SIMULATION OF TEXTILE COMPOSITE REINFORCEMENT USING ROTATION FREE SHELL FINITE ELEMENT

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8 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS SIMULATION OF TEXTILE COMPOSITE REINFORCEMENT USING ROTATION FREE SHELL FINITE ELEMENT P. Wang, N. Hamia *, P.

fr) Keywords: textie composites, forming, trianguar she eement, rotation free, woven fabric Introduction Numerica optimization of products and production processes becomes increasingy important in

1 8 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS SIMULATION OF TEXTILE COMPOSITE REINFORCEMENT USING ROTATION FREE SHELL FINITE ELEMENT P. Wang, N. Hamia *, P. Boisse Universite de Lyon, INSA-Lyon, LaMCoS, CNRS UMR 559, F-696, France * Corresponding author(nahiene.hamia@insa-yon.fr) Keywords: textie composites, forming, trianguar she eement, rotation free, woven fabric Introduction Numerica optimization of products and production processes becomes increasingy important in the design phase of composite structures. Numerica simuations of the composite forming processes are an essentia part of these optimization toos. They permit to determine the conditions of the feasibiity of a process without defect (wrining, fracture of yarns, porosities ) but above a, they give the fibre orientations after shaping. This is mainy important because redistribution of the fibres is inevitabe when doube curved products are considered. The fibre orientations strongy infuence the mechanica behaviour of the fina part and the permeabiity of the reinforcement and thus the injection of the resin in the case of a iquid mouding process []. For a physica anaysis of a composite forming process, the compete mode must incude a the equations for the mechanics, especiay equiibrium, constitutive equations, and boundary conditions. These equations must be soved numericay, with some approximations. Finite Eement anaysis of the composite forming process incudes the toos modeing, the contact and friction between the different parts, and above a, the mechanica behaviour of the composite during forming. If these modes are numericay costy, probems of computation time are steadiy reduced through improved processing capabiities. The main probem for the FE approach therefore ies in the requirement for accurate modes of a the significant aspects of the forming process. Mechanica Mode. Mechanica Behavior Textie composite reinforcements considered in this paper are made up of continuous fibres. The materia resuting from this assemby of continuous fibres exhibits a very specific mechanica behaviour since reative motions are possibe between the yarns and the fibres. In iquid composite mouding processes (LCM), the textie reinforcement pre-forming stage taes advantage of these possibe motions. The forming is made on dry reinforcement (i.e. without resin) since it is performed before the injection stage. Athough the fibrous reinforcement is not stricty continuous because of reative siding between fibres, severa mechanica behaviour modes have been proposed that consider the textie reinforcement as an anisotropic continuum []. Nevertheess there is no widey accepted mode that describes accuratey a of the main aspects of fabric mechanica behaviour [3]. Actuay, such a mode must convey the specificities of the composition of the textie made of yarns and fibres and above a tae into account the variation of the properties during the forming. These changes are very arge because of the variations of fibre directions and of the oca atera compression of the yarns due to the forming. The very specific mechanica behaviour of textie reinforcements has ed the aboratories that anayse the composite pre-forming to deveop mechanica tests that are quite specific to these materias.. Interna virtua wor Fig.. (a) Loads on a unit woven ce and resutants:(b) tensions, (c) in-pane shear moment, (d) bending moments. The textie composite reinforcement consists of woven unit ces. Its mechanica behaviour is

2 specific because of the possibe reative dispacements between yarns and between fibres within the yarns. Let s consider the oads on a unit woven ce such as Fig. a. The foowing resutants of these oads are considered: - The tensions T and T are the resutants of the oads respectivey on warp and weft yarn directions (Fig. b) - The in-pane shear moment Ms is the moment at the centre of the RUC, in the direction of the norma to the fabric, resuting from the in-pane oads on the unit woven ce (Fig. c). - The bending moments M and M resuting on the warp and weft yarns (Fig. d). The principe of virtua wor can be written: W ( η) W ( η ) = ext acc N c p p p p p p ( ) T L ( ) T L p= (b) ε η + ε η + p γ( η ) Ms (c) p p p p p p χ( η ) M L + χ( η) M L (d) () Fig.. Trianguar eement and its three neighbors. 3 Finite Eement Formuation Four node membrane finite eements based on this semi-discrete approach have been previousy proposed [4]. The objective of the present paper is to propose a three node semi-discrete she eement incuding membrane and bending stiffness for textie composite reinforcement forming simuations (Fig..). This bending stiffness is very sma due to the fibrous nature of the textie composite reinforcement. Nevertheess this second order rigidity can be important in some cases especiay when some wrines appear. This she eement composed of woven ces is rotationa-free, i.e. the noda variabes are ony dispacements [5]. In a dynamic expicit approach, the membrane and bending noda interior oads are defined according to the tensions, shear torque and bending moments given by the mechanica tests specific to textie reinforcements. 3. Trianguar eement made of woven ces Textie composite reinforcements considered in this paper are made up of continuous fibres. The materia coordinates r, r are defined aong the warp and weft directions (Figure 3). r is equa to zero on M M 3 and is equa to in M. r is equa to zero on M M and is equa to in M 3. These coordinates are reated to the coordinates in the reference eement ξ and ξ. (ξ = in M, ξ = 0 in M and M 3, ξ = in M 3, ξ = 0 in M and M (Figure 3)) r b ξ = r ab a ξ (8) with ξ =b in B and ξ =a in A (Figure 3). The materia coordinates r, r and ξ, ξ give the materia vectors:

SIMULATION OF TEXTILE COMPOSITE REINFORCEMENT USING ROTATION FREE SHELL FINITE ELEMENT g = r = ξ g = r = ξ (9) The associated contravariant vectors are defined by:. β = δ g.

3 SIMULATION OF TEXTILE COMPOSITE REINFORCEMENT USING ROTATION FREE SHELL FINITE ELEMENT g = r = ξ g = r = ξ (9) The associated contravariant vectors are defined by:. β = δ g.g = δ β β β (0) As the interpoation functions are the standard inear ones (N = - ξ - ξ, N = ξ, N 3 = ξ ), equation (9) eads to: is an index taing vaue or. η and are the component number (= to 3) respectivey of the virtua dispacement η and of vector in the goba frame and η, η, η 3 the vaues of these virtua dispacement components at nodes M, M, M 3. B are the components of the virtua axia strain interpoation. Consequenty, denoting n cee the number of woven ces in the eement under consideration, the noda tensie interior oad components are (=,3, =,3 ): te ( Fint ) = ncee B T ( ε, ε ) + B T ( ε, ε) (3) L L =AM =BM 3 g =M M g =M M 3 () with : B = (a-) B = B 3 = -a B = (b-) B = -b B 3 = (4) Fig.3. Curviinear coordinates of the finite eement. 3. Interna forces At the time step i, the noda tensie interior oads F for the eement under consideration are te int cacuated according to the tensions T and T in the eement. The virtua extension strains in warp and weft directions are given by the virtua symmetrica gradient: s η ε ( η ) = ( ( η) ) B = = η r () se The noda in pane shear interior oads F int for the eement under consideration are cacuated according to the shear torque C s in the woven ces of the eement. The virtua ange γ( η) between warp and weft directions is given by the virtua gradient: γ( η ) = η B + η = η B γ γ (5) are the components of the virtua in pane shear strain interpoation. Consequenty, the noda in pane shear interior oad components are (=,3, =,3 ): se ( ) Fint = n cee Bγ C s (6) In order to avoid to add suppementary degrees of freedom and consequenty for numerica efficiency, the bending stiffness is taen into account within an approach without rotationa degree of freedom [6]. In theses approaches the curvatures of the eement are computed from the positions and dispacements of the neighbouring nodes eements (Figure ). The curvatures are assumed to be constant in the eement. The interpoations of the curvatures in warp and weft directions are now defined: χ ( η ) = Bbmη m (7) 3

4 m= to 6 (index of the node), = to 3 (index of direction of the dispacement).the noda bending interior oad components are: be L L Fint = n m cee BbmM + Bb m M ( ) 3 Forming simuation of an ange bracet (8) in the fat part of the fabric. A first main objective of the simuations is to verify that these wrines do not propagate to the tetrahedron part of the fabric. For this the pressure on the ban hoders must be sufficient. A second important resut is the shear ange fied within the tetrahedron part. These anges are in the order of 0% in a arge part of the tetrahedron. These anges affect the mechanica properties of the composite part obtained after injection. The deformed shapes (Figures 5a and 5c) have been shown to be in good agreement with experiments performed in the ITOOL project [7] In Figure 5b and 5d, the simuations are performed with higher bending rigidities. The shear anges in the tetrahedron part are roughy the same but the wrines are much arger and ess numerous. These ast simuations confirm the importance of the bending stiffness regarding the number and the size of the wrines. Fig.4. Deep drawing of tetrahedron shape. Geometry of the toos. These forming tests have been deveoped by EADS company in order to test experimentay and numericay the manufacturing of an ange bracet by R.T.M. process. The shape of the part is a reguar tetrahedron (Figure 4). The fabric is the G5 interoc. This woven composite reinforcement has been studied within the ITOOL project [7]. Two bending rigidities are considered and specified in Figure 5. The measured vaue (5.0 - N.mm) is the vaue obtained by the cantiever bending test (Figures 5a and 5c). In order to show the infuence of the bending stiffness the simuations are performed with a higher vaue (50 N.mm Figure 5b and 5d) The textie reinforcement is maintained on the die by six square ban hoders (Figure 4). The force on each ban hoder is 800N. The simuation resuts are given for (0-90 ) initia orientation of the yarns (Figures 5a and 5b) and (±45 ) initia orientation of the yarns (Figures 5c and 5d). The geometry of the six ban hoders eads to a arge number of wrines References [] J. Sade, E.M. Sozer, S.G. Advani Fuid Impregnation of deformed preforms. J. Reinf. Past. Compos. Vo. 9, pp , 000. [] L. Dong, C. Leaou, M.G. Bader Processing of composites: simuations of the draping of fabrics with updated materia behaviour aw. J. Compos. Mater, Vo. 35, pp 38-63, 00. [3] M.J. King, P. Jearanaisiawong, S. Socrate. A continuum constitutive mode for the mechanica behavior of woven fabrics, Int. J. Soid Struct., Vo.4, pp , 005. [4] P. Boisse, B. Zouari, J. L. Danie Importance of In- Pane Shear Rigidity in Finite Eement Anayses of Woven Fabric Composite Preforming. Composites part A, Vo. 37, No. pp 0-, 006. [5] N. Hamia, P. Boisse, F. Sabourin and M. Brunet A semi-discrete she finite eement for textie composite reinforcement forming simuation. IJNME, Vo. 79, No. pp , 009. [6] Sabourin F., Brunet M., Anayses of pates and shes with a simpified 3 node trianguar eement. Thin Waed Structures, Vo., pp. 38-5, 995. [7] ITOOL Integrated Too for Simuation of Textie Composites, European Specific Targeted, Research Project, sixth framewor programme, Aeronautics and Space,

mm. Fig.5. (c) Initiae orientation ±45, Bending stiffness 5.0 - N.mm. Fig.5. (d) Initiae orientation ±45, Bending stiffness 50 N.

5 SIMULATION OF TEXTILE COMPOSITE REINFORCEMENT USING ROTATION FREE SHELL FINITE ELEMENT Fig.5. (a) Initiae orientation 0-90, Bending stiffness N.mm. Fig.5. (b)initiae orientation 0-90, Bending stiffness 50 N.mm. Fig.5. (c) Initiae orientation ±45, Bending stiffness N.mm. Fig.5. (d) Initiae orientation ±45, Bending stiffness 50 N.mm. 5

COMPOSITE REINFORCEMENT FORMING SIMULATION: A MULTISCALE APPROACH

COMPOSITE REINFORCEMENT FORMING SIMULATION: A MULTISCALE APPROACH N. Hamila A. Khan S. Gatouillat E. De Luycker E. Vidal-Sallé T. Mabrouki P. Boisse Université de Lyon, LaMCoS, INSA-Lyon Philippe.Boisse@insa-lyon.fr