Ceramic foams often have hollow cell walls as a result of the replication process used to make them. Derive an expression for the fracture toughness of an open-cell ceramic foam with hollow cell walls of circular cross section (thin-walled), in terms of the modulus of rupture of the cell wall, σfs , the relative density ρ∗/ρs , the cell size, l , and the ratio of the radius to wall thickness, r/t , and a constant C . Assume that the modulus of rupture of the cell wall material is constant. Please note: Due to limitations of the computer grader, you will need to enter ρ∗ as "rho".

K∗IC

As we know that ,the mechanical behaviours of ceramic foams greatly depend on their cell topology, including cell shape, cell size etc. as well as relative density and ceramic properties of the cell wall.

However, the cell shape effect on the ceramic behaviours of such materials appears to be ignored in previous research. In this paper, both analytic and finite element models are developed and employed to investigate the effect of cell shape on the mechanical behaviour of open-cell magnesium alloy (AZ91) foams under compression, including deformation modes and failure modes. For numerical modelling, both two-dimensional (2-D) and three-dimensional (3-D) finite element models are developed to predict the compressive behaviours of typical open-cell ceramic foams and capture the deformation modes and failure mechanisms. Two typical cell shapes i.e. cubic and diamond are taken into consideration. To validate these models, the analytic and numerical results are compared to the experimental data. Both the numerical and experimental data indicate that the cell shape significantly affects the compression behaviour of open-cell metal foams. In general, numerical results from the three-dimensional solid-element model show better agreement with the experimental results than those from other finite element models.