Fracture Toughness of Cellular Solids using Finite Element Based Micromechanics

Micromechanical methods to predict the fracture behavior and estimate the fracture toughness of cellular solids and foams are presented in this paper. The microstructure of the foam is modeled using finite elements. The struts of foam are modeled using either structural elements such as beams or three-dimensional solid elements. A portion of the foam containing an edge crack is modeled. Displacement boundary conditions are applied such that they correspond to a given value of stress intensity factor in the homogenized solid. The crack propagation is simulated by breaking the crack tip strut when the maximum stress in that strut exceeds the strength of the strut material. The results show that the displacements and stresses in the foam near the crack tip are very similar to that in an equivalent homogeneous material, and continuum fracture mechanics concepts can be applied to predict the fracture of a cellular medium. Numerical results are presented for Mode I fracture toughness tetrakaidecahedral foams.