Eq

where a is a constant that is generally taken to be 3. This, too, is an approximation based on the premises that the bulged film assumes a spherical shape and that the film is a plane at zero tension. The realization of true sphericity is questionable, but experimental results have shown that the meridional strain may be accurate within about 8% for strains up to 1% (Ref 5).

A serious criticism of bulge testing centers about the initial state of the film, that is, its flatness at zero pressure. Whenever bulge testing is carried out on films adherent to the substrate by removing the substrate over a given area, there may be residual compressive or tensile stresses in the film. In the former case, this results in buckling or wrinkling of the film, and in the latter case, in a film stressed in tension (Ref 6). These conditions must be taken into account when calculating the stress-strain relations obtained from the tests.

The bulge test presents an attractive method for determining mechanical properties of thin films, mainly because--in contrast to the uniaxial test--flaws at the edges of the film specimens do not affect bulge-test results. It is seen from the above comments, however, that the value of this method for the accurate determination of mechanical behavior of freestanding thin films is diminished because of the many imponderables with which the interpretation of bulge-testing data is fraught.

Beam-Bending Methods Applied to Free-standing Films. When a specimen in the shape of a beam is bent, the portion on one side of a longitudinal "neutral" plane is strained in tension, while the portion of the other side of the plane is strained in compression. If the specimen has a uniform composition, such as a freestanding film, the stress-strain relation of the material can be readily calculated from the load-deflection data determined during bending. In this technique, very small cantilever-beam specimens are used, which are produced by microelectronic fabrication methods. In such test, a Nanoindenter device can be employed that applies the load to the free end of the cantilever beam and simultaneously measures the deflection (Fig. 3). The elastic modulus and the yield strength of the material are determined from the load-deflection curve. The specimens for the microbeam method are prepared by creating the required pattern of the film and the subsequent removal of the substrate. Microbeam fabrication and testing are briefly reviewed in Ref 8. A detailed review of micromachining of beam specimens is given in Ref 9.

Fig. 3 Schematic drawing of a Nanoindenter used as a loading device on a microcantilever beam. Source: Ref 7

When the deflections are small and the material is considered to be uniform and isotropic and to deform elastically, the well-known equation for the cantilever-beam deflection S under a load P applied to the free end of a beam is given by:

0 0

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