Composite Structures 94 (2011) 246–252

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Composite Structures

journal homepage: www.elsevier .com/locate /compstruct

An efficient design method for multi-material bolted jointsused in the railway industry

G. Catalanotti a,⇑, P.P. Camanho a, P. Ghys b, A.T. Marques a

a DEMec, Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugalb ALSTOM Transport, Rue Albert Dhalenne, 48, 93482 Saint-Ouen, France

a r t i c l e i n f o

Article history:Available online 1 July 2011

Keywords:A. Hybrid structuresB. Bolted jointsC. Fast design tools

0263-8223/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.compstruct.2011.06.018

⇑ Corresponding author.E-mail address: giuseppe.catalanotti@fe.up.pt (G. C

a b s t r a c t

A methodology to design and analyze multi-material bolted joints in hybrid train structures is presented.This methodology enables the prediction of the response of a multi-material bolted joint in a shortamount of time and it is suitable to be used for large structures, where the number of bolts can be veryhigh. The method developed is applied to a real industrial case which consists on the connection betweenthe roof and the side of a carbody shell train structure. Experimental tests are performed on a full-sizesub-component. The comparison between the experimental data and the numerical results confirmsthe accuracy of the method.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The use of composites as the main load-carrying structures oftransport vehicles is often limited to the aerospace, marine andautomotive industries. While it is possible to find in the railwayindustry some examples of the use of composites as the mainload-carrying structures, they are mainly used in non-structuralparts (e.g., cab, skirts, interiors). This is justified by the fact thatthe use of composites requires an investment in know-how thatthe railway industry is not currently willing to make, and for thisreason metals are preferred.

However, the use of composites is vital for the future of the rail-way industry. In fact, the advantages of composites are numerous,namely:

� the reduction of the weight and, consequently, of the energynecessary for the railway transportation;� the reduction of the cost of manufacturing: it is possible to

obtain a simplification of the parts that form a structure and,consequently, a reduction of the time and of the costs requiredfor the assembly of the final structure;� the reduction of the recurring costs, because composite struc-

tures normally require less maintenance when compared withmetallic structures.

In the railway industry, the principal issue related with the useof composites is to find a way to substitute an original structure(that generally is manufactured in aluminum or steel) with another

ll rights reserved.

atalanotti).

one, manufactured using composites which provides the same orbetter performances. Obviously, the new technical solution canonly be accepted if gains in both mass and cost are obtained. There-fore, if the composite version of a structure does not ensure thesegains the solution cannot be accepted. Consequently, it is impor-tant to make a comparison between the different technologies toevaluate which one gives the best performance in reduction ofweight and cost. Three different carbody shells can be compared[1]:

� the carbody shell manufactured completely in aluminum (alu-minum carbody shell, standard);� the carbody shell manufactured completely in composites

(composite carbody shell);� the carbody shell manufactured using steel and composites

(hybrid carbody shell).

It was shown in [1] that the hybrid solution gives the best per-formances. It was estimated that an hybrid carbody shell leads to again in mass of about 12–24% and a gain in cost of about 20% [1]. Inaddition, improved performance can be obtained by developingaccurate and efficient design methods.

Similarly to other composite structures, one of the main designdrivers in hybrid structures is the calculation of the strength andthe response of the hybrid joints [2–6]. Normally, the predictionof the stiffness of hybrid structures is straightforward; the mainchallenge in the design of such of structures is the prediction offailure, which typically occurs at stress concentrations such asbolted joints.

It has been shown that three-dimensional numerical simula-tions can predict with accuracy both the value of the first peak load

rot

roc

Characteristiccurve

Y

X

Loadingdirection

Fig. 2. Characteristic curve.

G. Catalanotti et al. / Composite Structures 94 (2011) 246–252 247

and the extent and location of damage zones [7]. However, thecomputational cost of a 3D numerical simulation and the expertizenecessary to set it up are not suitable for large-scale industrialapplications.

A reliable, fast and easy method to predict the mechanical re-sponse of large-scale structures in an industrial environment is re-quired. Therefore, the objective of this paper is to define asimplified two-dimensional methodology to design joints betweendissimilar materials (hybrid joints) for train structures. Such amethodology should identify the critical joints, the failure modeand the failure load of hybrid structures.

2. Stress analysis and strength prediction in the compositestructure

Camanho and Lambert [8] proposed a methodology that enablesthe prediction of the elastic limit (i.e., of the first ply failure load)and of the ultimate failure load of composite bolted joints in ashort amount of time. The elastic limit is predicted using theLaRC03 failure criteria [9], while the ultimate failure is predictedusing a modification of the Yamada–Sun failure criterion [10]. Thismethodology uses the Complex Variable Theory of Elasticity(CVTE) to obtain analytical solutions for the stress distributionaround the hole avoiding the use of the Finite Element Method.Using the Classical Lamination Theory [11] the stress distributionis calculated for each ply.

Considering plane stress, the stress distribution around the holeis based on the use of the Airy stress function F and on the follow-ing equations that satisfy equilibrium:

rxx ¼@2F@y2 ð1Þ

ryy ¼@2F@x2 ð2Þ

rxy ¼ �@2F@x@y

ð3Þ

The general expression for the function F depends upon the rootof the characteristic equation and is defined as:

F ¼ 2R F1ðZ1Þ þ F2ðZ2Þf g ð4Þ

where F1(Z1) and F2(Z2) are analytical functions of the complex vari-ables Z1 = x + R1y and Z2 = x + R2y respectively.

The methodology used to define the function Fi(Zi) is based onthe work done by Garbo and Ogonowski [12]. The stress distribu-tion is considered as obtained by the superposition of the in-planebearing and by-pass loads as shown in Fig. 1.

The stress distribution of a laminate with a loaded hole isobtained superimposing two stress distributions: a cosinusoidal

Fig. 1. Superpositio

distribution of pressure on the contact zone of the hole (in-planebearing), and the stress distribution of a laminate with an openhole remotely loaded.

The resulting stress distribution is a good approximation of thereal stress state when the ratio w/d P 4 and e/d P 3, i.e. whenbearing failure mode is present. It should be noted that the stressdistribution is calculated under the hypothesis that no bending ispresent in the mid-plane of the laminate and when the pressurecan be assumed cosinusoidal (this happens when the laminate isquasi-isotropic and the clearance is small).

Equipped with the results of the stress analysis, it is now possi-ble to predict the elastic domains and the strength of the compos-ite bolted joint. The procedure used here follows the strengthprediction method proposed in [8]. For completeness, a summaryof the strength prediction method is presented in the following.

The prediction of the elastic domain is performed using theLaRC03 failure criteria [9], applying the corresponding equationsto the components of the stress tensor calculated for each ply usingthe previously described stress analysis. It is clear that, generally,first ply failure does not imply structural collapse. Therefore, thestrength prediction method used here is based on the applicationof failure criteria along a characteristic curve (Fig. 2), as proposedby Chang et al. [13].

The parameters rot and roc shown in Fig. 2 are respectively thecharacteristic distances in tension and in compression that areused to define the characteristic curve as:

rðhÞ ¼ Rþ rot þ ðroc � rotÞ cos h ð5Þ

n of load cases.

Fig. 4. Coupled and contour nodes.

Table 1Mechanical properties of the unidirectional ply.

E1 (MPa) 37,500E2 (MPa) 3000m12 0.35G12 (MPa) 2715XT (MPa) 1365XC (MPa) 1289YT (MPa) 62YC (MPa) 168SL (MPa) 20ST (MPa) 19

Table 2Relevant parameters of the bolts.

Ab 19.6 mm2

As 13.9 mm2

av 1.25cM2 0.6fub 1300 MPak2 0.9

Fig. 3. Proposed methodology.

248 G. Catalanotti et al. / Composite Structures 94 (2011) 246–252

where R is the radius of the hole.Final failure of the composite joint is predicted using the Yam-

ada–Sun failure criterion [10] applied to the material points lo-cated on the characteristic curve:

r11

XT

� �� 1 6 0; r11 > 0 ð6aÞ

r11

XC

� �2

þ r12

SL

� �2

� 1 6 0; r11 6 0 ð6bÞ

where XT is longitudinal tensile strength, XC is the longitudinal com-pressive strength and SL is the longitudinal shear strength.

The model proposed by Camanho and Lambert [8] was imple-mented in a FORTRAN code, FastComp [14], that can easily be usedin an industrial environment.

Fig. 5. Scheme of the

3. Strength prediction of the bolts

The failure indexes for the bolts (shear, traction, combinedshear/traction) are defined following NF EN 1993-1-8 norm [15].The failure index for shear, FIs, is:

FIs ¼ Ps=PRs ð7Þ

with:

sub-component.

Fig. 6. Loading configuration.

Fig. 7. Equipment setup.

Fig. 9. Load vs. displacement curve.

G. Catalanotti et al. / Composite Structures 94 (2011) 246–252 249

PRs ¼

av fubAb

cM2ð8Þ

where Ps is the shear load acting on the bolt, PRs is the shear load at

failure, Ab is the gross section area of the bolt, av is a parameter thatdepends on the class of the bolt, cM2 is the coefficient of assemblageand fub is the ultimate tensile strength of the bolt. For tension, thefailure index FIt is calculated as:

FIt ¼ Pt=PRt ð9Þ

Fig. 8. Connections between the sub-co

with:

PRt ¼

k2fubAs

cM2ð10Þ

where Pt is the tensile load acting on the bolt, PRt is the tensile load

at failure, As is the tensile stress area of the bolt, and k2 is a param-eter that is equal to 0.63 for countersunk bolts and 0.9 otherwise.The failure index for the combining presence of shear and traction,FIst, is calculated following the European Norm EN 1993-1-8 [15]:

FIst ¼ FIs þFIt

1:4ð11Þ

4. Proposed methodology

When the number of bolts is high the calculation of large multi-material train structures becomes complex and time consuming.The 2D methodology proposed here to solve this problem has thefollowing characteristics that are fundamental for an industrialenvironment:

� the method is fast;� different failure criteria can be implemented (for composite

parts, metal parts, bolts and rivets);� the method uses automatically the results of the FE analysis.

The numerical implementation of the model is done using Py-thon 2.6 [16] and Abaqus CAE [17]. Fig. 3 shows the flowchart ofthe methodology proposed to analyze large-scale hybrid trainstructures.

mponent and the testing machine.

Fig. 10. Failure modes of the multi-material sub-component.

Fastener 1 (nodes: 4334−20708)

Fastener 2(nodes: 4329−20711)

Omega beam

Side of thecarbody shell

Fig. 11. FE model of the sub-component.

Fig. 12. Determination of the characteristic lengths.

250 G. Catalanotti et al. / Composite Structures 94 (2011) 246–252

The model of the structure is generating using Abaqus CAE [17].After the creation of the FE model, a Python pre-processing routineis launched. This routine modifies the Abaqus [17] input file to ob-tain, during the post-processing, the relevant parameters that areused in the strength prediction method. These parameters arethe forces at each bolt and the forces per unit length applied inthe composite part in the vicinity of each bolt. This procedure iscompletely automatic and does not require the manual input ofnew data.

Afterwards, Abaqus [17] solves the FE model and an outputdatabase file is obtained. A second Python routine using the Aba-qus output database [17] is launched. The Python routine uses asinput the characteristic distances for each material section and cal-culates for each bolt the value of the bearing load, the by-pass loadand the orientations of each load.

Each bolt is represented by a kinematic constraint applied to thenodes located at the connection points.

For each node it is possible to consider a path of nodes that liearound the coupled node and the elements attached to them.Knowing the nodal forces it is possible to compute the bearingand the by-pass load. Fig. 4 shows1 the coupled node (in red),the contour nodes that lie in a path around the coupled node (inorange), and the attached elements.

Finally, for each bolt, the Python routine call the FastComp [14]software and computes the failure indexes for each material con-sidering both the elastic limit and the ultimate failure. In addition,

1 For interpretation of color in ‘Figs. 1–12’, the reader is referred to the web versionof this article.

the failure indexes for each bolt are computed using the equationsshown in point Section 3.

5. An industrial case study

An application of the proposed methodology to design multi-material joints of a sub-component of a train-structure will be de-scribed in the following points.

Fig. 13. Failure indexes as a function of the applied load.

Fig. 14. Load vs. displacement: comparison between predictions and experiments.

G. Catalanotti et al. / Composite Structures 94 (2011) 246–252 251

5.1. Sub-component design and manufacturing

The design of the industrial sub-component is shown in Fig. 5,where the connection between the side of the carbody shell (insteel, 1 in Fig. 5a) and the omega beam of the roof (in glass-fiber/epoxy, 2 in Fig. 5a) is shown.

The lay-up of the laminate is [(0/±45)6/0]s, where 0� corre-sponds to the longitudinal direction of the omega beam. The nom-inal thickness of the composite beam in the vicinity of the holes isequal to 11.8 mm. The omega beam was manufactured using thetechnique of the resin infusion. The mechanical properties of theunidirectional lamina (glass-fiber was supplied by SELCOM) areshown in Table 1, where E1 is the longitudinal Young’s modulus,E2 is the transverse Young’s modulus, m12 is the Poisson’s ratio,G12 is the shear modulus, XT is longitudinal tensile strength, XC isthe longitudinal compressive strength, YT is the transverse tensilestrength, YC is the transverse compressive strength, SL is the longi-tudinal shear strength and ST is the transverse shear strength.

The connection is made using the 5 mm UNBRAKO bolts (3 inFig. 5a). It should be noted that the torque used to install the boltsis very low [18] and therefore the bolts work in shear and not intraction (as normally occurs in metal structures). This means thatfor this type of application the use of bolts or rivets is indifferent.The relevant parameters used for the calculation of the failure in-dexes of the bolts are reported in Table 2.

5.2. Testing

To study the behavior of the joint under the bearing failuremode, the sub-component is tested as shown in Fig. 6. As the steelpanel is very flexible, the load has to be applied using a hinge in or-der to guarantee a predominant shear stress field on the plane ofthe bolts.

Fig. 7 shows the experimental setup of the Instron testing ma-chine used to test the sub-component. A 100 kN load cell was usedin a A1675-1016 servo-hydraulic actuator with a dynamic loadcapacity of 100 kN.

Fig. 8 shows the solution used to connect the component to thetest fixture. On the top, the component is connected to the mainframe (Fig. 8a). Bolts are used in conjunction with a drilled steel-plate to prevent damage in the composite during loading.

Fig. 8b shows the connection at the bottom of the sub-compo-nent. An hinge was designed to connect the component to thecylinder of the servo-hydraulic machine. The hinge allows testingthe sub-component in the presence of misalignment of the loadrig.

To reduce the value of the peak-load during the test, only twobolts were used to connect the two parts of the sub-component.The tests were performed in displacement control and a speed of1 mm/min was used.

Fig. 9 shows a representative load–displacement curve obtainedduring the experimental test compared with the elastic load–dis-placement curve (shown in red). The first non-linearity point isapproximatively for Pnl � 15,000 N and the peak-load isPmax = 25,800 N.

When the load P reaches the critical value Pnl the compositestart to fail (i.e. it reaches its elastic limit). The failure mode is bear-ing as shown in Fig. 10a. At the same load, also the steel panelexhibits bearing failure in the proximity of the bolts as shown inFig. 10b. Finally, when the load reaches the peak-load Pmax the boltsfail (see Fig. 10c) because of the combination of shear and tractionapplied.

Generally, in design, the elastic limit is considered as the limitcondition and not the ultimate failure of the bolt. The methodologydescribed in the following will also enable the prediction of theload at which the composite start to fail (i.e. the value of Pnl).

5.3. Numerical model

The numerical model of the sub-component was performedusing Abaqus CAE [17]. The corresponding FE mesh is shown inFig. 11. The two parts were connected together thanks to two bolts,indicated as Fastener 1 and Fastener 2, that were modeled ascoupled constraint. S4 general-purpose shell elements were used.Frictionless contact conditions were imposed between the twoparts.

The characteristic lengths were determined numerically usingthe methodology proposed by Kweon et al. [19] for two configura-tions: load applied in 0� and in 90� directions. Fig. 12 shows thelaminate mean stress as a function of the distance from the holeedge, along the bearing and the net-tension plane for compressionand tension respectively when an arbitrary load is applied. Therespective characteristic lengths for the different configurationsare calculated using Kweon’s model [19] as:

rot j0 ¼ 1:3 mm rotj90 ¼ 1:0 mm ð12Þrocj0 ¼ 0:4 mm rocj90 ¼ 1:0 mm ð13Þ

It should be highlighted that characteristic lengths depend on theloading direction. However, as usually quasi-isotropic compositesare used, the characteristic lengths can be considered independentof the load direction. Given that in the present case the material isnot quasi-isotropic and there are no alternative methods to com-

252 G. Catalanotti et al. / Composite Structures 94 (2011) 246–252

pute the characteristic lengths for an arbitrary direction, the charac-teristic length for a general load direction are computed simplyusing a linear interpolation based on the values shown in (12)and (13).

5.4. Comparison between predictions and experimental results

Fig. 13 shows the failure indexes as a function of the appliedload computed numerically. The failure indexes reported for thebolts are calculated using Eq. (11). The failure indexes reportedfor the composite are related to the Fastener 2 that, as clearlyshown in Fig. 13, is the critical one.

The model predicts:

� the onset of the damage in the composite at a load of 14,670 N(Fastener 2);� the fracture of the composite at a load of 23,770 N (Fastener2);� the fracture of the bolt (peak-load) at a load of 25,250 N.

The predictions are shown in Fig. 14 together with the experi-mental load–displacement curve. It is observed that the predic-tions agree very well with the experimental data. The predictedcomposite elastic limit corresponds to the first non-linearity pointin the load vs. displacements curve. The peak load is well predictedwith an error lower than 2.5%.

6. Conclusions

The methodology presented here is able to predict the onset ofdamage and the strength of a multi-material structure, wheremechanically fastened joints are used. The method is suitable tobe used in an industrial environment because it is fast, reliableand easy to use. A full-size sub-component has been tested andthe predictions were compared with the experimental results.Good agreement was found between the predicted damaged onsetand peak load and the corresponding experimental values. Themethod has the drawback of requiring the characteristic distances,which have to be calculated for each lay-up.

Acknowledgement

The first author acknowledges the financial support of the Euro-pean Commission under Contract No. MRTN-CT-2005-019198.

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