Residual curvature method

The thickness, density, and residual stress in sintered films can be determined by the methods described above. The X-ray diHfaction method of determining stress is generally more suitable for sintered films since it does not require the removal of the film, as do the substrate curvature methods. The surface roughness can be measured with a profilometer, whereas the adhesion of the film to the substrate can be determined by a pull test, in which a wire is bonded to the film and then pulled with the force needed to remove the film from the substrate. The amount of camber or warpage can also be determined with a profilometer. Grain and pore sizes can also be determined by the same techniques used for bulk ceramics. 

Thin-film residual stresses can be determined mainly by two different methods (i) the Stoney (1909) curvature method and (ii) X-ray diffraction if films are crystalline. We emphasize the curvature method, which is the most popular and widely used. The X-ray diffraction method is developed in Appendix L. 

There are several ways to test the linearity of a calibration line one can devise theory-based tests, or use common sense. The latter approach is suggested here because if only a few calibration points are available on which to rest one s judgement, a graph of the residuals will reveal a trend, if any is present, while numerical tests need to be adjusted to have the proper sensitivity. It is advisable to add two horizontal lines offset by the measure of repeatability accepted for the method unless the apparent curvature is such that points near the middle, respectively the end of the x-range are clearly outside this reproducibility band, no action need to be taken. 

The quasielastic method as developed by Schapery [26] is used in the development of the viscoelastic residual stress model. The use of the quasielastic method is motivated by the fact that the relaxation moduli are required in the viscoelastic analysis of residual stresses, whereas the experimental characterization of composite materials is usually in terms of the creep compliances. An excellent account of the development of the quasielastic method is given in [27]. The underlying restriction in the application of the quasielastic method is that the compliance response of the material shows little curvature when plotted versus log time [28]. Harper [27] shows excellent agreement between the quasielastic method and direct inversion for AS4/3510-6 graphite/epoxy composite. For most graphite/thermoset systems, the restrictions imposed by the quasielastic method are satisfied. 

To circumvent the drawbacks of the sin2 P-technique including the problem of a non-linearity of the modulus of elasticity, attempts have been made to apply other tests to obtain estimates of the residual stresses. The curvature measurement is probably one of the most widely used method for determining residual stress and involves measuring the bending of the coated sample in response to both quenching and thermal stresses. From the measured radius of curvature, the stress can be calculated according to the Stoney equation (Stoney, 1909) as... 

In particular, the lathe cut method (1) makes it possible to manufacture a lens with special curvature, this allows a high value-added lens specifically tailored to the user to be made. On the other hand, the direct method is suitable for mass production and is particularly suited for daily disposable lenses. Unfortunately, the current polymerization technique still has residual monomer and less molding precision than desired. 

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