Geometric Softening

Motivation

We observed grain-size reduction and the development of crystallographic preferred orientation (CPO) in our up-strain deformation experiments. However, the cause of strain weakening during deformation remains uncertain. Understanding this process is crucial, as it governs how ice transitions from a strong, strain-hardening regime to a weaker, strain-softening state, ultimately controlling the localisation of flow, the onset of shear zones, and the large-scale dynamics of glaciers and ice streams.

End-member Modelling - Grain Size

We used the dataset from Fan et al. (2020) as input and separately evaluated the effects of grain size and CPO on ice viscosity. The influence of grain size on viscosity can be illustrated using a deformation-mechanism map (left). Applying the grain-size-sensitive flow law of Goldsby and Kohlstedt (2001) (top), we estimated the corresponding stress evolution. The results show that, when grain size alone is considered, the stress remains nearly constant with increasing strain, contradicting the strain-weakening behaviour observed experimentally (right).

End-member Modelling - CPO

The influence of CPO on viscosity can be quantified using the reduced Schmid factor, a proxy for the shear stress resolved on the basal planes of ice crystals (left). We calculated the volume-weighted bulk reduced Schmid factor and incorporated it into the flow law proposed by Azuma (1995) (top), which isolates the effect of geometric softening on ice strength. The results show that when CPO alone is considered, the stress decreases with increasing strain, with both the trend and magnitude closely matching the strain-weakening behaviour observed in experiments (right).