|
UF
|
external work caused by the change of the potential energy of the liquid |
|
UF(a) |
the UF when r = a
|
|
Ua
|
energy absorbed by the enclosed air |
|
Ua(a) |
the Ua when r = a
|
|
Uef
|
elastic strain energy stored in the blistering thin film |
|
Uef(a) |
the Uef when r = a
|
|
Ud
|
energy released on the delamination region |
|
G
|
energy release rate |
|
K
|
proportional coefficient |
|
S
|
area of the circular delamination region |
|
a
|
radius of the circular delamination region |
|
R
0
|
radius of the hole in the rigid substrate |
|
R
|
inner radius of the container |
|
H
1
|
initial height of the air in left container |
|
H
|
height of the liquid added to the right container each time |
|
h
1,i
|
height of liquid in the left container after step i of loading operation |
|
h
2,i
|
height of liquid in the right container after step i of loading operation |
|
ρ
|
density of the liquid in the container |
|
g
|
acceleration of gravity |
|
P
|
pressure of gas |
|
V
|
volume of gas |
|
N
|
number of gas molecules per unit volume |
|
K
|
Boltzmann constant |
|
T
|
temperature of gas |
|
V
0
|
initial volume of the air in left container |
|
Vn
|
volume of the air in left container after the step n of loading operation |
|
r
|
radial coordinate |
|
w
|
transversal displacement |
|
u
|
radial displacement |
|
h
|
thickness of the membrane |
|
θ
|
slope angle of the deflected membrane |
|
σr
|
radial stress |
|
σt
|
circumferential stress |
|
er
|
radial strain |
|
et
|
circumferential strain |
|
E
|
Young’s modulus of elasticity |
|
|
Poisson’s ratio |
|
x
|
dimensionless form of r
|
|
Q
|
dimensionless form of q
|
|
W
|
dimensionless form of w
|
|
U
|
dimensionless form of u
|
|
Sr
|
dimensionless form of σr
|
|
St
|
dimensionless form of σt
|
|
bi, ci, di
|
coefficients of Sr, St and W
|