2013 Koiter Medal Paper: Crack-Tip Fields and Toughness of Two-Dimensional Elastoplastic Lattices

The dependence of the fracture toughness of,o-dimensional (2D) elastoplastic lattices upon relative density and ductility of cell wail material is obtained for four topologies: the triangular lattice, kugome lattice, diamond lattice, and the hexagonal lattice. Crack-tip fields are explored, including the plastic zone size and crack opening displacement. The cell walls are treated as beams, with a material response given by the Ramberg Osgood law. There is choice in the criterion Pr crack advance, and two extremes are considered: (i) the maximum local tensile strain (LTS) anywhere in the lattice attains the failure strain or (ii) the average tensile strain (AT,S') across the cell wall attains the failure strain which can be identified with the necking strain). The dependence of macroscopic fracture toughness upon failure strain, strain hardening exponent, and relative density is obtained for each lattice, and SCaling laws are derived. The role of impeifections in degrading the fracture toughness is assessed by random movement of the nodes. The paper provides a strategy for obtaining lattices of high toughness at low density, thereby Idling gaps in material property space.