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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