Effects of deflection on bulge test measurements of enhanced modulus in multilayered films

The bulge test is an experimental method to determine the yield behavior and biaxial elastic modulus of thin films. In a typical bulge test, pressure is applied to a free-standing foil. The bulge height h is measured as function of the applied pressure. The initial height h(0) of the bulge deflection must be considered when analyzing interferometric bulge-height measurements as the range of linearly elastic behavior and the magnitude of biaxial modulus enhancement are directly affected by it. Computation of the biaxial modulus over a linearly elastic range to 0.10% strain is shown to yield rule-of-mixtures values for homogeneous Ag/Pd and Cu/Pd multilayer foils. An apparent 500% modulus enhancement for a 1.47 nm Cu/Pd foil is reduced to 12% using an h(0) correction to produce a linear elastic response to 0.10% offset strain. For a 100% enhancement found in a 2.24 nm Ag/Pd foil, the ho correction reduces the enhancement to 51%. Analysis of bulge test results using an ho correction shows that modulus enhancement exists in metallic multilayers, but not to the extent found using a non-linear elastic analysis.