Roberta Massabò

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 [ ]. 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 [ ]. If [ ] 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, [ ] 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 [ ] 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 [ ].

The flexibility of the bonds between the adjacent layers of multi-layered systems and their degradation or the presence of delaminations strongly affect mechanical response and final collapse. The formulation of accurate and efficient models able to capture the complex local distributions of stresses and displacements, which arise due to the layered structure and imperfect bonding, is of great importance for the design and verification of the systems. In this paper a novel and effective “single-variable zigzag” theory is formulated to analyze beams with homogeneous layers made of the same material and imperfect interfaces, which allow sliding between the layers. The primal variable is a fictitious bending displacement, which is derived in order to define all other kinematic and static quantities in terms of it. The “zigzag” technique describes multilayer systems with imperfect interfaces as equivalent single-layers, so that the problem is governed by equations similar to those of the classical theories for homogeneous beams; the “single-variable” formulation facilitates the implementation into numerical schemes and eliminates well-known numerical problems. Explicit solutions are straightforwardly derived for simply supported beams subjected to uniform and sinusoidal transverse loads. The results for some exemplary structural elements confirm the accuracy and efficiency of the approach. The study is preliminary to the single-variable reformulation and numerical implementation of the zigzag models for laminates with elastic mismatch between the layers.

Upper and lower bounds for the parameters of one-dimensional theories used in the analysis of sandwich fracture specimens are derived by matching the energy release rate with two-dimensional elasticity solutions. The theory of a beam on an elastic foundation and modified beam theory are considered. Bounds are derived analytically for foundation modulus and crack length correction in single cantilever beam (SCB) sandwich specimens and verified using accurate finite element results and experimental data from the literature. Foundation modulus and crack length correction depend on the elastic mismatch between face sheets and core and are independent of the core thickness if this is above a limit value, which also depends on the elastic mismatch. The results in this paper clarify conflicting results in the literature, explain the approximate solutions, and highlight their limitations. The bounds of the model parameters can be applied directly to specimens satisfying specific geometrical/material ratios, which are given in the paper, or used to support and validate numerical calculations and define asymptotic limits.

Equivalent single layer theories for layered beams effectively and accurately predict global displacements and internal force and moment resultants using a limited number of displacement variables. However, they cannot reproduce local effects due to material architecture or weak/imperfect bonding of the layers, such as zigzag displacement fields, displacement jumps at the layer interfaces and complex transverse stress fields, nor can they simulate delamination damage growth. In this work we will present some applications and discuss advantages and limitations of a recently formulated zigzag model. The model, through a modification of the equilibrium equations of an equivalent single layer theory, which maintains the same number of variables, reproduces local effects and delamination fracture under mode II dominant conditions. The approach is based on a local enrichment of the displacement field of first order shear deformation theory, the introduction of cohesive interfaces and homogenization.