presented by didier baptiste ensam, lim, umr cnrs 8006 151...
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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
Déformation ε11 (%)
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
Déformation ε11 (%)
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
Déformation ε11 (%)
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
Déformation ε11 (%)
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
Déformation ε11 (%)
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
PredictionPrediction of the of the macroscopicmacroscopic behaviourbehaviour
-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
PredictionPrediction of the of the macroscopicmacroscopic behaviourbehaviour
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
PredictionPrediction of the of the macroscopicmacroscopic behaviourbehaviour
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 effecteffect of of the the differentdifferent microstructuremicrostructure
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
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