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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,
TENSYL
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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
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Continuous fibres, short fibres and matrix
• The fibers are continuous or short
The matrix prevents the motion between the fibres
The matrix is inactive during manufacturing
We consider continuous fibers
Composite wing ATR72
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Composite manufacturing processes
They are many.
LCM processes :Resin is injected on a dry preform
The preform can also be braided, obtained by fibre placement, knitting…
The preform is dry during forming(no resin)
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Composite manufacturing processes
Prepreg forming (or thermoforming)
Prepreg stackHeating
Forming at hightemperatureThermoplastic
Thermoset prepreg (1 ply)
Hand drapingor draping machine
Curing in an autoclaveT=180°C, P = 7 bars
> T fusion
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LCM processes: Resin is injected on a dry preform
Prepreg forming (or thermoforming)
Prepreg stackHeating
Forming
Modelling and simulations of composite reinforcements and prepreg forming
Preform
Dry reinforcememntforming
Many researchsconcerns resin injection
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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 materialsMainly, fibers and yarns have relative displacements during forming(There is no matrix or it is soft)
Expected results of the forming simulation of a fab ric: - 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)
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Macroscopique scale(scale of the part)
Mesoscopic scale(scale of the yarn and of the woven cell)
Microscopic scale(scale of the fibre)
The three possible scales of the textile composite reinforcements analyses
It is a continuous material. A macroscopic model is defined that has to account for the fibrous nature of the material
It is a set of yarns the size of which are mesoscopic � mesoscopic approaches(discrete number of yarns)
It is a set of fibres the size of which are microscopic � microscopic approaches (discrete number of fibres)
The three scales are simultaneously present in the reinforcementBut the analysis can be made considering:
(most of the forming analyses)
(some recent forming analyses)
(analyses of a small element)
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Approaches at the microscopic scaleThe 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]2-D woven fabric generated by multi-chain digital element model [Zhou et al, CST 04]
The simulation of a forming process is difficult (12 000 fibres by yarn…)Hundreds of yarns in a preform.
ANR MECAFIBRES
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Approaches at the
macroscopic scaleThe reinforcement is a set of fibresA 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]
1120 25 30 35 40 45 50 55 600
50
100
150
200
250
300
350
400
450
500
Volume fraction(%)C
ompa
ctio
n st
ress
(Kpa
)
1 layer2 layers 3 layers 4 layers 5 layers
The main experiments for mechanical behavior identification
Biaxial tensile test 50mm
70mm
230mm
40mm
Bending test
M(χ)
[De Bilbao et al, Exp Mech, 2010]
Compaction test
[Nguyen et al, Composites B, 2013]
[Buet-Gautier et al, Exp Mech, 2001]
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In plane shear tests
Shear Frame
Fabricsample
Picture frame test Bias extension test
Fibres oriented at ± 45°
There is a strong research activity concerning these tests because these tests are 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]
The tests must be performed at high temperature for thermoplastic prepregs.
Shear locking
[Wang et al, JTCM, 2013]
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The reinforcement is a continuous media .
∇ =σ C : D
Hypoelastic model
( )T Td. . . .
dt∇ =
σ Q Q σQ Q
Q must be the rotation of the fiber (not Jaumann, or Green Naghdi)
e20=f20
e10=f10e10
e20f2=h2
e1
e2g2
h1
θ1
θ2
f1=g1
e20=f20
e10=f10
[Badel et al, Composites A, 2009]
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Numerical (±45°)
Experimental (±45°)
100 mm
International benchmark : Double dome
∇ =σ C : D
Hypoelastic model
[Khan et al, JMPT, 2010] [J. Sherwood et al, to appear 2013 ]
[Peng and Rehman, Comp Sci Tech 2011]
[Lee and Cao, IJMF, 2009]
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• 6 deformation modes corresponding to 6 equivalent invariants
Extensions(warp/weft)
( ) ( )1,241lni
elongI I= = 3
41 42
1ln
2comp
II
I I
=
421
41 42
cp
II
I I= ( )1,2 4 3
4 43
= =i ict
i
II
I I
Compaction In plane shear Transverse shear(warp/weft)
[Charmetant et al, Comp. Sci. Tech., 2011 and 2012]
a. b. c.
f.e.d.
2 2 ..... ∂ ∂∂ ∂ ∂= = + ∂ ∂ ∂ ∂ ∂
elong ct
elong ct
I Iw w wS
C I C I C
Hyperelastic model for analyses of 3D composite per forms
( ) ( ) ( ) ( ) ( ) ( )( )2 2, , , , ,i i i j
w Tr C Tr C Det C Tr C G Tr C G Tr C G G⋅ ⋅ ⋅ ⋅
1 2 3 4 5 4i i ijI I I I I I��� ����� ����� ����� ����� �������
It is assumed here that the contribution of each deformation mode is independent from the others
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Hyperelastic model for analyses of 3D composite per forms
Shear angles on top and bottom faces
Transverse compaction strains.
The agreement with experimental strains is good
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Stress resultants
T11
T11
T22
T22
Tensions
t 11int 1
222
W ( ) ( ) T L
( ) T L
11
22
η = ε η
+ ε η
Internal virtual work
Ms
Ms
In plane shear
Internal virtual work
sint sW ( ) ( ) Mη = γ η
M11
M11
M22
M22
Bending
Internal virtual work
b 11int 1
222
W ( ) ( ) M L
( ) M L
11
22
η = χ η
+ χ η
unit cell
The semi-discrete approach
To avoidContinuous mechanical behavior model
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1 2
56
4
6d5d
4d
1β2β
3β
1n�
1t�
2n�
2t�
3n� 3t�
Rotation-free
triangular
shell element
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Deep drawing with a tetrahedron punch
• Tetrahedron punch• Triangular die• Six blank holders
Project ITOOL/ ANR LCM3M / EADS IW
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Interlock reinforcement - G1151®
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Upper ply ±45°
Central ply 0°-90°
Lower ply ±45°
25°
22°18°
23°
3.5°
17°
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W1
Wrinkle 1 (W1):
Test 1
Test2
Test 3
Average
Maxidiffere
nce
Simulati
o
20 mm
28 mm
25 mm
24mm
8 mm 23 mm
Wrinkle 2 (W2):
Test 1
Test2
Test 3
Average
Maxidiffere
nce
Simulati
o
30 mm
30 mm
25 mm
28.3mm
5 mm 32mm
W2
[Allaoui et al, Composites A, 2011]
[Boisse et al, Comp. Sci. Tech. 2011]
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15 mmR = 60 mm
R=15 mm
R=85 mm
L=150 mm
Blank holder
Blank holder
Hemispherical punch
Die Die
Composite woven fabric
Ewarp (N/yarn) Eweft (N/yarn)
50 0.2Polyamide fibres (nylon 6x6) 2x2 twillfor elastomer reinforcement
Hemispherical punching of a very unbalanced textile reinforcement
Nottingham university
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Tensile stiffness only
Tensile and in-plane shear rigidities
Tensile + in-plane shear + bending rigidities
Experimental forming
Hemispherical punching of a very unbalanced textile reinforcemen t
L1/L2=1.8
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Simulation of 3D Interlock Composite PreformingFan blades, Snecma engines
[D.Marsal, S. Otin
L. Marcin]
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Initial Déformé
Semi-discrete approach for 3D textile reinforcements
3D hexahedral finite elements are made of yarns
[De Luycker et al, Composite Structures 2009]
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Thermoforming simulation of multilayer composites with continuous fibres and thermoplastic matrix
[P. Wang, et al. Composites B, 2013][ten Thije et al, Composites A, 2009]
eff 1 e 2
eN
C H C
VH
F
µ = +η=
[Fetfatsidis et al, Composites A, 2007]
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Thermoforming simulation of multilayer composites with continuous fibres and thermoplastic matrix
320°C
370°C
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•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
FE model for the analysis of the behaviour of the unit cell.
FE model for simulations of the whole composite reinforcement forming.
Approaches at the mesoscopic scale
The reinforcement is a set of yarns in contact-friction with its neighbours
• Each yarn is a continuous material
(Virtuel tests)
47214 Dof. 416 Dof
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Ms
γ
Mesoscopic modeling
Picture frame Bias testExperiments
Experimental and virtual in plane shear biaxial tests
[P. Badel et al, Commat, 2007]
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Mesoscopic modeling. Constitutive model of the yarn
f1
f1
Main requirement:
strictly follow the direction f1
The yarn is made of thousands of fibers.
∇ =σ C : D
rotation of the fiber direction0
i i= = ⊗Q Φ f e
For fibrous materials:
Transverse mechanical behaviorCompaction Distortion
Fiber density changes Shape changes
Spherical (2D) transformation Deviatoric (2D) transformation
( ) ( )( ) ( )
22 22
33 33
23 23
A B 2 A B 2 0
A B 2 A B 2 0
0 0 B
∆σ + − ∆ε ∆σ = − + ∆ε ∆σ ∆ε
s 11
s
-pε nε0
-pε0
A = A e e
B = B e
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Simulations - Glass plain weave in -plane shear
Pure shear test :Picture frame
Objectif of the simulation:
Geometry of the deformed cellfor permeability determination
Vitual mechanical tests
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Tomography validation of the deformed geometry
Experimental deformed geometry obtained by X-ray tomography
In-plane shear
Mesoscopic F.E. analysis
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Tomography validation of the deformed geometry
In-plane shear
Width ratio w/w0
w0
Experiment 0.77Simulation 0.71
Experiment: 0.77Simulation: 0.74
[Badel et al, Comp. Sci. Tech., 2008]
Average area ratio S/S0
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Figure 5. Experimental and numerical shear curves.
Simulations - 2x2 carbon twill in -plane shear
Experimental deformed geometry obtained by X-ray tomography
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Comparison of the computed and experimental sheared geometries (slices in warp planes)
Tomography
Simulation
The initial shapes of the transverse sections are very different
-- Simulation
-- Bias tests
Shear angle
She
ar to
rque
Simulations - Interlock reinforcement - G1151® (Hexcel)Meilleure géométrie initiale:Simulation du tissageANR NUMTISS 2009 (F. Boussu)
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L3S Grenoble (Loix, Orgeas, et al)
Solid and fluid REV’s for a deformed configuration
Mesh of the fluid REV in the non deformed configuration
Newtonien or non-newtonien flow(K, permeability tensor)
Slices of velocity norm
Application of analyses at mesoscale : Numerical determination of the permeability of fibrous reinforcements
fluid RVE
[Loix et al, Comp. Sci. Tech., 2008 & 2009]
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FE model for simulations of the whole composite reinforcement forming. 416 Dof
Approaches at the mesoscopic scaleForming simulations
The reinforcement is a set of yarns in contact-friction with its neighbours
(Virtuel tests)
47214 Dof.
Shells with an hypoelastic membrane behaviour based on the rotation of the fibre
and a specific bending stiffness
[Creech and Pickett, JMS 2006]
[Gatouillat et al, IJMF 2010]
NCF meso modeling
[Duhovic and D. Bhattacharyya, composites A, 2006]
[Ben Boubaker and Ganghoffer, Mech. Res. Com. 2007]
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Analyse of the forming in case of lack of continuit y of the reinforcement
Strong blankholder loads
39[Gatouillat et al, Composites A, 2013]
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Thank you for your attention