Bubble Coalescence in Ice as a Tool for the Study of its Deformation History

An analysis is made of the rate of bubble coalescence in an ice mass that is deforming. A total strain of at least 8 is required before appreciable coalescence occurs. The analysis has been applied to deforming ice shelves and ice sheets. No appreciable coalescence is expected in ice shelves but coalescence should occur in ice sheets (or glaciers) if the shear strain-rate at the bottom surface is of the order of 0·075/year or larger. Measurements of bubble concentration are capable of setting limits on paleo-strain-rates of the present ice sheets. Bubble migration down temperature gradients presents complications to the study of bubble coalescence.

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Erebus Glacier Tongue, Mcmurdo Sound, Antarctica

Journal of Glaciology ◽

10.1017/s0022143000023340 ◽

1974 ◽

Vol 13 (67) ◽

pp. 27-35 ◽

Cited By ~ 39

Author(s):

G. Holdsworth

Keyword(s):

Shear Stress ◽

Strain Rate ◽

Shear Strain ◽

Longitudinal Strain ◽

Strain Rates ◽

Shear Strain Rate ◽

Mcmurdo Sound ◽

Glacier Tongue ◽

The Past ◽

Image Position

Examination of the past and present behaviour of the Erebus Glacier tongue over the last 60 years indicates that a major calving from the tongue appears to be imminent. Calculations of the regime of the tongue indicate that bottom melt rates may exceed 1 m a−1. By successive mapping of the ice tongue between the years 1947 and 1970, longitudinal strain-rates were determined using the change in distance between a set of 15 teeth, which are a prominent marginal feature of the tongue. Assuming a flow law for ice of the form where τ is the effective shear stress and is the effective shear strain-rate, values of the exponent n = 3 and B = 1 × 108 N m−2 are determined. These are in fair agreement with published values.

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The temperature change shortcut: effects of mid-experiment temperature changes on the deformation of polycrystalline ice

The Cryosphere ◽

10.5194/tc-15-2235-2021 ◽

2021 ◽

Vol 15 (5) ◽

pp. 2235-2250

Author(s):

Lisa Craw ◽

Adam Treverrow ◽

Sheng Fan ◽

Mark Peternell ◽

Sue Cook ◽

...

Keyword(s):

Strain Rate ◽

Temperature Change ◽

Constant Temperature ◽

Ice Sheets ◽

Strain Rates ◽

Temperature Step ◽

Ice Shelves ◽

Polycrystalline Ice ◽

Long Time ◽

Run Time

Abstract. It is vital to understand the mechanical properties of flowing ice to model the dynamics of ice sheets and ice shelves and to predict their behaviour in the future. We can increase our understanding of ice physical properties by performing deformation experiments on ice in laboratories and examining its mechanical and microstructural responses. However, natural conditions in ice sheets and ice shelves extend to low temperatures (≪-10 ∘C), and high octahedral strains (> 0.08), and emulating these conditions in laboratory experiments can take an impractically long time. It is possible to accelerate an experiment by running it at a higher temperature in the early stages and then lowering the temperature to meet the target conditions once the tertiary creep stage is reached. This can reduce total experiment run-time by > 1000 h; however it is not known whether this could affect the final strain rate or microstructure of the ice and potentially introduce a bias into the data. We deformed polycrystalline ice samples in uniaxial compression at −2 ∘C before lowering the temperature to either −7 or −10 ∘C, and we compared the results to constant-temperature experiments. Tertiary strain rates adjusted to the change in temperature very quickly (within 3 % of the total experiment run-time), with no significant deviation from strain rates measured in constant-temperature experiments. In experiments with a smaller temperature step (−2 to −7 ∘C) there is no observable difference in the final microstructure between changing-temperature and constant-temperature experiments which could introduce a bias into experimental results. For experiments with a larger temperature step (−2 to −10 ∘C), there are quantifiable differences in the microstructure. These differences are related to different recrystallisation mechanisms active at −10 ∘C, which are not as active when the first stages of the experiment are performed at −2 ∘C. For studies in which the main aim is obtaining tertiary strain rate data, we propose that a mid-experiment temperature change is a viable method for reducing the time taken to run low-stress and low-temperature experiments in the laboratory.

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Strain Rate Dependent Constitutive Model of Multiaxial Ratchetting of 63Sn–37Pb Solder

Journal of Electronic Packaging ◽

10.1115/1.2753917 ◽

2006 ◽

Vol 129 (3) ◽

pp. 278-286 ◽

Cited By ~ 5

Author(s):

Gang Chen ◽

Xu Chen ◽

Kwang Soo Kim ◽

Mohammad Abdel-Karim ◽

Masao Sakane

Keyword(s):

Constitutive Model ◽

Strain Rate ◽

Shear Strain ◽

Kinematic Hardening ◽

Axial Stress ◽

Strain Range ◽

Strain Rates ◽

Shear Strain Rate ◽

Viscous Term ◽

Ratcheting Strain

A series of multiaxial ratcheting tests were conducted on 63Sn–37Pb solder. A unified viscoplastic constitutive model was developed on the basis of the Ohno–Wang kinematic hardening model, and the rate dependence of the material was taken into consideration by introducing a viscous term. The stress-strain hysteresis loop of 63Sn–37Pb under different strain rates can be simulated reasonably well by the model. However, since the axial ratcheting strain rate of 63Sn–37Pb solder is strongly dependent on the applied shear strain rates in axial/torsional ratcheting, the original constitutive model fails to describe the effect of shear strain rate on the ratcheting strain. To improve the rate sensitivity of the model, the material parameter μi was correlated to the strain rate. Comparisons of the experimental and simulated results verify that the modified constitutive model is able to predict the complicated deformation of 63Sn–37Pb. The effects of axial stress, shear strain range, loading history, and strain rate on ratcheting behavior can be reflected fairly well.

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Deformation rates in combined compression and shear for ice which is initially isotropic and after the development of strong anisotropy

Annals of Glaciology ◽

10.3189/s0260305500013501 ◽

1996 ◽

Vol 23 ◽

pp. 247-252 ◽

Cited By ~ 9

Author(s):

Li Jun ◽

T.H Jacka ◽

W.F. Budd

Keyword(s):

Shear Stress ◽

Steady State ◽

Stress State ◽

Strain Rate ◽

Shear Strain ◽

Uniaxial Compression ◽

Simple Shear ◽

Strain Rates ◽

Shear Strain Rate ◽

State Dependent

Laboratory-prepared fine-grained, initially isotropic polycrystalline ice samples were deformed under conditions of simple shear with simultaneous uniaxial compression at a constant temperature of −2.0°C. The aim was to investigate the effects of stress configuration on the flow rate of initially isotropic ice and on ice with subsequent stress and strain-induced anisotropy. Experiments were carried out for various combinations of shear and compression with shear stress ranging from 0 to 0.49 MPa and compressive stress ranging from 0 to 0.98 MPa, but such that for every experiment the octahedral shear stress was 0.4 MPa.The strain curves resulting from the experiments clearly exhibit minimum strain rates while the ice is still isotropic, and steady-state tertiary strain rates along with the development of steady-state anisotropic fabric patterns. With constant octahedral stress (root-mean-square of the principal stress deviators), the minimum octahedral shear-strain rate has no dependence on stress configuration. This result supports the hypothesis that the flow of isotropic ice is dependent only on the second invariant of the stress tensor. This fundamental assumption has been used to provide a general description of ice-flow behaviour independent of the stress configuration (e.g. Nye, 1953; Glen, 1958; Budd, 1969).For the tertiary flow of anisotropic ice, the octahedral strain rate is stress-state dependent as a consequence of the developed crystal-orientation fabric, which is also stress-state dependent, and which develops with strain and rotation. The present tests indicate that the enhancement factor for steady-state tertiary octahedral shear-strain rate depends on the shear or compression fraction and varies from about 10 for simple shear (with zero compression) to about 3 for uniaxial compression (with zero shear).

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Erebus Glacier Tongue, Mcmurdo Sound, Antarctica

Journal of Glaciology ◽

10.3189/s0022143000023340 ◽

1974 ◽

Vol 13 (67) ◽

pp. 27-35 ◽

Cited By ~ 2

Author(s):

G. Holdsworth

Keyword(s):

Shear Stress ◽

Strain Rate ◽

Shear Strain ◽

Longitudinal Strain ◽

Strain Rates ◽

Shear Strain Rate ◽

Mcmurdo Sound ◽

Glacier Tongue ◽

The Past ◽

Image Position

Examination of the past and present behaviour of the Erebus Glacier tongue over the last 60 years indicates that a major calving from the tongue appears to be imminent. Calculations of the regime of the tongue indicate that bottom melt rates may exceed 1 m a−1. By successive mapping of the ice tongue between the years 1947 and 1970, longitudinal strain-rates were determined using the change in distance between a set of 15 teeth, which are a prominent marginal feature of the tongue. Assuming a flow law for ice of the form where τ is the effective shear stress and is the effective shear strain-rate, values of the exponent n = 3 and B = 1 × 108 N m−2 are determined. These are in fair agreement with published values.

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Velocity and strain rates derived from InSAR analysis over the Amery Ice Shelf, East Antarctica

Annals of Glaciology ◽

10.3189/172756402781817842 ◽

2002 ◽

Vol 34 ◽

pp. 228-234 ◽

Cited By ~ 44

Author(s):

N. W. Young ◽

G. Hyland

Keyword(s):

Strain Rate ◽

Shear Strain ◽

Transverse Shear ◽

Transverse Shear Strain ◽

Strain Rates ◽

Shear Strain Rate ◽

Ice Shelf ◽

Local Flow ◽

Synthetic Aperture Radar Data ◽

Amery Ice Shelf

AbstractWe use displacements derived from matching complex synthetic aperture radar data using maximum coherence to generate a dense network of velocity estimates over the Amery Ice Shelf. From these velocities we generate the horizontal strain-rate components and resolve them with respect to the local flow direction. We present the spatial distributions of velocity and transverse shear strain rate and use them to investigate features of the flow regime for the shelf. From the southern end of the shelf, velocity decreases from a high of about 800ma–1 to around 300 ma–1, and then increases to a maximum of about 1350ma–1 at the centre of the front. Strain rates vary systematically across and along the shelf. The pattern of the transverse shear strain rate clearly identifies the shear margins, where values exceed 0.1 a–1 in the southern section of the shelf. The pattern also shows longitudinal bands of enhanced shear strain rate containing ice with a strong preferred crystal fabric that was advected from shear margins upstream. In the northern section of the shelf, significant values of longitudinal and traverse stresses lead to enhanced shear deformation through their effect on the octahedral shear stress term.

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The temperature change shortcut: effects of mid-experiment temperature changes on the deformation of polycrystalline ice

10.5194/tc-2020-318 ◽

2020 ◽

Author(s):

Lisa Craw ◽

Adam Treverrow ◽

Sheng Fan ◽

Mark Peternell ◽

Sue Cook ◽

...

Keyword(s):

Strain Rate ◽

Temperature Change ◽

Constant Temperature ◽

Ice Sheets ◽

Strain Rates ◽

Temperature Step ◽

Ice Shelves ◽

Polycrystalline Ice ◽

Long Time ◽

Run Time

Abstract. It is vital to understand the mechanical properties of flowing ice to model the dynamics of ice sheets and ice shelves, and to predict their behaviour in the future. We can do this by performing deformation experiments on ice in laboratories, and examining its mechanical and microstructural responses. However, natural conditions in ice sheets and ice shelves extend to low temperatures ( 0.08), and emulating these conditions in laboratory experiments can take an impractically long time. It is possible to accelerate an experiment by running it at a higher temperature in the early stages, and then lowering the temperature to meet the target conditions once the tertiary creep stage is reached. This can reduce total experiment run-time by > 1000 hours, however it is not known if this could affect the final strain rate or microstructure of the ice and potentially introduce a bias into the data. We deformed polycrystalline ice samples in uniaxial compression at −2 °C before lowering the temperature to either −7 °C or −10 °C, and compared the results to constant temperature experiments. Tertiary strain rates adjusted to the change in temperature very quickly (within 3 % of the total experiment run-time), with no significant deviation from strain rates measured in constant-temperature experiments. In experiments with a smaller temperature step (−2 °C to −7 °C) there is no observable difference in the final microstructure between changing-temperature and constant-temperature experiments which could introduce a bias into experimental results. For experiments with a larger temperature step (−2 °C to −10 °C), there are quantifiable differences in the microstructure. These differences are related to different recrystallisation mechanisms active at −10 °C, which are not as active when the first stages of the experiment are performed at −2 °C. For studies in which the main aim is obtaining tertiary strain rate data, we propose that a mid-experiment temperature change is a viable method for reducing the time taken to run low stress and low temperature experiments in the laboratory.

Download Full-text

Deformation rates in combined compression and shear for ice which is initially isotropic and after the development of strong anisotropy

Annals of Glaciology ◽

10.1017/s0260305500013501 ◽

1996 ◽

Vol 23 ◽

pp. 247-252 ◽

Cited By ~ 29

Author(s):

Li Jun ◽

T.H Jacka ◽

W.F. Budd

Keyword(s):

Shear Stress ◽

Steady State ◽

Stress State ◽

Strain Rate ◽

Shear Strain ◽

Uniaxial Compression ◽

Simple Shear ◽

Strain Rates ◽

Shear Strain Rate ◽

State Dependent

Laboratory-prepared fine-grained, initially isotropic polycrystalline ice samples were deformed under conditions of simple shear with simultaneous uniaxial compression at a constant temperature of −2.0°C. The aim was to investigate the effects of stress configuration on the flow rate of initially isotropic ice and on ice with subsequent stress and strain-induced anisotropy. Experiments were carried out for various combinations of shear and compression with shear stress ranging from 0 to 0.49 MPa and compressive stress ranging from 0 to 0.98 MPa, but such that for every experiment the octahedral shear stress was 0.4 MPa. The strain curves resulting from the experiments clearly exhibit minimum strain rates while the ice is still isotropic, and steady-state tertiary strain rates along with the development of steady-state anisotropic fabric patterns. With constant octahedral stress (root-mean-square of the principal stress deviators), the minimum octahedral shear-strain rate has no dependence on stress configuration. This result supports the hypothesis that the flow of isotropic ice is dependent only on the second invariant of the stress tensor. This fundamental assumption has been used to provide a general description of ice-flow behaviour independent of the stress configuration (e.g. Nye, 1953; Glen, 1958; Budd, 1969). For the tertiary flow of anisotropic ice, the octahedral strain rate is stress-state dependent as a consequence of the developed crystal-orientation fabric, which is also stress-state dependent, and which develops with strain and rotation. The present tests indicate that the enhancement factor for steady-state tertiary octahedral shear-strain rate depends on the shear or compression fraction and varies from about 10 for simple shear (with zero compression) to about 3 for uniaxial compression (with zero shear).

Download Full-text