Ice flow relations for stress and strain-rate components from combined shear and compression laboratory experiments

Abstract

ABSTRACT. The generalized (Glen) flow relation for ice, involving the second invariants of the stress deviator and strain-rate tensors, is only expected to hold for isotropic polycrystalline ice. Previous single-stress experiments have shown that for the steady-state flow, which develops at large strains, the tertiary strain rate is greater than the minimum (secondary creep) value by an enhancement factor which is larger for shear than compression. Previous experiments combining shear with compression normal to the shear plane have shown that enhancement of the tertiary octahedral strain rate increases monotonically from compression alone to shear alone. Additional experiments and analyses presented here were conducted to further investigate how the separate tertiary shear and compression strain-rate components are related in combined stress situations. It is found that tertiary compression rates are more strongly influenced by the addition of shear than is given by a Glen-type flow relation, whereas shear is less influenced by additional compression. A scalar function formulation of the flow relation is proposed, which fits the tertiary creep data well and is readily adapted to a generalized form that can be extended to other stress configurations and applied in ice mass modelling. BACKGROUNDIn natural ice masses the most important and common state of deformation is arguably a combination of approximately bed-parallel shear and vertical compression. For deformational flow with a stationary boundary, a region of simple shear is associated in an essential way with bulk transport of ice in glaciers, ice sheets and ice shelves, and this is generally accompanied by normal deformations associated with increasing velocities along the flow and divergence or convergence transverse to the flow.For a coordinate system with x and y horizontal and z vertical, and corresponding component velocities (u, v, w), simple shear deformation in the x direction can be characterized by du/dz = c where we note that the horizontal planes on which the forces generating shear deformation act do not rotate, while compression normal to these planes is described by dw/dz = k, where c/2 and k are the respective shear and vertical compressive strain rates. The compressive flow may be confined or unconfined, and quite generally the accompanying horizontal normal strain rates are du dx ¼ ð À 1Þk and dv dy ¼ Àk where the factors involving indicate the proportions of the deformations in the horizontal directions, relative to the rate of vertical compression. Note that = 1/2 corresponds to uniaxial compression in the z direction, while = 1 corresponds to longitudinally confined compression in the experiments reported here (Fig. 1).The generalized flow relation for ice involving the second invariants of the stress deviator and strain-rate tensors (Nye, 1953;Glen, 1958) provides a useful formulation for the interactions between the individual stress and strain-rate components for isotropic ice. This relation is not expected to apply for anisotropic i...

Implementing an empirical scalar tertiary anisotropic rheology (ESTAR) into large-scale ice sheet models

“…This observation, in conjunction with the development of crystallographic preferred orientations during deformation of polycrystalline ice to high strains (e.g. Russell-Head and 25 Budd, 1979;Jacka and Maccagnan, 1984;Pimienta et al, 1987;Morgan et al, 1998;DiPrinzio et al, 2005;Durand et al, 2009;Budd et al, 2013;Montagnat et al, 2014), has driven the development of rheological descriptions in which the connection between deviatoric stresses and resulting strain-rates is regarded as an intrinsic material property determined by the effects of microstructure on bulk deformation processes, (e.g. Lile, 1978;Lliboutry, 1993;Azuma and Goto-Azuma, 1996;Staroszczyk and Gagliardini, 1999;Thorsteinsson, 2001;Gödert, 2003;Gillet-Chaulet et al, 2005;Pettit et al, 2007;Placidi et al, 2010).…”

“…While the Glen flow relation captures the observed nonlinear response of ice deformation to an applied stress, it is unable to account for the mechanical anisotropy of polycrystalline ice during tertiary creep (e.g., Nye, 1953;Glen, 1958;Budd et al, 2013). That is, it cannot explain the dependence of tertiary strain rates on the character of the applied stress.…”

“…The anisotropic flow relation proposed by Budd et al (2013) represents a continuation of this strand. They found that a scalar anisotropic flow relation, i.e., one maintaining the collinear relationship between the components ofε and σ (τ e is a scalar function of the second invariant of σ ) provides a good fit to laboratory data from combined compression and shear experiments.…”

“…Previous studies have used anisotropic flow models or approximations to assign regional values to E G (e.g., Ma et al, 2010) that may also vary according to the prevailing stress regime. Budd et al (2013) recently proposed an anisotropic flow relation based on results from laboratory ice deformation experiments in simple shear, compression, and combinations of these. As tertiary creep rates and the corresponding compatible fabrics were found to vary according to the relative proportions of the simple shear and compression stresses, Budd et al (2013) de-30 fined an enhancement factor E as an anisotropic function of the stress configuration, with separate, experimentally-determined enhancement factors for simple shear-alone and compression-alone.…”

“…Budd et al (2013) recently proposed an anisotropic flow relation based on results from laboratory ice deformation experiments in simple shear, compression, and combinations of these. As tertiary creep rates and the corresponding compatible fabrics were found to vary according to the relative proportions of the simple shear and compression stresses, Budd et al (2013) de-30 fined an enhancement factor E as an anisotropic function of the stress configuration, with separate, experimentally-determined enhancement factors for simple shear-alone and compression-alone. We refer to the generalised form of the anisotropic flow relation proposed by Budd et al (2013) as ESTAR (Empirical, Scalar, Tertiary, Anisotropic Rheology), since it is based on ter-tiary (steady-state) creep rates and features a scalar (collinear) relationship between the strain rate and deviatoric stress tensor components.…”