Closed-Form Solution and Experimental Verification for the Axisymmetric Deformation Problem of Blistering Circular Thin Polymer Films under Uniformly Distributed Gas Pressure

The existing studies indicate that the measurement formulas used in blister test techniques, which are used to measure the mechanical properties of thin-film/substrate systems, are usually given based on an approximation—that is, the applied direction of the uniformly distributed transverse load is always vertical, while the applied direction of the uniformly distributed gas pressure is always perpendicular to the surface of the thin film. This approximation will lead to a large measurement error. In this study, we obtained the analytical solution to the problem of axisymmetric deformation of blistering circular thin polymer films under the action of uniformly distributed gas pressure via the power series method. An example is given to illustrate the error caused by the approximation mentioned above, and the validity of the solution presented here is verified. The result shows that the chance of error caused by the approximation increases with the increase in the applied load, and it far exceeds the allowable error of measurement when the applied load is relatively large. In addition, the related experiments of the blistering circular thin polymer film under uniformly distributed gas pressure are carried out, and the experimental results are compared with the theoretical results. The comparison results show that the analytical solution given in this paper is correct. The solution presented here is of great significance to improve the measurement accuracy of the blister test technique.