Materials and Design 32 (2011) 1957–1966

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Materials and Design

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

A study of the braided corrugated hoses: Behavior and life estimation

H. Hachemi a,b,⇑, H. Kebir a, J.M. Roelandt a, E. Wintrebert b

a Roberval Laboratory, Université de Technologie de Compiègne (UTC), BP 20529, 60205 Compiègne Cedex, Franceb BOA Flexible Solutions, 14 rue de la Goutte d’Or F-02130 Fère-en-Tardenois, France

a r t i c l e i n f o

Article history:Received 14 July 2010Accepted 30 November 2010Available online 8 December 2010

Keywords:FatigueResidual stressBraid

0261-3069/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.matdes.2010.11.075

⇑ Corresponding author at: Roberval Laboratory, UCompiègne (UTC), BP 20529, 60205 Compiègne Cedex89.

E-mail address: hakim.hachemi@utc.fr (H. Hachem

a b s t r a c t

This work presents the virtual simulation of the hoses hydroforming; the main objective is to predictwhen and where cracks can appear during a cyclic loading.

A methodology has been proposed to investigate the effects of plastic strain and residual stress afterhydroforming on cyclic life fatigue.

First, an axisymmetric simulation of the hydroforming of flexible metal hoses was accomplished usingthe finite element method, then a cyclic loading is applied, finally the life cycle is estimated using a modelbased on Chaboche’s model.

The results are compared with experimental data, a good agreement is found if we take in account theresidual stress and the hardening due to hydroforming.

A mechanical behavior model has been developed to study the braid which is the second element of thebraided corrugated hoses; they are added to corrugated hoses in order to improve its radial and axialstiffness.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Flexible corrugated hoses of stainless steel (Fig. 1) are mechan-ical components which are used in many applications, for examplethey are used to minimize the effect of vibrations on piping and carengines, doing well for this purpose, these components can sufferdynamic loads from gas and liquid pulsation and fail.

It is well-known that the metallic material is subjected to largeirreversible deformation in hoses hydroforming, this leads to highstrain and high stress localization areas, these two parametershave great impact on cyclic life fatigue of the hydroformed hoses[1–12].

Significant advances have been made in recent years for obtain-ing more accurate and reliable determinations of residual stressdistributions. These include both experimental and numericalmethods [13–16].

The failures of the corrugated hoses frequently happen in theform of small holes or cracks, therefore the conditions of leak be-fore break is generally most frequent in prediction of damage; thisenables the reduction of the failure consequences in a workingenvironment [17]. Wang et al. [18] studied the effect of stampingon fatigue life FEM prediction using plastic strain and thicknessvariation Zapatero et al. [19] studied the influence of maximumload, the crack length and stress ration on the fatigue crack closure

ll rights reserved.

niversité de Technologie de, France. Fax: +333 44 23 46

i).

by means of finite element analysis. Matsui et al. [20] explored theinfluence of strain ratio on bending fatigue life and fatigue crackgrowth in TiNi shape-memory. Li et al. [21] used the finite elementmethod to simulate the cyclic stress/strain evolutions for multi-ax-ial fatigue life prediction. Marakami et al. [22] studied the effect ofhydrogen on cracks propagation of SUS316L flexible hoses ofhydrogen station, Marron et al. [23] dealt with the effect of formingin the design of deep drawn structural.

The objective of this study is to improve the fatigue analysisusing finite element method considering effects of hydroforming(residual stresses and plastic hardening) on cyclic life fatigue ofcorrugated hoses.

In addition to the accurate parameters of fatigue damage mod-els, the investigations of this work showed that the accurate esti-mations of the cyclic stresses, residual stresses and plastic strainsafter hydroforming are very important to have an accurate estima-tion of fatigue life, thus a performant element and a refined meshare required to do the analysis.

2. Hydroforming effects of the corrugated hose

The case selected in this study is a corrugated hose used in auto-mobile engines; the corrugated hose is manufactured from astraight tube. The original blank is a stainless steel tube (AISI316L), the mechanical properties are shown in Table 1 and thehardening curve is shown in Fig. 2, The initial thickness ofthe tubes 0.25 mm. A non-linear FEM code is used to simulatethe hydroforming process.

Fig. 1. Corrugated hose after hydroforming.

Table 1Mechanical properties of AISI 316L.

Young modulus 193000 MpaYield stress 250 MpaTensile strength 1170 MpaPoisson coefficient 0.3Density 7800 kg/m3

Fig. 2. Stress–strain curve: INOX 316L.

1958 H. Hachemi et al. / Materials and Design 32 (2011) 1957–1966

An eight-node axisymmetric element with nine point of inte-gration is used to simulate the hydroforming process, this elementis the most powerful element in axisymmetric calculus; it givesmore accurate results for less refined mesh both for geometricnon-linearity and plasticity [24]. The focus of this study is to in-clude the hydroforming effects of plastic strains and residual stres-ses in the subsequent fatigue FEM model. Fig. 3 shows the effectiveplastic strain and the Von Mises residual stress. The axisymmetricelement is used in the simulation of the hydroforming process forthe consideration of time saving.

The hydroformed hose is made by multiple steps (see Fig. 4),first the straight tube is fixed by tools called flanges, after that a

preforming step is made without tools displacements then a sec-ond forming, using the same pressure as in the preforming, withtools displacement is performed, finally the pressure is canceledand the tools are removed.

In order to validate our simulation, the geometrical dimensionsafter hydroforming are compared to the measured one; as we cansee in the Table 2, the Geometrical dimensions carried out from thesimulations are very close to the measured dimensions; in fact themaximum error does not exceed 1.2%.

3. Fatigue FEM analyses for the hydroformed tube

To study the fatigue behavior of corrugated hoses, we subjectthem to alternated cycles of axial loading of traction and compres-sion without internal pressure. Fig. 5 shows the hose after com-pression and elongation.

To take into account the tensorial character of the stresses, aflow surface of fatigue in terms of flow surface in plasticity is de-fined Eq. (1), chaboche has already defined a fatigue model for amulti-axial fatigue [25]:

ff ¼ AII � A�II ð1Þ

AII ¼12

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi32

rdevijmax � rdev

ijmin

� �rdev

ijmax � rdevijmin

� �r

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12ða1 � a2Þ2 þ ða2 � a3Þ2 þ ða3 � a1Þ2h ir

ð2Þ

The damage starts when ff becomes positive, rdevijmax;rdev

ijmin arerespectively the maximum and minimum deviatoric tensors ofstresses in a cyclic loading, the amplitudes of the principal stressesare defined as:

ai ¼ Dri=2 ð3Þ

The present model is based on the criteria of Sines [25,26], themost general criteria so we can write:

A�II ¼ rl0 ð1� 3b�rHÞ ð4Þ

where �rH is the average of the hydrostatic stress in a cycle load, r‘0

is the ultimate stress in alternative fatigue (when �r ¼ 0) and b is amaterial coefficient.

The damage evolution for a tensorial stress can be expressed asit is given for one dimension stress [25]:

dD ¼ ½1� ð1� DÞbþ1�aðAII ;�rH ;reqMaxÞ AII

Mð1� DÞ

� �B

dN ð5Þ

M ¼ M0ð1� 3b�rHÞ ð6Þ

a ¼ 1� aAII � A�II

ru � reqmax

� �ð7Þ

reqmax ¼ max

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi32

�rdev : �rdev

r !ð8Þ

reqMax ¼ Max1ffiffiffi2p ½ðr1 � r2Þ2 þ ðr2 � r3Þ2 þ ðr3 � r1Þ2�

12

� �ð9Þ

ru is the tensile strength, a, M0, b are material parameters definedby Wohler curves.

After integration of Eq. (5), the fatigue life Nf is defined as afunction of the amplitude of the stress:

Nf ¼AIIM

� ��b

ðbþ 1Þð1� aÞ ð10Þ

As in one dimension [25,26], we can introduce the influence of ini-tial hardening on the coefficients: ru;A

�II;M.

Fig. 3. Plastic strain and residual stress after hydroforming.

Fig. 4. Hydrofoming steps.

Table 2Geometrical dimensions for PARNOR� 1 in. and PARNOR� 6 in.

PARNOR� 1 in. (mm) PARNOR� 6 in. (mm)

Measure Simulation Measure Simulation

Inner diameter 25 24.95 150 149.95Thickness 0.20/0.24 0.22/0.25 0.45/0.485 0.47/0.5Outer diameter 36 36.01 174 173.8Pitch 7.1 7.0 15.70 15.60

Fig. 5. Stresses after compression and elon

H. Hachemi et al. / Materials and Design 32 (2011) 1957–1966 1959

aðrM; q; �rÞ ¼ 1� aAII � A�IIðqÞ

ruðqÞ � reqMax

� �ð11Þ

A�II ¼ r‘0ð1þ k1:ZðcÞÞð1� 3b�rHÞ ð12ÞruðqÞ ¼ ru0ð1þ k2zðcÞÞ ð13ÞMðqÞ ¼ M0ð1þ k3ZðcÞÞ ð14ÞZðcÞ ¼ ffiffiffi

cp ð15Þ

k1, k2, k3 are coefficients which are obtained from experiments, thevalues of ru0, rl0 were fixed from the experimental Wohler curves

gation for Xf = 6 mm (PARNOR� 1 in.).

Table 3Materiel coefficients.

Parameter rl0r‘0 k1 k2 k3 b M0 a b

Value 1170 Mpa 222 Mpa 0.4 2.2 1.6 5 1650 Mpa 0.9 0.25

1960 H. Hachemi et al. / Materials and Design 32 (2011) 1957–1966

[25], 316L Steel has the coefficients values shown in Table 3. For thetests with an initial hardening, c is equal to the initial effective plas-tic strain.

First we assess the life cycle fatigue at each integration point ofeach element of the modelized corrugated hose. The life cycle ofthe tube is the minimum of the fatigue lives for each integrationpoint. The stress used in life cycle estimation is the algebraicsum of the residual stress and the stress due to cyclic loading.the organigram of this method is shown in Fig. 6.

Fig. 7. Fatigue test (BOA group�).

4. Experiment results

In order to validate the model, we have performed some exper-iments, see Fig. 7.

Each hose used in these tests have 10 waves, for everydisplacement Xf, a sample of six hoses is used to get the mean lifetime.

The numbers of cycles indicated correspond to the appearanceof a crack which we can see by eyes in the corrugated tube.

Fig. 6. Fatigue estim

5. Comparison of estimations with experimental findings anddiscussion

Comparative results for two hoses (dimension 1 in. and 6 in.) atdifferent axial displacement Xf are presented in Figs. 8 and 9.

ation algorithm.

Fig. 8. Comparison tests/computed values (PARNOR� 1 in.).

Fig. 9. Comparison tests/computed values (PARNOR� 6 in.).

H. Hachemi et al. / Materials and Design 32 (2011) 1957–1966 1961

It is well seen that the computation results can be used to pre-dict the life fatigue estimation of tubes in a given loading condi-tion; in fact the estimated values are lower than those carriedout by experiment.

Fig. 10. Crack initiation area: simulation and experiment for PARNOR� 1 in.

Fig. 11. The braid use

The difference between the estimation results and the experi-mental results is due to several parameters, first The assumedassumptions in the simulation, for more correct results we musttake into account all the manufacturing processes of the tube insimulation (rolling, welding. . .etc.), these processes give residualstresses and strains which could be added to the hydroformingstrains and residual stresses, also the results obtained by experi-ment are for large cracks whereas those obtained by estimationare for micro cracks, secondly we can attribute the differences be-tween the experiment and computation results to the damagemodel used in calculations; indeed it is difficult to identify the con-stants of the model of damage with sufficient precision. Finally arefined mesh is required to get more precise stresses and strainswhich are very important in the estimation of cylic life fatigue.

As shown in Fig. 10, the calculated fragile area corresponds wellto the experiments

� it is located in the hollow of the wave, close to the blank, on theexternal surface of corrugated hose for the PARNOR� 1 in.� it is located in the hollow of the wave, on the interior surface of

the corrugated hose for the PARNOR� 6 in.

6. Braid modeling

The second part of our work is to model the braid which is thesecond most important part of the corrugated braided hoses. Thispart is used to improve the radial and axial stiffness of the tube.

Extensive investigation of textiles has been conducted these thelast two decades, Most of these efforts were concerned withweaves with orthogonal tows, modeling based or not on the finiteelement method have been developed to characterize the effectiveengineering properties [27–37] and few focused on braids [38–45],but the braids in the form of tubes, as shown in Fig. 11, are lessstudied especially to get a macro mechanical behavior.

The braid is manufactured by the diagonal intersection of sev-eral units of wires which are called spindles, in the conventionalmachine of braiding, half of the bundles turn clockwise and otherhalf in the counterclockwise direction, and different braids aremanufactured as shown in Fig. 12. [46,47].

In this study, we present a non-linear macro mechanical behav-ior for 2 � 2 helicoidal braid.

6.1. Linear elastic behavior of the braid, Hooke’s law

6.1.1. Density of the braidThe density of a braid is defined as the volume of the braid di-

vided by the volume of the enveloping cylinder:

n ¼N1 � N2

U2

cosðaÞ

ððDþ 5UÞ2 � D2Þð16Þ

where

N1: The number of spindlesN2: The number of wires of each spindleU: The diameter of wirea: The angle of braiding

d in experiment.

Fig. 13. Change of the coordinate system.

Fig. 12. Braiding procedure.

1962 H. Hachemi et al. / Materials and Design 32 (2011) 1957–1966

D: The external diameter of hose (internal diameter of thebraid))

6.1.2. Stiffness matrix of the braidBy using the Hook’s law and the definition of the density we

get:The stiffness matrix in the case of one spindle (in the global

coordinate system (y0, z0))

Cwiresljkl ¼

0 0 0 0 0 00 E � cos4 a E � sin2 a cos2 a E � cos3 a sina 0 00 E � sin2 a cos2 a E � sin4 a E � cos3 a sina 0 00 0 0 0 0 00 0 0 0 0 00 E � sin a cos3 a E � sin3 a cos a 0 0 E � cos2 a sin2 a

2666666664

3777777775� � �

e11

e22

e33

c12

c13

c23

2666666664

3777777775

By taking two spindles and adding the radial stiffness, we find thestiffness matrix of the braid in the global coordinate system(x0, y0, z0) (see Fig. 13):

Cbraidijkl ¼

E � n 0 0 0 00 2 � E � n � cos4 a 2 � E � n � cos2 a sin2 a 0 00 2 � E � n � cos2 a sin2 a 2 � E � n � sin4 a 0 00 0 0 0 00 0 0 0 00 0 0 0 0 2E

2666666664

6.2. Variation of the angle

When the corrugated hose is subjected to internal pressure,the braiding angle a decreases under the effect of thiselongation.

By means of some mathematical operations we can find a rela-tion between the variations of the angle a and the longitudinalstrain e22 in the global coordinate system (see Fig. 14b).

The longitudinal strain e22 is calculated from the length varia-tion of the braid.

00000

� n � cos2 a sin2 a

3777777775� � �

e11

e22

e33

c12

c13

c23

2666666664

3777777775

Fig. 14. Representative unit cell (left) and braiding angle change (right).

Fig. 15. Implementation in ABAQUS.

H. Hachemi et al. / Materials and Design 32 (2011) 1957–1966 1963

Fig. 16. Evolution of the braid during traction and numerical simulation results.

1964 H. Hachemi et al. / Materials and Design 32 (2011) 1957–1966

da ¼ e22 � sinðaÞ � cosðaÞ1þ e22 � cos2ðaÞ ð17Þ

With:

e22 ¼dpp

ð18Þ

6.3. The elongation of the braid yarns

An elongation dp of the braid causes automatically elongationsof the yarns.

Using some mathematical operations we can find a relation be-tween the yarn strain, the current braiding angle and the longitu-dinal strain:

OA0 ¼ cosða� daÞ � dP þ cosðdaÞ �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðpÞ2 þ ðPDÞ2

qð19Þ

ef ¼ cosða� daÞ � pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffip2 þ ðPDÞ2

q e22 þ cosðdaÞ � 1 ð20Þ

ef ¼ cosða� daÞ � cosðaÞ � e22 �ðdaÞ2

2ð21Þ

6.4. Variation of the braid diameter and length

When the pressure loading is applied the braid elongates with-out plastic deformation until it reaches a critical angle ac.

The relation between the initial diameter D0, the current radiusD, the current and initial angle a and a0, is obtained by using therepresentative unit cell (see Fig. 14a).

Fig. 17. Braid elongation/applied force.

H. Hachemi et al. / Materials and Design 32 (2011) 1957–1966 1965

D ¼ D0sinðb2Þsinðb0

2 Þ¼ D0

sinðaÞsinða0Þ

ð22Þ

The same thing can be done for the length:

L ¼ L0cosðb2Þcosðb0

2 Þ¼ L0

cosðaÞcosða0Þ

ð23Þ

The cell locks when S ¼ 0 and we get ac ¼12� arcsin

W‘

� �ð24Þ

where ‘ is the length of the unit cell measured along the tows and Wis the width of the spindles.

The model has been incremented in ABAQUS using the UMATsubroutine, as shown in Fig. 15.

A traction test on a universal testing machine was carried out tovalidate the developed model; the measures are taken from threedifferent positions, the Fig. 16 illustrates this test.

The Characteristics of the braid used in testing and simulationare:

Length of the braid(mm)

250

Diameter to bebraided (mm)

41

External diameter (mm) 43

Diameter of wire(mm)

0.4

Density (compactness) 0.54

Number of wire byspindles

10

Braiding angle 37.17�

Number of thespindles

48

Length of wire for 1 mof braiding

1.25

Braiding pitch (mm)

174 Mass of braid (kg/m) 0.6

As we can see in the force/elongation curves (see Fig. 17): we have avery good agreement until we reach 25 mm of elongation whichcorresponds to 10% of elongation, this divergence between thecurves is due to the lock of the cells, this lock induce plasticityand hard contact of wires.

7. Conclusions

On the basis of the research on corrugated hoses, this paper car-ried out simulations on hydroforming, estimation cyclic life fatiguethen modeling braid behavior under external loading, and the fol-lowing conclusions were drawn:

(a) In this work a methodology for estimating cyclic life fatiguehas been developed, as the elongation increase the number

of cycles decreases, taking into account residual stressesallows more accurate results, the numerical estimation arelower than the experimental results (2–3 times). The locali-zation of the crack weak area was detected, this presentedmodeling shows good agreement with experimental resultsand may be used by hoses designers to predict and improvehydroformed hoses performance.

(b) In the second part of this work a modal has been developedto simulate the behavior of the braid subjected to axial loads,the curve force/elongation shows very good agreement withexperiment until 10% of elongation (25 mm) where we havethe lock of the cells of the braid.

(c) This modeling can be used to study the braided corrugatedhoses under internal pressure to estimate the fatigue life ofbraided hoses. The modeling could be improved by takinginto account the plasticity of the wires after cells lock.

References

[1] Webster GA, Ezeilo AN. Residual stress distributions and their influence onfatigue lifetimes. Int J Fatigue 2001;23 [S375-S383STP 1004, 1988].

[2] Glinka G. Residual stresses in fatigue and fracture: theoretical analyses andexperiments. In: Niku-Lari A, editor. Advances in surface treatment andresidual stresses. Pergamon Press; 1987. p. 413–54.

[3] Webster GA. In: Lieurade HP, editor. Fatigue and stress. France: IITTInternational, Gournay-sur-Marne; 1989. p. 9–20.

[4] Suresh S. Fatigue of materials. Cambridge University Press; 1991.[5] Newman JC. Fatigue-life prediction methodology using a crack-closure model.

Eng Mater Technol 1995;117:433–9.[6] Almer JD, Cohen JB, Winholtz RA. The effects of residual macrostresses and

microstresses on fatigue crack propagation. Metall Mater Trans1998;29A:2127–36.

[7] Webster GA, Ezeilo AN. Principles of the measurement of residual stress byneutron diffraction. In: Furrer A, editor. PSI proceedings of the 96002. ISSN1019-6447, new instruments and science around SINGQ, November 1996. p.217–34.

[8] Sadananda K, Vasudevan AK. Short crack growth behavior. In: Piascik RS et al.,editors. Fatigue and fracture mechanics, vol. 27. ASTM-STP; 1997. p. 301–16.1296.

[9] Sadananda K, Vasudevan AK. Application of unified fatigue damage approachto compression–tension region. Int J Fatigue 1999;21(Suppl. 1):263–73.

[10] Moshier MA, Hillberry BM. The inclusion of compressive residual stresseffects in crack growth modeling. Fatigue Fract Eng Mater Struct 1999;22(2):519–26.

[11] Wang H, Buchholz F-G, Richard HA, Jagg S, Scholtes B. Numerical andexperimental analysis of residual stresses for fatigue crack growth. ComputMater Sci 1999;16:104–12.

[12] Almer JD, Cohen JB, Moran B. The effect of residual macrostresses andmicrostresses on fatigue crack initiation. Mater Sci Eng 2000;A284:268–79.

[13] Webster GA. ECRS-5, Holland. Role of residual stress in engineeringapplications. September 1999. Materials Science Forum, 347–349, 1–9.Switzerland: Trans Tech Publ; 2000.

[14] Webster GA, Ezeilo AN. Neutron scattering in engineering applications.Physica B 1997;234–236:949–55.

[15] Tauchert TR, Webster GA, Reed RC. Thermoelastoplastic analysis of a stainlesssteel plate considering phase transformations. In: Crespo da Silva MRM,Mazzilli CEN, editors. Mechanics Pan-America 1993. Appl Mech Rev 1993; 46(Part 2): S12–S20.

[16] Tauchert TR, Webster GA, Ezeilo A. Residual stresses in a surface-heat-treatedsteel specimens. In: Godoy LA, Idelsohn SR, Laura PAA, Mook DT, editors.Applied mechanics in the Americas, vol. III. Santa Fe (Argentina): AAM &AMCA; 1995. p. 185–9.

[17] Wener Aichberger, Harlard Riener, Helmut Dannbauer. Regarding InfluencesProcesses on Material Parameters in Fatigue Life Prediction. MAGONA POWERTRAIN-Engineering Center Steyr GmbH&CoKG, St. Valentin, Austria 2007-01-1650.

[18] Wu-rong Wang, Guanlong Chen, Zhong-qin Lin. The study on the fatigueFEM analysis considering the effect of stamping. Mater Des 2009;30:1588–94.

[19] Zapatero J, Moreno B, Gonzalez-Herrera A. Fatigue crack closure determinationby means of finite element analysis. Eng Fract Mech 2008;75:41–5.

[20] Ryosuke Matsui, Yoshiyasu Makino, Hisaaki Tobushi, Yuji Furuichi, FusahitoYoshida. Influence of strain ratio on bending fatigue life and fatigue crackgrowth in TiNi shape-memory alloy thin wires. Mater Trans 2006;47:759–65.

[21] Li B, Reis L, de Freitas M. Simulation of cyclic stress/strain evolutions formultiaxial fatigue life prediction. Int J Fatigue 2006;28:451–8.

[22] Murakami Y, Kanezaki T, Fukushima Y, Tanaka H, Tomuro J, Kuboyama K, et al.Failure analysis of SUS316L flexible hose for hydrogen station and fatigue lifeprediction method. The Japan Society of Mechanical Engineers, No. 08-0544;2009.

1966 H. Hachemi et al. / Materials and Design 32 (2011) 1957–1966

[23] Marron Guy C, Patou Pascal F. Effect of forming in the design of deep-drawnstructural parts. In: Proceedings of the 1998 TMS annual meeting, February1998. p. 25–36.

[24] ABAQUS Documentation V 6.7.1.[25] Lemaitre J, Chaboche JL. Mécanique des matériaux solides. 3éme édition; 2001.[26] Chaboche JL. Sur les effets d’interaction de l’écrouissage et de

l’endommagement dans l’acier 316L. Rech. Aérosp, Mi–Juin 1980.[27] Bathias C, Bailon JP. La fatigue des matériaux et des structures. 2éme édition,

Hermès, Paris; 1997.[28] Dumonta François, Hiveta Gilles, Rotinata René, Launay Jean, Boissea Philippe,

Vacherb Pierre. Field measurements for shear tests on woven reinforcements.Mécanique Ind 2003;4:627–63.

[29] Cox BN, Flanagan G. Handbook of analytical methods for textile composites.NASA CR 4570; 1997.

[30] Tan P, Tong L, Steven GP. Modeling for predicting the mechanical properties oftextile composites – a review. Composites: Part A 1997;28A:903–22.

[31] Bystron J, Jekabsons N, Varna J. An evaluation of different models forprediction of elastic properties of woven composites. Composites: Part B2000;31B:7–20.

[32] Ishikawa T, Chou T-W. Stiffness and strength behavior of woven fabriccomposites. J Mater Sci 1982;17:3211–20.

[33] Naik NK, Shembekar PS. Elastic behavior of woven fabric composites: I –lamina analysis. J Compos Mater 1992;26:2196–225.

[34] Whitcomb JD, Tang X. Routine three-dimensional analysis of wovencomposites. In: Proceedings of the 12th international conference ofcomposite materials. Paris, France; 1999.

[35] Tang X. Micromechanics of 2D woven composites, Ph.D. Dissertation,Department of Aerospace Engineering, Texas A&M University, CollegeStation, Texas, December; 2001.

[36] Whitcomb JD, Chapman CD, Tang X. Derivation of boundary conditions formicromechanics analyses of plain and satin weave composites. J ComposMater 2000;34(9):724–47.

[37] Tang X, Whitcomb JD. General techniques for exploiting periodicity andsymmetries in micromechanics analysis of textile composites. J Compos Mater2003;37(13):1167–89.

[38] Whitcomb JD, Tang X. Effective moduli of woven composite. J Compos Mater2001;35(23):2127–44.

[39] Tang X, Whitcomb JD, Goyal D, Kelkar AD. Effect of braid angle and wavinessratio on effective moduli of 2�2 biaxial braided composites. In: Proceedings ofthe 44th AIAA/ASME/ASCE/AHS structures, structural dynamics, and materialsconference, April 7–10, 2003. Norfolk, Virginia, AIAA-2003-1877; 2003.

[40] Ma CL, Yang JM, Chou TW. Elastic stiffness of three-dimensional braided textilestructure composites. In: Proceedings of the composite materials: testing anddesign (7th conference), ASTM893; 1986.

[41] Naik RA. Failure analysis of woven and braided fabric reinforced composites. JCompos Mater 1995;29:2334–63.

[42] Byun J-H. The analytical characterization of 2-D braided textile composites.Compos Sci Technol 2000;60:705–16.

[43] Cox BN, Carter WC, Fleck NA. A binary model of textile composites: Iformulation. Acta Metal Mater 1994;42:3463–79 [(2009) Nihon Kikai GakkaiRonbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers,Part A, 75 (1), pp. 93–102].

[44] Miravete A, Clementeand R, Castejon L. Macro mechanical analysis of 3-Dtextile reinforced composites. In: Miravete A, editor. 3-D Textilereinforcements in composite materials. Cambridge (England): WoodheadPublishing; 1999.

[45] Márquez A, Fazzini PG, Otegui JL. Failure analysis of flexible metal hose atcompressor discharge. Eng Fail Anal 2009;16(6):1912–21.

[46] Potluri P. Geometrical modeling and control of a triaxial braiding machine forproducing 3D performs. Composites: Part A 2003;34:481–92.

[47] Tada Makiko. Structure and machine braiding procedure of coupled squarebraids with various cross sections. Composites: Part A 2001;32:1485–9.