mechanical behaviour of silica filled silicon rubber: an optical two-dimensional extensometer...
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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
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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
CompTest 2003 6
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
CompTest 2003 7
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
CompTest 2003 12
Experimental Tests
Non-homogeneous tests
FEABC
ED
DIC
IA
ER
M
Realistic mesh
Realistic BC
CompTest 2003 13
Experimental Tests
Non-homogeneous tests
FEABC
ED
DIC
IA
ER
M
Transverse profiles : axial stretch ratio
evolution
CompTest 2003 14
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
CompTest 2003 20
Results and Discussion
DENT Tests
CompTest 2003 21
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