Fracture toughness of foams with tetrakaidecahedral unit cells using finite element based micromechanics

Fracture toughness of open-cell foams consisting of tetrakaidecahedral unit cells is predicted by simulating crack propagation using a finite element (FE) based micromechanical model. The inputs to the model are the geometric parameters required to model the repeating unit cell and tensile strength of the foam ligament or strut. Cracks are created by removing certain number of cells pertaining to a crack length. The FE model consists of a local micro-scale region surrounding the crack tip. For an assumed stress intensity factor, the displacements along the boundary of the local model are calculated based on linear elastic fracture mechanics for orthotropic materials. The stresses in the ligaments ahead of the crack tip calculated from this micro-model in conjunction with the tensile strength of the strut material are used to predict fracture toughness. A parametric study with different micro-model sizes and different crack lengths is performed to check for convergence of predicted Mode-I, Mode-II and mixed mode fracture toughness values. The effect of applying rotations as additional boundary conditions along with translational displacement boundary conditions on the predicted fracture toughness values is also studied.