Une formulation numerique pour Ia caracterisation de Ia deformation des tissus composites par mise en forme
Keywords:
composites, warps and weft fibres behaviour, resin behaviour, shaping processes, corotational formulation, finite strains, truss finite element and membrane finite elementAbstract
High performance reinforced composite structures are generally obtained by shaping process. These reinforced composites are used in aeronautical and automotive industries. The proposed study concerns the simulation of the shaping process and permits to determine if the deformation operation is possible before manufacturing of tools. The numerical approach is proposed to model the behaviour of the prep reg woven fabric during the forming deformation. The global behaviour of composite fabric is modelled by a linear truss element system representative of warp and weft fibres behaviour and a isotropic elastic (or viscoelastic) membrane representative of resin behaviour. Comparisons with experiment results and simulations prove the efficiency of the proposed model.
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References
[BAS 89] BASER G., "A Mechanical Approach to the Determination of the geometry of a
woven fabric and to analysis of subsequent changes in the geometry. Part 2: the
development of a geometry of plain-woven fabric in the loom state and a theory of
weaving contractions", J. Text. lnst, 1989, Vo180 N" 4, p. 521-534.
[BEL 98] BELHOUS S., CHEROUAT A. & BILLOET J.L., ''Two-component finite element model
for the simulation of shaping prepreg woven fabric", 2"d International Conference on
Integrated Design and Manufacturing in Mechanical Engineering, Compiegne 1998,
Vol 2, p. 523-530.
[BER 88] BERGSMA O.K & HUISMAN J., "Deep drawing of fabrics reinforced thermoplastics",
Proceeding of the 2nd int. Conf on Computer Aided Design in Composite Material
Technology, 1988. p. 323-333.
[B1L 93] BILLOET J.L., Introduction aux materiaux composites a hautes performances,
Teknea, 1993.
[BIL 96] BILLOET J.L., Contribution a Ia Comprehension des Problemes en Grandes
Transformations, Rapport interne LM2S ENSAM, Paris, 1996.
[BIL 99] BILLOET J.L. & CHEROUAT A., "Numerical behaviour of prepreg woven fabric for
the simulation of shaping deformation", Proceeding of Numeslzeet'99, The 4th Int. Conf.
and Workshop on Numerical Simulation of 3D sheet Forming Processes, Vol I, p. 5.67-
, Besanr;on, 1999.
[BLA 93] BLANLOT R., 8ILLOET J.L. & GACHON G., << Modelisation du comportement
mecanique non lineaire de tissus preimpregnes en phase non-polymerisee >>, Actes du I r
Congres Franrais de Mecanique, 1993, Vol 4, p. 125-128.
[BLA 96 a] BLANLOT R. & BILLOET J.L., "Simulation of the shaping of woven fabrics",
/CCE/3 New Orleans, 1996. p.ll7-118.
[BLA 96 b] BLANLOT R. & BILLOET J.L., << Loi de comportement orthotrope evolutive pour Ia
simulation de Ia mise en forme des tissus composites >>, JNC 9, 1996, p. 761-772
94] BOISSE P., CHEROUAT A., GELIN. J.C. & SABHI H., <
composites par le procede RTM simulation numerique de I' operation d'emboutissage >>;
JNC9 1994 Volt, p. 95-104.
97] 80ISSE P., BORR M., 8UET K. & CHEROUAT A., "Finite element simulation of textile
composite forming including the biaxial fabric behavior", Composite Part B Engineering
Journal,1997, W 28 p. 453-464.
[BOR 95] BORR M. CHEROUAT. A., & GELIN J.C., "Modelling large biaxial deformation of
glass fibres fabrics and application to shaping processes", Euromeclz Symposium 334,
Lyon, 1995, p. 129-139.
[CHE 94] CHEROUAT A., Simulation numerique du preformage des tissus de fibres de verre
par Ia methode des elements finis, these de Doctoral de I'Universite de Franche Comte,
[CHE 95] CHEROUAT A., GELIN J.C, BOISSE P. & SABHI H.,<< Modelisation de l'emboutissage
des tissus de fibres de verre par Ia methode des elements finis >>, Revue Europeenne des
Elements finis, Vo14, W2, 1995, p. 159-182.
[CHE 98] CHEROUAT A., BILLOET J.L. & BELHOUS S., "New Finite element approach for the
simulation of shaping prepreg woven fabric", Fifth International Conference on
Composites Engineering, ICCE 5, Las Vegas USA, 1998, p. 181-182.
[CHE 99] CHEROUAT A. & BILLOET J.L., "Computational simulation of the shaping process of
reinforced composite fabric by the finite element method", Proceeding of Numeslzeet'99,
The 4th Int. Conf. and Workshop on Numerical Simulation of 3D sheet Forming
Processes, Vol I, p. 573-578, Besanr;on, 1999.
[CUR 83] CURTIN M.E., SPEAR K., "On the relationship between the logarithmic strain rate
and the stretching tensor", lnt 1. Solids Structllres, Vol 19, W 5, p. 437-444,1983.
[DAL 94] DALLEMAGNE G. & BLANLOT R., «Identification des viscosites dynamiques
complexes d'un pre-polymere epoxyde pour modeliser Ia mise en a:uvre des tissus preimpregnes
>>, JNC/0, 1994, p. 45-58
[GAY 96] GAY D. & CARRONNIER D.,« Approche integree du RTM >>,Revue des Composites
et des materiaux Avances, Vol6, 1996, Hermes.
(GEL 96) GELIN J.C., CHEROUAT A, BOISSE P. & SABHI H., "Manufacture of thin composite
structures by the RTM process: Numerical simulation of the shaping operation",
Composites Science and Technology 56,1996, p. 711-718.
(GIL 93 a) GILORMINI P., ROUDIER P. & ROUGEE P., Utilisation des deformations cumulees
tensorielles dans l'analyse du cisaillement simple de materiaux anisotropes, A.C.
Academic des Sciences Paris, 316, Serie II, 1993, p. 1659-1666.
(GIL 93 b) GILORMINI P., ROUDIER P. & ROUGEE P., Les deformations cumulees tensorielles,
A.C. Academic des Sciences Paris, 316, Serie II, 1993, p. 1499-1504.
[GIL 93 c) GtLORMINI P., Sur les referentiels locaux objectifs en mecanique des milieux
continus, A.C. Academic des Sciences Paris, 316, Serie II, 1993, p. 1153-1159.
[GIL 93 d) GILORMINI P.& ROUDIER P., Abaqus and Finite Strain, Rapport interne LMT
Cachan W 140, Paris, 1993.
[GRO 66] GRODERSBERG P. &. KEDIA S., 'The Mechanical Properties of Woven Fabrics, Part
I: The Initial Load Extension Modulus of Woven Fabrics", J. Text. Res, 1966, Vol 36, p.
-87.
(HIB 95) HIBBIT, KARLSSON & SORESEN, Abaqus theory, User's Manual Version 5.5, 1995.
[HOG 86] HoGER A., 'The material time derivation of logarithmic strain", b11 J. Solids
Structures, 1986, Vol 22, W 9, p. 1019-1032.
[HOG 87] HOGER A., 'The stress conjugate to logarithmic strain", bll J. Solids Structures,
, Vo123, W 12, p. 1645-1656.
[ISH 83]1SHIKAWA. T & CHOU. T, "Non linear behaviour of the woven fabric composites", J.
of Composites Materials, 1983, p. 399-413.
[KAW 73) KAWABATA S., NITWA M., KAWAI H., 'The finite deformation theory of plain
weave fabrics, Part 1: the biaxial deformation theory", J. of the Textile Institute, 1973, Vol
, p. 62-83.
[LEH 91] LEHMANN T., Guo Z.& LIANG H.; "The conjugacy between Cauchy stress and
logarithm of the left stretch tensor", Eur J. Mech. A/Solids, I 0, W 4, 1991, p. 395-404.
(LON 95) LONG A.C., Ruoo C.D., BLAGDON M., KENDALL K.N. & DEMERI M.Y.,
"Deformation mechanics of engineered fabrics during prefom manufacture", Proceeding
of ICCM- 10, Whisler, B.C. Canada, Vol III, 1995, p. 205-212.
(REA 93) REALFF M.C., MARCY C., BACKERS., "A Micromechanical approach to modelling
tensile behaviour of woven fabrics", MD, Vol 46, Use of Plastic and Plastic Composites :
Material and Mechanics Issues ASME. 1993,64,285-294.
[SOW 87] SOWERBY R.& CHU E., "Rotation, stress rates and strain mesures in homogeneous
deformation process", lnt J. Solids Structures, 1987 Vol20, W 11112, p. 1037-1048.
[SAB 93] SABHI H. Etude experimentale et modelisation mecanique et numerique du
comportement des tissus de fibres de verre tors de leur preformage, These de doctoral de
I'Universite de Franche-Comte, 1993.
[SAB 93] SABHI H, Etude experimentale et modelisation mecanique et numerique du
comportement des tissus de fibres de verre lors de leur preformage, These de doctoral de
I'Universite de Franche-Comte, 1993.
[SAB 95] SABHI H., GELIN J.C. & RtMLINGER L., <
mecanique du comportement des tissus de meches de verre >>, Mecanique Jndustrie et
Materiaux, Vol48- N" 2, 1995, p. 59-61.
[SAB 94] SABOURIN F., Contribution a I' etude d'elements finis triangulaires a trois na:uds de
type coque: proposition d'un element simplifie et application a l'emboutissage, These de
I' lnstitut National des Sciences Appliquees de Lyon, 1994.
[SID 82] SIDOR OFF F., Cours sur les grandes deformations, Rapport GRECO N" 5111982.
[VAN 91] VAN DE WEEN F., Algorithms for draping fabrics on doubly curved surfaces, Int. J.
Num. Meth. Engineering, 1991, N" 31, p. 1415-1426.
