Characterization of residual stress distribution of film/substrate structure with elastic boundary: Theoretical modeling and experimental identification

Film/substrate structures are extensively utilized in many fields due to their unique properties. Curvature-based techniques (CBTs) are employed to measure and analyze residual stresses within these structures. While existing theories have relaxed many limitations of CBTs, they primarily focus on the free boundaries of circular objects. To address this issue, this work presents an analytical method for evaluating residual stresses in film/substrate structures subjected to arbitrary misfit strains under elastic boundary conditions for the first time, and the proposed theory can be applied to objects of arbitrary shape. Based on linear elasticity theory, a system of coupled governing equations involving seven variables is established. The equations are decoupled and solved using Fourier series expansion and the method of constant variation. Random displacement fields with uniform, normal, and exponential distributions are utilized to examine the convergence of the results under various boundary stiffness conditions. Finite Element Method (FEM) is employed to validate the film stresses under different boundary conditions. Using Stoney formula as a rough estimate, an iterative algorithm has been developed to calculate equivalent boundary conditions for circular measurement boundaries. This algorithm enables dividing the object into multiple circular regions for individual measurement, facilitating the assessment of arbitrarily shaped objects. Finally, a monoscopic fringe reflectometry measurement system is developed to experimentally characterize the topography of specular surface. This system provides precise and efficient measurement of the topography of film/substrate structure. Utilizing this data, the full-field distribution of residual stresses is subsequently determined through an inversion process.