The role of grain-size evolution on the rheology of ice: Implications for reconciling laboratory creep data and the Glen flow law

Abstract

Abstract. Viscous flow in ice is often described by the Glen flow law – a non-Newtonian, power-law relationship between stress and strain-rate with a stress exponent n ~ 3. The Glen law is attributed to grain-size-insensitive dislocation creep; however, laboratory and field studies demonstrate that deformation in ice can be strongly dependent on grain size. This has led to the hypothesis that at sufficiently low stresses, ice flow is controlled by grain boundary sliding, which explicitly incorporates the grain-size dependence of ice rheology. Experimental studies find that neither dislocation creep (n ~ 4) nor grain boundary sliding (n ~ 1.8) have stress exponents that match the value of n ~ 3 in the Glen law. Thus, although the Glen law provides an approximate description of ice flow in glaciers and ice sheets, its functional form is not explained by a single deformation mechanism. Here we seek to understand the origin of the n ~ 3 dependence of the Glen law by using the wattmeter to model grain-size evolution in ice. The wattmeter posits that grain size is controlled by a balance between the mechanical work required for grain growth and dynamic grain size reduction. Using the wattmeter, we calculate grain size evolution in two end-member cases: (1) a 1-D shear zone, and (2) as a function of depth within an ice-sheet. Calculated grain sizes match both laboratory data and ice core observations for the interior of ice sheets. Finally, we show that variations in grain size with deformation conditions result in an effective stress exponent intermediate between grain boundary sliding and dislocation creep, which is consistent with a value of n = 3 ± 0.5 over the range of strain rates found in most natural systems.

Crystallographic Preferred Orientation (CPO) Development Governs Strain Weakening in Ice: Insights From High‐Temperature Deformation Experiments

“…Table 3 Parameters of Glen's Flow Law, Durham's Flow Law, and Goldsby-Kohlstedt Composite Flow Law modeling by Behn et al (2020) likewise suggests that combined dislocation creep and GBS produces an apparent stress exponent of n = 3 for ice sheets. We use the simplified composite flow law (Equation 6)-hereafter referred to as the "grain-size-sensitive model"-to estimate ice strength evolution arising from grain size evolution, using the revised composite flow law parameters provided in Table 3 .…”

Modelling the influence of marine ice on the dynamics of an idealised ice shelf

“…We have chosen to focus on these values as they lie in the middle of a range of what could reasonably be expected based on our limited knowledge of marine ice rheology. Specifically, this was informed by the possible effects of CPO orientations (Duval and others, 1983; Budd and Jacka, 1989; Dierckx and others, 2014), grain size (Cole, 1987; Behn and others, 2021) and impurity content (Hammonds and Baker, 2016; Craw and others, 2018; Hammonds and Baker, 2018) on the viscosity of polycrystalline ice, as well as the experiments of Dierckx and Tison (2013), as outlined in the Introduction.…”

“…We have attempted to investigate the effects of strengthening and weakening in the marine ice that we consider to be possible as a result of these properties based on existing observations and modelling studies (e.g. Budd and Jacka, 1989; Rommelaere and MacAyeal, 1997; Craven and others, 2009; Dierckx and Tison, 2013; Dierckx and others, 2014; Hammonds and Baker, 2016, 2018; Craw and others, 2018; Behn and others, 2021) but these may vary widely across an actual ice shelf. Further laboratory studies to measure the microstructural characteristics, chemical content and mechanical response to stress of marine ice, particularly in tertiary creep, would be extremely valuable for improving the way ice flow relations capture those effects.…”

“…Finer grain sizes in ice generally lead to rheological weakness, due to an increase in grain-size sensitive creep mechanisms (Paterson, 1991; Goldsby and Kohlstedt, 1997). In glaciers and ice sheets, Behn and others (2021) have shown that while the traditional Glen flow relation using n = 3 may apply on a large scale, the appropriate parameters on a small scale (including through the thickness of the ice shelf) can vary substantially from n ≈ 2 to n ≈ 4 due to variations in grain size. The appropriate value for n can be related to the balance of deformation and recovery mechanisms, which is controlled by temperature and grain size; in warm ice with larger grain sizes, ice is likely to be less viscous due to the dominance of dislocation creep (Ranganathan and others, 2021).…”

Assessment of Quartz Grain Growth and the Application of the Wattmeter to Predict Quartz Recrystallized Grain Sizes

“…was formulated byShinevar et al (2015), who empirically fit the thermodynamic database ofPitzer and Sterner (1994) to determine a single equation that provides a good fit to the fugacity data for a wide range of crustal geotherms and determined A1 = 5521 MPa, A2 = 31.28 kJ/mol, and A3 = -2.009  10 -5 m3 . Equation 4 is also used to determine the water fugacity in the flow laws.…”