ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Sain, -6 June 04 INFLUENCE OF BEARING DEGRADATION ON THE BEHAVIOUR OF MULTI-BOLT COMPOSITE JOINTS WITH HOLE-LOCATION ERROR J. Lecomte a,b*, C. Bois a, H. Wargnier a, J.-C. Wahl a a Université Bordeaux, Institut de Mécanique et d Ingénierie de Bordeaux (IM), IUT Bordeaux - 5, rue Naudet - CS 007-3375 - Gradignan Cedex France b ASTF, 8 Avenue du Val d Or, 33700 Mérignac *julie.lecomte@u-bordeaux.fr Keywords: multi-bolt joint, location error, load transfer, clearance Abstract In the aircraft industry, the method for designing metal-comosite joints is mainly based on conservative metallic calculation rules and on alying high safety factors. The reason is that the influence of errors due to manufacturing is not well-nown, and few studies deal with this issue. This study first resents the evolution of load transfer inside a double-la joint with two bolts, in resence of bolt-hole clearance and osition error. Then, a -D analytical numerical model is detailed, in order to evaluate the load distribution in multi-bolt shell structures.. Introduction The increasing use of comosite materials in the aeronautical field leads to metal-comosite joints with a large number of fasteners. The choice of joint dimensions, fastener diameter, number of fasteners, sacing between rows of fasteners, is well understood now, thans to many studies about their influence [], [], [3]. However, the effect of hole-location errors on the assembly mechanical erformance is less well controlled. To reduce location error and thus ensure mechanical erformance, fastener holes are made in a single drilling oeration which requires a comlex flow-rocess grid. This assembly rocess is incomatible with costefficient interchangeability rules and contributes in the increase in joint manufacturing and maintenance costs. Few studies have been ublished dealing with the influence of geometrical errors on the mechanical behaviour of joined structures. This can be exlained by the fact that this issue needs an accurate stiffness model for each constituent of the assembly (joined arts, fasteners) which controls load distribution between fasteners. Moreover, even for low hole-location errors or clearance, load distribution between fasteners is controlled by non-linear behaviour of materials, which generates a local softening [4], [5]. Another roblem, related to exerimental validation, is found in introducing a controlled flaw into samles and develoing secific instrumentation to analyse the effect of the flaw [4]. The load distribution in bolted joints has been investigated with different levels of comlexity. Some studies tae the fasteners as rigid bodies and define the material behaviour of structures as elastic linear [6], others integrate nonlinearities due to contact issues (clearance, friction, etc.) and also bolt stiffness [7], [8], [9], [0]. These models do not usually include nonlinear behaviour due to material damage in the fastener or around the hole. Some
Transmitted load (N) ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Sain, -6 June 04 studies tae into account material damage [5], [], [], [3], [4], [5], [6], [7], [8]. In [5], [], [3], [8], a 3-D finite element model is used to study the rogressive degradation imlied by bearing loading. Thus several damage mechanisms are introduced in this model, such as delamination, matrix cracing and fiber comressive failure. However, such a comlex model cannot be alied to a large structure with multi-bolt joining with a view to study the effect of design arameters. In [], the most critically loaded fastener is first determined using a linear analysis, and then a secific study including damage mechanisms focuses on this location. Nevertheless, the effect of local softening on load redistribution between fasteners is not reresented. In [5], [7], a -D analytical model is roosed in which each bolt is modelled by a sring with a nonlinear force dislacement law in order to reresent the local softening due to bearing damage. The evolution of load transfer rate during loading is thus more easily redicted according to joint dimensions and material behaviours. It should be noted that clearance can be included in the sring force dislacement law. Gray and McCarthy [6] included nonlinear bolt behaviour reviously roosed [5] in a user-defined 0-node suer finite element which can be used with shell elements to simulate large-scale structures. Results on 0-bolt joints are resented and comared with exerimental data in terms of strain distribution. Although good agreement is found, the effect of nonlinear behaviour is not addressed. The aroach roosed in this wor consists in develoing two models with different levels of comlexity. The first one is a -D analytical model which is dedicated to study the influence of joint arameters in reliminary design stages. The second model is a -D analytical numerical model which is dedicated to evaluate the mechanical erformance of actual multi-bolt joint by taing into account joint and art architectures. In these two models, bolt comliance, nonlinear bolt behaviour (i.e. contact with clearance and damage), and holelocation error are taen in account. While nonlinear bolt behaviour is introduced at the bolt scale in the -D analytical model under the form of a force-dislacement resonse, it is exlicitly introduced in the -D model with local behaviours.. Descrition of the -D analytical model.5 3 x 04 () () (3) (4) (5).5 0.5 0 F Analytical model, no bearing F Analytical model, no bearing F Analytical model, with bearing F Analytical model, with bearing F FEM (no bearing) F FEM (no bearing) -0.5 0 3 Total load F (N) 4 5 6 x 0 4 Figure. Loads transmitted by the bolts versus alied load for Cgeom = 0.05 mm and δ = 0.50 mm.
ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Sain, -6 June 04 The model consists in dividing the n-bolt joint in n+ sections. Each adherent section and each bolt are considered as a sring. Elastic linear behavior are assumed for adherent section srings while a non-linear behavior is used for bolt sring in order to account clearance, rogressive contact establishing and comosite damage. Hole-location errors are introduced in term of initial dislacement conditions. The model statement and identification are fully described in [9]. The model was validated by a 3D finite element model and exerimental tests on double-la aluminum-comosite joints with two bolts. The evolution of the load transmitted by each fastener is lotted in Figure for both the analytical model and the FEM for a clearance of 0.05mm and a location error of 0.50mm. Several stages can be identified along the curves obtained with the analytical model. Preload caused by hole-location error generates two oosite loads on bolts. During the first stage of external load alication (), the second bolt is unloaded while the first bolt is loaded more. When the second bolt is totally unloaded, the clearance recovery stage () starts. During this stage, the first bolt transfers the whole alied load. Once the clearance has recovered, the second bolt is in contact with the adherent holes again, and both bolts can be rogressively loaded simultaneously (3). Bolt # reaches the bearing degradation threshold F, first, which imlies a decrease in load transfer rate (4). b Consequently the load is transferred to the second bolt, until it reaches F in its turn (5). b Furthermore, from Figure it can be concluded that the analytical model is able to relace a comlex finite element model for load transfer estimation in a multi-bolt joint with clearance and location error. The FEM, which contains 760,000 degrees of freedom, needs about hours of calculation time, whereas the analytical model only taes a few seconds. This analytical model is quite simle and taes a lot of arameters and henomena into account, but it can only be alied to joints with one row of bolts loaded in the bolts line. 3. Descrition of the -D model y x Adherent y Adherent x y Y x X Figure. Descrition of a multi-bolt joint with coordinates systems 3.. Problem statement We focus on a multi-bolt comosite-comosite or metal-comosite joint, made of a art, with a thicness h and called adherent, and a art, with a thicness h and called adherent 3
ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Sain, -6 June 04 (Figure ). The global coordinate system is defined as XY,. The Figure 3 shows the local olar coordinate systems x, y and u, v, whose origins are located at the center of the fastener in. x is defined as the direction of the loads F transmitted by the adherents # to the fastener. The radius of the fastener # is equal to R a, where a is the hole radius of adherents # associated to fastener # and is the radial bolt-hole clearance associated to fastener #. For each bolt #, a and are assumed equal for the two adherents. Adherents and are modelled by continuum shell elements which allow reresenting comlex geometry with a reasonable calculation time. Adherent holes are exlicitly reresented with a moderately refined mesh which allows accessing the stress field around the hole. Hole-location error can then be directly integrated on adherent geometry. Bolt and adherent-bolt contact models are based on the Madenci s model roosed in [8]. y v u R O x a Figure 3. Definition of olar coordinate systems and holes dimensions for the fastener # Actual osition of fastener in section in mid-lan of adherent Actual osition of fastener in section in mid-lan of adherent x Initial osition of fastener in O O I I Hole section of adherent Hole section of adherent Figure 4. Descrition of contact between fastener # and hole boundary 4
ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Sain, -6 June 04 As roosed by Xiong and Poon [9] by modelling the fastener as a short beam, the comliance S of fastener # can be calculated as follow: S 3 R h h EI F h EI GA h h () where F F x is the amlitude of the load transmitted by fastener # and is the relative dislacement between the two fastener in sections in mid-lane of each adherent as illustrated in Figure 3. is a shear coefficient arameter which is equal to.33, EI is the bending stiffness and GAis the shear stiffness of the fastener in. The relative normal dislacement U alied to adherents between contact center oints and I defined in Figure 4 are then related to the transmitted load by the following equation: where,, 0, 0 U u a u a S F () u a is the normal (i.e. on u ) dislacements of adherent #. The bolt load is transmitted through the contact zones between fastener and adherent holes. In resence of friction between fastener in and adherent holes, the contact zone in each adherent # for each fastener # is divided in no-sli and sli zones, delimited by angles,, and (Figure 4). The boundary conditions along the fastener holes can then be defined as: where,, 0cos u a u a, with,,, 0sin v a u a, with, a, f a, I (3) (4), with, (5) a, f a,, with, a a,, 0, with, (6) v is the tangential (i.e. on v ) dislacement of adherent #, f is the friction coefficient, and are resectively the normal and shear stress in the adherent #. The continuity equations which define the contact angles give: a, 0, with, (7) a a,, 0 (8) 5
ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Sain, -6 June 04 The equilibrium of the fastener # gives: a, a, (9) a, a, (0) F F 0 () The last equation gives the relation between the force transmitted by the adherent # to fastener # and the stress field in adherent #: 3.. Solving method 0 h a a, cos a, sin d F 0 () For solving this roblem, Madenci [8] uses the boundary collocation technique, made ossible by the use of the comlex analytic functions introduced by Lehnitsii [0] to reresent the adherent elastic deformations. In the resent study, an iterative rocedure is roosed to solve both the analytical bolt and adherent-bolt contact formulation and a finite element model (FEM) is used for the adherents. At each iteration, the stress field obtained from the FEM is used to calculate the load transmitted by each fastener (Equation ()) and to readjust the contact angles according to Equations (7) to (). Equations () to (6) allow then to udate the boundary conditions on each adherent hole. Without hole-location error, bolt and adherent holes being initially coaxial, the clearance disables the contact. Contact angles are thus initially taen equal to zero. Hole-location error can otherwise be introduced rogressively in a first ste by decreasing a virtually augmented clearance u to the actual value. This iterative rocedure can be imlemented in an imlicit or exlicit scheme. The user-subroutine facilities of Abaqus software were exloited to combine the analytical equations with the FEM. First simulations were dedicated to double-la aluminum-comosite joints with two bolts in order to comare the -D model to 3-D FEM and -D model. Comarison mainly aims at evaluating the relative erformances in term of calculation time since the henomena imlied in the three different models are identical. First results are encouraging even if the calculation time roves to be quite deendent to the iterative rocedure algorithm. 4. Conclusions Two models with different levels of comlexity were develoed in order to study the effect of hole-location error on the load distribution in multi-bolt joints. The wor uts emhasis on non-linear behaviour generated by friction henomena and clearance in bolt-adherent contact and material damage. An analytical model was devoted to double-la joint with several bolts lined u in a row. This time-efficient model allows arameters influence studies, but cannot be alied to comlex structures. The -D model elaborated here is balanced between a numerical art, to reresent the geometry of assembled arts including hole-location error, and an analytical art, for contact issues, bolt-hole clearance and bolt in deformation. This model maes ossible to obtain the load in each bolt and lan stress field of comosite arts while avoiding the 6
ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Sain, -6 June 04 meshing of fasteners. The comromise between calculation time and result accuracy aears very interesting. References [] P. P. Camanho and F. L. Matthews, Stress analysis and strength rediction of mechanically fastened joints in FRP: a review, Comos. Part Al. Sci. Manuf., vol. 8, no. 6,. 59 547, 997. [] S. Chutima and A. P. Blacie, Effect of itch distance, row sacing, end distance and bolt diameter on multi-fastened comosite joints, Comos. Part Al. Sci. Manuf., vol. 7, no.,. 05 0, Jan. 996. [3] L. J. Hart-Smith, Bolted joint analysis for comosite structures, in Joining and Reair of Comosites Structures, Kansas City, MO, 004. [4] V. P. Lawlor, M. A. McCarthy, and W. F. Stanley, An exerimental study of bolt-hole clearance effects in double-la, multi-bolt comosite joints, Comos. Struct., vol. 7, no.,. 76 90, 005. [5] C. T. McCarthy, M. A. McCarthy, and V. P. Lawlor, Progressive damage analysis of multi-bolt comosite joints with variable bolt-hole clearances, Comos. Part B Eng., vol. 36, no. 4,. 90 305, 005. [6] R. E. Rowlands, M. U. Rahman, T. L. Wilinson, and Y. I. Chiang, Single- and multile-bolted joints in orthotroic materials, Comosites, vol. 3, no. 3,. 73 79, Jul. 98. [7] L. Ingvar Erisson, Contact stresses in bolted joints of comosite laminates, Comos. Struct., vol. 6, no. 3,. 57 75, 986. [8] E. Madenci, S. Sharayev, B. Sergeev, D. W. Olinger, and P. Shyryevich, Analysis of comosite laminates with multile fasteners, Int. J. Solids Struct., vol. 35, no. 5,. 793 8, May 998. [9] Y. Xiong, An analytical method for failure rediction of multi-fastener comosite joints, Int. J. Solids Struct., vol. 33, no. 9,. 4395 4409, Dec. 996. [0] A. Stricher, Tolérancement flexible d assemblages de grandes structures aéronautiques, École normale suérieure de Cachan - ENS Cachan, 03. [] F.-X. Irisarri, F. Laurin, N. Carrere, and J.-F. Maire, Progressive damage and failure of mechanically fastened joints in CFRP laminates - Part I: Refined Finite Element modelling of single-fastener joints, Comos. Struct., vol. 94, no. 8,. 69 77, 0. [] F.-X. Irisarri, F. Laurin, N. Carrere, and J.-F. Maire, Progressive damage and failure of mechanically fastened joints in CFRP laminates - Part II: Failure rediction of an industrial junction, Comos. Struct., vol. 94, no. 8,. 78 84, 0. [3] G. Gohorianu, Interaction entre les défauts d usinage et la tenue en matage d assemblages boulonnés en carbone/éoxy, Université Toulouse III, 008. [4] P. J. Gray and C. T. McCarthy, A global bolted joint model for finite element analysis of load distributions in multi-bolt comosite joints, Comos. Part B Eng., vol. 4, no. 4,. 37 35, Jun. 00. [5] C. T. McCarthy and P. J. Gray, An analytical model for the rediction of load distribution in highly torqued multi-bolt comosite joints, Comos. Struct., vol. 93, no.,. 87 98, 0. [6] P. J. Gray and C. T. McCarthy, A highly efficient user-defined finite element for load distribution analysis of large-scale bolted comosite structures, Comos. Sci. Technol., vol. 7, no.,. 57 57, 0. 7
ECCM6-6 TH EUROPEAN CONFERENCE ON COMPOSITE MATERIALS, Seville, Sain, -6 June 04 [7] C. Bois, H. Wargnier, J.-C. Wahl, and E. Le Goff, An analytical model for the strength rediction of hybrid (bolted/bonded) comosite joints, Comos. Struct., vol. 97, no. 0,. 5 60, 03. [8] E. Le Goff, Etude des transferts de charges dans les alésages comosites, alication aux renforcements ar bague frettée collée, Université Bordeaux, 03. [9] J. Lecomte, C. Bois, H. Wargnier, and J.-C. Wahl, Effect of geometric errors on the behaviour of multi-bolt comosite joints, in The 9th international conference on comosite materials, Montréal, Canada, 03. [0] S. G. Lehnitsii, Anisotroic lates, Gordon and Breach Science Publishers, New Yor, 968 8