Closed form solution for the energy release rate and mode partitioning of the single cantilever beam sandwich debond from an elastic foundation analysis

Abstract

The goal of this paper is to derive closed form expressions for the energy release rate and mode partitioning offace/core debonds for the Single Cantilever Beam Sandwich Composite testing configuration, which is loaded with an applied shear force and/or bending moment. This is achieved by an elastic foundation approach, in which a finite length sandwich beam is treated as having a free “debonded” section and a “joined” section where a series of springs exists between the face and the substrate (core and bottom face). The elastic foundation analysis is done for a general asymmetric sandwich construction. A J-integral approach is subsequently used to derive a closed form expression for the energy release rate. It is also shown that the energy release rate is very close to the differential energy stored in the springs at the beginning of the elastic foundation, i.e. the energy released by the “broken” differential spring element as the debond propagates. In the context of this elastic foundation model, a mode partitioning measure is defined based on the transverse and axial displacements at the beginning of the elastic foundation. Since the normal springs account for the transverse compressibility of the core but not for the shear, a correction for the shear of the substrate is included by deriving the expression for the corresponding shear angle and accounting for the additional horizontal “tip” displacement. The results are compared with finite element results for a range of core materials and show very good agreement.