Undamaged Ice Research Articles

A Maxwell elasto-brittle rheology for sea ice modelling

Abstract. A new rheological model is developed that builds on an elasto-brittle (EB) framework used for sea ice and rock mechanics, with the intent of representing both the small elastic deformations associated with fracturing processes and the larger deformations occurring along the faults/leads once the material is highly damaged and fragmented. A viscous-like relaxation term is added to the linear-elastic constitutive law together with an effective viscosity that evolves according to the local level of damage of the material, like its elastic modulus. The coupling between the level of damage and both mechanical parameters is such that within an undamaged ice cover the viscosity is infinitely large and deformations are strictly elastic, while along highly damaged zones the elastic modulus vanishes and most of the stress is dissipated through permanent deformations. A healing mechanism is also introduced, counterbalancing the effects of damaging over large timescales. In this new model, named Maxwell-EB after the Maxwell rheology, the irreversible and reversible deformations are solved for simultaneously; hence drift velocities are defined naturally. First idealized simulations without advection show that the model reproduces the main characteristics of sea ice mechanics and deformation: strain localization, anisotropy, intermittency and associated scaling laws.

Effects of prestrain on the ductile-to-brittle transition of ice

The ductile-to-brittle transition was investigated in prestrained columnar ice at −10 °C. Laboratory-grown specimens of freshwater and saline ice were prestrained under uniaxial across-column compression (to levels from εp = 0.003 to εp = 0.20, at constant strain rates in the ductile regime) and likewise reloaded (at rates from 1 × 10−6s−1 to 3 × 10−2s−1). Prestrain caused solid-state recrystallization as well as damage in the form of non-propagating microcracks. The ductile-to-brittle transition strain rate ε˙D/B increased by a factor of 3–10 after prestrain of εp = 0.035 in both freshwater and saline ice, compared to that of initially undamaged ice of the same type. Additional prestrain had little further effect on ε˙D/B. The results are interpreted within the framework of a model (proposed by Schulson, 1990, and Renshaw and Schulson, 2001) that predicts the transition strain rate based on the micromechanical boundary between creep and fracture processes. Model parameters primarily affected by prestrain were the power-law creep coefficient B (more so than the creep exponent n), Young's modulus E and, by extension, the fracture toughness KIc.

Experiments on the damage process in ice under compressive states of stress

AbstractDuring ice-structure interaction, ice will fail in a brittle manner dominated by two processes. The first corresponds to the formation of macrocracks and the consequent spalling-off of large ice pieces. The second includes an intense shear-damage process in zones, termed critical zones, where high pressures are transmitted to the structure. The shear-damage process results in microstructural changes including microcrack formation and recrystallization. A range of tests on laboratory-prepared granular ice have been conducted to determine the fundamental behaviour of ice under various stress states and stress history, particularly as it relates to changes in microstructure. The test series was designed to study three aspects: the intrinsic creep properties of intact, undamaged ice; the enhancement of creep and changes in microstructure due to damage; and the effects of different stress paths. Tests on intact ice with triaxial confining pressures and low deviatoric stresses, aimed at defining the intrinsic creep response in the absence of microcracking, showed that an accelerated creep rate occurred at relatively low deviatoric stresses. Hence, a minimum Creep rate occurred under these conditions. Recrystallization to a smaller grain-size and void formation were observed. Ice damaged uniaxially and triaxially prior to testing showed enhancement of creep under both uniaxial and triaxial loading conditions Creep rates in triaxially damaged ice were found to be non-linear with high deviatoric stresses, corresponding to a power-law dependence of creep rate. Uniaxially damaged specimens contained microcracks parallel to the stressed direction which tended to close under triaxial confinement. Damage under triaxial conditions at low confining pressures produced small recrystallized grains near zones of microcracking. At high confining pressures, a fine-grained recrystallized structure with no apparent cracking was observed uniformly across the specimen. The recrystallization process contributes significantly to the enhanced creep rates found in damaged specimens.

Experiments on the damage process in ice under compressive states of stress

AbstractDuring ice-structure interaction, ice will fail in a brittle manner dominated by two processes. The first corresponds to the formation of macrocracks and the consequent spalling-off of large ice pieces. The second includes an intense shear-damage process in zones, termed critical zones, where high pressures are transmitted to the structure. The shear-damage process results in microstructural changes including microcrack formation and recrystallization. A range of tests on laboratory-prepared granular ice have been conducted to determine the fundamental behaviour of ice under various stress states and stress history, particularly as it relates to changes in microstructure. The test series was designed to study three aspects: the intrinsic creep properties of intact, undamaged ice; the enhancement of creep and changes in microstructure due to damage; and the effects of different stress paths. Tests on intact ice with triaxial confining pressures and low deviatoric stresses, aimed at defining the intrinsic creep response in the absence of microcracking, showed that an accelerated creep rate occurred at relatively low deviatoric stresses. Hence, a minimum Creep rate occurred under these conditions. Recrystallization to a smaller grain-size and void formation were observed. Ice damaged uniaxially and triaxially prior to testing showed enhancement of creep under both uniaxial and triaxial loading conditions Creep rates in triaxially damaged ice were found to be non-linear with high deviatoric stresses, corresponding to a power-law dependence of creep rate. Uniaxially damaged specimens contained microcracks parallel to the stressed direction which tended to close under triaxial confinement. Damage under triaxial conditions at low confining pressures produced small recrystallized grains near zones of microcracking. At high confining pressures, a fine-grained recrystallized structure with no apparent cracking was observed uniformly across the specimen. The recrystallization process contributes significantly to the enhanced creep rates found in damaged specimens.

Generation of melt during crushing experiments on freshwater ice

A stainless-steel platen, with arrays of pressure sensors and thermocouples on the front face, has been used to crush mono-crystalline, bubble-free freshwater ice samples at −10°C and −5°C at various constant speeds. One of the thermocouples was located at the center of the platen's central pressure transducer. Video records of the ice/steel contact zone during crushing were obtained by mounting samples on a thick plexiglas plate which permitted viewing through the specimens to the ice/steel interface. Total load and pressure records exhibited a sawtooth pattern. The relative movement of the ice towards the platen was not uniform but was much slower on the ascending side of each sawtooth, where elastic energy built up in the ice and apparatus, than on the steep descending portion, where the energy was released and the main damage of the ice occurred. This mode of periodic failure was caused by the compliance of the ice and the testing apparatus. Peak pressures were in the pressure melting range for the temperatures investigated. Contact between the platen and the ice consisted of low pressure zones of highly damaged crushed and/or refrozen ice, opaque in appearance, and regions of relatively undamaged ice, transparent in appearance, where ∼88% of the load was borne and the pressure was ⩾ 70 MPa. Specific energy calculations for the ejecta extruded from high pressure zones, based on video and load records, and temperature measurements indicated that the ejecta was partially liquid and that pressure melting and heat generation by viscous flow of liquid plays an important role in ice crushing. The process was responsible for at least ∼64% of the energy dissipated in these tests.

Melt-layer thickness measurements during crushing experiments on fresh-water ice

AbstractA stainless-steel platen, with a centrally located pressure sensor on the front face, has been used to crush mono-crystalline, bubble-free fresh-water ice samples. Two electrical conductors, located on the face of the pressure sensor, were connected to a bridge circuit so that the presence of liquid between the two conductors could be detected and its thickness measured. Video records of the ice/ steel contact zone during crushing were obtained by mounting samples on a thick Plexiglas plate which permitted viewing through the specimen to the ice/steel interface. Total load and pressure records exhibited a sawtooth pattern due to the compliance of the ice and the testing apparatus, and spalling of ice from the contact zone. When the region of contact was in the vicinity of the pressure transducer, liquid was detected and peaks occurred in the liquid sensor output when load drops occurred. Contact between the platen and the ice consisted of low pressure zones of highly damaged crushed and/or refrozen ice, opaque in appearance, and transparent, high-pressure regions of relatively undamaged ice. Upper limits for the liquid-layer thickness on the high-pressure undamaged ice were ~3 µm on the ascending sides of the sawteeth in the load records and ~ 21 µ on the sharp descending sides.

Melt-layer thickness measurements during crushing experiments on fresh-water ice

AbstractA stainless-steel platen, with a centrally located pressure sensor on the front face, has been used to crush mono-crystalline, bubble-free fresh-water ice samples. Two electrical conductors, located on the face of the pressure sensor, were connected to a bridge circuit so that the presence of liquid between the two conductors could be detected and its thickness measured. Video records of the ice/ steel contact zone during crushing were obtained by mounting samples on a thick Plexiglas plate which permitted viewing through the specimen to the ice/steel interface. Total load and pressure records exhibited a sawtooth pattern due to the compliance of the ice and the testing apparatus, and spalling of ice from the contact zone. When the region of contact was in the vicinity of the pressure transducer, liquid was detected and peaks occurred in the liquid sensor output when load drops occurred. Contact between the platen and the ice consisted of low pressure zones of highly damaged crushed and/or refrozen ice, opaque in appearance, and transparent, high-pressure regions of relatively undamaged ice. Upper limits for the liquid-layer thickness on the high-pressure undamaged ice were ~3 µm on the ascending sides of the sawteeth in the load records and ~ 21 µ on the sharp descending sides.

Transient creep of polycrystalline ice under uniaxial compression: an assessment of internal state variable models

The efforts to develop damage models for ice cannot be disconnected from a better knowledge of the undamaged ice behaviour. In this respect the transient behaviour of polycrystalline ice still needs to be investigated. The present paper is a contribution to the development of rheological models which can be used in varying load situations. The deformation processes which should be the foundation of the models are described. The models of Le Gac and Duval (1980) and of Sunder and Wu (1989a) are tested against two uniaxial compression tests on isotropic granular ice under varying load. They fail to describe both primary creep and the response to increments/decrements of the applied load. A new model, based on a decomposition of the viscoplastic strain into two components which account separately for kinematic and isotropic hardening, is shown to give better results.

Transient creep of polycrystalline ice under uniaxial compression: an assessment of internal state variable models

The efforts to develop damage models for ice cannot be disconnected from a better knowledge of the undamaged ice behaviour. In this respect the transient behaviour of polycrystalline ice still needs to be investigated. The present paper is a contribution to the development of rheological models which can be used in varying load situations. The deformation processes which should be the foundation of the models are described. The models of Le Gac and Duval (1980) and of Sunder and Wu (1989a) are tested against two uniaxial compression tests on isotropic granular ice under varying load. They fail to describe both primary creep and the response to increments/decrements of the applied load. A new model, based on a decomposition of the viscoplastic strain into two components which account separately for kinematic and isotropic hardening, is shown to give better results.

Effect of microcracking on the deformation of ice

Tests in the field and full-scale experience with arctic structures show that the crushing of ice is accompanied by large fluctuations in load. Field experiments show that, in addition to variations of load in time, significant spatial variations across the contact surface also occur. The deformation is observed to take place in a thin layer of damaged ice, which appears near the structure or indenter surface. It is important to model the deformation and strength of ice in this zone. Various aspects of modelling are discussed in the paper, in particular, measures of damage and the relation to the deformation of ice. The relevance of various components of deformation (elastic, viscous, delayed elastic) is outlined, and two mathematical formulations for the deformation are discussed. The behaviour was investigated by a series of tests at constant strain rate as well as tests in which the strain response to stress of damaged and undamaged ice was measured. The creep rate in damaged ice is shown to be significantly enhanced, even for short-term loading. Comparisons of theory and experiment are given for constant strain-rate tests. The models have been calibrated to the experimental data described in the paper. It is a matter for future research to generalize the models to all damage levels and stress states. Key words : creep, damage, deformation, ice, microcracking, visco-elasticity.

Dynamic response of narrow structures to ice crushing

A new model is developed for the ice-induced vibration of offshore structures. The dynamic equations of equilibrium for the structure and the undamaged ice field are coupled by a nonlinear element describing the crushing and clearing processes at the ice-structure interface. Sample calculations show good agreement with the results of a model test and a series of full-scale measurements.

Impurity Effects on the Basal Plane Solidification Kinetics of Supercooled Water

Growth rates of ice on the basal plane from pure water and from dilute solutions of selected ionic salts, surfactants, and water-soluble polymers were measured by an improved technique of capillary crystallization for supercoolings ranging from 0.03° to 0.2°C. The corresponding velocities ranged from 10-6 cm/sec to 5×10-4 cm/sec. Corrections for bulk mass transfer and heat transfer effects were applied to the kinetic data. The kinetic data for pure water, although in agreement with those of Hillig near supercoolings of 0.07°C, diverge from the earlier results toward lower velocities at both lower and higher supercoolings. The data nonetheless support the general conclusion of Hillig that growth of undamaged ice crystals on the basal plane proceeds by two-dimensional nucleation. Both growth-rate enhancements (up to a factor of about five) and retardations (up to a factor of about three) were observed during crystallization in the presence of additives. The type of effect and its magnitude were dependent on the nature of the additive, its concentration, and upon the degree of supercooling. Certain effects of ionic salts appear related to freezing potential phenomena reported by several earlier workers. Growth acceleration, found to occur to varying degrees with all classes of additive, may have been a consequence of dislocations introduced in the crystal by the additive during growth.