Large Deflection Effects on the Energy Release Rate and Mode Partitioning of the Single Cantilever Beam Sandwich Debond Configuration

Abstract

This paper investigates the effects of large deflections on the energy release rate and mode partitioning of face/core debonds for the Single Cantilever Beam Sandwich Composite testing configuration, which is loaded with an applied shear force and/or a bending moment. Studies in this topic have been done by employing geometrically linear theories (either Euler-Bernoulli or Timoshenko beam theory). This assumes that the deflection at the tip of the loaded debonded part is small, which is not always the case. To address this effect, we employ the elastica theory, which is a nonlinear theory, for the debonded part. An elastic foundation analysis and the linear Euler Bernoulli theory is employed for the “joined” section where a series of springs exists between the face and the substrate (core and bottom face). A closed form expression for the energy release rate is derived by use of 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. Furthermore, a mode partitioning angle is defined based on the displacement field solution. Results for a range of core materials are in very good agreement with the corresponding ones from a finite element analysis. The results show that large deflection effects reduce the energy release rate but do not have a noteworthy effect on the mode partitioning. A small deflection assumption can significantly overestimate the energy release rate for relatively large applied loads and/or relatively long debonds.