On determining mixed-mode traction–separation relations for interfaces

Traction–separation relations can be used to represent the adhesive interactions of a bimaterial interface during fracture. In this paper, a direct method is proposed to determine mixed-mode traction–separation relations based on a combination of global and local measurements including load-displacement, crack extension, crack tip opening displacement, and fracture resistance curves. Mixed-mode interfacial fracture experiments were conducted using the end loaded split (ELS) configuration for a silicon-epoxy interface, where the epoxy thickness was used to control the phase angle of the fracture mode-mix. Infra-red crack opening interferometry was used to measure the normal crack opening displacements, while both normal and shear components of the crack-tip opening displacements were obtained by digital image correlation. For the resistance curves, an approximate value of the J-integral was calculated based on a beam-on-elastic-foundation model that referenced the measured load-displacement data. A damage-based cohesive zone model with mixed-mode traction–separation relations was then adopted in finite element analyses, with the interfacial properties determined directly from the experiments. With the mode-I fracture toughness from a previous study, the model was used to predict mixed-mode fracture of the silicon/epoxy interfaces for phase angles ranging from -42∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-42^{\circ }$$\end{document} to 0∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0^{\circ }$$\end{document}. Results from experiments using ELS specimens with phase angles that differed from those employed in parameter extraction were used to validate the model. Additional measurements would be necessary to further extend the reach of the model to mode-II dominant conditions.