| A finite element method based micromechanical analysis is used to understand the fracture behavior of homogeneous and functionally graded foams. Both rectangular prism and tetrakaidecahedral unit cells are studied. Two approaches of predicting fracture toughness of foams and other cellular materials are used in this study. In one approach, the finite element analysis uses a micromechanical model in conjunction with a macro-mechanical model in order to relate the stress intensity factor to the stresses in the struts of the foam. The stress intensity factor at the crack tip of the macro-mechanical model can be evaluated using either the J-contour integral or the stresses in the singularity-dominated zone. The other approach is to directly apply displacements based on the K-field on the boundary of the micromechanical model.;Using the first approach, the mode I fracture toughness is evaluated for various crack positions and length. Both homogeneous foam and graded foam are studied to investigate the effect of stress gradients in the vicinity of the crack-tip on the fracture toughness. Various types of loading such as remotely applied displacements, remote traction are studied. Preliminary results of this study show that the stress gradient has slight effects on the fracture toughness. However, since the effects are relatively small, KIc can be defined as a material property. Then the relationship between the fracture toughness of the graded foam and the local density at the crack tip is studied.;The second approach is easy to apply in predicting the fracture toughness of homogeneous foam. By using this approach, convergence study of a micromechanical model is conducted. Also, an analytical model for the mode I fracture toughness of foams with rectangular prism cells is introduced. The mode I and mode II fracture toughness of homogeneous foam consisting of tetrakaidecahedral unit cells are predicted. A parametric study is performed to understand the effect of the geometric parameters of the unit cell and tensile strength of the foam ligament and also dislocation imperfection in the foam. |
