Crack initiation and fracture toughness of random Voronoi honeycombs

The competing effects of cell-regularity and relative density upon the toughness of Voronoi honeycombs are investigated for different loading modes using finite elements. Mode I toughness is shown to be the more sensitive to microstructural variations than mode II although both retain a strong quadratic dependence upon relative density. Crack initiation is shown to occur at up to six cells from the crack-tip in regions of high localised strain and/or high strain gradient. The inclusion of T-stress dramatically changes the location of ligament fracture and the normalised effective toughness of a lattice. Ligament fracture is predominantly due to bending.