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An investigation of the effects of particles on creep of polycrystalline ice
Scripta Materialia 55 (2006) 91–94 www.actamat-journals.com
An investigation of the effects of particles on creep of polycrystalline ice Min Song,a,* David M. Coleb and Ian Bakerc a
State Key Laboratory for Powder Metallurgy, Central South University, Changsha 410083, China b US Army Cold Regions Research and Engineering Laboratory, Hanover, NH 03755, USA c Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA Received 9 December 2005; revised 3 January 2006; accepted 16 March 2006 Available online 12 April 2006
The effects of particles on the creep of polycrystalline ice have been studied at temperatures from 20 C to 2 C. It has been shown that particles do not affect the creep stress exponent. Both particle-free ice and particle-containing ice show n = 3 power-law behavior. Calculation indicates that activation energies are 70 kJ mol1 for both particle-free ice and particle-containing ice from 20 C to 10 C. However, the activation energy increases to 120 kJ mol1 for particle-free ice when the temperature is above 10 C due to grain boundary sliding, which is inhibited in the particle-containing ice. 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Creep; Dislocations; Grain boundaries; Ice; Stress dependence
It has been shown that the stress dependence of the minimum strain rate for polycrystalline ice at temperatures from 0.05 C to 50 C [1] fits a power-law (also known as Glen’s law [2] in glaciology), i.e. Q 3 ð1Þ e_ min ¼ Ar exp kT where n is the stress exponent, A is a constant, Q is the activation energy for creep, k is the Boltzmann constant and T is the absolute temperature. Unlike single crystal ice, which has a creep activation energy of 60– 70 kJ mol1 up to the melting point [3,4], polycrystalline ice shows a higher activation energy of 120– 140 kJ mol1 from 10 C to the melting point [5,6]. This increase in activation energy may be due to an increase in liquid water along the grain boundaries, and to grain boundary sliding at high temperatures [6]. The existence of particles in glacier ice, especially ice in contact with the ground, has been of considerable interest [7–13]. Studies of the creep of ice containing particles have embraced a large range of particle sizes, from ultra-fine (15 nm) particles [8,10] to sand-sized (150 lm) particles [9]. Ice with ultra-fine amorphous silica particles shows a similar mechanical behavior to * Corresponding author. Tel.: +86 7318836773/86 13875857025; fax: +86 7318710855; e-mail: [email protected]
particle-strengthened metals, in which, at low concentrations, the strength increases as the particle concentration increases. However, when the particle size increases to that of silt (4–64 lm) and sand (70–200 lm), most studies indicate that the particles increase the creep rate at low concentrations. For example, the authors’ previous study [13] found an increased creep rate with up to 4 wt.% of silt (50 lm) particles at 12 C, while Baker and Gerberich [9] found that 1.3–6.6 vol.% of solid inclusions increased the creep strain rate for temperatures from 20 C to 5 C. Shoji and Langway [12] also found an increased flow rate for dirty basal ice from Camp Century compared with clean basal ice, and Holdsworth and Bull [7] observed an enhanced flow rate in the basal amber-colored ice of the Meserve Glacier. All the above studies of the effect of particles on creep focused on a fixed stress level, and insufficient data are available to quantify the effect of silt and sand-sized particles on the stress dependence. Additionally, previous findings [9] regarding the effect of particles on the activation energy were inconclusive. Consequently, the present paper examines the effects of silt-sized particles on the creep stress exponent and the activation energy for creep. Deionized, distilled and degassed water was used to grow thin plates of large-grained ice. These ice plates were then broken up, and a 3–5 mm sieve fraction was obtained. These grains were used to seed granular
1359-6462/$ - see front matter 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2006.03.029
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freshwater ice specimens using the method of Cole [14]. Briefly, the seed grains were put into an aluminum cylindrical mold, 215.9 mm in length, 50.8 mm inner diameter and 69.8 mm outer diameter (hollow between outer and inner walls). Degassed water at 0 C flowed continually through the unfrozen core of the specimen to maintain a relatively low concentration of dissolved gas at the freezing front while at the same time accommodating the volume changes resulting from the phase change. The temperature of the mold was decreased from 0 C to 10 C by a refrigerated circulating bath. The final specimen dimensions were 127 mm in length and 50.4 mm in diameter. For ice specimens with particles, water with silt-sized soil particles (50 ± 10 lm) was frozen to a thickness of about 5 mm from bottom to top using a cooling plate. Another layer of ice with particles was then grown on the top of the first layer. This procedure was repeated several times until the thickness of the ice plate was about 30 mm. Growing a multilayer ice plate was necessary to distribute the particles throughout the ice grains. The ice plate was subsequently broken up, and a 3– 5 mm sieve fraction was obtained. These grains were then used to seed granular ice specimens as described above. Both types of ice had an initial average grain size of about 5 mm. Figure 1 shows a thin section of ice with 1 wt.% particles distributed both along the grain boundaries and in the grain interiors. It can be seen that the particles are uniformly distributed: some of the particles are along the grain boundaries, while the other are in the grain interiors. It should be noted that for the particle size of 50 lm, even when the particle concentration is as low as 1 wt.% (0.43 vol.%), the number of the particles could be as large as 8.2 · 109 m3. Creep and cyclic loading tests were performed using a creep jig [15] located in a cold room with a temperature 2 C lower than the test temperatures (20 C to 2 C). Two insulated boxes were used to isolate the jig from the cold room, and a temperature regulating system was located between the boxes. This method controlled the temperature in the inner box to deviations of less than ±0.1 C. Creep tests used air pressure to determine the creep rate as a function of creep stress and temperature, while the cyclic loading tests used an MTS actuator to determine the contribution of grain
boundary sliding to the creep. Cyclic loading tests use the sinusoidal waveforms to generate stress/strain hysteresis loops areas to study the anelasticity caused by both the dislocation relaxation process and grain boundary relaxation process, and thus provide an indirect way to understand the contribution of grain boundary sliding to the creep rate and creep activation energy. Figure 2 shows the stress dependence for particlefree ice and particle-containing ice at temperatures from 20 C to 2 C. At temperatures from 20 C to 5 C, particle-containing ice showed higher creep rates compared to particle-free ice at the same stress. The difference between the creep rates is small at and above 5 C. Significantly, the particles do not affect the power-law behavior at any temperature. Both types of ice show power-law creep with a stress exponent of 3 from 20 to 2 C and for stresses from 0.4 MPa to 1.4 MPa, in agreement with a previous study on freshwater polycrystalline ice [1]. It is well-known that non-basal plane deformation of ice crystals needs a much higher stress than that for basal slip at the same strain rate. For polycrystalline ice, the difference in resistance to creep between basal and non-basal plane causes large internal stress, and thus gives two types of hardening – directional and non-directional hardening [16]. Directional hardening is caused by short-range interactions between dislocations on parallel planes (Taylor hardening) or on intersecting planes (Forest hardening); while nondirectional hardening is caused between moving dislocations and arrays of dislocations forming cell walls. Since ice exhibits high amount of anelastic strain, a previous study [16] has indicated that recovery processes control the creep of polycrystalline ice. For single crystal ice, the rate-controlling might be glide and the stress exponent is 2, while for polycrystalline ice, the rate-controlling might be recovery and the stress exponent is 3. Our tests on ice with particles show that the stress exponent is not affected by the presence of particles. Since the particle concentration is low, the spacing (0.5 mm) between particles is very large compared to the slip line spacing (several microns). Thus, dislocation movement during creep is apparently not impeded by the particles, and the particles’ main effect is probably to act as dislocation multiplication sources. The creep
Figure 1. Micrographs of the thin section of particle-containing (1 wt.%) ice viewed through crossed polarizers.
Figure 2. Minimum strain rate as a function of creep stress for particle-free ice and particle-containing ice from 20 C to 2 C.
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rate is affected by the increase in dislocation density, but the rate-controlling mechanism remains the same. Thus, the stress exponent is not affected. Figure 3 shows the effects of temperature on the minimum creep rate of both particle-free ice and particle-containing ice at various stress levels. It can be seen that particle-containing ice shows a linear relationship between log minimum creep rate and reciprocal temperature over the entire temperature range, while there is clearly a change in slope for the particle-free ice at around 10 C (1/T = 3.8 · 103 K1). Detailed calculations indicate the activation energy is 70 kJ mol1 for particle-containing ice from 20 C and 2 C, while for particle-free ice, the activation energy is 74 kJ mol1 from 20 C to 10 C, but increases to 120 kJ mol1 from 10 C to 2 C. The activation energies are roughly independent of creep stress from 0.4 MPa to 1.4 MPa. The value 70 kJ mol1 below 10 C for both types of granular ice agrees well with previous data [6,19,20]. Generally, polycrystalline ice has a similar activation energy to single crystal ice (normally 63 kJ mol1, [17,18]) below 10 C. The slight difference in activation energy might be due to the difference in rate-controlling processes – glide for single crystal ice and recovery for polycrystalline ice. Normally polycrystalline ice has an activation energy somewhat higher at temperatures above 10 C. This increased activation energy was also observed in the present study for particle-free polycrystalline ice at temperatures above 10 C. However, it is emphasized that the activation energy for particle-
containing ice above 10 C is the same as that below 10 C. The difference between the behavior of polycrystalline ice and single crystal ice is due to the influence of grain boundaries. A previous study [5] attributed the higher activation energy above 10 C for polycrystalline ice to a liquid phase at the grain boundaries, and to grain boundary sliding. If this is so, equivalent experiments on single crystal ice should not show such an increase in activation energy. For example, the work by Jones and Brunet [21] indicated that in single crystal ice, the activation energy has a constant value 70 kJ mol1 from 20 to 0.2 C. It has been shown using cyclic loading [22] that a dislocation relaxation peak exists at 2 · 104 Hz and a grain boundary relaxation peak exists at 5 Hz at 10 C. The peaks will shift to lower frequencies as the temperature decreases. The higher the temperature, the shorter is the relaxation time and the higher is the frequency of the relaxation peak [23]. Figures 4 and 5 show the stress/strain hysteresis loop areas (anelastic relaxation strength) for particle-free ice and particle-containing ice after creep at various stresses at 20 C and 15 C. The hysteresis loop area is a measure of energy dissipation due to dislocation motion and grain boundary sliding. The variations in hysteresis loop area for both types of ice at low cyclic frequencies up to 101 Hz are due to the variations in dislocation densities, and the variations in hysteresis loop area at high cyclic frequencies (above 101 Hz) are due to the variations in the contribution of grain boundary sliding [22]. Grain boundary sliding peaks can be observed at 0.5 Hz at 20 C and 1 Hz at 15 C for particlefree ice because these peaks have been shifted from 5 Hz at 10 C to 0.5 Hz at 20 C and 1 Hz at 15 C. However, these peaks are not observed for ice with particles. Some of the particles distributed along
Figure 3. Effect of temperature on the creep rate of (a) particle-free ice and (b) particle-containing ice.
Figure 4. Hysteresis loop area as a function of frequency at T = 20 C: (a) particle-free ice and (b) particle-containing ice.
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Creep experiments have been performed on polycrystalline particle-free ice and particle-containing ice to study the effects of particles on the creep stress exponent and the activation energy for creep from 20 C to 2 C. Particles affect the creep rate but do not affect the creep stress exponent. n 3 power-law creep has been observed for both particle-free ice and particlescontaining ice. Particles do not affect the power-law behavior but decrease the activation energy above 10 C by inhibiting grain boundary sliding, which causes the activation energy to increase from 70 kJ mol1 below 10 C to 120 kJ mol1 above 10 C. This research was supported by NSF Office of Polar Programs, Arctic Natural Sciences Program (OPP 011737). We thank Glenn Durell for his valuable assistance in developing the creep and cyclic loading equipment.
Figure 5. Hysteresis loop area as a function of frequency at T = 15 C: (a) particle-free ice and (b) particle-containing ice.
the grain boundaries inhibit the grain boundary sliding, and cause the grain boundary relaxation peak to disappear. A previous study [24] also observed this phenomenon in metals (Cu–Fe and Cu–SiO2). When the particles are located at grain boundaries, the particles retard grain boundary sliding through the development of internal stresses, which decrease the free sliding distance and the relaxation time, thus increasing the modulus and decreasing the internal friction. It is evident that the increase in activation energy above 10 C is due to the increased grain boundary sliding at high temperatures. Since particles inhibit grain boundary sliding at temperatures above 10 C, they prevent the increase in activation energy evident in particle-free ice. Thus, polycrystalline ice with particles shows a similar activation energy to polycrystalline ice without particles at lower temperatures (below 10 C), at which grain boundary sliding is inhibited. However, this does not mean there is no grain boundary sliding when temperatures are below 10 C. Grain boundary sliding is a diffusion-based, thermally activated process and increases exponentially with increasing temperature. At temperatures below 10 C, the contributions of grain boundary sliding are present but not important. However, it becomes more important at temperatures above 10 C, and hence is responsible for the increase in activation energy for polycrystalline particle-free ice. A previous study [5] indicated that at temperatures above 10 C, the grain boundary structure changes to a quasi-liquid phase. This quasi-liquid phase can absorb dislocations and thus affect the internal stress field and increase the grain boundary sliding, which inevitably increases the activation energy for particle-free polycrystalline ice above 10 C.
[1] W.F. Budd, T.H. Jacka, Cold Reg. Sci. Technol. 16 (1989) 107. [2] J.W. Glen, in: Union Geodesique et Geophysique Internationale. Association Internationale d’Hydrologie Scientifique, Symposium de Chamonix, 16–24 September 1958, pp. 267–275. [3] A. Higashi, S. Konimua, S. Mae, Jpn. J. Appl. Phys. 4 (1965) 575. [4] S.J. Jones, J.W. Glen, in: General Assembly of Bern, Commission of Snow and IceInt. Union Geod. Geophys., vol. 79, IASH Publisher, 1968, p. 326. [5] J.W. Glen, Proc. R. Soc. London Ser. A 228 (1955) 111. [6] P. Barnes, D. Tabor, J.C.F. Walker, Proc. R. Soc. London Ser. A 324 (1971) 127. [7] G. Holdsworth, C. Bull, Int. Assoc. Sci. Hydrol Publ. 86 (1970) 204. [8] H.S. Nayar, F.V. Lenel, G.S. Ansell, J. Appl. Phys. 42 (10) (1971) 3786. [9] R.W. Baker, W.W. Gerberich, J. Glaciol. 24 (90) (1979) 179. [10] M.A. Lange, T.J. Ahrens, J. Geophys. Res. 88 (B2) (1983) 1197. [11] W.B. Durham, J. Geophys. Res. 97 (E12) (1992) 20883. [12] H. Shoji, C.C. Langway, Ann. Glaciol. 6 (1985) 305. [13] M. Song, D.M. Cole, I. Baker, Ann. Glaciol. 39 (2004) 397. [14] D.M. Cole, Cold Reg. Sci. Technol. 1 (1979) 153. [15] M. Song, D.M. Cole, I. Baker, J. Glaciol 51 (2005) 210. [16] P. Duval, M.F. Ashby, I. Anderman, J. Phys. Chem. 87 (1983) 4066. [17] J. Muguruma, Brit. J. Appl. Phys. (J. Phys. D) 2 (1969) 1517. [18] L.W. Gold, Activation energy for creep of columnargrained ice, in: E. Whalley, S.J. Jones, L.W. Gold (Eds.), Physics and Chemistry of Ice, Royal Society of Canada Press, Ottawa, 1973, p. 362. [19] D.S. Russell-Head, W.F. Budd, J. Glaciol. 24 (1979) 117. [20] M. Mellor, R. Testa, J. Glaciol. 8 (1969) 131. [21] S.J. Jones, J.G. Brunet, J. Glaciol. 21 (85) (1978) 445. [22] D.M. Cole, Philos. Mag. A. 72 (1) (1995) 231. [23] A.S. Nowick, B.S. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, New York, NY, 1972. [24] N. Shigenaka, R. Monzen, T. Mori, Acta Metall. 31 (12) (1983) 2087.
An investigation of the effects of particles on creep of polycrystalline ice Min Song,a,* David M. Coleb and Ian Bakerc a
State Key Laboratory for Powder Metallurgy, Central South University, Changsha 410083, China b US Army Cold Regions Research and Engineering Laboratory, Hanover, NH 03755, USA c Thayer School of Engineering, Dartmouth College, Hanover, NH 03755, USA Received 9 December 2005; revised 3 January 2006; accepted 16 March 2006 Available online 12 April 2006
The effects of particles on the creep of polycrystalline ice have been studied at temperatures from 20 C to 2 C. It has been shown that particles do not affect the creep stress exponent. Both particle-free ice and particle-containing ice show n = 3 power-law behavior. Calculation indicates that activation energies are 70 kJ mol1 for both particle-free ice and particle-containing ice from 20 C to 10 C. However, the activation energy increases to 120 kJ mol1 for particle-free ice when the temperature is above 10 C due to grain boundary sliding, which is inhibited in the particle-containing ice. 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Creep; Dislocations; Grain boundaries; Ice; Stress dependence
It has been shown that the stress dependence of the minimum strain rate for polycrystalline ice at temperatures from 0.05 C to 50 C [1] fits a power-law (also known as Glen’s law [2] in glaciology), i.e. Q 3 ð1Þ e_ min ¼ Ar exp kT where n is the stress exponent, A is a constant, Q is the activation energy for creep, k is the Boltzmann constant and T is the absolute temperature. Unlike single crystal ice, which has a creep activation energy of 60– 70 kJ mol1 up to the melting point [3,4], polycrystalline ice shows a higher activation energy of 120– 140 kJ mol1 from 10 C to the melting point [5,6]. This increase in activation energy may be due to an increase in liquid water along the grain boundaries, and to grain boundary sliding at high temperatures [6]. The existence of particles in glacier ice, especially ice in contact with the ground, has been of considerable interest [7–13]. Studies of the creep of ice containing particles have embraced a large range of particle sizes, from ultra-fine (15 nm) particles [8,10] to sand-sized (150 lm) particles [9]. Ice with ultra-fine amorphous silica particles shows a similar mechanical behavior to * Corresponding author. Tel.: +86 7318836773/86 13875857025; fax: +86 7318710855; e-mail: [email protected]
particle-strengthened metals, in which, at low concentrations, the strength increases as the particle concentration increases. However, when the particle size increases to that of silt (4–64 lm) and sand (70–200 lm), most studies indicate that the particles increase the creep rate at low concentrations. For example, the authors’ previous study [13] found an increased creep rate with up to 4 wt.% of silt (50 lm) particles at 12 C, while Baker and Gerberich [9] found that 1.3–6.6 vol.% of solid inclusions increased the creep strain rate for temperatures from 20 C to 5 C. Shoji and Langway [12] also found an increased flow rate for dirty basal ice from Camp Century compared with clean basal ice, and Holdsworth and Bull [7] observed an enhanced flow rate in the basal amber-colored ice of the Meserve Glacier. All the above studies of the effect of particles on creep focused on a fixed stress level, and insufficient data are available to quantify the effect of silt and sand-sized particles on the stress dependence. Additionally, previous findings [9] regarding the effect of particles on the activation energy were inconclusive. Consequently, the present paper examines the effects of silt-sized particles on the creep stress exponent and the activation energy for creep. Deionized, distilled and degassed water was used to grow thin plates of large-grained ice. These ice plates were then broken up, and a 3–5 mm sieve fraction was obtained. These grains were used to seed granular
1359-6462/$ - see front matter 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2006.03.029
92
M. Song et al. / Scripta Materialia 55 (2006) 91–94
freshwater ice specimens using the method of Cole [14]. Briefly, the seed grains were put into an aluminum cylindrical mold, 215.9 mm in length, 50.8 mm inner diameter and 69.8 mm outer diameter (hollow between outer and inner walls). Degassed water at 0 C flowed continually through the unfrozen core of the specimen to maintain a relatively low concentration of dissolved gas at the freezing front while at the same time accommodating the volume changes resulting from the phase change. The temperature of the mold was decreased from 0 C to 10 C by a refrigerated circulating bath. The final specimen dimensions were 127 mm in length and 50.4 mm in diameter. For ice specimens with particles, water with silt-sized soil particles (50 ± 10 lm) was frozen to a thickness of about 5 mm from bottom to top using a cooling plate. Another layer of ice with particles was then grown on the top of the first layer. This procedure was repeated several times until the thickness of the ice plate was about 30 mm. Growing a multilayer ice plate was necessary to distribute the particles throughout the ice grains. The ice plate was subsequently broken up, and a 3– 5 mm sieve fraction was obtained. These grains were then used to seed granular ice specimens as described above. Both types of ice had an initial average grain size of about 5 mm. Figure 1 shows a thin section of ice with 1 wt.% particles distributed both along the grain boundaries and in the grain interiors. It can be seen that the particles are uniformly distributed: some of the particles are along the grain boundaries, while the other are in the grain interiors. It should be noted that for the particle size of 50 lm, even when the particle concentration is as low as 1 wt.% (0.43 vol.%), the number of the particles could be as large as 8.2 · 109 m3. Creep and cyclic loading tests were performed using a creep jig [15] located in a cold room with a temperature 2 C lower than the test temperatures (20 C to 2 C). Two insulated boxes were used to isolate the jig from the cold room, and a temperature regulating system was located between the boxes. This method controlled the temperature in the inner box to deviations of less than ±0.1 C. Creep tests used air pressure to determine the creep rate as a function of creep stress and temperature, while the cyclic loading tests used an MTS actuator to determine the contribution of grain
boundary sliding to the creep. Cyclic loading tests use the sinusoidal waveforms to generate stress/strain hysteresis loops areas to study the anelasticity caused by both the dislocation relaxation process and grain boundary relaxation process, and thus provide an indirect way to understand the contribution of grain boundary sliding to the creep rate and creep activation energy. Figure 2 shows the stress dependence for particlefree ice and particle-containing ice at temperatures from 20 C to 2 C. At temperatures from 20 C to 5 C, particle-containing ice showed higher creep rates compared to particle-free ice at the same stress. The difference between the creep rates is small at and above 5 C. Significantly, the particles do not affect the power-law behavior at any temperature. Both types of ice show power-law creep with a stress exponent of 3 from 20 to 2 C and for stresses from 0.4 MPa to 1.4 MPa, in agreement with a previous study on freshwater polycrystalline ice [1]. It is well-known that non-basal plane deformation of ice crystals needs a much higher stress than that for basal slip at the same strain rate. For polycrystalline ice, the difference in resistance to creep between basal and non-basal plane causes large internal stress, and thus gives two types of hardening – directional and non-directional hardening [16]. Directional hardening is caused by short-range interactions between dislocations on parallel planes (Taylor hardening) or on intersecting planes (Forest hardening); while nondirectional hardening is caused between moving dislocations and arrays of dislocations forming cell walls. Since ice exhibits high amount of anelastic strain, a previous study [16] has indicated that recovery processes control the creep of polycrystalline ice. For single crystal ice, the rate-controlling might be glide and the stress exponent is 2, while for polycrystalline ice, the rate-controlling might be recovery and the stress exponent is 3. Our tests on ice with particles show that the stress exponent is not affected by the presence of particles. Since the particle concentration is low, the spacing (0.5 mm) between particles is very large compared to the slip line spacing (several microns). Thus, dislocation movement during creep is apparently not impeded by the particles, and the particles’ main effect is probably to act as dislocation multiplication sources. The creep
Figure 1. Micrographs of the thin section of particle-containing (1 wt.%) ice viewed through crossed polarizers.
Figure 2. Minimum strain rate as a function of creep stress for particle-free ice and particle-containing ice from 20 C to 2 C.
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rate is affected by the increase in dislocation density, but the rate-controlling mechanism remains the same. Thus, the stress exponent is not affected. Figure 3 shows the effects of temperature on the minimum creep rate of both particle-free ice and particle-containing ice at various stress levels. It can be seen that particle-containing ice shows a linear relationship between log minimum creep rate and reciprocal temperature over the entire temperature range, while there is clearly a change in slope for the particle-free ice at around 10 C (1/T = 3.8 · 103 K1). Detailed calculations indicate the activation energy is 70 kJ mol1 for particle-containing ice from 20 C and 2 C, while for particle-free ice, the activation energy is 74 kJ mol1 from 20 C to 10 C, but increases to 120 kJ mol1 from 10 C to 2 C. The activation energies are roughly independent of creep stress from 0.4 MPa to 1.4 MPa. The value 70 kJ mol1 below 10 C for both types of granular ice agrees well with previous data [6,19,20]. Generally, polycrystalline ice has a similar activation energy to single crystal ice (normally 63 kJ mol1, [17,18]) below 10 C. The slight difference in activation energy might be due to the difference in rate-controlling processes – glide for single crystal ice and recovery for polycrystalline ice. Normally polycrystalline ice has an activation energy somewhat higher at temperatures above 10 C. This increased activation energy was also observed in the present study for particle-free polycrystalline ice at temperatures above 10 C. However, it is emphasized that the activation energy for particle-
containing ice above 10 C is the same as that below 10 C. The difference between the behavior of polycrystalline ice and single crystal ice is due to the influence of grain boundaries. A previous study [5] attributed the higher activation energy above 10 C for polycrystalline ice to a liquid phase at the grain boundaries, and to grain boundary sliding. If this is so, equivalent experiments on single crystal ice should not show such an increase in activation energy. For example, the work by Jones and Brunet [21] indicated that in single crystal ice, the activation energy has a constant value 70 kJ mol1 from 20 to 0.2 C. It has been shown using cyclic loading [22] that a dislocation relaxation peak exists at 2 · 104 Hz and a grain boundary relaxation peak exists at 5 Hz at 10 C. The peaks will shift to lower frequencies as the temperature decreases. The higher the temperature, the shorter is the relaxation time and the higher is the frequency of the relaxation peak [23]. Figures 4 and 5 show the stress/strain hysteresis loop areas (anelastic relaxation strength) for particle-free ice and particle-containing ice after creep at various stresses at 20 C and 15 C. The hysteresis loop area is a measure of energy dissipation due to dislocation motion and grain boundary sliding. The variations in hysteresis loop area for both types of ice at low cyclic frequencies up to 101 Hz are due to the variations in dislocation densities, and the variations in hysteresis loop area at high cyclic frequencies (above 101 Hz) are due to the variations in the contribution of grain boundary sliding [22]. Grain boundary sliding peaks can be observed at 0.5 Hz at 20 C and 1 Hz at 15 C for particlefree ice because these peaks have been shifted from 5 Hz at 10 C to 0.5 Hz at 20 C and 1 Hz at 15 C. However, these peaks are not observed for ice with particles. Some of the particles distributed along
Figure 3. Effect of temperature on the creep rate of (a) particle-free ice and (b) particle-containing ice.
Figure 4. Hysteresis loop area as a function of frequency at T = 20 C: (a) particle-free ice and (b) particle-containing ice.
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Creep experiments have been performed on polycrystalline particle-free ice and particle-containing ice to study the effects of particles on the creep stress exponent and the activation energy for creep from 20 C to 2 C. Particles affect the creep rate but do not affect the creep stress exponent. n 3 power-law creep has been observed for both particle-free ice and particlescontaining ice. Particles do not affect the power-law behavior but decrease the activation energy above 10 C by inhibiting grain boundary sliding, which causes the activation energy to increase from 70 kJ mol1 below 10 C to 120 kJ mol1 above 10 C. This research was supported by NSF Office of Polar Programs, Arctic Natural Sciences Program (OPP 011737). We thank Glenn Durell for his valuable assistance in developing the creep and cyclic loading equipment.
Figure 5. Hysteresis loop area as a function of frequency at T = 15 C: (a) particle-free ice and (b) particle-containing ice.
the grain boundaries inhibit the grain boundary sliding, and cause the grain boundary relaxation peak to disappear. A previous study [24] also observed this phenomenon in metals (Cu–Fe and Cu–SiO2). When the particles are located at grain boundaries, the particles retard grain boundary sliding through the development of internal stresses, which decrease the free sliding distance and the relaxation time, thus increasing the modulus and decreasing the internal friction. It is evident that the increase in activation energy above 10 C is due to the increased grain boundary sliding at high temperatures. Since particles inhibit grain boundary sliding at temperatures above 10 C, they prevent the increase in activation energy evident in particle-free ice. Thus, polycrystalline ice with particles shows a similar activation energy to polycrystalline ice without particles at lower temperatures (below 10 C), at which grain boundary sliding is inhibited. However, this does not mean there is no grain boundary sliding when temperatures are below 10 C. Grain boundary sliding is a diffusion-based, thermally activated process and increases exponentially with increasing temperature. At temperatures below 10 C, the contributions of grain boundary sliding are present but not important. However, it becomes more important at temperatures above 10 C, and hence is responsible for the increase in activation energy for polycrystalline particle-free ice. A previous study [5] indicated that at temperatures above 10 C, the grain boundary structure changes to a quasi-liquid phase. This quasi-liquid phase can absorb dislocations and thus affect the internal stress field and increase the grain boundary sliding, which inevitably increases the activation energy for particle-free polycrystalline ice above 10 C.
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