Blister Test Analysis Methods
- PDF / 804,117 Bytes
- 6 Pages / 414.72 x 648 pts Page_size
- 31 Downloads / 218 Views
materials[ l,2,3,4]. Pressure applied to one side of a free-standing thin-film "window" causes it to deflect outward. When pressure is sufficiently high, the film begins to debond from the substrate, forming a blister whose radius increases steadily (see figure 1). The adhesion energy is determined from measurements of pressure and deflection during blister growth. A closely related technique is the bulge test, in which the pressure- deflection behavior prior to any debonding is analyzed to determine the film's elastic modulus and residual stress[5,61.
S ...
..
a
a +Aa
l3efore debondingý Figure 1:
[Blister growth Schematic of the blister test
585
Mat. Res. Soc. Symp. Proc. Vol. 356 01995 Materials Research Society
The bulge equations The relation between pressure (p) and deflection (h) for a thin film window may be expressed as:
p
cl(ot h + c2 Et a4 (-v) a2
h3
(1)
where c I and c2 are geometric parameters, t is the film thickness, oo is the residual stress, E is Young's modulus, and v is Poisson's ratio. For additional simplicity, we rewrite eq. (1) as: p= where ic1 = cl (0 t and
1K2= C2 E
a2
h +
- h3 a4
(2)
t/(l-v).
The form of eq. (1) is the same as that obtained for the idealized "spherical cap" model, in which stress is assumed to be biaxial throughout the membrane. Small [7] showed that eq. (1) could be used to describe finite-element simulations of pressurized circular membranes. Vlassak[6] used an energy minimization technique to demonstrate the validity of eq. (1) for square and rectangular membranes. Geometric parameters ci and C2 are summarized for several geometries in table I. Table I: Geometric Parameters for Bulge Equation Geometry Cl c2 Ideal Spherical Cap[9] 4 2.667 Circular Film[8] 4 2.667 (1.014 - 0.244 v) Square Window[8] 3.393 (0.792 + 0.085 v)-3 Long rectangular window[8] 2 1.333 (1+ v)- 1 The volume of a blister is related to its radius and height through a volume parameter V = Kv a2 h
Kv:
(3)
The volume parameter for circular blisters is generally somewhat larger than the value of 7t/2 obtained from the idealized "spherical cap" model. In finite element simulations we have observed values ranging from 1.57 to 1.66. However, the variation within any given test over the range of interest is not large. From these results it is reasonable to assume that the volume parameter remains constant throughout a blister test.
Derivation of a blister equation The conditions under which a blister will grow (increase its radius) can be examined using a thermodynamic argument. We calculate the change in energy associated with a radius increase da and require the energy change to be negative for blister growth to proceed spontaneously. Three terms contribute to the total energy of the system: the strain energy of the bulged film (Ustrain), the work done by the pressurized fluid as the blister grows (Wexternal), and the energy of the film-substrate interface (Uinterface). When the blister radius increases, the amount of work done by the pressurized fluid is greater than the change in t
Data Loading...
