A series solution approach to an analytical load-deflection relation for the measurement of mechanical properties of thin films

The load-deflection technique is a popular technique to measure mechanical properties such as internal stress and Young's modulus of thin films. The measurement of internal stress and Young's modulus depends on the determination of the analytical load-deflection relation. In this paper, a series solution approach is presented to obtain the analytical load-deflection relation for a circular membrane. To determine the number of terms required for the results to settle to a stable value, a convergence study is carried out. The present study found that to obtain the analytical load-deflection relation using a series solution approach, the transverse displacement can only admit one term solution, while the in-plane displacement can have a series solution. The present approach has been verified with a finite-element solution obtained using Macneal-Schwendler Corporation Nastran by comparing maximum deflections as well as deflection curves. The agreement is excellent.