Stress-induced crystal preferred orientation in the poromechanics of in-pore crystallization

Abstract

A non-hydrostatic stress field affects the orientation of crystals growing in the pore network of an elastic porous medium. The hypothesis of a hydrostatic state of stress within the crystal has been implicitly made in the recent extension of poromechanics to in-pore crystalization ( Coussy, 2006). This underlying hypothesis is revisited on a small-scale conceptual model based on Eshelby's problem and shows that chemo-mechanical equilibrium requires that the crystal adapts its shape and orientation to the far-field stress, therefore resulting at equilibrium in a hydrostatic state of stress within the crystal. The optimum crystal shape as a function of the far-field stress is consistently investigated, highlighting limiting cases. The small scale model allows to understand the macroscopic effects associated with deviatoric stresses in the poromechanics of in-pore crystallization. Moreover, it provides the building block for an up-scaling of the macroscopic tangent poroelastic properties, which depend on both the current crystal saturation and the state of stress. A dilute micromechanical scheme illustrates the variation of the macroscopic Biot's coefficient tensor as a function of deviatoric stresses. A simple configuration akin to a potential laboratory experiment finally illustrates the strong induced anisotropy of the crystallization induced macroscopic strain when deviatoric stresses are applied to the material prior to crystallization.