Mechanical Behaviour of silica filled Silicon Rubber:

an Optical two-dimensional Extensometer Application

Mechanics of Materials and Structures Lab (2MS) Engineering Materials Center (CMGD)Ales School of Mines (EMA)

M. Giton, P. Ienny, R. Piques

CompTest 2003 2

Introduction

Tear Strength: Common Approach Principle: analytical model in Fracture Mechanics Drawback:

– no realistic approximation of the behaviour– dependency of the tear strength on

• specimen geometry• loading conditions (type of the test)

Local Approach Principle: stress concentration analysis

– Mechanical behavior of the material– Simulated test by FEA

ds

dfy

x

CompTest 2003 3

Experiment Optimization processus

FiniteElementAnalysis

Load and Digitalkinematic field

constitutive law

Boundary Conditions

Mesh

Optimization Procedure

Experimental Datas

Digital Image Correlation

Image Analysis

Experimental Results

FEABC

ED

DIC

IA

ER

M

E(t)

F(t)

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Digital Image Correlation

F(t)

u(t)

Experimental setup

FEABC

ED

DIC

IA

ER

M

Image sequence

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Digital Image Correlation

Principle of the method

two-dimensional displacement measurements

t,XU i

mes

t,i

FEABC

ED

DIC

IA

ER

M

mes

tiF

,

Linear fit of displacement field

tIFFLi

Tmes

ti,

,

In-plane tensor of strain

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Digital Image Correlation

Image 2

X1

Y1

Y

XX2

Y2

P1 (x1 ; y1)

M1

M2

P2 (x2 ; y2)

Image 1

Processing method

FEABC

ED

DIC

IA

ER

M

•Elastomers: large strain

•Tear Study: local phenomena

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Digital Image Correlation

Image 2

X1

Y1

Y

XX2

Y2

[F]-1

P1 (x1 ; y1)

M1

M2

P2 (x2 ; y2)

Image 1

221

11 PMFPM

Improvement of the processing method

FEABC

ED

DIC

IA

ER

M

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Digital Image Correlation

New correlation functions

u

u

u

uPuPP

uFMuFMM

uPuFMPM

2Im2Im

1Im1Im

2Im1Im,

Where

2Im

111Im

12Im,1Im

PM

PMPMTc

2Im1Im

2Im,1Im ,,

Iterative fine search method:•lower number of intermediate images•better localisation measurement

u:Pattern of M

FEABC

ED

DIC

IA

ER

M

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Experimental Tests

V

UCUT

BT

B.C.

Homogeneous tests

FEABC

ED

DIC

IA

ER

M

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Experimental Tests

Exemple of experimental results in UT

FEABC

ED

DIC

IA

ER

M

0

1

2

3

4

5

6

7

-0.5 1.5 3.5 5.5

Experimental Strains

Nom

inal

Str

ess

(MPa

)

Exx

Exy

Eyy

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Experimental Tests

Non-homogeneous tests

L R

a

L

geometry

b

Alignment defaults

FEABC

ED

DIC

IA

ER

M

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Experimental Tests

Non-homogeneous tests

FEABC

ED

DIC

IA

ER

M

Realistic mesh

Realistic BC

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Experimental Tests

Non-homogeneous tests

FEABC

ED

DIC

IA

ER

M

Transverse profiles : axial stretch ratio

evolution

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Phenomenological modelFEA

BC

ED

DIC

IA

ER

M

4

8

2

4

14

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Experimental Study Numerical Study

EXPERI

MENT

Testing

Images

Collection

FiniteElementAnalysis

Load and Digitalkinematic field

viscous hyper-elastic law’sparametrersBoundary

Conditions

Mesh

Optimization Procedure

FiniteElementAnalysis

Load and Digitalkinematic field

constitutive law

Boundary Conditions

Mesh

Experimental Datas

Digital Image Correlation

Image Analysis

Experimental Results

FEABC

ED

DIC

IA

ER

M

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FiniteElementAnalysis

constitutive law

Boundary Conditions

Mesh

Optimization Procedure

Law cost Function

FEABC

ED

DIC

IA

ER

M

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Results and Discussion

Uniaxial Tensile Test

0

1

2

3

4

5

6

7

0.5 0.6 0.7 0.8 0.9 1

stretch ratio

No

min

al S

tre

ss

(M

Pa

)

0

1

2

3

4

5

6

7

1 2 3 4

stretch ratio

No

min

al S

tre

ss

(M

Pa

)

UT - v1

UT - v2

UT - v3

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Results and Discussion

Biaxial Tensile Test

0

1

2

3

4

5

6

0.85 0.9 0.95 1stretch ratio

No

min

al S

tre

ss

(M

Pa

)

0

1

2

3

4

5

6

1 1.5 2 2.5 3stretch ratio

No

min

al S

tre

ss

(M

Pa

)

BT - v1

BT - v2

BT - v3

Pure shear

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Results and Discussion

DENT Test

0

10

20

30

40

0 200 400 600 800 1000

time (s)

Lo

ad

(N

)

s imulation

experiment

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Results and Discussion

DENT Tests

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Concluding and remarks

Strain sollicitations diagram

1

1.5

2

2.5

3

3.5

4

0.5 1 1.5Transversal Stretch Ratio

Axi

al S

tre

tch

Ra

tio

DENT exp.

DENT sim.

UT

BT

Multiaxial tests with localisation zone

Fracture criteria

CompTest 2003 22

Concluding and remarks

FEA + Two-dimensional Digital Extensometer

•Realistic Boundary Conditions

•Identical meshes for FEA/DIC

•Identification bases on Multiaxial Tests

Inverse Approach