biaxial bulge testing of thin films and foils miroslav cieslar faculty of mathematics and physics...
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Biaxial bulge testing of thin films and foils
Miroslav CieslarFaculty of Mathematics and Physics
Charles University, Prague
Czech Republic
J.L. Martin, A. Karimi: EPFL Lausanne, SwitzerlandC. Fressengeas: LPMM, Université de Metz, France
Schedule
• Introduction to small structure testing
• Bulge test
• Applications– Recrystallization of thin foils– Plastic instabilities in Al foils– Plastic deformation of thin metallic films
Most common experimental methods
• Films adhered to substrate– Nanoindentation (hardness, modulus)– Microbeam bending (fatigue, bending)– Wafer curvature (biaxial strain, thermal fatigue)
• Free standing films– Tensile test (difficult sample preparation)– Microbeam bending – Biaxial bulge test
Industrial requirements for reliable biaxial tests
Biaxial bulge test
Testing of membranes in micro- and nano-devices
Finstocks for heat exchangers
Spherical cap model
pR
2t
Ra2 h2
2ha2
2h
2h2
3a2
Biaxial bulge test
Biaxial test with a constant fluid flow-rate
0
20
40
60
80
100
120
0 200 400 600 800 1000 1200 1400 1600
Time [s]
Str
ess [
MP
a]
0.00022 ml/s
0.00130 ml/s
0.00260 ml/s
0.00433 ml/s
Time [s]
Str
ess
[MP
a]
Biaxial test under constant stress-rate
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 100 200 300 400 500 600 700 800
Time [s]
Str
ess r
ate
[M
Pa/s
]
0.00022 ml/s
0.00130 ml/s
0.00260 ml/s
0.00433 ml/s
Time [s]
Str
ess-
rate
[M
Pa/
s]
Examples
• Thin Al-Fe-Si foils (thickness 8.5 m)
Element Fe Si Cu Mn Mg Zn Ti Al
wt. % 0.51 0.61 0.007 0.020 0.0066 0.022 0.024 bal.
Initial microstructure after homogenization 590 °C/30 min
Stress – strain curves obtained from bulge tests during prestraining and after annealing at indicated
temperatures.
Recrystallization of thin foils
Yield stress variation of predeformed aluminium foils with annealing temperature
Microstructure after predeformation and annealing
200 °C initial
380 °C 590 °C
Plastic instabilities in Al–Fe-Si foils
0
50
100
150
0 0.8 1.6 2.4 3.2
as received
590 °C
630 °C
stre
ss [
MP
a]
strain [%]
Instabilities after strain rate jump
0
30
60
90
120
0 0.75 1.5 2.25
stre
ss [
MP
a]
strain [%]
as received
TA = 590°C
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Instabilities after an instant increase of stress
by 3 MPa
0
30
60
90
120
0 1 2
TD = R.T.
TD = 120°C
stre
ss [
MP
a]
strain [%]
Portevin – Le Chatelier effect?
Stress or strain oscillations?
Stability analysis
Constitutive equation
Evolution of perturbations
Homogeneous solution
Stability analysis
Instability grow
The rate of perturbations growth
>0
Stability analysis
Hill’s criterion
For negative SRS
For positive SRS
e~ єen
Simulations
Ring-shaped zone of localized intense strain rate
Simulations
Thin film plastic deformation
Biaxial plastic deformation of Al thin films
0
40
80
120
160
0 0.2 0.4 0.6
stre
ss [
MP
a]
Strain [%]
0.55 m
1.1 m
4.4 m
TD=R.T.
60
80
100
120
140
160
180
0.4 0.6 0.8 1 1.2 1.4
Rp0.
2 [M
Pa]
d-1/2
[m-1/2
]
Al 5N5
TA = 450 °C
TD = R.T.
Biaxial plastic deformation of Al thin films
Influence of temperature
70
80
90
100
110
120
130
0 50 100 150 200 250
Rp0.
2 [M
Pa]
deformation temperature [°C]
Al 5N5
TA= 450 °C
1.1 m
Biaxial plastic deformation of Al thin films
Creep-fatigue tests
0.2
0.3
0.4
0.5
0.6
0.7
0 20 40 60 80 100 120
stra
in m
ax.
[%]
cycle
Al 5N51.1 m
TD= R.T.
96
100
104
108
112
0.26 0.28 0.3 0.32 0.34
stre
ss [
MP
a]
strain [%]
Al 5N5
TD= R.T.1.1 m
Variation of maximum strain with the number of cycles
Deformation loops received during cycling
Deformation processes in Al-Zn-Mg-Cu thin films
4 m thin films from AA 7075 alloy
0
100
200
300
400
500
600
0 0.5 1 1.5 2
as depositedT
A=350°C, T
D=R.T.
TA=350°C, T
D=120°C
TA=350°C, T
D=160°C
TA=350°C, T
D=200°C
TA=350°C, T
D=280°C
stre
ss [
MP
a]
strain [%]
0
100
200
300
400
500
600
0 50 100 150 200 250 300
Rp
0.2
[M
Pa]
Deformation temperature [°C]
Al-Zn-Mg-Cu
TA = 350 °C