Micromechanics-Derived Scaling Relations for Poroelasticity and Strength of Brittle Porous Polycrystals

Abstract

There are lots of ceramic geological and biological materials whose microscopic load carrying behavior is not dominated by bending of structural units, but by the three-dimensional interaction of disorderedly arranged single crystals. A particularly interesting solution to capture this so-called polycrystalline behavior has emerged in the form of self-consistent homogenization methods based on an infinite amount of nonspherical (needle or disk-shaped) solid crystal phases and one spherical pore phase. Based on eigenstressed matrix-inclusion problems, together with the concentration and influence tensor concept, we arrive at the following results: Young’s modulus and the poroelastic Biot modulus of the porous polycrystal scale linearly with the Young’s modulus of the single crystals, the former independently of the Poisson’s ratio of the single crystals. Biot coefficients are independent of the single crystals’ Young’s modulus. The uniaxial strength of a pore pressure-free porous polycrystal, as well as the blasting pore pressure of a macroscopic stress-free polycrystal, scale linearly with the tensile strength of the single crystals, independently of all other elastic and strength properties of the single crystals. This is confirmed by experiments on a wide range of bio- and geomaterials, and it is of great interest for numerical simulations of structures built up by such polycrystals.