The subject of the study are alumina foams produced by gelcasting method. The results of micro-computed tomography of the foam samples are used to create the numerical model reconstructing the real structure of the foam skeleton as well as the simplified periodic open-cell structure models. The aim of the paper is to present a new idea of the energy-based assessment of failure strength under uniaxial compression of real alumina foams of various porosity with use of the periodic structure model of the same porosity. Considering two kinds of cellular structures: the periodic one, for instance of fcc type, and the random structure of real alumina foam it is possible to justify the hypothesis, computationally and experimentally, that the same elastic energy density cumulated in the both structures of the same porosity allows to determine the close values of fracture strength under compression. Application of finite element computations for the analysis of deformation and failure processes in real ceramic foams is time consuming. Therefore, the use of simplified periodic cell structure models for the assessment of elastic moduli and failure strength appears very attractive from the point of view of practical applications.
The work reports on the development of random three-dimensional Laguerre-Voronoi computational models for open cell foams. The proposed method can accurately generate foam models having randomly distributed parameter values. A three-dimensional model of ceramic foams having pre-selected cell volumes distribution with stochastic coordinates and orientations was created in the software package ANSYSTM. Different groups of finite element models were then generated using the developed foam modeling procedure. The size sensitivity study shows that each of foam specimens at least contains 125 LV-cells. The developed foam models were used to simulate the macroscopic elastic properties of open cell foams under uni-axial and bi-axial loading and were compared with the existing open cell foam models in the literature. In the high porosity regime, it is found that the elastic properties predicted by random Laguerre-Voronoi foam models are almost the same as those predicted by the perfect Kelvin foam models. In the low porosity regime the results of the present work deviate significantly from those of other models in the literature. The results presented here are generally in better agreement with experimental data than other models. Thus, the Laguerre-Voronoi foam models generated in this work are quite close to real foam topology and yields more accurate results than other open cell foam models.