Fracture toughness of open-cell Kelvin foam

Brittle fracture behavior of a perfect open-cell Kelvin foam is considered. The foam is modeled as a spatial lattice consisting of brittle elastic struts rigidly connected to each other at the nodal points. The fracture toughness is determined from the analysis of a quasi-plane problem for a slice of the foam with an embedded finite length crack generated by broken struts. The crack plane is chosen on the basis of a previous study of crack nucleation phenomenon, and the crack length, which assures the self-similar K-field in the tip vicinity, is established by numerical experiments. For the considered densities range the crack includes several hundreds of broken struts and, consequently, the portion of the foam to be considered in the analysis has a very large number of nodal degrees of freedom. The computational cost is reduced significantly by using for the analysis the representative cell method based on the discrete Fourier transform. As a result, the initial problem for the foam slice is reduced to the problem for the repetitive cell which includes 12 struts. pendence of the Mode I and Mode II fracture toughness of the considered bending dominated foam upon its relative density is determined and found to be different from known results for the stretch dominated cubic cell lattice. On the other hand, the results obtained for Mode I meet the experimental data and theoretical predictions for random foams. For the case of struts with hollow cross-section the analysis predicts linear dependence of the fracture toughness upon cross-section gyration radius.