Modelling of elastic properties of sintered porous materials

Models for prediction of the elastic characteristics of natural and synthetic porous materials are re-examined and new models are introduced. First, the Vavakin–Salganik (VS) model for materials with isolated spherical pores is extended in order to take into account various statistical distributions of pore sizes. It is shown that the predictions of the extended VS model are in good agreement with experimental data for porous materials with isolated pores such as foamed titanium, porous glass and sandstone. However, the model is in a considerable disagreement with the experimental data for materials sintered from metal powders. The disagreement is explained by the presence of merged and open pores whose shapes cannot be well approximated as spheres. Using the theory of geometrical probabilities, the amount of pores that are close enough to overlap is estimated, and a model is introduced where merging pores are modelled as corresponding ellipsoids. Another modification is proposed to take into account open pores. This modification is based on the classical Rabotnov–Kachanov approach to damage accumulation in the loaded material. Finally, predictions given by the above models, and their combination is compared with experiments. A good agreement is observed between the combined model and the available experimental data for a variety of sintered materials.