A micromechanical method to predict the fracture toughness of cellular materials

The Mode I, Mode II and mixed mode fracture toughness of a cellular medium is predicted by simulating the crack propagation using a finite element model. Displacement boundary conditions are applied such that they correspond to a given value of stress intensity factor in a homogeneous solid that has the same elastic constants as the cellular medium. 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. Based on the finite element results a semi-empirical formula is also derived to predict the Mode I and Mode II fracture toughness of cellular solids as a function of relative density. 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. The forces acting in the crack tip strut can be considered as the resultant of stresses over an effective length in the corresponding continuum model. A relation for this effective length has been derived in terms of the relative density of the cellular medium.