Re-Examining the Bulge Test: Methods for Improving Accuracy and Reliability
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RE-EXAMINING THE BULGE TEST: METHODS FOR IMPROVING ACCURACY AND RELIABILITY MARTHA K. SMALL, JOOST J. VLASSAK AND WILLIAM D. NIX Department of Materials Science and Engineering, Stanford University, Stanford, California 94305 ABSTRACT Since its first application to thin films in the 1950's, the bulge test has had a prominent place in the field of thin film mechanical properties. The major appeal of the technique is that it is analogous to the familiar uniaxial tension test, which is commonly applied to bulk materials. At the same time, it avoids the sample tearing and alignment problems associated with micro-tensile tests. Unfortunately, bulge test results have been sometimes controversial and difficult to reproduce. In this paper we address possible causes for these inconsistencies and describe a method by which the bulge test technique can be made to produce accurate and reliable results. INTRODUCTION The bulge test was an early response to the question of how to test the mechanical properties of thin films. In this test a film is clamped over an orifice and pressure applied to one side, as shown in Fig. 1. The pressure-deflection curve obtained is a function not only of sample geometry and of the mechanical properties of the material, but also of residual stress and slack or wrinkling in the film. Uncertainty in the starting height that sometimes accompanies interferometric displacement measurements can also alter the shape of the curve and the apparent stiffness of the material. Ignoring any of these factors in analyzing bulge test data can completely invalidate the output of the test. This fact may account for reported differences of hundreds of percent in the elastic properties of seemingly identical materials measured in the bulge test [1, 2]. In this paper we will show how the finite element method has h been used to quantify sources of error in the test and prescribe a procedure for analyzing bulge P test results that should help to eliminate such variations. Figure 1. Bulge test schematic. FINITE ELEMENT MODEL FORMULATION The bulge test was modeled using axisymmetric thin shell elements with an isoparametric formulation. The boundary conditions for a test are that the center of the film remain at the center and noi rotate, so as to maintain a smooth top to the bulge, and that the edge of the film remain fixed and not rotate. The elastic properties of aluminum (E=71 GPa, v=.345) are used for the film unless otherwise specified. A slack film is modeled by first allowing the edge to slide inward while a small pressure is applied to one side of the film. Upon reaching the desired Mat. Res. Soc. Symp. Proc. Vol. 239. @1992 Materials Research Society
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height the film is clamped and then unloaded to determine the initial height of the bulge. The procedure is analogous to fitting the edge of a film of radius a to a hole of radius a-8, where 8 is small and positive. This models a film, part of which is free-standing, that is in compression on its substrate. A taut film is modeled by simply applying an initia
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