h. chalal, f. meraghni , f. pierron & m. grÉdiac *
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CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
DIRECT IDENTIFICATION OF THE DAMAGED BEHAVIOUR OF
COMPOSITE MATERIALS USING THE VIRTUAL FIELDS METHOD
H. CHALAL, H. CHALAL, F. MERAGHNIF. MERAGHNI, F. PIERRON & , F. PIERRON & M. GRÉDIACM. GRÉDIAC**
LMPFLMPF, JE 2381 , JE 2381 – ENSAM Châlons en Champagne– ENSAM Châlons en Champagne
**LERMES – Univ. Blaise Pascal, Clermont Ferrand IILERMES – Univ. Blaise Pascal, Clermont Ferrand II
Université Blaise Pascal
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
OUTLINEOUTLINE
Introduction
The Virtual Fields Method
Damage Meso-modelling
Non linear Constitutive Law Implementation
Application : Iosipescu Configuration Test
Results : Numerical Aspects and Parametric Study
Conclusions
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
INTRODUCTIONINTRODUCTION
Objective
To identify an in-plane non-linear behaviour law for orthotropic composite materials
- Performing several mechanical tests
- Unable to extract the coupling terms (tensoriel damage approach)
Local strain measurements
Inverseproblem
Heterogeneous stress fields
Usual technique :
Novel Strategy
Involves the whole set of material parameters
Whole-Field MeasurementsWhole-Field Measurements ( great amount of information)
Uniform stain/stress fields (closed-form solution)
(no closed-form solution)
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
How to link WFM to the identified parameters ?
Among the techniques : FE models Updating•• Iterative process
•• Need to introduce initial values
Novel strategy for in-plane orthotropic composites :
The Virtual Fields Method (VFM) : Grédiac M. (1989)
Whole-kinematic fields are processed
INTRODUCTIONINTRODUCTION
Principle : Global equilibrium of a structure
Principle of Virtual Work .A.Ku, *0dSu.PdV:fS
*
V
*
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
How to find virtual kinematic fields ? (filtering information)
- analytically (found intuitively)
- automatic generation
Special virtual fields (recent improvements)
Grédiac M. proposed polynomial functions
m
i
n
j
ji
ij H
y
L
xAU
0 0
*~
Virtual Fields MethodVirtual Fields Method
K2 K1
x
y
S3 S2 S1
L
H
Thickness : e
uy ~
uy ~
P
Unnotched Iosipescu test
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
Damage Damage MMeso-modeleso-modelllinging
ss
yy
xx
d000d000d
d
Anisotropic Damage : Meso-model proposed by Anisotropic Damage : Meso-model proposed by Ladevèze (1986)Ladevèze (1986)
damage evolution is modelled by a quadratic damage evolution is modelled by a quadratic
function of the shear strainfunction of the shear strain
ddssss = = K/QK/Qssss . . ss22
only the in-plane shear damage is considered
In the present work :
Non linearity Non linearity of the behaviour is assumed to beof the behaviour is assumed to be due mainly to damage. due mainly to damage.
IIn-plane stressn-plane stress
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
Non Linear Behaviour LawNon Linear Behaviour Law
PVW
dSKdSQdSQdSQdSQS
ss
S
ssssyx
S
xyxy
S
yyyy
S
xxxx *3***** )(e
LUP y )(. *
Identification requires at least 5 different virtual fields
, P (resulting force) : KnownKnownsγεε y,x,
Qxx, Qyy, Qxy, Qss, K : Unknown parametersUnknown parameters
s
yx
2sss
yyxy
xyxx
s
yx
γεε
)Kγ(Q000QQ0QQ
σσσIn-plane orthotropic compositeIn-plane orthotropic composite
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
dSKdSQdSQdSQdSQS
ss
S
ssssyx
S
xyxy
S
yyyy
S
xxxx *3***** )(e
LUP y )(. *
=1 =0 =0=0 =0
eUPQ y
xx
*)1(. Uy(1)* : first special virtual displacement
To extract Qxx..
According to the same scheme, Qyy Qxy, Qss and K are determined
……...eUPQ y
yy
*)2(.eUPK y
*)5(.
Virtual Fields MethodVirtual Fields Method
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
2.3 ssss
ss KQJ
In the present study, these are nIn the present study, these are numerically simulated umerically simulated usingusing FE FE analysisanalysis
FE Implementation of the considered behaviour law FE Implementation of the considered behaviour law
development of development of a a UMATUMAT (ABAQUS) routine : Incremental (ABAQUS) routine : Incremental stress estimationstress estimation
)(.)()1( iJii
IMPLEMENTATIONIMPLEMENTATION
Actual strain fields : Experimental measurements using optical methodsActual strain fields : Experimental measurements using optical methods
( grid method, ESPI, …) ( grid method, ESPI, …)
lk
ijijklJ
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
A
C
B
RESULTSRESULTS
Finite element model (ABAQUS 6.2- UMAT)
15000 (2D) 4-nodes plane stress element (CPS4)
In-plane shear strain field simulated for the damaged compositeIn-plane shear strain field simulated for the damaged composite
Unnotched Iosipescu specimenUnnotched Iosipescu specimen
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
Linear shear response Non-linear shear response
RESULTSRESULTS
UD : Glass /epoxy (M10) compositeUD : Glass /epoxy (M10) composite
FE inputs
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
Identification from Noisy Data
= 5% = 10%
Amplitude noise = . Max(mean(|x|), mean(|y|), mean(|s|))
RESULTSRESULTS
UD : Glass /epoxy (M10) compositeUD : Glass /epoxy (M10) composite
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
L 15000 elements
SENSITIVITY TO THE LENGTHSENSITIVITY TO THE LENGTH
Increasing L : bending stresses increaseDecreasing L : shear and transverse compression stresses increase
Optimal L ?
UD : Glass /epoxy (M10) compositeUD : Glass /epoxy (M10) composite
40
30
20
10
Qxx
(G
Pa)
5040302010L (mm)
Identification Reference
14
12
10
8
6
Qyy
(G
Pa)
5040302010 L (mm)
6
5
4
3
2
1
0
Qxy
(G
Pa)
5040302010L (mm)
5.0
4.5
4.0
3.5
3.0
Qss
(G
Pa)
504540353025201510L (mm)
7000
6000
5000
4000
3000
2000
K (
GP
a)
504540353025201510L (mm)
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
L
Noisy strain fields
Mean values of 30 identifications
40
30
20
10
Qxx
(G
Pa)
5040302010L (mm)
Identification without noise Reference Noisy data (5%)
14
12
10
8
6
Qyy
(G
Pa)
5040302010 L (mm)
6
5
4
3
2
1
0
Qxy
(G
Pa)
5040302010L (mm)
5.0
4.5
4.0
3.5
3.0
Qss
(G
Pa)
504540353025201510L (mm)
7000
6000
5000
4000
3000
2000
K (
GP
a)
504540353025201510L (mm)
SENSITIVITY TO THE LENGTHSENSITIVITY TO THE LENGTH
UD : Glass /epoxy (M10) compositeUD : Glass /epoxy (M10) composite
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
UD : Carbon/epoxy (T300/914)
r = 13.7
SENSITIVITY TO THE ORTHOTROPIC RATIO
both materials
L=30 mm
UD : Glass /epoxy (M10) composite (r = UD : Glass /epoxy (M10) composite (r = QQxxxx /Q /Qyyyy = 2.5) = 2.5)
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
Identification from Noisy Data
= 5%
L=30 mm is probably not the optimal length for the T300/914
SENSITIVITY TO THE ORTHOTROPIC RATIO
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
CONCLUSIONCONCLUSION
Capability of the VFM to process Whole-fields measurments
Identification of material parameters governing a damage model
VFM : proved numerically robust and less sensitive to moderate noisy data
Interaction between specimen length and material orthotropic ratio
VFM : less sensitive to the specimen length when the strain gradients are well described (numerically or experimentally)
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
Identification Identification : Off-axis orthotropic behaviour: Off-axis orthotropic behaviour
Coupling termsCoupling terms
(6 constants to be identified simultaneously)(6 constants to be identified simultaneously)
ss
ysyy
xsxyxx
QSYMQQQQQ
Q.
.
FURTHER WORKFURTHER WORK
Coupled damage modelCoupled damage model
ss
yy
d..SYM0d.000
d
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
-2.0
-1.8
-1.6
-1.4
-1.2
-1.0
Ga
mm
a1
2 (%
)
20x103 16141210
Nombre d'éléments dans la zone acitve
Point A
-50x10-3
-40
-30
-20
-10
0
Ga
mm
a1
2 (%
)
20x103 16141210
Nombre d'éléments dans la zone acitve
Point C
-80x10-3
-60
-40
-20
0
20
40
Ga
mm
a1
2 (%
)
20x103 16141210
Nombre d'éléments dans la zone acitve
Point B
Convergence spatialeConvergence spatiale
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
L
5.0
4.5
4.0
3.5
3.0
Qss
(G
Pa)
504540353025201510L (mm)
Identification Référence
5000
4500
4000
3500
3000
2500
2000
K (
GP
a)
504540353025201510L (mm)
Identification Référence
30
29
28
27
26
25
24
23
Qxx
(G
Pa)
5040302010 L (mm)
Identification Référence
4.0
3.8
3.6
3.4
3.2
3.0
Qxy
(G
Pa)
5040302010L (mm)
10.8
10.6
10.4
10.2
10.0Q
yy (
GP
a)
5040302010L (mm)
Identification Référence
9600 elements
SPATIAL CONVERGENCESPATIAL CONVERGENCE
CompTest 2003CompTest 2003 :: ENSAM-Châlons en Champagne,ENSAM-Châlons en Champagne, 28-30 January 200328-30 January 2003
Virtual Fields MethodVirtual Fields Method
Global equilibrium of a structurePrinciple
Principle of Virtual Work0dSu.PdV:
fS
*
V
* .A.Ku, *
Basic idea : Grédiac M. (1989)
Known : P (global load), and specimen geometry
Introduction of the behaviour law which form is a priori known
Writing : PVW with as many virtual fields (u*) as unknown parameters
A set of linear equations system
Resolution : direct and simultaneous determination of the parameters
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