Vibrational Technique for Stress Measurement in Films: II, Extensions and Complicating Effects

Abstract

Several extensions and complicating effects in the vibrational technique for the measurement of stress in films are discussed in this, the second part of the study. The principles of the technique, based on ideal membrane behavior, and some applications were presented in the companion paper. Several complicating effects can be important due to deviation from ideal behavior. For low-density polymer membranes, air loading can shift the natural frequencies considerably. This effect is studied by measuring stress at different air pressures and compared to a theoretical model for the correction of air loading effects. The effect of bending stiffness can be important for thick and stiff films. This effect has been studied systematically and it is shown that it can be used to measure the stress and stiffness of the film simultaneously. A powerful extension of the technique to the measurement of anisotropic biaxial stresses is also demonstrated.

A resonant method for determining the residual stress and elastic modulus of a thin film

“…3 for comparison. Considering the effect of inhomogeneity of the film material on the testing and the inaccuracies of these two testing methods, 24,31 the experimental results are in reasonably good agreement with the results obtained using from the resonant method.…”

“…[19][20][21][22] In particular, when a thin film is stretched across a circular hole in a substrate, the natural frequencies of the film membrane can be related to the in-plane stress within the film. [23][24][25] Linear vibration analysis of membranes and plates has been a classic problem in solid mechanics. When a circular membrane lies in a plane with no resistance to bending and its material is elastic, its vibrations can be modelled by two-dimensional wave equations and the solution to the equations is analytically exact.…”

“…27 However, the introduction of residual stress into a membrane or plate makes the problem far more complex as it adds stiffness to the membrane or alters the stiffness of the plate. Several approximate methods 24,28 have been proposed to determine the residual stress and elastic modulus of a film employing resonant vibration measurement. An analytic solution to this problem would provide a simple and explicit method for determining residual stress in a thin film, which has great importance in engineering as circular membranes are widely used in pumps, microphones, mobile phones, and so on.…”

A New Analytical and Experimental Approach To Rubber Thermodynamics

“…This technique allows resolution of one or more of the principal stresses of a thin film in either uniaxial extension or isotropic and anisotropic biaxial extension to a degree of high accuracy. Holographic interferometry allows a variety of other measurements to be made, including directly measuring the total state of stress, the through the thickness diffusion coefficients of a thin film, and the linear elastic constants. − …”

Stress determination of micromembranes using laser vibrometry

“…11,12 In addition, dynamic techniques have been used where the resonant frequencies of vibrating membranes are used ͑as elaborated below͒ for determining stress. 1,[13][14][15] A new dynamic technique for membrane stress determi-nation utilizing laser vibrometry is described in the present article. Specifically, a tightly focused laser spot is used for interrogating the driven ͑vibrating͒ membrane surface while extracting displacement and velocity spot measurements from an interferometric analysis of the retroreflection.…”