Onset of failure in aluminum honeycombs under general in-plane loading

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Of interest here is the theoretical prediction of the onset of failure in aluminum honeycombs under arbitrary macroscopic loading conditions. A failure surface is defined in macroscopic stress space by the onset of the first buckling-type instability encountered along proportional load paths, where each load path is defined by a fixed macroscopic load orientation and a fixed ratio of principal macroscopic stresses. The influence of specimen size (i.e., geometric scale effects), and the influence of geometric microstructural imperfections on these failure surfaces, are investigated through a combination of analytical (i.e., Bloch wave) and numerical (i.e., finite element) techniques. All of the analyses presented here are carried out for commercially available honeycombs, and the results show an extreme sensitivity of the onset of failure in these materials to the macroscopic load orientation and the principal macroscopic stress ratio. In addition, the failure surface for a perfectly periodic honeycomb of infinite extent, is found to be an upper bound for the failure surfaces of the corresponding finite honeycomb specimens with microstructural imperfections. Moreover, the construction of the failure surfaces for the imperfect specimens requires the numerical solution for large, multicell models, while the failure surface for the finite, perfectly periodic model is obtained with less computational effort, since calculations involving only the unit cell are required. The methodology proposed in this investigation, therefore, provides a useful predictive tool for the design of these materials.