Micromechanical model for predicting the fracture toughness of functionally graded foams

A finite element analysis based micromechanical method is developed in order to understand the fracture behavior of functionally graded foams. The finite element analysis uses a micromechanical model in conjunction with a macromechanical model in order to relate the stress intensity factor to the stresses in the struts of the foam. The continuum material properties for the macromechanical model were derived by using simple unit cell configuration (cubic unit cell). The stress intensity factor of the macromechanical model at the crack tip was evaluated. The fracture toughness was obtained for various crack positions and lengths within the functionally graded foam. Then the relationship between the fracture toughness of foams and the local density at the crack tip was studied. In addition, convergence tests for both macromechanical and micromechanical model analysis were conducted. Furthermore, fracture toughness was estimated for various loading conditions such as remote loading and local crack surface loading. Local effect was studied by crack face traction conditions. The principle of superposition was used to analyze the deviation caused by local loading conditions such as crack surface traction and temperature gradients. From the thermal protection system point of view the behavior of graded foams under thermal loading was investigated, and fracture toughness was estimated. The methods discussed here will help in understanding the usefulness of functionally graded foam in the thermal protection systems of future space vehicles. However, further research is needed to focus on more realistic cell configurations, which capture the complexity of foam and predicts more accurately its mechanical property changes, such as relative density and modulus in functionally graded foam, in order to provide more accurate predictions.