h. chalal, f. meraghni , f. pierron & m. grÉdiac *

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


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


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)


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

*


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


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


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


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(.



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


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


Linear shear response Non-linear shear response

RESULTSRESULTS

UD : Glass /epoxy (M10) compositeUD : Glass /epoxy (M10) composite

FE inputs


Identification from Noisy Data

= 5% = 10%

Amplitude noise = . Max(mean(|x|), mean(|y|), mean(|s|))

RESULTSRESULTS



L 15000 elements

SENSITIVITY TO THE LENGTHSENSITIVITY TO THE LENGTH

Increasing L : bending stresses increaseDecreasing L : shear and transverse compression stresses increase

Optimal L ?


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)


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 : 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)


Identification from Noisy Data

= 5%

L=30 mm is probably not the optimal length for the T300/914

SENSITIVITY TO THE ORTHOTROPIC RATIO


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)


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


-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


Point C

-80x10-3

-60

-40

-20

0

20

40

Ga

mm

a1

2 (%

)

20x103 16141210


Point B

Convergence spatialeConvergence spatiale


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)


30

29

28

27

26

25

24

23

Qxx

(G

Pa)

5040302010 L (mm)


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)


9600 elements

SPATIAL CONVERGENCESPATIAL CONVERGENCE



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

h. chalal, f. meraghni , f. pierron & m. grÉdiac *

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