Elastic Foundation Solution for the Energy Release Rate and Mode Partitioning of the Mixed-Mode Bending Sandwich Configuration

This paper presents a closed form solution for the Mixed Mode Bending debond test configuration in sandwich composites. The solution is for the energy release rate and the mode partitioning. The finite-length sandwich specimen is considered to be a beam consisting of a debonded part (top face) and a substrate part (core and bottom face). A finite debond exists at the interface between the top face and the core. In the intact region, the two parts are considered to be joined through an elastic foundation, which is a uniform distribution of normal and shear springs. Based on the Euler-Bernoulli beam theory, the solution for a general asymmetric sandwich construction is derived. The energy release rate solution is derived via the J-integral and also from the energy of the broken springs in the elastic foundation. In this approach, the elastic foundation mode partitioning is defined based on the opening and shearing displacement at the tip of the elastic foundation (where the debond ends). The results are computed for a range of load configurations, core/face materials, core/face thicknesses and debond lengths. The results are also compared with the ones from a finite element study and show good agreement, except for the very small debond lengths.