Modélisation et simulation de la mise en œuvre de matériaux composites. Philippe Boisse, INSA-Lyon, France

Transcription

1 Modélisation et simulation de la mise en œuvre de matériaux composites Philippe Boisse, INSA-Lyon, France Projets ANR MatetPro MecaFibres 2007 et LCM3M 2007 MECAFIBRES: coordinateur JF Gangoffer, LEMTA, LMSSMat, LPMT, LaMCoS, SNECMA, CETELOR, H. BASTIEN LCM3M: coordinateur J. Bréard, LOCM, LaMCoS, PRISME, CEMEF, ONERA, SNECMA, HEXCEL, EADS, PROTAC, 1 TENSYL

2 Composite materials, are used in applications in which light weight and high specific modulus and strength are critical issues. aerospace industry automotive industry refurbishment of buildings and bridges medical implants sports industry Composites contribute to the sustainable development within our society There is a strong increase in the use of composite materials in some fields 2

3 Continuous fibres, short fibres and matrix The fibers are continuous or short Composite wing ATR72 The matrix prevents the motion between the fibres We consider continuous fibers The matrix is inactive during manufacturing 3

4 They are many. Composite manufacturing processes LCM processes: Resin is injected on a dry preform The preform is dry during forming (no resin) The preform can also be braided, obtained by fibre placement, knitting 4

5 Composite manufacturing processes Prepreg forming (or thermoforming) Thermoset prepreg (1 ply) Curing in an autoclave T=180 C, P = 7 bars Hand draping or draping machine Thermoplastic Prepreg stack Heating Forming at high temperature > T fusion 5

6 Modelling and simulations of composite reinforcements and prepreg forming LCM processes: Resin is injected on a dry preform Preform Many researchs concerns resin injection Dry reinforcememnt forming Prepreg forming (or thermoforming) Forming Prepreg stack Heating 6

7 Achievement of double curved shapes by forming requires in plane strains of textile reinforcements, mainly shear strains The mechanisms of the forming are specific to fibrous materials Mainly, fibers and yarns have relative displacements during forming (There is no matrix or it is soft) Expected results of the forming simulation of a fabric: - Conditions for the forming feasibility - Detection of defects (wrinkles, porosities, fractures) - Direction and density of the reinforcements after forming (Very important for the further mechanical analyses in service and for injection simulations) 7

8 The three possible scales of the textile composite reinforcements analyses Macroscopique scale (scale of the part) Mesoscopic scale (scale of the yarn and of the woven cell) The three scales are simultaneously present in the reinforcement But the analysis can be made considering: Microscopic scale (scale of the fibre) It is a continuous material. A macroscopic model is defined that has to account for the fibrous nature of the material (most of the forming analyses) It is a set of yarns the size of which are mesoscopic mesoscopic approaches (discrete number of yarns) (some recent forming analyses) It is a set of fibres the size of which are microscopic microscopic approaches 8 (discrete number of fibres) (analyses of a small element)

9 Approaches at the microscopic scale The reinforcement is a set of fibres [Zhou et al, CST, 04] [Durville,JMS 05] [Duhovic & Bhattacharya, CompA 06] [Grave & Kyosev, Greenville 09] Each fibre is modeled (for instance by beam FE) Shear test [Durville, IJMF 2010] ANR MECAFIBRES 2-D woven fabric generated by multi-chain digital element model [Zhou et al, CST 04] The simulation of a forming process is difficult ( fibres by yarn ) Hundreds of yarns in a preform. 9

10 Approaches at the macroscopic scale The reinforcement is a set of fibres A macroscopic model is defined that has to give an account of the fibrous nature of the material This is not simple, especially in large strains because the models have to be very anisotropic, must strictly take fibre direction update and it consequences into account and remain simple. [Spencer, CompA, 2000][Lamers et al, IJFP, 2002] [Yu et al, CompA, 2002] [Cao et al, CompA 2003, 05][King et al, IJSS, 2005][Boisse et al, JMS, 2005] [Ten Thije et al, CMAME, 2007],[Charmetant et al, CSTE, 2012] There is no widely accepted model ; Continuous models cannot describe slidings between yarns [Allaoui, IJMF 2012] 10

11 The main experiments for mechanical behavior identification Biaxial tensile test 230mm 70mm 50mm 40mm Bending test M(χ) 500 Compaction test 450 Compaction stress(kpa) [Buet-Gautier et al, Exp Mech, 2001] layer 2 layers 3 layers 4 layers 5 layers [De Bilbao et al, Exp Mech, 2010] Volume fraction(%) [Nguyen et al, Composites B, 2013]

12 Picture frame test In plane shear tests Bias extension test Shear Frame Fabric sample Fibres oriented at ± 45 There is a strong research activity concerning these tests because these Shear tests are locking important for forming modeling and difficult (International Benchmark). The in plane shear can be disrupted by the very strong tensile stiffness [Cao et al, Composites A, 2008] [Wang et al, JTCM, 2013] The tests must be performed at high temperature for thermoplastic prepregs. 12

13 The reinforcement is a continuous media. Hypoelastic model e 20 =f 20 g 2 e 2 e 20 =f 20 e 20 f 2 =h 2 θ 2 σ = C : D e 10 =f 10 e e =f 10 f 1 =g 1 θ 1 e 1 h 1 d ( T... ) σ = Q Q σ Q. Q dt T Q must be the rotation of the fiber (not Jaumann, or Green Naghdi) [Badel et al, Composites A, 2009] 13

14 Hypoelastic model σ = C : D Experimental (±45 ) 100 mm Numerical (±45 ) [Lee and Cao, IJMF, 2009] International benchmark : Double dome [Khan et al, JMPT, 2010] [J. Sherwood et al, to appear 2013 ] 14 [Peng and Rehman, Comp Sci Tech 2011]

15 6 deformation modes corresponding to 6 equivalent invariants I Hyperelastic model for analyses of 3D composite performs Extensions (warp/weft) ( i= 1,2) elong ln ( I41 ) S w w Ielong w Ict = 2 = C Ielong C Ict C ( ), 2 ( ), ( ), 2 ( ), ( ), i i ( i j ) ( ) w Tr C Tr C Det C Tr C G Tr C G Tr C G G I1 I2 I3 I4i I5i I4ij 1 I = ln 3 = comp 2 I41I42 I Compaction In plane shear Transverse shear (warp/weft) I cp = I 421 I I I ( i= ) ct = I 1,2 4i3 I I 4i 43 a. b. c. d. It is assumed here that the contribution of each e. f. deformation mode is independent from the others 15 [Charmetant et al, Comp. Sci. Tech., 2011 and 2012]

16 Hyperelastic model for analyses of 3D composite performs Shear angles on top and bottom faces Transverse compaction strains. The agreement with experimental strains is good 16

17 The semi-discrete approach To avoid Continuous mechanical behavior model unit cell Stress resultants T 22 6 d 6 n 2 t 2 T 11 T 11 T Tensions t Internal virtual work Rotation-free W triangular ( η ) = ε ( η) T L + shell ε η element t 11 int ( ) T L2 3 β 3 β1 β2 n 3 3 t1 d 4 4 n 1 d 5 M s M s In plane shear Internal virtual work W ( η ) = γ( η) M s int 5 s M 22 M 11 M 11 M 22 Bending Internal virtual work W ( η ) = χ ( η) M L b 11 int χ η ( ) M L2 17

18 Deep drawing with a tetrahedron punch Project ITOOL/ ANR LCM3M / EADS IW Tetrahedron punch Triangular die Six blank holders 18

19 Interlock reinforcement - G

20 Upper ply ± Central ply Lower ply ±

21 Wrinkle 1 (W1): Test 1 Test 2 Test 3 Aver age Maxi differe nce Sim ulati o 20 mm 28 mm 25 mm 24 mm 8 mm 23 mm W1 W2 Wrinkle 2 (W2): Test 1 30 mm Test 2 30 mm Test 3 25 mm Aver age 28.3 mm Maxi differe nce Sim ulati o 5 mm 32 mm [Allaoui et al, Composites A, 2011] [Boisse et al, Comp. Sci. Tech. 2011] 21

22 Hemispherical punching of a very unbalanced textile reinforcement Hemispheri cal punch Blank holder L=150 mm Die R = 60 mm R=85 mm Composite woven fabric 15 mm R=15 mm Die Blank holder Nottingham university Polyamide fibres (nylon 6x6) 2x2 twill for elastomer reinforcement E warp (N/yarn) E weft (N/yarn)

23 Hemispherical punching of a very unbalanced textile reinforcement Tensile stiffness only Tensile + in-plane shear + bending rigidities L 1 /L 2 =1.8 Tensile and in-plane shear rigidities Experimental forming 23

24 Simulation of 3D Interlock Composite Preforming Fan blades, Snecma engines [D.Marsal, S. Otin L. Marcin] 24

25 Semi-discrete approach for 3D textile reinforcements Initial Déformé 3D hexahedral finite elements are made of yarns [De Luycker et al, Composite Structures 2009] 25

26 Thermoforming simulation of multilayer composites with continuous fibres and thermoplastic matrix µ = C H + C H eff 1 e 2 e ηv = F N [Fetfatsidis et al, Composites A, 2007] [ten Thije et al, Composites A, 2009] [P. Wang, et al. Composites B, 2013] 26

27 Thermoforming simulation of multilayer composites 370 C with continuous fibres and thermoplastic matrix 320 C 27

28 Approaches at the mesoscopic scale The reinforcement is a set of yarns in contact-friction with its neighbours Each yarn is a continuous material The woven nature of the reinforcement is naturally taken into account The mechanical behaviour of the yarn (made of thousands of fibers) must be described by a specific model The numerical model must be simple enough to analyze a unit cell.. or a forming process Dof. 416 Dof FE model for the analysis of the behaviour of the unit cell. (Virtuel tests) FE model for simulations of the whole composite reinforcement forming. 28

29 Experimental and virtual in plane shear biaxial tests [P. Badel et al, Commat, 2007] Picture frame Experiments Bias test M s Mesoscopic modeling γ 29

30 Mesoscopic modeling. Constitutive model of the yarn The yarn is made of thousands of fibers. Main requirement: f 1 f 1 strictly follow the direction f 1 σ = C : D For fibrous materials: Transverse mechanical behavior Compaction Q = Φ = f e i 0 i rotation of the fiber direction Distortion Fiber density changes Shape changes Spherical (2D) transformation Deviatoric (2D) transformation ( ) ( ) ( ) ( ) σ 22 A + B 2 A B 2 0 ε22 σ = A B 2 A + B 2 0 ε σ B ε23 A = A e 0 B = B e 0 -pεs nε11 -pεs e 30

31 Simulations - Glass plain weave in-plane shear Objectif of the simulation: Geometry of the deformed cell for permeability determination Vitual mechanical tests Pure shear test 31 : Picture frame

32 Tomography validation of the deformed geometry In-plane shear Mesoscopic F.E. analysis Experimental deformed geometry obtained by X-ray tomography 32

33 Tomography validation of the deformed geometry In-plane shear w 0 Width ratio w/w 0 Experiment: 0.77 Simulation: 0.74 Average area ratio S/S 0 Experiment 0.77 Simulation [Badel et al, Comp. Sci. Tech., 2008]

34 Simulations - 2x2 carbon twill in-plane shear Experimental deformed geometry obtained by X-ray tomography Figure 5. Experimental and numerical shear curves. 34

35 Simulations - Interlock reinforcement - G1151 (Hexcel) Meilleure géométrie initiale: Simulation The initial du shapes tissage of the transverse sections are very different ANR NUMTISS 2009 (F. Boussu) Comparison of the computed and experimental sheared geometries (slices in warp planes) -- Simulation Simulation Shear torque -- Bias tests Shear angle Tomography 35

36 Application of analyses at mesoscale : Numerical determination of the permeability of fibrous reinforcements L3S Grenoble (Loix, Orgeas, et al) fluid RVE Solid and fluid REV s for a deformed configuration Newtonien or non-newtonien flow (K, permeability tensor) Slices of velocity norm Mesh of the fluid REV in the non deformed configuration 36 [Loix et al, Comp. Sci. Tech., 2008 & 2009]

37 Approaches at the mesoscopic scale Forming simulations The reinforcement is a set of yarns in contact-friction with its neighbours (Virtuel tests) Dof. [Gatouillat et al, IJMF 2010] NCF meso modeling FE model for simulations of the whole composite reinforcement forming. 416 Dof Shells with an hypoelastic membrane behaviour based on the rotation of the fibre and a specific bending stiffness [Creech and Pickett, JMS 2006] [Duhovic and D. Bhattacharyya, composites A, 2006] [Ben Boubaker and Ganghoffer, Mech. Res. Com. 2007] 37

38 Analyse of the forming in case of lack of continuity of the reinforcement Strong blank holder loads 38

39 [Gatouillat et al, Composites A, 2013] 39

40 Thank you for your attention 40