1. INTRODUCTION:
This study is aimed at determining additional abilities, weaknesses and strength of the bulge testing technique. In particular, the possibility to evaluate Poisson’s Ratio and the properties of films with high residual stress is analyzeds. The manufacturing of thin films has an extremely large number of factors that influences the properties of the final film. In the bulge testing method, pressure is applied on the backside of a micromachined thin film membrane. The film consequently deflects and forms a bulge, we can see that in Fig. 1 and
Figure. 1: Bulge Testing: Dimensions of the Bulge
The applied pressure is recorded and the bulge height is measured, how that is can be seen in fig 2: Bulge cross section. The pressure p and membrane center displacement deflection h are directly related to the in-plane properties Elastic Modulus and residual stress in the film.
Figure. 2: Bulge Cross-Section
A suitable model is developed that converts the pressure-displacement data to stress and strain, from which the unknowns can be calculated.
The
general bulge testing procedure is to incorporate a model that relates the
applied pressure and the membrane deflection to the unknown parameters of the
film. During inflation of the bulge, pressure (p) and membrane center
deflection (h) are measured. A curve of the general shape p=Ah3+Bh
is fit through the experimental data. This exact shape of the function is
dependent on the specific model that is used, but in general A is a function of
Young’s modulus (E) and B is dependent on the residual stress 
of the film. The constants A and B are then determined from the curve
fit and the film parameters E and 
can be solved.
2. LITERATURE REVIEW:
J. J. Vlassak, and W. D. Nix, et al., investigated new bulge test method for the determination of young’s modulus and poion’s ratio of thin films. D. Srikanth Rao and N. Gopikrishna et al., evaluated strain release rate. B. Erdem Alacaa) and K. Bugra Toga et al., developed Strain controlled bulge test for determination of poison’s ratio using a test called bulge. N. Gopikrishna et al., and D. Srikanth Rao et al., evaluated Mode – I fracture toughness. J. SLOTA, E. SPIÁK et al., determined flow stress by hydraulic bulge test.
GENERAL BULGE EQUATION:
These are standard procedures to determine the membrane geometry with great accuracy. A and B then become functions of Young’s Modulus (E), Poisson’s Ratio (v) and the residual stress only. These unknowns are the geometry-independent material parameters that shall be determined by bulge testing.
Fundamental Principle
Bulge test for circular membrane: For the thin-walled sphere, the stress σ in a spherical pressure vessel of the thin film membrane can be expressed as the formula:
where R is the radius of spherical; P is the applied pressure; and t is the thickness of the thin film.
In bulge test, the model derived from Beam was based on the assumption of line diagram of bulging as shown in Fig.3 and Schematic layout of the Bulge test as shown in Fig.4. The circular membrane have a radius a. When the pressure is applied to the specimens, the deformation of the membrane produced a height h.
Using equations (13) and (14) one can measure E and υ by a bulge test performed on the same material in a square and rectangular geometry. The 2 measured deflections will lead to 2 equations with 2 unknowns (E and υ). Application of the bulge test for the first time to atomic scale membranes to extract the elastic constants of graphene. The experiments in this thesis only measured a combination of and υ and not each independently since we studied only a square membrane.It can be found that the Young’s modulus and residual stress form the experimental result by curve fitting. There are different assumptions for equation of circular membrane. The determination of constants C1 and C2 by different research [6, 9-11] are summarized in table 1.
Table.1: Different assumptions of C2 value
|
For circular membrane |
Different Assumptions |
The constant value C2 |
Poisson’s ratio 0.25 |
|
Beam’s [6] |
Spherical cap |
8/3 |
13.33% |
|
Hohlfelder [10] |
Hencky’s [9] Numerical approximation |
8/3(1.015-0.247v) |
10.47% |
|
Lin’s [11] |
Energy minimization |
(7-v)/3 |
11.68% |
Design of the Equipment
A simple test equipment which could be used by any skilled worker, an attempt has been made to design an apparatus with materials which either available or can be fabricated locally. From the data available, it was observed from the literature, that metal foils would bulge to rupture at pressures of 4-5 kg/cm2.
A leg operated air pump which could transmit the air pressure to the specimen up to 10 kgf/cm2 was procured. A cylinder which could act as the base plate for holding a specimen as well as store compressed air and transmit pressure was to be machined. The diameter of the specimen to be bulged was arbitrarily fixed at 102 mm. For transmitting the air pressure under the specimen a hole of 20mm thick and ½ inch outer diameter.
The following considerations of the bulge test make a bulge test apparatus for conducting bulge test for thin films which is designed and realized and such samples were prepared. In this work the design criteria are presented, the control, the data acquisition and the data processing of the apparatus and the microscope are discussed and the sample preparation explained in this work. Finally, the realized bulge test apparatus was presented.
Design Considerations: The basic components of the bulge testing equipment designed consist of the following four components
Figure 5: Schematics representing the Basic Components
The sample holders designed for this simple bulge test equipment are of two types:
Circular Type Sample Holder:
It is designed using two plates, one free from the set up and the other welded together with the tapered frame through which the air from the compressor is passed. The free plate is used to fix the film to be tested using the other fixed plate as the support to it. The sample holder is designed in such a way that the air should not leak out through the sample. The sample holder shown in the fig above is of circular type
The Hemispherical Cap Type Sample Holder:
It is a single cast sample holder, which requires a cylindrical bar of mentioned diameter tapered from its center along its length as per the design requirements. Bottom of the set-up is drilled such that the pipe from the compressor should get merged into it. The sample is to be placed on top of tapered bar and is enclosed by a round cap so as to make the set-up air tight.
Figure 6: Circular type sample holder
Figure 7: Hemispherical Cap Type Sample Holder
Differential Pressure Control: Differential pressure control is one of the key in the testing set-up. It is used to provide the required maximum pressure that a film bears without bursting off. Generally in automated systems the pressure is controlled by giving standard inputs to the system, but in case of manual system as of this set up we are using a valve of the compressors provided to it for maintaining differential pressure.
Bulge Height Measuring System: A bulge height measuring system consists of a height measuring device. Generally LVDT’s are used in automated systems for higher accuracies. Any such devices like digital indicators, dial and pointer type indicators, manual scales can also be used for measuring bulge height of the film. Here in our experiments we are preferred to use plunger type indicator as shown in fig. 9(dial and pointer type) with magnetic stands, having least count (L.C) of 0.01mm and the maximum range of 20 mm.
Figure 8: Plunger type indicator
Figure 9: Air Compressor
Air Compressor:
This forms the source of pressure input to the film. Initially air is stored in the compressor (shown in fig. 10)with some predefined pressure, then pressure regulating valve is slightly opened so that the film sealed inside the set up bulges to the maximum extent.
3. RESULTS AND DISCUSSIONS:
Tests with Brass
From the experiments conducted,
Thickness of the film, t = 1.5 mm
Pressure input, 
=
2.6 bars
Bulge radius, a = 51 mm
Bulge height, z = 5.4 mm
Stress in the film due to the pressure induced is given by
4. CONCLUSION:
All measurement techniques listed above show limitations and drawbacks for measuring both, the elastic modulus and the residual stress in thin films. While some of them achieve good results in the determination of either of these properties, none of the techniques seems appropriate for the determination of both properties independently in one measurement.
Suggested improvement in Bulge Testing
Although Bulge Testing has gained acceptation as a standard technique for measuring material properties of thin films, the full capacities and the limits of this technique have not fully been explored yet. The purpose of this work is to broaden the knowledge of Bulge Testing in general and to determine special limitations and capabilities of this technique.
REFERENCES:
M. K. Small, J. J. Vlassak, and W. D. Nix, in Thin Films: Stresses and Mechanical Properties HI, edited by William D. Nix, John C. Bravman, Edward Arzt, and L. Ben Freund (Mater. Res. Soc Symp. Proc. 239, Pittsburgh, PA, 1992).
D. Srikanth Rao and N. Gopikrishna - International Education and Research Journal. 2017; 3(1): 44-46.
B. Erdem Alaca et al.: Strain-controlled bulge test , J. Mater. Res.2008; 23(12): 3295-3302.
N. Gopikrishna and D. Srikanth Rao. - International Journal of Innovative Research in Science, Engineering and Technology.2017; 6(1): 925-931.
J. Slota, E. Spiák Determination of flow stress by the hydraulic bulge test – Metalurgija. 2008; 47(1): 13-17
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Received on 13.10.2017 Accepted on 05.02.2018 ©A&V Publications all right reserved Research J. Engineering and Tech. 2018;9(1): 75-84 DOI: 10.5958/2321-581X.2018.00012.0 |
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