A two-scale model for predicting elastic properties of porous titanium formed with space-holders

This study proposes a model for the effective Young's modulus of porous titanium produced by space-holder technique. Unlike conventional foams, it contains porosities at two scales: macro-pores formed by the space-holder and micro-pores formed by incomplete sintering of the titanium powder. The structure of the porous body is therefore defined in terms of two state parameters: the relative density at the macro- and micro-scale. It is proposed that the interaction between the two scales is small, and models of each type of porosity are developed separately. It is found that the micro-scale model is in good agreement with the experiment data, as it is expected to be less sensitive to random variations in the powder structure. The macro-model is found to under-estimate the effect of the pores arising from the space-holder, as the distribution of these tends to be highly variable in size, shape and spatial distribution.