Crack nucleation due to elastic anisotropy in polycrystalline ice

Abstract

This paper presents a theoretical analysis of crack nucleation in isotropic polycrystalline ice due to the elastic anisotropy of the constituent crystals. The singularity of the associated stress concentrations near a grain-boundary facet junction provides the mechanism for inducing microcrack precursors, if similar nuclei do not already exist. The first-order microstructural stress field created by the elastic anisotropy mechanism is linearly superposed on the applied stress field. This total stress field causes the precursors to nucleate into microcracks. 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 energy of either the grain boundary or the solid-vapor interface. Model predictions show that: (a) the stress required to nucleate cracks in compression is about 2.5 times that in tension, unlike other microstructural models which predict them to be equal; (b) elastic anisotropy rather than dislocation pile-up as proposed by others may govern crack nucleation in tension over a wide range of strain rates; (c) 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; (d) the grain size effect due to the elastic anisotropy mechanism is similar to that due to the dislocation pile-up mechanism over the typical range of grain sizes encountered in nature; and (e) 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 excellent phenomenological approximation of the nucleation surface under multiaxial states of stress.