Increasing contribution of grain boundary compliance to polycrystalline ice elasticity as temperature increases

Abstract

ABSTRACT. Measured elastic stiffnesses of ice polycrystals decrease with increasing temperature due to a decrease in grain boundary stiffness with increasing temperature. In this paper, we represent grain boundaries as imperfectly bonded interfaces, across which traction is continuous, but displacement may be discontinuous. We express the additional compliance due to grain boundaries in terms of a second-rank and a fourth-rank tensor, which quantify the effect on elastic wave velocities of the orientation distribution as well as the normal and shear compliances of the grain boundaries. Measurement of the elastic stiffnesses allows determination of the components of these tensors. Application of the method to resonant ultrasound spectroscopy measurements made on ice polycrystals enables determination of the ratio B N /B S of the normal to shear compliance of the grain boundaries, which are found to be more compliant in shear than in compression. The ratio B N /B S is small at low temperatures, but increases as temperature increases, implying that the normal compliance increases relative to the shear compliance as temperature increases.

Ultrasonic and seismic constraints on crystallographic preferred orientations of the Priestley Glacier shear margin, Antarctica

“…The ability of a CPO model to explain measured seismic anisotropy is assessed by introduction of a misfit between synthetic forward modelled seismic properties and observations. We found that CPO predicted seismic velocities are consistently faster than observed velocities, an effect which can be attributed to the absence of grain boundary effects (Sayers, 2018) or air bubbles…”

Ultrasonic and seismic constraints on crystallographic preferred orientations of the Priestley Glacier shear margin, Antarctica

“…The ability of a CPO model to explain measured seismic anisotropy is assessed by introduction of a misfit between synthetic forward-modelled seismic properties and observations. We found that CPO-predicted seismic velocities are consistently faster than observed velocities, an effect which can be attributed to the absence of grain boundary effects (Sayers, 2018) or air bubbles (Hellmann et al, 2021) in synthetic CPOs. The elasticity tensor by Gammon et al (1983) was derived using oscillations in gigahertz (GHz) frequencies; therefore dispersion is another potential factor to introduce differences between modelled and observed seismic or ultrasonic velocities with hertz (Hz) to kilohertz (kHz) frequencies.…”

“…At the site the glacier is ∼ 1000 m thick and 8 km wide (Frezzotti et al, 2000). Ice flow velocities are measured to increase from ∼ 45 m yr −1 close to the glacier margin to ∼ 130 m yr −1 towards the centre (Mouginot et al, 2019;Thomas et al, 2021), resulting in strong shear, with shear strain rates at the site calculated to be 6 × 10 −10 s −1 (Still et al, 2022;Thomas et al, 2021). Core samples were analysed for CPO using electron backscatter diffraction (EBSD) measurements (Thomas et al, 2021), and a strong horizontal clustering of c axes was observed throughout the entire length of the core.…”

Porosity dependence of elastic moduli of snow and firn

“…It then follows (Sayers and Han, 2002; Sayers, 2018) that the bulk and shear moduli of the medium in the presence of imperfect bonds between the ice particles are:where K 0 and μ 0 are the bulk and shear moduli that would result if the bonds between ice particles were perfect. It follows from Eqns (15) and (16) that 5 β /(3α) = ( B N / B S ) − 1, assuming an isotropic distribution of normal vectors n i .…”

“…Assuming that snow and firn are isotropic, the non-vanishing components of α ij and β ijkl are: It then follows (Sayers and Han, 2002;Sayers, 2018) that the bulk and shear moduli of the medium in the presence of imperfect bonds between the ice particles are:…”