Elastic Foundation Solution for the End-Notched Flexure Mode II Sandwich Configuration

This article presents a closed-form solution for the energy release rate of face/core debonds in the mode II end-notched flexure (ENF) sandwich configuration. The finite-length sandwich specimen is considered to have a "debonded" region and a "joined" region. In the later, the interface between the top face and the substrate (core and bottom face) is modeled by an elastic foundation, which is a uniform distribution of shear and normal springs. Based on the Timoshenko beam theory, the solution for a general asymmetric sandwich construction is derived. The energy release rate expression is derived via the J-integral. Another closed-form expression for the energy release rate is derived from the energy released by a differential spring as the debond propagates. In this closed-form solution, there is no fitting and everything, including the foundation constants, are given in a closed form. Results are produced for a range of face/core stiffness ratios and debond length/core thickness ratios and are compared with the corresponding ones from a finite element solution. A very good agreement is observed except for small debond lengths versus specimen thickness.