Modified Stoney formula for obtainment of stress within thin films on large deformed isotropic circular plates

TL;DR

This paper introduces a modified Stoney formula that accurately estimates residual stress in thin films on large-deformed isotropic circular plates by accounting for nonlinear deformation effects.

Contribution

A new nonlinear extension of the Stoney formula is proposed, incorporating a parameter related to plate properties to improve stress measurement accuracy under large deformations.

Findings

The modified formula reduces errors in stress estimation for large deformations.

The coefficient p relates curvature to stress as a function of plate parameters.

The formula is validated for various plate dimensions and materials.

Abstract

Stoney formula is widely used to obtain the residual stress in the films on isotropic circular plates. However, significant errors would be introduced for large deformations because of the assumption of small deformation in the Stoney formula. In this study, a modified Stoney formula was proposed to extend its scope of application to the nonlinear domain. One-phase exponential decay function with coefficient p was used to relate the curvature of the substrate to the stress in the film. The coefficient p could be expressed as a function of the thickness, diameter, Young's modulus, and Poisson's ratio of the circular plate. The linear fitting technique was applied to ascertain the relationship between the coefficient p and the aforementioned parameters. The simple yet accurate modified Stoney formula could be used to calculate the residual stress in the film directly from the measured curvature of isotropic circular plates with various dimensions and materials.