Size-Dependent Analysis of Strain Energy Release Rate of Buckling Delamination Based on the Modified Couple Stress Theory

In micro-electro-mechanical systems, interface expansion issues are commonly encountered, and due to their small size, they often exist at the micro- or nano-scale. The influence of the micro-structural effect on interface mechanics cannot be ignored. This paper focuses on studying the impact of micro-structural effect on interface crack propagation. Modified couple stress theory (MCST) is used to study the buckling delamination of ultra-thin film-substrate systems. The equivalent elastic modulus (EEM) and equivalent flexural rigidity (EFR) are derived based on MCST. Substituting EEM and EFR into the classical Kirchhoff plate theory, the governing equations of ultra-thin film-substrate system with micro-structural effect can be obtained. The finite element method (FEM) was used to calculate the critical strain energy release rate for crack extension. Differences between the three theoretical approaches of MCST, classical theory (CT), and FEM were compared. The effects of stress ratio sigma sigma c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{\sigma }{{\sigma_{c} }}$$\end{document}, initial crack length, film thickness, and micro-structural effect parameters on crack extension were analyzed. The results show that the FEM calculations coincide with the CT calculations. The stress ratio sigma sigma c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{\sigma }{{\sigma_{c} }}$$\end{document}, initial crack length, film thickness, and micro-structural effect parameters have significantly influence crack extension.