Relating stiffness changes in porous materials to the evolution of pore space

The work aims at relating stiffness changes in porous materials to the evolution of pore space geometry. After a brief review of the relevant micromechanics tools, we apply them to case studies on several metals. In particular, it is clarified, when porosity can or cannot be used as a single quantitative characteristic of the pore space in whose terms the effective stiffness is to be expressed, and when it must be changed to crack density. Namely, the use of porosity parameter is legitimate in cases of isotropic mixtures of pores having approximately equal shape factors, provided the shapes are not strongly oblate (aspect ratios larger than about 0.08). Considered examples show that, in cases of strongly oblate, crack-like pores, noticeable stiffness changes may occur at very low values of porosity; in such cases, the crack density parameter must be used. Besides predicting the effective stiffness in terms of proper characteristics of the pore space, the developed methodology allows monitoring the evolution of pore shapes based on stiffness changes and porosity data. In our analysis, pore geometries are modeled by spheroids of appropriate aspect ratios; they provide sufficient flexibility and allow quantitative modeling. The adequacy of such modeling is supported by agreement of the theoretical results with experimental data.