Crack nucleation due to elastic anisotropy in porous ice

Abstract This paper presents a theoretical analysis of crack nucleation in isotropic but porous ice due to the elastic anisotropy of the constituent crystals. Samples of freshwater polycrystalline ice made in the laboratory and those found in nature are in general porous materials. Even relatively dense samples of laboratory ice contain bubbles with average diameters in the range of 0.06–0.12 mm and average bubble densities of 350−6500 bubbles-cm −3 . Concentrated stress fields are produced both due to geometrical discontinuities such as grain-boundary-facet junctions and the presence of the pores which are often located in the vicinity of grain boundaries. The singularity of the microstructural stress field produced by crystal anisotropy provides the mechanism for inducing microcrack precursors on the surface of the pores, if similar nuclei do not already exist. Formation of the precursor relieves the stress singularity and a first-order approximation is adequate to characterize the remaining microstructural field. The precursors can nucleate into microcracks through the local intensification of the concentrated stress field around the pore produced by the applied stresses and the first-order microstructural stresses. The analysis of the nucleation stress is based on a solution to the general problem of an extending precursor in a combined stress field including the effects of Coulombic frictional resistance. The local material resistance is characterized in terms of a critical value for the maximum principal tensile stress which can be determined from the surface free energies of either the grain boundary or the solid-vapor interface. The stress gradients acting along the plane of the precursor due to the presence of the pore are taken into account in modeling frictional effects and computing the stress-intensity factors. Model predictions for relatively dense polycrystalline ice show that: (i) the presence of the pore influences the nucleation stresses at smaller grain sizes, i.e., less than about 5 mm, where the precursor and pore become comparable in size; (ii) the stress required to nucleate cracks in compression varies between 2.25–3.60 times that in tension, the larger values occur as the grain size decreases below 5 mm; (iii) the nucleation stress in tension closely follows the well-known linear Hall-Petch relationship with the inverse square root of grain size exhibited by experimental data; (iv) the stress required to nucleate a crack in compression is strongly dependent on crystal orientation and, as a consequence of the random orientation of crystals in isotropic polycrystalline ice, there can be a distinct beginning and end to the microcrack-nucleation phase when stress is increased and if failure does not occur prematurely; (v) the pore serves to change the nature of first crack nucleation from a shearing or mixed-mode phenomenon to a tension-dominated phenomenon as the grain size decreases below 5 mm, and this tends to align the microcracks perpendicular to the loading axis in tension and parallel to it in compression; (vi) a generalization of the limiting tensile-strain criterion proposed by Shyam Sunder and Ting (1985) which accounts for the anisotropy of the constituent crystals is an adequate phenomenological approximation of the nucleation surface under multiaxial states of stress.