Effects of buckling struts on the fracture toughness of triangular lattices

The effect of strut-buckling on the fracture toughness of elastic-brittle triangular lattices is investigated using the finite element method. Buckling of struts in the vicinity of a crack-tip is shown to precede fracture contingent on the relative density and strut material. Under idealised $K$-field conditions, it was found that the buckling struts act as a toughening mechanism in Mode I loading and lead to a knockdown in fracture toughness in Mode II. Linear perturbation analyses reveal the transition relative density below which strut-buckling precedes fracture, and its dependence upon the fracture strain of the strut material. A power-law scaling relationship between fracture toughness and relative density is proposed for the regime where buckling of constituent struts can occur before fracture. It will be shown that strut-buckling can lead to elastic crack-tip blunting and to the development of compliant layers of cells with reduced stiffness. Subsequently, the effects of mode mixity and T-stress on the transition relative density and deviation from the traditional fracture toughness scaling law are addressed. Buckling struts act as a toughening mechanism in modes with predominantly Mode I influence and lead to a knockdown in toughness for modes with more than 25% Mode II contribution. The inclusion of negative T-stress leads to an increase in the transition relative density and to significant toughness knockdown after the onset of buckling in Mode I.