming further that the fasteners are located at the center of each ‘‘effective’’ hole through both plates, i.e. that dci1 ¼ dai2 and that all clearances are non-negative, makes it possible to solve for the unknown clearances. Estimation of the clearances with this method yields that the clearances at the inner fasteners are zero whereas the clearance is maximum (22 lm) at the outer fasteners, i.e. the clearances are such that for the given hole sizes, maximum load is shifted from the outer fasteners to the inner fasteners. This will be accounted for in the FE-model. All calculated clearances are presented in Table 3.
Table 2 Mean values of measured row spacing Material
rs1 (mm)
rs2 (mm)
rs3 (mm)
Composite Aluminium
32.077 31.998
32.043 32.013
31.941 32.011
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
879
Fig. 4. Bolt hole clearances.
Table 3 Bolt-hole clearances (mm) Plate
d11
d12
d21
d22
d31
d32
d41
d42
Composite Aluminium
0.022 0.036
0 0.022
0 0.058
0.022 0
0 0.058
0.022 0
0.022 0.036
0 0.022
4.2. Measurement of bolt loads 4.2.1. Instrumented fastener Load carried by each bolt in the joint was measured with a fastener instrumented in such a way that its output signal is only affected by shear deformation of the fastener in the vicinity of the joint shear plane. This is achieved by machining slots in a regular titanium fastener and installing four strain gauges in a 45° angle to the bolt axis direction, two on either side of the fastener as illustrated in Fig. 5. The two gauges on each side of the fastener were mounted equidistant to, and on opposite sides of the joint shear plane. This type of instrumented fastener was previously used by Palmberg [22]. The load submitted to a fastener in a single shear joint is a combination of shear, torsion, bending and axial forces. Torquing the nut in assembling the joint submits torsional and axial forces. Tension or compression loading of the joint results in shear forces and bending of the fastener over the transverse direction (BT) of the joint. Secondary bending could imply twisting of the joint, depending on the stacking sequence used in the composite laminate, which
would cause the fastener to bend over the longitudinal direction (BL). In order to make the fastener output signal insensitive to all forces except the shear force, the four gauges were connected into a full Wheatstone bridge. Mapping the cylindrical surface of the bolt shank on a Cartesian coordinate system implies that the strain gauges are located according to Fig. 6(a). The electric potential in points a,. . .,d in Fig. 6(b) can be written as, a ¼ V in
b ¼ V in ;
c ¼ V in
G4 ; G3 þ G4
d ¼ 0; ð5Þ
where Gi is the resistance of gauge i, under the assumption that the potential in point d is zero. Output voltage, Vout, can be written as the potential in point c subtracted from the potential in point a which yields
a
Fig. 5. Machined slots and installed strain gauges in instrumented fastener.
G1 ; G1 þ G2
b
Fig. 6. (a) Strain gauges on the instrumented bolt are located equidistant from the joint shear plane and on either side of the bolt shank. (b) Strain gauges connected into a full Wheatstone bridge. Strain gauge configuration in instrumented bolt.
880
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
V out ¼ a c ¼ V in
G1 G4 V in . G1 þ G2 G3 þ G4
ð6Þ
Each of the forces subjected to the fastener will introduce strains in the gauges that could be tensional or compressive, which results in changed electrical resistance by DG and DG, respectively, as tabulated in Table 4. Introducing the contributions to the resistance from Table 4 into Eq. (6) for each type of load implies that the output voltage (Vout) is affected according to Eq. (7). Thus, Vout is only affected by the shear load subjected to the fastener. G þ DG G DG DG V in ¼ V in ; 2G 2G G G þ DG G þ DG V in ¼ 0; V torsion ¼ V in out 2G 2G G þ DG G þ DG V in ¼ 0; V bt out ¼ V in 2G þ 2DG 2G þ 2DG G þ DG G þ DG V in ¼ 0; V axial out ¼ V in 2G þ 2DG 2G þ 2DG G þ DG G DG V in ¼ 0. V bl out ¼ V in 2G þ 2DG 2G 2DG
V shear out ¼ V in
ð7Þ
The bolt was calibrated in a finger tightened, single fastener, single shear lap joint in order to establish a relation between output voltage and load carried by the fastener. This relation could then be used to calculate the approximate bolt load for any bolt for which the output signal had been recorded. 4.3. Testing procedure All plates were cleaned individually with ultrasonic technique in order to remove any grease from handling the plates, and loose particles from the drilling process. This cleaning process is in accordance with the process used when measuring the coefficient of friction [24] which was used in the finite element modeling. The level of torque was either 6 Nm or finger tight for all fasteners within the same joint. As only one instrumented fastener was available, each joint utilized three regular fasteners and the test was repeated four times with the instrumented fastener shifting position. The joint was completely disassembled between each test in order to remove all frictional forces built up during the test. The joints were mounted in an hydraulic test machine and subjected to displacement controlled, quasi-static (loading rate = 0.1 mm/min, max load = 18 kN) tension loading. Table 4 Change in electrical resistance at each gauge due to loading
Shear Torsion BT Axial BL
G1
G2
G3
G4
DG DG DG DG DG
DG DG DG DG DG
DG DG DG DG DG
DG DG DG DG DG
5. Results and discussion 5.1. Load transfer in single shear lap joints Results obtained with the continuum FE-model described in Section 3 are presented below in order to illustrate some fundamental characteristics of multifastener single shear lap joints. A four fastener composite-to-composite (equal thickness) joint with perfect fit, torqued fasteners was selected as an example. The coefficient of friction was set to be larger between the plates compared to all other contact surfaces. An external longitudinal tension load is transferred from one plate to the other through a number of contact surfaces, each of which contributes to fulfill the force equilibrium. Contact forces could be either normal, tangential (friction) or both and are presented in Fig. 7(a) in terms of their longitudinal components summed over all four fasteners. Individual normal bolt loads are shown in Fig. 7(b). Large frictional forces develop between the plates in the vicinity of the holes due to the clamping force generated by the fasteners and the load transfer is dominated by this friction when the level of applied load is low. At some point, when the load is increased, friction is fully developed and the plates start to slide relative to each other, which causes the load to be picked up by the fasteners through contact between the bolt shanks and the hole edges. Once sliding has started, the load transferred by friction between the plates remains essentially constant during further increase of the applied load. Deviations from this constant value can be explained by local changes in contact pressure between the plates. The compressive stresses in the plates close to the bolt-hole contact implies that the thickness of the plates is increased locally, due to the Poisson effect, which could increase the contact pressure between the plates. In other regions, the tensional bypass loads leads to a decreased thickness of the plates. The separation of the plates at the ends of the overlap region also affects the contact pressure between the plates. It appears that the net effect of these mechanisms leads to a reduced contact pressure between the plates for the joint presented in Fig. 7(a) which is reflected in the slightly decreased frictional load when the applied load is increased. Since the two member plates are identical, the joint is almost anti-symmetric with respect to a vertical line between bolts 2 and 3 in Fig. 2(a). The only deviation from antisymmetry is that the nuts are thicker than the bolt heads. Perfect anti-symmetry would imply that the two outer bolts would carry equal load as would the two inner bolts. Therefor, result from only one outer and one inner fastener is presented in Fig. 7(b). It can be seen that the outer fastener carries significantly more load than the inner fastener. The load is picked up earlier and is increasing at a higher rate as the applied load increases. This behavior is well known and is mainly attributed to the relative displacements of the hole centers. The outer fastener hole is displaced more from the anti-symmetry plane due to its
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
a
881
b
Fig. 7. Typical load transfer characteristics of a four fastener, antisymmetric single shear lap joint. (a) Longitudinal components of total normal bolt loads, total tangential bolt loads, total friction between washers and one plate and friction between the plates. (b) Longitudinal components of the normal contact load for one outer and one inner bolt.
larger distance from the plane, compared to that of the inner fastener, which is reflected in the distribution of load between the fasteners. 5.2. Comparison between experiments and FE-model In order to validate the FE-model, detailed comparisons with experiments were made regarding individual bolt loads. The experimental curves are mean values of results from all tested specimens and are assumed to represent the average behavior of the joint. Variations between the joints were found to be small. Output signal from the instrumented fastener is affected by shear strains in the fastener according to the previous discussion. Thus, all longitudinal load contributions that affects the shear
deformation in the fastener are taken into account in the FE-model, including normal and tangential bolt-hole contact forces and friction between washers and bolt heads. All results regarding hole sizes and positions, and the resulting clearances presented in Section 4.1, were used in the FE-model in order to describe the real test specimens as accurately as possible. The coefficient of friction between the plates was set to 0.235 according to measurements by Scho¨n [24] and to 0.05 at all other contact surfaces due to the solid film lubricant coating on the fasteners. Results for finger tightened fasteners (200 N axial load in FE-models) are presented in Fig. 8. Load pick-up is delayed at the outer bolts, and more load is carried by the inner bolts, due to the bolt-hole clearances at the outer bolts.
a
b
c
d
Fig. 8. Comparison between FE-models and experiments with finger tightened fasteners. (a) Bolt 1, (b) Bolt 2, (c) Bolt 3 and (d) Bolt 4.
882
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
The total amount of load transferred by the fasteners is 17.5 kN for the FE-model and 16.5 kN for the experiments which indicates that a small portion of the applied load is transferred by friction between the plates despite the lack of clamping pressure. The discrepancy between the model and the experiments can be attributed to small differences in clamping force, coefficient of friction and fastener compliance. According to Section 4.2.1, small slots were machined in the instrumented fastener to accommodate the installation of the strain gauges. This resulted in a reduction of the cross-sectional area of the fastener, at the shear plane of the joint, of approximately 7% which would make the fastener less stiff and possibly shift some load to the other fasteners. Since the only available instrumented fastener was used in different positions, in conjunction with three regular fasteners, it could imply that it consistently carried less load due to its reduced stiffness. However, it appeared that this effect was small as the agreement with the FE-model was good. Results for joints with torqued fasteners (6 Nm in experiments, 3740 N axial force in FE-models [5]) are presented in Fig. 9. Again, the FE-model generates results in good agreement with the experiments. Load pick-up is delayed at all bolts due to the friction between the plates but once load is picked up by the fasteners, the load distribution is similar to that of the finger tight case. Experimental load pick-up is more smooth compared to the FE-models which could indicate that the coefficient of friction at all surfaces except the faying surface, was set too low (0.05) in the FEmodel. Small amounts of load is picked up in a smooth
process for the FE-model and an increased coefficient of friction would cause the FE-curve to approach the experimental curve in Fig. 9(a) and (d). However, explicit, non-physics related fine tuning of the FE-models have consistently been avoided in the present work and the first assumption that the lubricant on the fasteners would generate a low coefficient of friction is maintained. It was concluded that the FE-model accurately accounts for the mechanisms affecting the load transfer and that it is capable of predicting individual bolt loads with good accuracy. 5.3. Influence of various mechanisms on load transfer Results presented in Figs. 8, 9 show that a detailed 3D continuum FE-model is capable of predicting individual fastener loads in complex multifastener joints. However, in developing the FE-model, detailed information regarding hole diameters, hole positions, surface conditions and fastener clamp-up force was taken into account. This information was obtained by means of several test programmes and it can be assumed that this information is in general not available in a regular design process of an aircraft structure. It is therefore of interest to investigate the relative importance of the different pieces of information in order to establish what needs to be accounted for and what can be neglected in accurate predictions of fastener loads using a continuum FE-model. The investigation was conducted by means of a series of analyses using the FE-model described in Section 3. A
a
b
c
d
Fig. 9. Comparison between FE-models and experiments with torqued fasteners. (a) Bolt 1, (b) Bolt 2, (c) Bolt 3 and (d) Bolt 4.
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
number of modifications were applied to the model in such a way that in each analysis, only one modification of the original model was in effect. The original FE-model is referred to as the ‘‘baseline’’ model in the remainder of this text. Modified FE-models are listed in Table 5. Results are presented in Fig. 10 in terms of fastener load fractions and absolute fastener loads. Fastener load fracf tion is defined as Fbbi where fbi is the load carried by fastener i and Fb is the total amount of load carried by all fasteners, i.e. the frictional load between the plates subtracted from the applied load. Regarding the load fractions (see Fig. 10(a)) it can be seen that hole eccentricity between the member plates has a large impact. The analyses with perfect fit fasteners and with clearance with concentric holes, differs significantly from the baseline model in the sense that load is shifted from the inner fasteners (2 and 3) to the outer fasteners (1 and 4). However, load fractions are almost identical for the two cases which implies that the parameter of importance is the difference in clearance between the holes rather than the magnitude. It appears that friction, torque and kinematical formulation (linear or non-linear) have a smaller influence on the load fractions compared to the bolt-hole clearance. However, in all cases, neglecting one of these parameters leads to a more even distribution of load fractions compared to the baseline model. Absolute fastener loads are presented in Fig. 10(b) and the effect of friction between member plates and fastener torque is illustrated. Neglecting either of these two parameters will cause the fasteners to carry more load compared to the baseline model. Table 5 Identification tag and description of conducted analyses ID
Modification
No clearance No ecc. No friction No torque Small disp.
No bolt hole clearance Concentric holes No friction between plates Finger tightened fasteners Linear kinematics
883
Thus, neglecting bolt clamp-up force or member plate friction would essentially preserve the relations between individual fastener loads compared to the baseline model but increase the amount of load carried by each fastener. Using linear kinematics generates a more even load distribution and in particular predicts a lower load carried by the most heavily loaded fastener compared to the baseline model, i.e. it may be unconservative to use linear kinematics. Neglecting any differences between the holes in effective bolt-hole clearances affects the results drastically which implies that meaningful evaluation of the results may be prevented. 5.4. Influence of temperature The strong influence on the load distribution of having different clearances at the holes caused by eccentricity of the holes opens a discussion about the influence of temperature. Thermal expansion in a composite laminate is depending on the thermal properties of the material constituents, their relative proportions and the laminate stacking sequence. In composite laminates used in aircraft structures, the thermal expansion coefficient can be assumed to be smaller than that of aluminium which implies that hole eccentricity could change if the temperature changes. In order to illustrate the effect of having member plates with different coefficient of expansion, an analysis was conducted with coefficients according to Table 6. The joint with concentric holes and different hole sizes in the two materials according to Section 4.1 was used. Effective
Table 6 Coefficients of thermal expansion Material
a (106/°C)
Aluminium Composite Titanium Steel
23 10 8.8 15
Fig. 10. Influence of various mechanisms on fastener load distribution. (a) Fractions of total fastener reacted load. Fastener numbers according to Fig. 2. (b) Individual fastener loads. Fastener numbers according to Fig. 2.
884
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885
Table 7 Bolt-hole clearances (mm) Temperature (°C)
Clearance
d1
d2
d3
d4
20 20 20 50 50 50
Composite Aluminium Effective Composite Aluminium Effective
0.011 0.029 0.040 0.021 0.043 0.064
0.011 0.029 0.040 0.012 0.032 0.044
0.011 0.029 0.040 0.010 0.025 0.035
0.011 0.029 0.040 0.003 0.012 0.015
Fig. 11. Influence of temperature on fastener load fractions.
clearance at fastener i, di, denotes the relative displacement of the member plates required before the fastener starts to pick up load, i.e. it is the sum of the clearance in the composite and the aluminium plate. An additional load step was defined where a temperature load of DT = 70 °C was applied after torquing the fasteners but before applying the tensional load. Boundary conditions specified in the first load step were maintained in the added load step. This would approximately correspond to a situation where the joint was manufactured and assembled in room temperature and the aircraft was operating in a temperature of 50 °C. The main effect of the applied temperature load is that the aluminium plate contracts more than the composite plate which result in changed clearances according to Table 7. At 20 °C the effective clearance was 0.040 mm at all fasteners, but at 50 °C the effective clearance varies from 0.064 mm at bolt 1 down to 0.015 mm at bolt 4. This is clearly reflected in load transfer, which is illustrated in Fig. 11. The fastener load fraction is reduced for bolts 1 and 2 where the effective clearances were increased, and increased for bolts 3 and 4 where the clearances were decreased. The effect is more significant at the outermost fasteners where the change in clearance is larger compared to the innermost fasteners. 6. Summary and conclusions A detailed 3D, continuum finite element model was developed for a single shear, multifastener, composite-tometal lap joint in order to predict the joint load transfer. The model accounted for all mechanisms that were ex-
pected to affect the load transfer including fastener clamp-up force, member plate friction, bolt-hole clearance and nonlinear kinematics. In particular, the exact geometry regarding hole sizes and positions in the composite and in the aluminium plates was established by means of a coordinate measurement machine. Predicted results were found to agree well with experimental results obtained with instrumented fasteners. The developed FE-model proved to be accurate in terms of load transfer but it was also found to be numerically expensive and thus not suitable for systematic parametric studies in a design process. A parametric study was conducted to investigate whether any of the accounted for mechanisms could be neglected in order to simplify the model. Bolt-hole clearance was found to be the most important parameter. Any difference in clearance between the holes drastically shifted load towards the fasteners where the smallest clearances occurred. An important consequence of this is that changes in temperature could have a strong impact on the load distribution if member plates with different thermal expansion coefficient are used. Clearance appeared to have no effect as long as identical clearance was present at each fastener. Member plate friction and bolt clamp-up force had only small effects on the fastener load fractions but the absence of either friction or clamp-up significantly increased the load carried by each fastener. Assuming linear kinematics generated a more even load distribution and may thus be an unconservative assumption. It can be concluded that accurate predictions of load transfer requires that all the discussed mechanisms are accounted for. This implies that any significant reduction in computation time would require a different modeling approach, possibly involving structural finite elements rather than continuum elements.
Acknowledgements ‘‘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’’. ABB AB, Corporate Research is acknowledged for financial support and for providing computer resources. References [1] Marshall IH, Arnold WS, Wood J, Mousley RF. Observations on bolted connections in composite structures. Composites 1989;13(1): 133–51. [2] Camanho PP, Matthews FL. Delamination onset prediction in mechanically fastened joints in composite laminates. J Compos Mater 1999;33:906–27. [3] Chang F-K, Scott RA, Springer GS. Strength of mechanically fastened composite joints. J Compos Mater 1982;16(November): 470–94.
J. Ekh, J. Scho¨n / Composites Science and Technology 66 (2006) 875–885 [4] DiNicola AJ, Fantle SC. Bearing strength behavior of clearance-fit fastener holes in toughened graphite/epoxy laminates. Compos Mater: Testing Des 1993;11:220–37E.T. Camponeschi, Jr., (Ed.), ASTM STP 1206, American Society for Testing and Materials, Philadelphia. [5] Ekh J, Scho¨n J, Melin LG. Secondary bending in multi fastener, composite-to-aluminium single shear lap joints. Composites Part B: Engineering 2005;36(3):195–208. [6] P. Ericsson, Besta¨mning av sekunda¨rbo¨jning och lasto¨verfo¨ringsfo¨rdelningar hos enska¨rigt bultfo¨rband. Technical report, The Aeronautical Research Institute of Sweden, 1983. FFA TN 1983-17 [in Swedish]. [7] Eriksson I, Ba¨cklund J, Mo¨ller P. Design of multiple-row bolted composite joints under general in-plane loading. Compos Eng 1995;8(5):1051–68. [8] Hamada H, Maekawa Z-I, Haruna K. Strength prediction of mechanically fastened quasi-isotropic carbon/epoxy joints. J Compos Mater 1996;30(14):1596–612. [9] Hart-Smith LJ. Bolted joints in graphite-epoxy composites. Technical Report NASA CR-144899, Douglas Aircraft Company, June 1976. [10] Hart-Smith LJ. The design of efficient bolted and riveted fibrous composite structures. Technical Report Douglas Paper 8335, Douglas Aircraft Company, USA, July 1989. [11] Hibbit, Karlsson & Sorensen, Inc. ABAQUS/Standard UserÕs Manual, 6.4 ed., 2003. [12] Hollman K. Failure analysis of bolted composite joints exhibiting inplane failure modes. J Compos Mater 1996;30(3):358–83. [13] Hyer MW, Chastain PA. Effect of bolt load proportioning on the capacity of multiple-bolt composite joints. J Aircraft 1987;25:184–9. [14] Ireman T. Three-dimensional stress analysis of bolted single-lap composite joints. Compos Struct 1998;43:195–216. [15] Jarfall L. Shear loaded fastener installations. Int J Vehicle Des 1986;7:337–80.
885
[16] Crews Jr JH, Naik RA. Combined bearing and bypass loading on a graphite/epoxy laminate. Compos Struct 1986;6:21–40. [17] Jurf RA, Vinston JR. Failure analysis of bolted joints in composite laminates. In: Garbo SP, editor. Composite materials: testing and design (Ninth Volume), ASTM STP 1059. Philadelphia: American Society for Testing and Materials; 1990. p. 165–90. [18] Lessard LB, Shokrieh MM. Two-dimensional modeling of composite pinned-joint failure. J Compos Mater 1995;29:671–97. [19] McCarthy MA, McCarthy CT. Three-dimensional finite element analysis of single-bolt, single-lap composite bolted joints: part 2effects of bolt-hole clearance. Compos Struct 2005; in press. Available online 10 November 2004. [20] McCarthy MA, McCarthy CT. Finite element analysis of the effects of clearance on single-shear, composite bolted joints. J Plastics, Rubber Compos 2002;32(2):1–11. [21] McCarthy MA, McCarthy CT, Lawlor VP, Stanley WF. Threedimensional finite element analysis of single-bolt, single-lap composite bolted joints: part 1-model development and validation. Compos Struct 2005; in press. Available online 5 November 2004. [22] Palmberg B. Instrumented bolts for measurements of their shear load transfer in single and double shear joints. Technical report, The Aeronautical Research Institute of Sweden, 1991. FFA TN 1991-09. [23] Park H-J. Bearing failure analysis of mechanically fastened joints in composite laminates. Compos Struct 2001;53:199–211. [24] Scho¨n J. Coefficient of friction for Aluminium in contact with a carbon fiber epoxy composite. Tribol Int 2004;37(5): 395–404. [25] Smith PA, Pascoe KJ, Polak C, Stroud DO. The behavior of singlelap bolted joints in CFRP laminates. Compos Struct 1986;6: 41–55. [26] Stanley WF, McCarthy MA, Lawlor VP. Measurement of load distribution in multi-bolt, composite joints, in the presence of varying clearance. J Plastics, Rubber Compos 2002;31(9):412–8.