Simultaneous extraction of tensile and shear interactions at interfaces

Abstract

A simple beam analysis is developed that accounts for the tensile and shear interactions between the surfaces of two beams that have been brought into contact. The generally coupled differential equations for the relative normal and tangential displacements between the interacting surfaces and the normal and shear components of the traction between the two surfaces are decoupled when a balance condition involving the bending stiffness and height of each beam is satisfied. This condition also allows the normal and shear components of the J-integral and the crack tip displacement to be obtained from measurements of the applied loads along with load point displacement and rotation of each beam. As a result, the derivative of each component of the J-integral with respect to its associated crack tip displacement simultaneously provides both the normal and shear traction–separation relations at any value of the mode-mix without invoking any assumption on the particular form. As an application of this method, the normal and shear traction–separation relations for a silicon/epoxy interface were determined over nominal mode-mixes ranging from −53° to 87.5° using non-symmetric end-loaded split (ELS) and end-notched flexure (ENF) specimens. It is found that many of the assumptions made previously in developing traction–separation relations based on potential or damage-based approaches do not apply to this particular interface, which should motivate future theoretical developments.