Validation by asymptotic development of the empirical bulge test formula

The non-linear elastic bending of a thin axi-symmetrical film layer clamped at its edges has been investigated under pressure in the framework of the Föppl–von Karman theory of thin plates. The mechanical equilibrium equations have been solved for the pressurized layer by developing the relaxed stress and layer deflection in power of a pressure dependent parameter. The obtained expression allows for a better understanding of the different terms of the empirical bulge test formula and validates the use of this empirical expression by the materials science community for determining the elastic coefficients of thin films and coatings.