presented by didier baptiste ensam, lim, umr cnrs 8006 151...

MultiscaleMultiscale analyses of the analyses of the behaviourbehaviour and damage of and damage of

composite composite materialsmaterials

PresentedPresented by Didier BAPTISTEby Didier BAPTISTE

ENSAM, LIM, UMR CNRS 8006ENSAM, LIM, UMR CNRS 8006151 boulevard de l151 boulevard de l’’hôpital 75013 PARIS, hôpital 75013 PARIS,

FranceFrance

ResearchResearch worksworks fromfrom: : K.DerrienK.Derrien, , J.FitoussiJ.Fitoussi, F. , F. MeraghniMeraghni, , E.LepenE.Lepen, , G.GuoG.Guo, M. Levesque, , M. Levesque, Z.JendliZ.Jendli..

VariabilityVariability of the short of the short fibres orientationfibres orientation

From B. Ohl, Schneider

From B. OLH, Schneide

Microtomography X: volume view of the fibres distribution

ExampleExample of a of a disperseddispersedmicrostructure: S.M.C.microstructure: S.M.C.

WhatWhat are the are the difficultiesdifficulties??

MechanicalMechanical propertiesproperties dependingdepending on on the the analysedanalysed zone of the structure.zone of the structure.Initial Initial anisotropyanisotropy dependingdepending on the on the distribution of fibres orientationdistribution of fibres orientationEvolution of Evolution of thisthis anisotropyanisotropy withwith the the loadingloading

DifficultiesDifficulties of the of the macroscopicmacroscopic approachapproach

TensileTensile tests in tests in differentdifferent directionsdirectionsManyMany tensiletensile tests tests withwith unloadingunloading to to determinedetermine the the evolutionevolution of all the of all the stiffnessstiffness parametersparameters due to damagedue to damageIdentification of a Identification of a macroscopicmacroscopicbehaviourbehaviour lawlaw takingtaking intointo accountaccountdamage damage evolutionevolution. (exemple SMC: 27 . (exemple SMC: 27 coefficients)coefficients)

Objective:Objective:

ExperimentalExperimental determinationdetermination of all the of all the mechanicalmechanical propertiesproperties fromfrom::–– one one givengiven distribution of the distribution of the

microstructure microstructure –– One One loadingloading directiondirection

ObjectiveObjective

PredictionPrediction of the of the mechanicalmechanical propertiesproperties

–– for for otherother distributions of microstructuredistributions of microstructure

–– for for otherother pathpath loadingsloadings ((otherother directions, directions, bibi--traction, traction, shearshear,,…….).)

ObjectiveObjective

Identification of an Identification of an anisotropicanisotropic behaviourbehaviour lawlawfromfrom the simulation of the simulation of loadingloading tests on a tests on a R.V.E. for R.V.E. for otherother distributions of the distributions of the microstructure and microstructure and differentdifferent loadingloading pathspaths..

VIRTUAL TEST MACHINE

EquivalentEquivalenthomogeneoushomogeneous

materialmaterial

HomogenizationHomogenizationModel:Model:

MoriMori and Tanakaand TanakaMatrixMatrix

ReinforcementReinforcement::Distributions:Distributions:Aspect ratio Aspect ratio Orientation, Orientation,

Volume fraction, Volume fraction, MechanicalMechanical propertiesproperties

DamageDamageMicroMicro--crackscracks

Matrix Behaviour law:Elasticity

ViscoelasticityPlasticity

PROCESSPROCESS

MULTIMULTI--SCALE BEHAVIOUR SCALE BEHAVIOUR MODELLINGMODELLING

StatisticalStatistical approach:Weibullapproach:WeibullLocal Local failurefailure criteriacriteria

ExperimentalExperimental investigationinvestigationLoadingLoading --unloadingunloading teststests

In situ In situ tensiletensile test test insideinside SEMSEMQuantification of micro cracks Quantification of micro cracks kineticskinetics

Objective: To predict the composite properties from the components ones.

DESCRIPTIONof the Representative Volume Element

LOCALIZATION

BEHAVIOUR

HOMOGENEISATION

ellipsoïdes(λi, fvi, θi, φi)

EimpΣ = L(?) Eimp

MICRO –MACRO BEHAVIOUR MODELLING

ε0=B0Ε

εr=BrΕσ0= L0 ε0

σr= Lr εr

Σ = < σi> i=0,…N

Interface damage Interface damage criterioncriterion

Interfacial criterion:(σ/σ0)2+ (τ/τ0)2 < R interface

σ τ Orientation θΣInterfacialstresses calculated byMori and Tanaka model

interface damage interface damage lawlaw: : StatisticalStatistical approachapproach

Damagedinterface

Undamagedinterface

σ

σ

Interface Failure Probability:

Pf=Vfd/Vf =1-exp[(((σ/σ0)2+ (τ/τ0)2 )/σu)]m

((σσ00,,ττ00, m) = f (, m) = f (εε)).

Interface mechanical properties

= Volume fraction of broken interface fibre/ Volume Fraction of total fibrefor a given orientation

FailureFailure particule particule criterioncriterion

DiapDiap KatellKatell

Σ = 494 MPa Σ = 509 MPa

Σ Σ ΣΣ

Al-SiCp

ReinforcementReinforcement failurefailure lawlaw

σ1

σ3

σ2

V : Particule volume( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛−−=

m

uVVV

σσσ

0exp1,Pr

Brittle fracture of the reinforcement

Damage criterion: σ< R particule

Statistical particule failure law

σ : Maximun principal stress in the particule

MatrixMatrix damage damage lawlaw

( ) h

h

pe e

m

fpRdR

σσ

ε 23491+

=

CavityCavity growthgrowth criterioncriterionMatrix cracking

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−−=

m

uσσexp1

density cracks Maximumdensity Cracks

σ: stresses in the matrix

or

ModellingModelling of the of the damageddamagedmicrostructuremicrostructure

Mori et Tanaka :

Building of the stress-strainanswer by an incremental

method

Σ

Σ = Σ + δΣ

Local damagecriteriaΔd (θ)

Introduction of a crack volume fraction

(new microstructure)

Simulation of a stressSimulation of a stress--strainstrain responseresponse

Identification of the Identification of the materialmaterial parametersparameters of the of the behaviourbehaviour lawlaw

Distribution of Distribution of reinforcementreinforcement ::

–– TomographyTomography

–– UltrasonicUltrasonic waveswaves

–– Flow Flow numericalnumerical simulation of the simulation of the processprocess

MicrotomographyMicrotomography

FromFrom B. B. OlhOlh Schneider ESRFSchneider ESRF

UltrasonicsUltrasonics measurementmeasurement

Wave propagation time measurement

under bi-tension

Specimen

Ultrasonic transducers

DeterminationDetermination of the distribution of fibresof the distribution of fibres

Cii = ρ vOL²

Cij = ρ vOT²

Mori and Tanaka model: volume fraction and distribution of fibres orientation

Ccomp = f°(fv,f(θ),Cm,Cr…)

1480

1500

1520

1540

1560

1580

1600

1620

0 30 60 90 120 150 180 210 240 270 300 330 360

Angle de rotation de l'échantillon (°)

Vite

sse

des

OT

(m/s

)

Rotation angle of the specimen

Tra

nsve

rsw

ave

rate

Damage quantification Damage quantification atat the the microscalemicroscale

Microscopic damage

In situ tensile test ( inside a S.E.M.)10 cm

Specimen

∑

Specimen

36*9*3,2 mm3

Quantitative analyses of damage at the microscopic scale

High High strainstrain rate damage rate damage caracterisationcaracterisation

σ

Fuse

Tensile test up to 20m/s

0

20

40

60

80

100

120

140

0 0.5 1 1.5 2 2.5Strain (%)

Stre

ss (M

Pa)

Stag e 1Elas t ic behaviour

Stag e 2Damag e init iat io n Stag e 3

Micro -cracks co alescence and d amag e accumulat io n

Evolution of damage for Evolution of damage for SMCSMC

Quantification of damage Quantification of damage evolutionevolution

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.5 1 1.5 2

0.0002 s-18 s-120.5 s-1

d m

icro

scop

ic

dε/dt (%)

ε_ult

d= Number of broken interface fibresTotal number of fibres

ε

The interface The interface failurefailure criterioncriterion isis a a functionfunction of the of the strainstrain rate. rate.

Identification of the Identification of the viscovisco--damage damage lawlaw atat the micro the micro scalescale

d=Pr = 1 - exp[(σ/σ0)2+(τ/τ0)2]m

(σ0, τ0, m) = f ( ).ε

minimisation algorithme:Levenberge marquardt+ Hessien calculation

Identification (Identification (matlabmatlab))

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

déformation (%)

d-m

icro

PROB-OPTDOM-EXPPROB-INT

3 m/s

STRAIN

8/s

20/s

ModelExperiments

STRAIN

PredictionPrediction of the of the lostlost of of stiffnessstiffness

0

2000

4000

6000

8000

10000

12000

14000

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

Déformation ε11(%)

E11

(MP

a)

E11-eps11-- 20s-1(Simulation)

E11-eps11(élastique)-- 20s-1(Expérience)

Exp.

Mod.

20 s-1

STRAIN

Strain rate:

AnisotropicAnisotropic stiffnessstiffness evolutionevolution of composite SMCof composite SMC--R26 R26 For For strainstrain rates: rates: 2.102.10--44, 20 et 250 s, 20 et 250 s--11.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5

Déformation ε11 (%)

E1/E

1° (M

Pa)

250 s-1

20 s-1

2.10-4 s-1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5


E2/E

2° (M

Pa)

250 s-120 s-12.10-4 s-1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5


E3/E

3° (M

Pa)

250 s-120 s-12.10-4 s-1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5


G12

/G12

° (M

Pa)

250 s-120 s-12.10-4 s-1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5


G23

/G23

° (M

Pa)

250 s-120 s-1

2.10-4 s-1

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5


G13

/G13

° (M

Pa)

250 s-120 s-12.10-4 s-1

11

2233

PredictionPrediction of the of the anisotropicanisotropic evolutionevolutionof all the of all the stiffnessstiffness coefficientscoefficients

PredictionPrediction of the of the macroscopicmacroscopic behaviourbehaviour

0

100

200

300

400

500

600

0 1 2 3 4 5D éform ation m acroscopique en %

Σ (M

Pa)

1 5% m odèle m =415% ex périence 20% m odèle m =420% ex périence

STRAIN

Al-SiCp

from K.DERRIEN

Elasticity + plasticity + damage + failure


-200

-100

0

100

200

-0,01 -0,006 -0,002 0 0,002 0,006 0,01

Total strain

Stre

ss (

Mpa

)

expérience

simulation

Al-Al2O3

From E. LEPEN

Elasticity + plasticity with kinematic and isotropic hardening + damage


S.M.C.Elasticity + viscodamage

0

20

40

60

80

100

120

140

160

-1 -0,5 0 0,5 1 1,5 2 2,5Strain (%)

Ten

sile

str

ess

(MPa

)

Model 22s-1: stress-strain22Model 22s-1: stress-strain1Experimental (22 s-1)Mode 150s-1: stress-strain11Mode 150s-1l: stress-strain22Experimental (150 s-1)

ε11

ε 11ε 22

ε =22 s -1

ε =150 s -1

From Z. JENDLI

02468

101214161820

0 0.2 0.4 0.6 0.8 1Strain (%)

Stre

ss (M

Pa)

10 MPa/s - Model10 MPa/s - FE1 MPa/s - Model1 MPa/s - FE0.1 MPa/s - Model0.1 MPa/s - FE


Glass reinforced thermoplastic

Non linear viscoelasticity

From M. LEVESQUE

PredictionPrediction of the of the effecteffect of of the the differentdifferent microstructuremicrostructure

PredictionPrediction of the of the behaviourbehaviour and damage and damage evolutionevolution for for differentdifferent loadingloading pathspaths..

Simulation micro-macro Matériaux CIC RANGERComparaison simulation-expérience

Essais quasistatiques

0

10

20

30

40

50

60

70

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Déformation (%)

Con

trai

nte

(MP

a)

Fibre à 90°

Endo interface seulsans endo matricielle

Fibre à 0°

Endo interface+

endo matricielle

ModelLoading in the 0°direction

Loading in the 90°direction

Experiences

C.I.C.

From J.FITOUSSI

STR

ESS

STRAIN

0

0,01

0,02

0,03

0,04

0,05

Fi/Ff

Distribution d'orientation des fibresFibres orientation distribution

PredictionPrediction of the of the behaviourbehaviourunderunder multiaxial sollicitationsmultiaxial sollicitations

Objective: Objective: to to performperform virtualvirtual multiaxial tests (multiaxial tests (bibi--tensiontension, , shearshear+tension, +tension, ……..)..)To To identifyidentify of a of a macroscopicmacroscopic damage damage criterioncriterionTo To identifyidentify the the evolutionevolution of of thisthisdamage surface damage surface withwith loadingloading

Simulation of Simulation of differentdifferent loadingloadingpathspaths : Iso: Iso--damage damage criterioncriterion

S.M.C.

From G. GUO

IsoIso--damage surface damage surface evolutionevolution

S.M.C.

From J. FITOUSSI

-60

-40

-20

0

20

40

60

-60 -40 -20 0 20 40 60

0/1

-1/1 1/1

σ1

σ2

1%5%

10%

20%

30%

Iso relative fraction of

broken interface fibres

Biaxial loading paths

Volume fraction of broken interface fibres

function of the fibres orientation:Vfb

-100 -80 -60 -40 -20 0 20 40 60 80 1000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Tension

Vfb18MPa

Angle

Micro damage Micro damage evolutionevolution for for differentdifferent biaxialbiaxial loadingloading pathspaths

-100 -80 -60 -40 -20 0 20 40 60 80 1000

0.05

0.1

0.15

0.2

0.25

Tension-compression

Angle

Vfb

18MPa

-100 -80 -60 -40 -20 0 20 40 60 80 1000

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Bi-tension

Angle

Vfb18MPa

HeterogeneousHeterogeneous structure structure behaviourbehaviour simulationsimulation

ThesesTheses virtualvirtual tests tests allowallow to to identifyidentify a a threethreedimensionnaldimensionnal anisotropicanisotropic behaviourbehaviour lawlaw..PossibilityPossibility to to performperform finitefinite elementselementscalculationscalculations: :

2 solutions:2 solutions:1. 1. MacroscopicMacroscopic lawlaw identifiedidentified by the micro by the micro

macro macro relationshiprelationship2. Micro2. Micro--macro model macro model introducedintroduced in the FEM in the FEM

code (code (UmatUmat, , AbaqusAbaqus))

IntegratedIntegrated DesignDesign

FiniteFinite elementselements calculationscalculations of the of the processprocess to to getget the distribution of fibres orientation.the distribution of fibres orientation.

FiniteFinite elementselements calculationscalculations of the of the deformationdeformationand damage of an and damage of an heterogeneousheterogeneous structure structure takingtaking intointo accountaccount the spatial distribution of the spatial distribution of the microstructure.the microstructure.

• mesh Moldflow

• Simulation of the process

( ex: Moldflow, …)

Interpolation of the fibres

orientation matrices

•Mesh(ex:Radioss,Abaqus…)

•Imput material data file

•Simulation of the deformation and the

damage of the structure

Coupling of process simulation with structure design simulation

F.E. MESH Differentmaterial data files

Simulation of the mouldfilling by injection of short fibres composites .

From P. CHINESTA

PredictionPrediction of the fibres orientationof the fibres orientation

From P. CHINESTA

Simulation of Simulation of bendingbending + + torsion of S.M.C. structuretorsion of S.M.C. structure

From G. GUO

ABAQUS+ UMAT

MICRO-MACRO LAW

Simulation of the Simulation of the behaviourbehaviour of a of a structure structure usingusing a microa micro--macomaco lawlawfor S.M.C.for S.M.C.

0

50

100

150

200

250

300

350

400

450

-1,50% -1,00% -0,50% 0,00% 0,50% 1,00% 1,50% 2,00%

Longitudinal strain ε22(%)

Force (N)

F. E. Face in tractionTest, Face in tractionF.E. Face in compressionTest, Face in compression

From G. GUO

Simulation of the Simulation of the lostlost of of stiffnessstiffness due to damagedue to damage

From G. GUO

0.25 1 1.5 2.25 2.75 3.5 4 4.751.5

69

13.516.5

2124

28.5

0

2.5

5

7.5

10

12.5

15

Longitudinal Young’smodulus (GPa)

thickness (mm)

width (mm)

0 à 5%5 à 10%10 à 15%15 à 20%20 à 25 %25 à 30%35 à 40%40 à 45%

Different volume fraction, different distribution of fibres orientation. due to the injection process.

Futur: Futur: PossibilityPossibility to to simulatesimulate the the behaviourbehaviour of a real of a real heterogeneousheterogeneouscomposite structurecomposite structure

From P. COUDRON INOPLAST

CONCLUSIONCONCLUSION

DiscontinuousDiscontinuous reinforcementreinforcement lawslaws basedbased on on homogeneisationhomogeneisation techniques techniques Introduction of micro damage Introduction of micro damage lawslaws for for eacheachdamage damage mechanismsmechanismsIdentification of the Identification of the micmic--macmac lawlaw fromfrom ultrasonicultrasonicmeasurementsmeasurements, , tomographytomography, and in situ , and in situ tensiletensiletests tests PredictionPrediction of the of the macroscopicmacroscopic behaviorbehavior and damage and damage effecteffect up to up to failurefailure for multiaxial stress statesfor multiaxial stress statesPredictionPrediction of the of the deformationdeformation and damage of an and damage of an heterogeneousheterogeneous structure by structure by couplingcoupling processprocess and and structure structure finitefinite elementselements simulations.simulations.

THANK YOU

presented by didier baptiste ensam, lim, umr cnrs 8006 151...

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