Analysis of the accuracy of the bulge test in determining the mechanical properties of thin films
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Since its first application to thin films in the 1950's the bulge test has become a standard technique for measuring thin film mechanical properties. While the apparatus required for the test is simple, interpretation of the data is not. Failure to recognize this fact has led to inconsistencies in the reported values of properties obtained using the bulge test. For this reason we have used the finite element method to model the deformation behavior of a thin film in a bulge test for a variety of initial conditions and material properties. In this paper we will review several of the existing models for describing the deformation behavior of a circular thin film in a bulge test, and then analyze these models in light of the finite element results. The product of this work is a set of equations and procedures for analyzing bulge test data that will improve the accuracy and reliability of this technique.
I. INTRODUCTION In the past 30 years the bulge test has become a standard technique for measuring thin film mechanical properties. Though sample preparation can be somewhat involved, the test is unique in that it allows the determination not only of film modulus, yield strength, and fracture strength, but of residual stress as well. The test involves clamping a free-standing thin film over an orifice and applying pressure to one side. Several models have been used in the past to convert the pressuredisplacement data obtained from this test into stress and strain. Since the solutions are based on different bulge shapes and boundary conditions, they naturally predict somewhat different deformation behaviors. As a result, researchers using different models can report different mechanical properties for the same material. In addition, initial conditions and experimental uncertainties have a substantial effect on the apparent film stiffness, and these are not always accounted for in the evaluation of bulge test data. It is perhaps not surprising, then, that bulge test results have often been difficult to reproduce or to substantiate by other mechanical testing methods. In bulge tests on Cu-Pd and Au-Ni multilayers, for example, Yang1 reported the biaxial modulus at small values of the modulation wavelength to be approximately four and two times that of a bulk mixture, respectively. Later work using the bulge test2 on Cu-Pd films and indentation and microbeam deflection3 on Au-Ni thin films found no enhancement. Much of the variation in the measured properties of identical materials can be attributed to an incomplete understanding of the bulge test itself. It is necessary to model the behavior of a film in a bulge test in order to find ways to improve the accuracy of our methods of data J. Mater. Res., Vol. 7, No. 6, Jun 1992 http://journals.cambridge.org
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analysis. In this paper we will first discuss the underlying assumptions and limitations of some previously derived models of the bulge test and then compare these models with our finite element model results. The goals of this work are (1) to tes
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