A Model to Predict the Elastic Properties of Reticulated Porous Ceramics

Abstract

Reticulated porous ceramics (RPCs) have a number of useful applications, but utilizing them in structural applications is hampered by the lack of models to accurately predict their elastic properties. The existing models for the elastic properties of foams do not take into account the features present in RPCs, specifically the distinctive shape of the cross sections of the ligaments. The work herein presents the development of an analytical model to predict the elastic material properties of RPCs based on the realistic ligament matrix geometry. Also presented is a validation of the elastic modulus model using experimental results for a cerium dioxide (ceria) RPC and data from the literature of other RPCs. The RPC is represented by a repeating unit structure of truncated octahedrons (tetrakaidecahedrons) with the ligaments represented by the cell edges. The deformations of the ligaments in the cellular structure under applied loads are used to determine the effective elastic modulus, shear modulus, and Poisson's ratio of the bulk material. The model is the first to consider the effect of the features of ligaments of RPCs on the elastic moduli of the bulk material. The ligament cross section is represented as having a Plateau border exterior surface with a cusp half-angle that is varied between zero and 90 degrees, and a Plateau border interior void with a cusp half-angle of zero, representative of the range seen in RPCs. The ligament cross-sectional area is permitted to vary along its length and the distance between internal and external cusps is assumed constant. The relative density of the foam, corresponding to the length, cusp distances, and external-cusp half-angle of the ligaments, is determined using solid geometry. The relative elastic properties of the RPC are presented in relation to the relative density. The moduli depends largely on the relative density. For example, the relative elastic modulus increases by ~4000% from a relative density of 0.03 to 0.30. The impact of the normalized length of the ligament is less important. The normalized ligament length only varies the moduli by 11-49% in the same relative density range. The impact of the external shape of a ligament on the relative moduli is insignificant. The model was validated through comparisons with the measured elastic properties of RPCs in the literature. Additional validation of the elastic modulus model was performed using experimental results from flexural tests performed on ceria RPCs. The new model agrees within 30% of the ceria RPC elastic modulus experimental measurements, a significant improvement compared to the 95% over prediction by a previous model that uses a staggered cubic structure. The elastic modulus and four-point flexural strength of a gelcast ceramic, cerium dioxide (ceria), with a microporosity of nominally 20% and a grain size of 11 um from 23 to 1500 degrees C was measured. The ceria tested is representative of that constituting the ligaments of a reticulated porous ceramic. The data augment the sparse data published for ceria and extend previous results by 150 degrees C. The elastic modulus decreases from 90 GPa at 23 degrees C to 16 GPa at 1500 degrees C. The flexural strength is 78 MPa below 900 degrees C and then decreases rapidly to 5 MPa at 1500 degrees C. These trends are consistent with data reported for other ceramics. Comparing the measured elastic modulus to prior data obtained for lower porosity shows the minimum solid area model can be used to extend the modulus data to other porosities. Similarly, the flexural strength data agree with prior data when the effects of specimen size, porosity, and grain size are taken into account. The data provide a means of projecting the ceria RPC elastic properties to different temperatures.