Strengthening and weakening of induced anisotropy in polar ice

Abstract

Reorientation of individual crystal glide planes as ice is deformed during its descent from the free surface to depth in an ice sheet creates a fabric and associated anisotropy. A macroscopic description in which the material glide planes are rotated towards planes normal to an axis of compression, and away from planes normal to an axis of extension, has already been applied to derive an associated orthotropic viscous law which expresses the deviatoric stress in terms of the strain rate, strain and three structure tensors based on the principal stretch axes. At high strain rate, or high shear stress, however, with critical magnitudes decreasing as temperature increases, dynamic (migration) recrystallization occurs and leads to loss of fabric strength and return to isotropic response. The orthotropic viscous law is now extended to incorporate this response, specifically to a behaviour in which anisotropy weakens continuously over a finite range of shear strain rate before isotropy is restored. Six different constructions are considered, and their associated directional viscosity properties examined, which show that only one construction is consistent. Continuous axial and shearing responses are illustrated for that law, and the shearing response is shown to have an unexpected behaviour. An alternative approach first reformulates the original orthotropic law as an additive decomposition into isotropic and anisotropic parts, and applies the fabric weakening directly to the latter. This formulation is shown to describe consistent and sensible behaviour in all the test simulations.