Introduction

The kinetic friction coefficient of ice sliding against itself is important in sea-ice ridge building(Hopkins and Hibler, Reference Hopkins, Hibler III., Sinha, Sodhi and Chung1989) and in the brittle compressive fracture (Schulson, Reference Schulson1990) of the material. Despite its importance, the topic has not yet been extensively studied, especially at low velocities.In both applications, the sliding velocities are quite low (< 0.1 m s⁻¹). Earlier work on fresh-water ice (Barnes and others, Reference Barnes and Walker1971) showed that large changes in ice friction occur in the 10⁻⁵ to 10⁻²ms⁻¹ velocity range. This paper considers the effectsof temperature (-3° to —40°C) and sliding velocity (10⁻⁶ to 5 × 10⁻² m s⁻¹) on the friction coefficient, defined as the ratio of the tangential force resisting sliding to the force applied normal to the plane of sliding.

Experimental Design

Ice was manufactured according to general procedures developed at the Thayer School of Engineering Ice Research Laboratory (Kuehn and others, Reference Kuehn, Lee, Nixon, Schulson, Sodhi, Luk and Sinha1988). The test material was grown from water of 20 parts per thousand (ppt) salt concentration (obtained using “Instant Ocean”, a commercial product recreating the composition of ocean water) which was contained within a 10001 insulated tank. Heat was removed unidirectionally through a cooling plate, producing a puck of ice approximately 1 m in diameter and upto 0.35 m in

Table 1. Characteristics of the test ice and first-year sea ice (Kuehn and others, 1988)

thickness. The ice was columnar (Fig. 1), and similar in characteristics (c-axis orientation, salinity, brine pocket sizes) to first-year sea ice (Table 1).

Blocks of two sizes, 50 by 50 by 20 mm³ and 70 by 220 by 20 mm³ were machined from the puck, with columns perpendicular to the sliding surfaces. Prior to every test, the mating surfaces were each re-surfaced using a Leitz 1400 Sledge Base Microtome to a depth of approximately

Fig. 1. Horizontal (a) and vertical (b) sections of laboratory-grown saline ice.

1.25 mm. Additionally, the edges of the smaller blocks were bevelled with a razor blade to remove anysharp corners which might otherwise plow into the surfaces of the larger blocks. The process was followed to create clean and fresh test surfaces, which would exhibit test traces independent of previoustest runs.

To perform the testing, an attachment to a uniaxial Material Testing System (MTS) testing machine wasconstructed to provide a pair of balanced, opposing test surfaces. The apparatus is shown in Figure 2. The larger ice specimens (220 mm long) were bonded to aluminum

Fig. 2. Friction coefficient apparatus with stationary and mobile ice blocks.

plates attached to a sensitive load transducer which measured the friction force. The load cell was mounted to the MTS hydraulic actuator, which was programmed to provide the desired sliding velocity. In contact with the two larger ice blocks were the laterally-loaded smaller, stationary ice blocks. The loading mechanisms were connected to the stationary cross-piece of the MTS testing machine.

A test constituted a single pass of the opposing block and slab faces, loaded under 17.8kPa. The datawere collected by two methods: (a) load, displacement and elapsed time were recorded using a data acquisition program, ASYST; and (b) the frictional force was plotted versus the sliding distance. The data were combined to obtain the mean and the variance of the steady-state kinetic friction coefficientfor a given test. For each condition, at least four tests were performed and the averages obtained.

Results

The majority of the tests was characterized, to some extent, by “stick-slip”. This occurred when the opposing surfaces were held in contact temporarily until the tangential forces were sufficiently great to release the surfaces. On the traces of force versus test-time (Fig. 3), the stick-slip conditionappeared as a sawtooth. Stick-slip was observed in all tests at sliding velocities ≥ 5 × 10⁻⁵m s⁻¹, and in the tests at -3°C at velocities as low as 10⁻⁵ms⁻¹. At these lowest velocities, the variation (given as the standard deviation) in the friction coefficient owing to

Fig. 3. Force (newtons) versus time (s) test trace, illustrating “stick-slip”.

stick-slip was about one-twentieth of the mean, compared with the variation at the higher velocities (~ 10⁻³m s⁻¹), which was about one-fifth of the mean.

Figure 4 shows the mean kinetic friction coefficient, μ, versus the sliding velocity, at each of the four temperatures investigated. The standard deviations are depicted by the error bars. Two points are noteworthy. (i) The curves at -10° and -3°C display three regions: the first is from 10⁻⁶ m s-1 to about 10⁻⁵ms⁻¹ where μ is approximately constant at ~0.5; the second region is from about 5 × 10-5 m s⁻¹ to about 10⁻³ m s⁻¹, where μtends to level off at ≤ 0.1. At -20°C and at -40°C, μrose from about 0.5 at 10⁻⁶ ms⁻¹ to a maximum at an intermediate velocity between 5 × 10⁻⁵ and 10⁻⁴ m s⁻¹, and then decreased rapidly to about 0.1 at 10⁻² m s⁻¹. The peak was more pronounced at the lower temperature. Curiously, the results of these tests on salt-water ice were similar to those found in friction experiments on freshwater granular ice tested under similar conditions using the same testing apparatus (Jones, Reference Jones1989). The similarity suggests that brine pockets do not influence the kinetic frictioncoefficient significantly. (ii) Generally, the kinetic friction coefficient increased with decreasingtemperature (e.g. at v = 10⁻⁴ m s⁻¹, μincreased from 0.25 at — 3°C to 0.63 at -40°C).

The other noteworthy feature was the surface of the ice blocks. Following sliding under certain conditions, the surfaces exhibited a liquid film which formed droplets upon separation of the ice samples. This characteristic was present for all sliding velocities at temperatures -3°C and -10°C, and for velocity 10⁻² m s⁻¹ at -20°C and -40°C. For the fresh-water ice testing, the icesamples exhibited the surface droplets only at the sliding velocities 10⁻² m s⁻¹ at -3°C and 5 × 10⁻² m s⁻¹ at -10°C. The variation about the mean coefficient value for fresh-water ice was in general greater than that of saline ice under the same conditions, attributed to the lack of surface droplets.

Discussion

Comparisons to previous work on the kinetic friction of ice are difficult, because the majority of the earlier work considered friction of ice against certain metals and plastic coating generally at higher sliding velocities.

The general decrease in the kinetic friction coefficient with both increasing velocity and increasingtemperature has already been noted. Tabata and Tsushima (1979)

Fig. 4. Fig: 4. Temperature dependence of kinetic friction of saline ice versus sliding velocity.

observed these behaviors for steel moving beneath sea ice under ~100 kPa at -5°C for the range 3.5 × 10⁻⁷ ≤ ν ≤ 5 × 10⁻² m s⁻¹. Saeki and others (Reference Saeki and Tanaka.1986) reported, for sea-ice sliding against both uncoated steel and concrete at -8°C under200 kPa, that μdecreases from 0.1 for steel and ~0.2 for concrete at 5 × 10⁻⁴m s⁻¹ to a steady value of about 0.04 for both materials at 1.0 m s⁻¹. Oksanen and Keinonen (Reference Oksanen and Keinonen.1982) indicated, for frozen tap water sliding against itself at ~2.5 kPa, that μdecreases from 0.038 at 0.5 m s⁻¹ and -15°C to 0.016 at 3 m s⁻¹ and -15°C, and to 0.23 at 0.5 m s⁻¹ and -5°C.

The curves in Figure 4, exhibiting peak values of kinetic friction coefficient at intermediate velocities at the lower temperatures (-20°C and -40°C), compare favorably with results obtained by Barnes and others (Reference Barnes and Walker1971). They observed bell-shaped μversus νcurves for polycrystalline fresh-water ice sliding on both polished granite and glass at about 1 MPa normal pressure, -18.5°C ≤ Τ ≤ -0.5°C, and 10⁻⁸ m s⁻¹ ≤ v ≤ 10⁻¹ m s⁻¹. Below -10°C, the ice adhered to the granite and, thus, at the lower temperatures the friction coefficient was for ice on ice. Coefficients reached a peak at ~10⁻⁵ms⁻¹ for polished granite and at ~10⁻² m s⁻¹ for glass, independent oftemperature. Barnes and others (Reference Barnes and Walker1971) attributed the peaks to a combination of processes, including creep, recrystallization, shearing of interfacial bonds and frictional heating. Their description doesnot fully explain the observations of the present study, in part because thin sections of tested saline specimens revealed no evidence of recrystallization. Instead, we propose the following explanation.

The friction force at the ice/ice interface originates within the real area of contact between asperities on the surfaces. A portion of the friction force can be attributed to adhesion; i.e. the making and breaking of bonds between contacting ice crystals. This contribution is nearly eliminated if a thin liquid film, acting as a lubricant, develops at the contact interface, through frictional heating and melting. This is probably responsible for the general decrease in the friction coefficient with increases in sliding velocity, as originally proposed by Bowden and Hughes (Reference Bowden and Hughes1939). In addition to the adhesive contribution to the friction, there is another important contributor: deformation of the contacting surfaces. Since both contacting surfaces have a finite roughness, asperities on the two specimens come into contact, or interlock, and must move by each other as sliding motion occurs. This may require deformation or fracture of one or both asperities. An important mechanism of deformation of ice is creep, with the creep rate increasing as the temperature approaches the melting point. A consideration of creep deformation can explain the shape of the friction versus velocity curve (Fig. 4) at low temperatures (-20° to -40°C).

At the lowest sliding velocities, creep deformation of contacting asperities has time to occur beforethe asperities move past each other, even at low ambient temperatures. As the sliding velocity increases, however, the depressed creep rate at low temperatures does not allow the asperities to deform sufficiently during the time they are in contact, so an increased tangential force is required to shearthe asperities. This is responsible for the peak in the friction coefficient at the low temperatures.If the velocity increases sufficiently, frictional heating increases the contact temperatures, resulting in higher creep rates and a decrease in the force required to deform the asperities. Eventually, at still higher velocities, melting of the asperity peaks occurs and the friction force drops more rapidly.

The above description of the sliding process is quite consistent with the sawtooth traces of the friction force versus time (and sliding distance) observed in this study, especially at low or intermediate sliding velocities (Fig. 3). The friction force would increase as the asperities interlocked and then decrease as they sheared or fractured.

The results of this work point out clearly the importance of temperature increases due to frictional heating. The temperature increases are related to the sliding velocity, the hardness of the ice (which influences the contact area), the thermal conductivity of the contacting materials and the frictioncoefficient. In addition, pressurized contact would cause a lowering in the melting point of the ice.Depression in the melting point, approximated by the Clausius-Clapeyron equation, would then reduce the amount of ΔT due to frictional heating necessary to produce melting. Although conditions were not sufficient to produce melting alone, calculations (Jones, Reference Jones1989) indicated that, in conjunction, ΔΤ should be sufficient to cause surface melting for velocities ≥ 10⁻² m s⁻¹ at Τ ≤ -10°C and for υ≤ 10⁻³m s⁻¹ at Τ = -3°C.

Conclusions

The following conclusions were drawn from experiments on the kinetic friction of saline ice against itself:

(i) The kinetic friction coefficient, μ,of salt-water ice was determined to be highly dependent upon the ambient test temperature (between -3° and -40°C) and the sliding velocity from 10⁻⁶ to 5 × 10⁻²m s⁻¹. The velocity dependence was partitioned into three sections: one region of near constant μ(approximately 0.5) for velocities ranging from 10⁻⁶m s⁻¹ to about 10⁻⁵ m s⁻¹; the transition zone, exhibiting a significant decrease in coefficient values for velocities between 10⁻⁵ and 10⁻³ m s⁻¹, and the third region, where apparent frictional-heating effects result in steady and low (0.1 or less) values of μat velocities ≥ 10⁻³m s⁻¹.

(ii) The temperature dependence of the friction coefficients was manifested in two forms. A general increase in μwas measured for decreasing temperatures: at 10⁻⁴¹ m s⁻¹ sliding velocity, for example, coefficients ranged from 0.25 at -3°C to 0.63 at -40°C. At lower testing temperatures (-20°C and -40°C), the friction coefficient curves exhibited a peak value at a sliding velocity of approximately 5 × 10⁻⁵m s⁻¹.

Acknowledgements

The work was supported by the Office of Naval Research, grant no. N00014-86K-0695, and was performed in the Ice Research Laboratory of the Thayer School of Engineering. The laboratory is operated through the additional support of the Army Research Office, Minerals Management Service, U.S. Coast Guard, Amoco, Conoco, Exxon, Mobil, Shell, and Unocal.