Biaxial bulge testing of thin films
and foils
Miroslav Cieslar
Faculty of Mathematics and Physics
Charles University, Prague
Czech Republic
J.L. Martin, A. Karimi: EPFL Lausanne, Switzerland
C. 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
Biaxial bulge test
Industrial requirements
for reliable biaxial tests
Testing of membranes in
micro- and nano-devices
Finstocks for heat
exchangers
Biaxial bulge test
Spherical cap model
pR

2t
a2  h2 a2
R

2h
2h
2
2h
 2
3a
Biaxial test with a constant fluid flow-rate
120
Stress [MPa]
Stress [MPa]
100
80
60
40
0.00022 ml/s
0.00130 ml/s
0.00260 ml/s
20
0.00433 ml/s
0
0
200
400
600
800
1000
Tim e [s ]
Time [s]
1200
1400
1600
Biaxial test under constant stress-rate
3
2
0.00022 ml/s
1.5
Stress rate [MPa/s]
Stress-rate [MPa/s]
2.5
0.00130 ml/s
0.00260 ml/s
1
0.00433 ml/s
0.5
0
-0.5
-1
-1.5
-2
0
100
200
300
400
500
Tim e [s ]
Time [s]
600
700
800
Examples
• Thin Al-Fe-Si foils (thickness 8.5 mm)
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
Recrystallization of thin foils
Stress – strain curves obtained from bulge tests
during prestraining and after annealing at indicated
temperatures.
Yield stress variation of predeformed aluminium foils
with annealing temperature
Microstructure after predeformation and
annealing
initial
200 °C
380 °C
590 °C
Plastic instabilities in Al–Fe-Si foils
stress [MPa]
150
100
as received
50
590 °C
630 °C
0
0
0.8
1.6
2.4
strain [% ]
3.2
Instabilities after strain rate jump
120
•
•

90
•
stress [MPa]

•
•




•

60
T = 590°C

A



•

•

30

•
•


•
•


•



as received
•
•
  



0
0
0.75
1.5
strain [% ]
2.25
Instabilities after an instant increase of stress
by 3 MPa
stress [MPa]
120
90
TD = R.T.
60
TD = 120°C
30
0
0
1
2
strain [% ]
Portevin – Le Chatelier effect?
Stress or strain oscillations?
Stability analysis
Constitutive equation
Homogeneous solution
Evolution of perturbations
Stability analysis
The rate of perturbations growth
Instability grow
w>0
Stability analysis
For positive SRS
e~  en
Hill’s criterion
For negative SRS
Simulations
Ring-shaped zone
of localized
intense strain rate
Simulations
Thin film plastic deformation
Biaxial plastic deformation of Al thin films
180
160
0.55 mm
1.1 mm
R 0.2 [MPa]
80
4.4 mm
100
T = R.T.
80
D
0
0.2
120
TA = 450 °C
T =R.T.
0
140
p
stress [MPa]
120
40
Al 5N5
160
0.4
Strain [% ]
0.6
60
0.4
D
0.6
0.8
-1/2
d
1
-1/2
[mm
1.2
]
1.4
Biaxial plastic deformation of Al thin
films
Influence of temperature
130
120
110
100
p
R 0.2 [MPa]
Al 5N5
1.1 mm
90
T = 450 °C
80
A
70
0
50
100
150
200
deformation temperature [°C]
250
Biaxial plastic deformation of Al thin
films
Creep-fatigue tests
0.7
Al 5N5
112
108
stress [MPa]
strain max. [%]
0.6
0.5
Al 5N5
1.1 mm
0.4
104
100
T = R.T.
0.3
D
1.1 mm
96
0.2
0
20
40
60
80
100
cycle
Variation of maximum strain
with the number of cycles
120
0.26
0.28
0.3
strain [%]
T = R.T.
D
0.32
Deformation loops received
during cycling
0.34
Deformation processes in Al-Zn-MgCu thin films
4 mm thin films from AA 7075 alloy
600
600
500
500
400
Rp0.2 [MPa]
stress [MPa]
Al-Zn-Mg-Cu
as deposited
TA=350°C, T D=R.T.
300
TA=350°C, T D=120°C
TA=350°C, T D=160°C
200
TA=350°C, T D=200°C
400
300
200
T A = 350 °C
TA=350°C, T D=280°C
100
100
0
0
0
0.5
1
strain [%]
1.5
2
0
50
100
150
200
250
Deformation temperature [°C]
300