Accuracy and Reliability of Bulge Test Experiments
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ACCURACY AND RELIABILITY OF BULGE TEST EXPERIMENTS MARTHA K. SMALL, JOOST J. VLASSAK, STEPHEN F. POWELL, BRIAN J. DANIELS AND WILLIAM D. NIX Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305 ABSTRACT In this paper we address possible causes for inconsistencies in bulge test results and describe methods by which the bulge test technique can be made to produce accurate and reliable results. Experiments have been conducted on a variety of materials: polyimide (PIQ13) and polycarbonate (Lexan), silver and silver-palladium multilayers, and silicon nitride. All the materials tested yield biaxial moduli that are in the range of expected values for the bulk material. In addition, the tests show that the technique can be used to differentiate between the elastic properties of materials throughout the range of elastic stiffnesses, with even crystallographic texture having a notable impact on the measured modulus. These results will be presented along with the methods used for preparing bulge test samples. INTRODUCTION With the bulge test one applies pressure behind a freestanding thin film clamped over an orifice. From the deflection of the film as a function of pressure one can determine such quantities as elastic modulus, residual stress and yield stress in the film. 1 The sources of error in the bulge test have been discussed in detail elsewhere. 2' 3 These are caused primarily by uncertainty in the film geometry. The deflection of a membrane under pressure is extremely sensitive to its dimensions. Thus, uncertainty in the film dimensions leads to considerable scatter in the measured modulus. Also, an initial, unmeasured bulge height can lead to large increases in the measured elastic modulus as well as apparently non linear elastic deformation. Finally, residual compressive stresses in a film cause it to buckle and become wrinkled. This wrinkling is eliminated gradually under pressure, but results in an additional deformation component that is difficult to quantify and is not included in any of the currently available bulge test models. It is possible to avoid all of these problems by producing initially flat films of welldefined dimensions. A simple curve-fitting procedure can be used to measure and eliminate the slight initial film height that is usually present in bulge test data. In the following sections we will show how this has been done and the bulge test applied to materials over a wide range of elastic properties. The results will be presented along with the methods used to obtain them. THE BULGE TEST
Analysis As mentioned above, the principle behind the bulge test is very simple. One applies pressure to one side of a freestanding film and measures the resulting deflection. For a linearlyelastic material, the equation that relates pressure, P, and deflection, h, is as follows,
P
ht f(v)Y h(
where 2 a is the film diameter (circular films) or side length (square films), t is thickness, o'o is the residual tensile stress in the film, and Y is biaxial modulus, E/(l-v), whe
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