The effective crack extension and its implications on the single cantilever beam test for sandwich composites

Abstract

The response of Single Cantilever Beam sandwich specimens may be analyzed effectively through one-dimensional theories accounting for the actual deformation of the core and its effects on fracture parameters and compliance. The model of a beam on an elastic Winkler foundation describes the detaching facesheet as an Euler–Bernoulli beam resting, in the bonded region, on an elastic foundation which generates oscillating deflections with characteristic length $1/\lambda$ . Modified beam theory (MBT) describes the debonded part of the face sheet as a cantilever beam, built-in at the debond tip, with an effective length which is longer than the actual detached length, by a quantity $\mathrm{\Delta }$ . If $\mathrm{\Delta }=1/\lambda$ the two models predict the same energy release rate and similar load-point displacements. Effective crack extension and characteristic length depend on the thicknesses and elastic constants of facesheets and core and may be derived through experimental measurements of the specimen compliance at various increments of crack growth, as prescribed by experimental protocols. In the theoretical analyses, $\mathrm{\Delta }$ is typically assumed, either by directly using formulas proposed for other specimens or by calibrating their parameters to case specific finite element results. In this paper, we investigate the applicability of such formulas to a wide selection of sandwich composites for naval and aeronautical applications having thicknesses or materials other than those used for the original fitting; we then highlight their limitations and effects on the design of experimental protocols for material characterization. The applicability of a recent isotropic-elasticity based formula for $\mathrm{\Delta }$ is then verified using extensive data from the literature and novel finite element (FE) results for typical sandwich composites. Finally, a novel elasticity solution for the load-point displacement of a layer on a half plane is derived which supports the test data reduction procedure for $\mathrm{\Delta }$ .