A theoretical analysis of crack nucleation due to grain boundary dislocation pile-ups in a random ice microstructure

Abstract

The nucleation of cracks is generally recognized as the precursor to the macroscopic fracture of many brittle materials. In this paper, the existence of load-induced cracks in polycrystalline S2 ice is investigated theoretically in terms of the pile-ups of grain boundary dislocations around grain triple points. Stress concentrations due to the elastic or thermal expansion anisotropy of the ice crystals are taken into account. Considering a random microstructure, the numerical results show that: (i) both stable and unstable cracks can be nucleated during loading, (ii) the microstructural stresses due to either type of crystal anisotropy obey a Gaussian distribution, (iii) the sizes of the stable cracks obey a gamma-type distribution with a small mean and a large skewness, (iv) the orientations of the stable cracks are approximately uniformly distributed, and (v) the crack statistics is a function of the microstructure and the loading conditions.