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Generation of melt during crushing experiments on freshwater ice
cold regions science and technology ELSEVIER
Cold Regions Science and Technology 22 (1994) 385-398
Generation of melt during crushing experiments on freshwater ice R.E. G a g n o n Institute for Marine Dynamics, National Research Council of Canada, St. John's, Nfld. A 1B 3T5, Canada (Received 22 October 1992; accepted after revision 18 June 1993)
Abstract
A stainless-steel platen, with arrays of pressure sensors and thermocouples on the front face, has been used to crush mono-crystaUine, bubble-free freshwater ice samples at - 10 oC 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.
1. Introduction In recent years the processes involved in ice impacts and crushing have been the focus of several investigations. These studies include visual observations of the contact zone between the crushing instrument and the ice (Riska et al., 1990; Gagnon and Molgaard, 1991; Fransson et al., 1991 ). In the recent work of Gagnon and Molgaard ( 1991 ) and Gagnon and Sinha ( 1991 ) it has been shown that pressure melting and generation of heat by viscous flow of the melt is an important mechanism. This paper reports resuits from experiments carefully designed to fur-
ther investigate this mechanism through visual records and measurements of pressure, load, and temperature at the ice/indentor interface. A preliminary report of these results has already been presented (Gagnon, 1992).
2. Apparatus Fig. 1 shows the ice specimen mounting holder. It consisted of a 5 cm X 13 cm X 17 cm plexiglas plate on which the ice samples sat. Confining plates for the sides of the specimen bolted to the plexiglas. The plexiglas plate was reinforced to
0165-232X/94/$07.00 © 1994 Elsevier Science B.V. All fights reserved SSDI O165-232X ( 93 )EOOI 7-D
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
386
MATING
,
PLATE
I ',
.
FOR
MTS
FRAME
MIRROR
J
.
.
.
.
.
.
PERIPHERAL REINFORCEMENT
l
! "
TRANSPARENT
'
PLEXIGLAS
PLATE
CONFINING
PLATE
~.
ICE
l INSTRUMENTED L
CRUSHING
-
PLATEN . . . .
ACTUATOR PISTON
Fig. 1. Crushing apparatus with mirror for viewing the contact zone during experiments.
minimize flexure by a 4 cm thick stainless steel rectangular backing structure which ran around the perimeter of the back face of the plexiglas plate. The reinforced plate was supported on opposite sides by two pillars of A1, 12.5 c m × 8 cm X 2.5 cm. A cross member attached to the base of the pillars and mated with the load cell of the testing frame. Between the pillars a mirror was situated at a 45 ° angle so that a video camera could view from the side through the plexiglas and ice to the region of contact between the ice and the steel platen that it was crushed against. A flood lamp was used to illuminate the ice and
platen along the same view path by placing it beside the video camera. The 4 cm × 20 cm X 20 cm platen which the ice was crushed against was made of stainless steel and instrumented with piston/diaphragm type pressure transducers (Fig. 2). Thermocouples (copper-constantan) were also installed in the platen by drilling and tapping small holes through the platen into which the thermocouples were inserted till they protruded slightly and filling the holes with 5 minute epoxy. When the epoxy had set the protruding portions were sanded off so the thermocouple tips were flush with the surface of the platen. An additional thermocouple was installed through the center of the central pressure transducer piston. This permitted direct measurement of temperature and pressure at one site. During tests the passive ends of the thermocouple wires were exposed to the ambient air temperature in the cold room, where they connected to the data acquisition system. Hence the temperature measured at the active ends of the thermocouples was relative to the ambient temperature of the cold room. The diameter of the four peripheral pressure transducers was 16 m m while the central one was 8 m m in diameter. Total load was monitored by a load cell attached to the crosshead of the loading frame. Data were acquired using a Data Translation analog to digital acquisition board with a throughput of 150,000 sampIes/s with 12 bit resolution. This was used in conjunction with an Empac 486 computer. The software package Viewdac (Keithley-Asyst) was used to control the acquisition board and to analyze the data. Typically 24,000 samples were acquired from each channel per test. All tests were run at fixed actuator speeds with durations ranging from 2 to 13 seconds, which allowed for a variety of sampling rates to be used, 2-18 kHz. The video recording system consisted of a Sony Hi8 camcorder capable of shutter speeds as high as 1/10,000 s at 30 frames/s and a Sony Hi8 VCR. During tests the VCR was connected to the camcorder so that two video records were obtained for each test. The shutter speed for all tests was 1/2000 s. In standard video format 60 video fields/s are acquired and in real-time playback
R.E. Gagnon / Cold Regions Science and Technology22 (1994) 385-398
STAINLESS
STEEL
387
PLATEN
PRESSURE
TRANSDUCER
THERMOCOUPLE
COMBINED AND
PRESSURE
SENSOR
THERMOCOUPLE
Fig. 2. Stainless steel crushing platen showing the configuration of pressure and temperature sensors.
two are interlaced to make up one frame to yield 30 frames/s. However, on still-frame playback only every second field is shown, with half the resolution of real-time playback. Connecting the VCR to the camcorder had the added advantage of sometimes gaining access to the full 60 fields/ s, that is, the camcorder video record, on stillframe playback, was shifted 1/60 s from the VCR record on still-frame playback. The video records were analyzed with the assistance of a frame grabber board (Targa M8 (Truevision)) and Java (Jandel) video analysis software, An LED was used to synchronize the video records with the data acquisition system. An elementary circuit caused the LED to start blinking at ~ 31 Hz, with a duty cycle of 50%, when activated by a 5 V signal from the data acquisition system at the start of a test. Because the LED blinked at a slightly different rate than the number of frames per second recorded by the video camera, subsequent video records would show
the LED on for several consecutive frames and then off for an equal number of consecutive frames, where the apparent on/off frequency was just the beat frequency of the LED/camcorder system i.e. Apparent Blink Rate =
( 1)
F(actual blink rate) -- Fframes/s
Synchronization was achieved by using the fraction of one full cycle of the apparent blink rate which appears on the video record at the beginning of a test to determine where in the first 1/30 s of the test that the first video frame was taken. This method yielded synchronization to within + 0.001 s.
3. Sample preparation The method of visual observation of the crushing process at the ice/indentor interface was
388
R.E. Gagnon /CoM Regions Science and Technology 22 (1994) 385-398
similar to that described by Gagnon and Molgaard (1991), that is, to make use of the transparency of the ice to view the process by looking through the ice specimen. In this case samples were cut from large single crystals of bubble-free freshwater ice with the c-axis vertical. The specimens were blocks initially 13 cm X 13 cm × 10 cm with the top portion trimmed to the shape of a truncated pyramid with a slope of ~ 40 °. Sharp edges and corners were rounded by melting and the very top of the peak was smoothed, by rubbing with a glove, to prevent premature cracking at low loads. Single crystal specimens were used to guarantee good visual observation by eliminating obscuring reflections off grain boundaries, and also crack formation associated with grain boundaries which would block the view. Specimens were mounted on the thick ( 5 cm) plexiglas plate by heating the plate's surface to just above 0 ° C and placing the sample (prewarmed to 0°C) onto it causing the ice to melt slightly and match the plate surface exactly. After wiping off excess water the plexiglas and ice were then put into the cold room at - 10 °C to freeze the melt layer. When the melt refroze the central annular region, comprising more that 50% of the bottom surface of the ice specimen was perfectly bonded to the plexiglas. The outer area had lifted slightly because of the expansion of the water on freezing. The gap between the ice and plexiglas in this region was very small, because Newton's interference rings were visible. The confining plates were then installed and a cclamp with a styrofoam pad was used to clamp the sample to the plexiglas to prevent separation when water, at 0°C, was poured in around the sides to fill the small gap between the confining walls and the ice, ~ 1-2 mm. These precautions were essential in preventing unwanted cracks in the bulk specimens during testing, due to improper bonding of ice to plexiglas, which would block the view of the ice/indentor interface. The large single crystals of freshwater ice were grown by placing a container with insulated sides and bottom filled partially with de-aired and deionised water in the cold room at - 10 ° C. The top of the container was covered with cardboard except for an opening at one end of the rectan-
gular container. Cold air blowing in through the opening at one end caused the growth of very long single crystal plates on the water surface. One of these continued to grow to take up the majority of the surface area, 20 cm × 60 cm. When a few centimeters thickness of this ice had grown it was removed from the container and the remaining water was dumped. In a room at 0 ° C, the ice plate was then placed in the bottom of the empty container and degassed water at 0 °C added through a small hose placed under the ice plate. As the water entered, the ice floated on the surface preventing air from saturating the liquid. When ~ 15 cm depth of water had been added, the container was put into the cold room at - 1 0 ° C which caused the gap between the ice edge and the sides of the container to quickly freeze sealing the water completely from the air. The ice plate behaved as a template and grew in thickness primarily as one large single crystal with no bubbles. When the ice had grown to the desired thickness it was removed from the container and a layer of a few centimeters thickness was cut from its top surface to serve as a template for the next refill of the ice growing container.
4. Data analysis Fig. 3 shows the pressure time series record from the central pressure/temperature sensor and the total load time series from the load celt for a typical run at - 10°C with an actuator speed of 1.5 cm/s. The total ice penetration was ~ 1 cm. The sampling rate was 18,5 kHz. Because of the symmetry of the confinement o f the ice and its pyramid shape most of the ice/platen contact occurred in the vicinity of the central pressure/ temperature sensor. The load and pressure records exhibit a sawtooth periodic breaking pattern often characteristic of ice crushing and indentation (Gagnon and Molgaard, 1991; Gagnon and Sinha, 1991; Michel and Blanchet, 1983; Evans et al., 1984; Frederking et al., 1990; Sodhi and Morris, 1984; Mii~ttiinen, 1983; Timco and Jordaan, 1988 ). The temperature sensor record (Fig. 4 ) shows that once the crushing process had gotten under way that the temperature at the in-
389
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398 70 60 5040
I
30 20 10 0 -10 50 4O
,-,
30
10 0 -10 0.0
L
I
J
I
0.2
0.4
0.6
0.8
~
1.0
(s)
Fig. 3. Pressure ( c e n t e r t r a n s d u c e r ) a n d load record for a test r u n at - l 0 °C with an a c t u a t o r speed o f 1.5 c m / s .
terface increased. The thermocouple temperature sensor had considerable thermal inertia because it was imbedded in epoxy which in turn was surrounded by metal and only the very tip of the sensor was at the platen's surface. For these reasons the temperature changes which registered were less than the actual changes in temperature at the platen's surface caused by its exposure to warm material produced in the ice crushing process. In other work on ice indentation (Gagnon and M~lgaard, 1991; Gagnon and Sinha, 1991 ), evidence has been presented that indicates that as a result of the indentation and crushing process liquid water is produced. To verify whether the thermocouple record from the
test indicated the presence of liquid and ice at 0°C the central transducer's response was recorded when a mass of fine wet snow was hand pressed against the center of the platen at - l 0 ° C. Fig. 4 shows the comparison of the thermocouple outputs from the test in Fig. 3 and the test with the wet snow. Clearly the trends and magnitude are very similar. While this is not an absolute calibration of the temperature sensor, it shows that it is very likely that liquid, produced by the ice crushing process, made contact with the sensor. The video records invariably showed the same characteristics for tests where specimens were confined properly and bonded well to the plex-
R.E. Gagnon / CoM Regions Science and Technology 22 (1994) 385-398
390
-0.20 > v
T E S T IN FIG.3
t~
m r.,o Z 0
-0.16
m
-0.12
m
m 0 0 0~
-0.08
-0.04
A M B I E N T T E M P E R A T U R E = -10oC
E-
0.00 0.00
I
I
0.22
0.44
I
0.66
0.88
1.10
T I M E (s) Fig. 4. Comparison of the response of the center temperature sensor during the test shown in Fig. 3 with its response when wet snow was hand pressed against the central region of the crushing platen.
iglas plate. The region of contact consisted of a central zone where the ice appeared to be undamaged, because the crushing platen was clearly visible through it, surrounded by a dense mixture of fine and coarse particles of ice that was opaque. This has also been observed by Gagnon and Molgaard ( 1991 ) using a different apparatus. As crushing occurred during a test the contact region would change in shape, size and position. Table 1 shows results from a number of tests from this test series where samples were well behaved because of proper confinement and good bonding to the plexiglas. Experiments were run at - 10°C and - 5 °C and for a range of actuator speeds, 0.15-2 cm/s. The table shows the maximum load for a penetration of 1 era, the ambient temperature, actuator speed, maximum pressure registered by the central pressure transducer for the whole test and the average sawtooth frequency for the whole test. There appeared to be no correlation between actuator speed and maximum load or maximum pressure at either temperature. In general higher maximum loads and maximum pressures were attained at the lower temperature. The mean maximum loads and
mean maximum pressures at - 10 oC and - 5 ° C were 28.7 kN and 22.1 kN respectively and 59.3 MPa and 47.4 MPa respectively. The sawtooth frequency of the load drops was strongly correlated with actuator speed at both temperatures, Fig. 5. The slope of the linear fit to the data at - 1 0 ° C implies an average actuator displacement of -,, 0.12 mm between sawteeth regardless of the actuator speed. It was noted in the slowest actuator speed tests at - 10 oC and occasionally in faster tests that in those instances where the time interval between load drops encompassed more than one video frame, i.e. longer than 1/30 see, that the size of the transparent area increased as the load increased. To cheek that in general for any test the size of the transparent contact spots correlated with load a series of contact areas were digitized from the video records (Table 2) from two tests run at - 10°C, one with an actuator speed of 1.5 c m / s and the other at 1.0 cm/s. A significant correlation was evident when the areas were measured and plotted against the corresixmding loads (Fig. 6). The slope of the linear fit was 0.126 eme/kN with a correlation coefficient of 0.86. One question arising from these experi-
391
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398 Table 1
Summary of results from tests at - 5°C and - 10°C Temperature (°C)
Actuator speed (cm/s)
Maximum pressure (MPa)
-
0.15 0.15 0.50 0.50 0.50 1.00 1.00 1.50 2.00 2.00 2.00 0.20 1.00 2.00
56.59 53.89 62.15 46.33 61.01 59.16 37.50 a 59.73 64.43 41.78 a 69.71 49.18 49.33 45.05
10 10 10 10 10 10 10 10 10 10 10 -5 - 5 - 5
Breaking frequency (Hz)
Maximum load to 1 cm (kN)
9 10 42 33 37 77 84 165 143 164 158 < 17 44 143
33.55 16.95 22.56 32.91 24.00 26.00 34.77 31.47 36.11 32.52 24.40 21.46 24.70 20.14
"Not used for average pressure calculation referred to in t e x t b e c a u s e of non-central contact and early cracking. 21111
Table 2
Transparent contact areas and corresponding loads from two
FIT FOR CIRCLES Y -1~7.5 + 82.81 X
t e s t s at - 10 ° C
=
O
Load (kN)
~120
Transparent contact area
Load (kN)
(cm2)
Transparent contact area
(cm2)
z
u.
41)
0.00
i
I
I
I
0.46
0.92
1-38
1.84
2.30
ACTUATOR SPEED (era/s) Fig. 5. Average frequency of the sawtooth load pattern versus
actuator speed for tests run at - 10°C and - 5°C.
ments and other ice crushing experiments is how the load is distributed relative to the transparent areas and the peripheral opaque snow-like material. The distribution of load was estimated in this ease by considering the measured pressure typical of the transparent spots, where the highest pressure measured during this test series by the center pressure transducer was 70 MPa at - 10*C. According to the slope of the line in Fig. 6, which yields a pressure of 79 MPa, this indi-
14.77 15.10 16.77 17.37 29.20 11.60 13.70 19.90 25.50 10.17 14.49 7.40 13.14 5.49 11.74 10.06 6.59 8.26 6.78 10.38
2.82 2.00 2.22 2.94 4.00 2.78 2.34 3.28 3.54 1.84 1.63 1.54 1.94 0.52 1.37 2.27 1.00 2.61 1.22 1.32
10.99 14.11 21.46 19.70 4.20 7.99 7.23 7.14 12.23 9.39 5.33 13.24 11.53 9.39 10.43 9.95 14.82 14.48 21.32 32.04
2.07 2.08 3.14 2.86 0.47 0.64 1.17 1.90 1.74 1.16 2.00 2.38 1.41 2.18 1.43 2.09 1.52 2.57 3.49 4.55
cates that in these experiments approximately 88% of the load is borne by the transparent spots, on the ascending side of the sawteeth at least. The
R.E. Gagnon / Cold Regions Scwnce and Technology. 22 (l 994) 385-398
392 6.0
IAREA = 0.449 + 0.126 x LOADI
4.8
t <
3.6
<
2.4
IPla,on.men,l\
8x104
D O I~
6x104
Z
4x10 ~
<
2x10 ~
t21 rn
1.2
J~'J D
Displacement Of Ice Against]
/
OxlO°
The Crushing Platen
/
J
0.0 0
8
16
24
32
40
LOAD (kN) Fig. 6. T r a n s p a r e n t contact area v e r s u s load for several video frames taken from two tests run at - l 0 ° C.
continuous wetting and softening of the opaque material by freshly produced liquid is probably responsible for the fact that the opaque material bears only 12% of the load. During the increase in load and the size of the hard spot the actual movement of the ice against the platen was ~ 0.3 × l0 -s m / N . This was determined by taking the difference between the apparent compliance of the ice/apparatus system as determined for ascending portions of the load record and the actual compliance as determined from elastic loading and unloading on previously damaged ice. Fig. 7 shows the true relative displacement of ice against the platen using the true compliance ( ~ 0.7× l0 -s m / N for the portion of the load record shown) of the ice/apparatus system. In general the compliance of the ice/apparatus system decreased as a sample was crushed. Fig. 8 illustrates the load, penetration and spot size relationships for the undamaged ice, assuming circular contact. The importance of the role of the transparent areas of contact has been noted and studied before (Gagnon and Melgaard, 1991; Gagnon and Sinha, 1991; Riska et al., 1990; Fransson et al., 1991 ). In particular Gagnon and Melgaard ( 1991 ) introduced the mechanism of pressure melting and heat generation by flow of melt during the rapid load drops as a means of explaining the visual and load and displacement data from ice crushing. In the present test results it is clear
_2xlO 4 0.00
0.01
0.02
0.03
...... 0.04
TIME (s) Fig. 7. Sections o f the t i m e series o f the c r u s h i n g platen disp l a c e m e n t a n d the relative d i s p l a c e m e n t o f the ice against the platen, d e t e r m i n e d using a c o m p l i a n c e o f 0 . 7 × 10 - 8 m / N, for the test s h o w n in Fig. 3.
that the same mechanism is also operating during the ascending portions of the load records. In this formulation the pressure is high enough on the transparent areas to initiate pressure melting Fig. 9. The thin layer of liquid which forms flows under the extreme pressure and generates heat from viscosity which goes into further melting. On moving towards the outer region of the high pressure zones the pressure is reduced and the melting temperature elevated so that refreezing occurs by dumping heat into the cold surrounding ice and metal. On leaving the high pressure zone the liquid has partially refrozen. This is consistent with several observations of refrozen liquid produced in indentation and impact on ice, e.g. (Gagnon and Molgaard, 1991; Gagnon and Sinha, 1991; Kheysin and Cherepanov, 1970). It is important to note that due to the size of the central pressure sensor, 0.5 cm 2, and the size and irregular shapes of the transparent contact spots (Fig. 10) that the sensor rarely, and then only marginally, was encompassed by the contact spot. The measured pressure was in fact an average pressure where the actual pressure was lower than average at the outer regions and higher than average at the center. This is why the pressure determined from the video and load records was
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
............... F .........
............ ~ ..........
393
F-16.7
..........
p t ~ R I M E T E R E X T E N T (era) Fig. 8. Surface characterization of the undamaged contact zone showing load, area and depth relationships, assuming circular contact.
Fig. 9. Schematic of the process of pressure melting and viscous flow of melt which occurs when the ice moves against the platen. The relative velocity of the ice towards the platen is ~ 0.5 c m / s on the ascending side of a sawtooth and ~ 18 cm/s on the descending side at a load drop. The fluid layer thickness is on the order of microns.
comparable to the highest measured by the transducer. A smaller pressure sensor would probably have recorded higher pressures when located in the center of a transparent contact spot. An average pressure of ~ 70 MPa is consistent with pressures required for pressure melting because a uniform layer of melt on a circular shaped transparent spot would imply a parabolic pressure distribution peaking to 140 MPa at the center (Bowden and Tabor, 1986, p. 274), which is adequate for melting at - 10 ° C .
The mechanism of pressure melting and viscous flow of melt, referred to above, implies a certain pattern of pressure and temperature across the transparent high pressure zones. The visual records and the configuration of sensors in the present experimental setup can, in principle, provide data on the distribution of pressure and temperature within these zones of contact. From the video records it was clear that whenever one of the transparent spots partially or completely (a very infrequent occurrence) covered the central pressure transducer that the pressure registered was very high. Because the frequency of the sawtooth breaks exceeded the rate at which video frames were captured and because of the thermal inertia of the temperature sensor most tests did not reveal any information about the temperature and pressure distribution within the hard spots. The experiments run at the lowest actuator speeds (0.2 c m / s ) and - 5 ° C did, however, provide some information. The time between the occurrence of large cracks was sometimes greater than 1 second and the behavior of a transparent spot as the actuator moved
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
394
^^^
2j ^ A A
^^
i 0
forward was easily captured in several video frames. The evolution of the spots at - 5 °C with an actuator speed of 0.2 c m / s seemed to be somewhat different from higher rate tests at the same temperature, and all tests at - 1 0 ° C . While the major drops in load governed the shape of the spots as before, more energy seemed to be consumed between major spalling events than for other tests. This was probably due to very tiny micro-spalls, evident in the video records, which continuously developed around the peripheries of the spots as the platen moved against the ice between major spalling events. Bearing this difference in mind, it is still reasonable to expect similar distributions of temperature and pressure across the transparent spots for all tests. Fig. 11 shows the pressure and therrnocouple readings for a segment of one of the tests at - 5 °C and 0.2 cm/s. As the crushing occurred the video record showed a transparent hard spot surrounded by opaque material. The size and position changed as the platen moved between major cracking events, such as at point A. In the figure points A, B, C, D corresponded exactly to the times when the hard spot had moved directly over the temperature and pressure transducer. Although the temperature record was not an absolute measurement of the actual temperature at the interface, for reasons discussed above, the trend in temperature from the outer to inner re-
u~-^
80
-5.5 A
C
60
:
D
-4.s
~-
-3,5 m
3
SCALE
cm
-2.5
:
0
J 2
3
' 4
~
-1,5
T I M E (s)
Fig. 10. Severalvideo framestaken at 1/60 s intervals showing the evolutionof the transparentcontactspotfromthe test in Fig. 3. The crosshatchedareas correspondto the opaque material surroundingthe hardspots.
Fig. 11. Comparisonof the trends in pressure and temperature at the centertransducersfor a test run at - 5°C with an actuator speed of 0.2 cm/s.
R.E. Gagnon I Cold Regions Science and Technology 22 (1994) 385-398
gion of the hard spot could be seen as the spot moved into position over the sensors, that is, higher at the outer regions and approaching the lower ambient temperature at the center. A similar inverse pattern of pressure was reflected in the pressure record. These observation are consistent with the mechanism of pressure melting described above. The video records and the sensor data revealed that the size, shape and position of the transparent spots were determined by two mechanisms, the pressure melting and extrusion of liquid process and the spalling process. This is best described by considering what happens in a typical test from a trough in the load record to the next trough (Fig. 12 ). T will denote the load at the top of the peak and, for convenience, B will be the load at the beginning of the section and the bottom of the load drop. On the ascending side the transparent spot area grew in size as the load increased according to the fit in Fig. 6. According to the values for the true and apparent compliance above, approximately 27% of the energy supplied by the actuator is associated with the growth of the transparent spot since 88% of the load is borne on it. 70% of the actuator energy goes into elastic energy of the ice/apparatus, given by C/2 × (T 2 - B 2) where the compliance, C, is 0.7× l0 -s m / N . Eventually, as the strain increased, the load on the ice reached a
395
point where a large crack(s) occurred and a spall(s) broke away from the area of contact (Fig. 13 ). This lead to a sudden rise in pressure on the remaining ice (Fig. 12) and rapid release of the built up elastic strain by movement of the ice against the platen. The load record and compliance indicate that even though the actuator was moving at a fixed rate of 1.5 cm/s, the relative displacement of the ice and platen towards one another occurred at ~ 18 cm/s until the consequent reduction in load and increase in hard spot area reduced the pressure on the ice to that which was present on the ascending portion of the sawtooth pattern and the cycle started again. It was clear from the results of the test program that more of the energy dissipated in the tests occurred during the rapid load drops than on the ascending sides of the sawteeth in the load records. A conservative estimate for the portion of that energy which is attributable to pressure melting and viscous flow of the melt can be obtained by determining the volume of hard spot ice removed by the process for a given load drop and multiplying it by the measured pressure obtained for the hard spots, ~ 70 MPa. This yields B
Ehardspot=70MPax
f
(Lx0.126+499)
2B-- T
X 10-7mE)<0.7X
lO-am/NdL
= 3.087 X 10-9 (4BT - 3B 2 - T 2) +2.2× 10-5(T-B) 411
(2)
3O
~1
The limits for the integration were established by recognizing that when a spall breaks away at the peak in the load the remaining hard spot area
Fig. 12. Sections of the pressure and load records, on an expanded scale, for the test shown in Fig. 3. The high frequency, low amplitude modulation in the load record corresponds to resonance in the apparatus. This corresponds to the same time segment shown in Fig. 7.
Fig. 13. Schematic of the spalling process that occurs at a load drop.
20
20
10
LOAD
SPALL E V E N T
0
10
-10 -20 0
~ 0.01
0.02
J 0.03
~ 0.04
0
TIME(s)
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
396
is small and grows to its eventual size at the bottom of the load drop as a result of the ice moving against the platen during the drop with a total displacement 0.7 X 10 - s ( T - B) m. This occurs according to the relationships of load, penetration and area illustrated in Fig. 8. This can be compared to the total energy expended by the apparatus/ice system according to
1.4 1.2 oe~ 1.0 u~ zm 0.8
[]
[-
o
/~../m
Y~= 0.134 + .423 X 1
c3D
/
/, /.-
/
cl
0.6 0.4
Etota,=(1/2)xO.7xIO-Sx(T2-B 2)
(3)
Table 3 and Fig. 14 show results of this comparison for several load drop events in the test shown in Fig. 3. In the mid-range the fit indicates that approximately 53% of the load drop energy was dissipated in the pressure melting and viscous flow of melt process. A percentage closer to 88% would be a reasonable expectation, however, due to the fraction of the load supported by the hard spots determined above for the ascending sides of the sawteeth. This implies that the pressure on the hard spot ice during the load drop was probably 66% greater than on the ascending portions of the load record, i.e. 116 MPa, Fig. 12 shows substantial rises in the pressure on the re-
Table 3 Calculated energies associated with the compliance of the ice and apparatus, and the transparent hard spots, for several load drops from the test in Fig. 3 Top load (kN)
Bottom load (kN)
Hard spot energy (J)
Compliant energy (J)
32.3 23.6 23.7 27.4 21.1 20.3 16.2 12.0 10.7 11.1 8.9 8.1 3.8 24.0 22.3
16.9 17.4 12.4 12.7 13.7 11.4 8.8 8.1 6.5 4.2 5.5 3.9 2.3 16.4 15.0
1.21 0.68 0.72 0.88 0.62 0.58 0.40 0.23 0.21 0.22 0.15 0.14 0.05 0.76 0.67
2.64 0.88 1.61 2.07 0.90 0.99 0.64 0.27 0.25 0.36 0.18 0.18 0.04 1.08 0.95
0.2 0.0 0.0
;
0.5
1
i
1.0 1.5 2.0 COMPLIANT ENERGY ( J )
2.5
3.0
Fig. 14. Energy associated with transparent contact areas versus energy calculated from the load data and compliance, Each point corresponds to a specific load drop event in the test shown in Fig. 3.
maining ice at load drops resulting from spalling which supports this conclusion, even though the central pressure transducer was not completely encompassed by the hard spots. We may conclude that since 88% of the energy dissipated on ascending portions of the load records and at least 53% on descending portions is associated with the hard spots that at least 6 4 % , i.e. 88% × 30% + 53% X 70%, of the total energy dissipated in the tests is attributable to the pressure melting process. The rest ofthe energy was probably dissipated as heat due to vibration in the apparatus and in the extrusion of the opaque material surrounding the spots. The goodness of the fit in Fig. 14 (the correlation factor was 0.95) implies that load drops occur in a manner such that the tops and bottoms of the drops closely satisfy the expression 0.13+0.21 X C( T2-B2)=Enardspot
(4)
where Ehardspot is given in Eq. (2). For a typical load drop from 22 kN to 15 kN the volume of ice removed by the melting process according to the expressions in Eq. (2) is 9.3 × 10 -9 m 3. The energy absorbed by the ice in the process is at least 0.65 J. This is sufficient to elevate the ice to 0°C and melt approximately
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
397
19% of it. Hence the ejecta that leaves the transparent high pressure zones is at least 19% liquid. A similar result was obtained by Gaguon and Molgaard ( 1991 ) based on data from tests using a different apparatus. We may also estimate the thickness of the liquid layer on both sides of the sawtooth using an expression from the theory of squeeze films (Bowden and Tabor, 1986, p. 274 ), assuming a circular contact area;
h= ( 3~lVR2/2P) i/3
(5)
where h is the layer thickness, q is the viscosity of water at 0°C ( 1750X 10 -6 Pa.s), Vis the velocity of the ice moving against the platen (0.005 and 0.18 m/s for the ascending and descending sides of the sawtooth respectively), P is the average pressure over the contact spot (70 MPa) and R is the radius of the spot (0.94X 10 -2 and 0.78× 10 -2 m on average for the ascending and descending sides of the sawtooth respectively). Using these values an average liquid layer thickheSS of 2.5 #m is obtained for the ascending side and 7.4 #In for the descending side. The evolution of the size and shape of a transparent contact spot is illustrated in Fig. 10 in a series of video frames, each separated by 1/60 s. These are from the test shown in Fig. 3 where the frequency of load drops was approximately 165 Hz. This implies that at least 2 spalling events occurred between each frame. Frame # 10 of Fig. 10 shows the last transparent zone created during the test. To demonstrate that during a test the ice in the high pressure zone was primarily removed by pressure melting and viscous flow of the thin layer of liquid, a thin section in the plane of the c-axis, was taken through the center of the spot in frame #10 (Fig. 15 ). Apart from a few cracks, some of which occurred during unloading at the end of the test, the figure clearly shows the ice through crossed polarized filters to be macroscopically undamaged in the zone, that is, no layer of crushed ice can be seen. Similar results have also been reported by Gagnon and Malgaard (1991 ) for crushing experiments on bubble-free freshwater ice. In the region of the high pressure zone it would be reasonable to expect densification and considerable cracking and recrystallization if the virgin ice has bubbles and/
Fig. 15. View through cross-polarized filters of a thin section (light area) taken through the last transparent spot in Fig. 10. Apart from a vertically oriented crack, which occurred during unloading, the ice is macroscopically undamaged in the central zone (A). The accumulation of dark material at the sides (B) corresponds to the opaque snow-like material surrounding the transparent spots in the video records. The unit on the scale is cm.
or brine channels, e.g. sea ice (Meaney et al., 1991). In the present setup the ice/(ice holder) system was not massive so that inertial effects did not play a large role during the sudden drops in load. However in the case of massive systems inertial effects lead to overshooting at the end of the load drops. Because of the overshoot in one cycle the pressure on the ice during load accumulation on the next cycle is not high enough for pressure melting and consequently the movement of the actuator results only in the build up of elastic strain in the system. This period of elastic build up when no fresh liquid is being produced by pressure melting provides time for refreezing of partially liquid opaque material extruded from the high pressure zone previously. Hence the opaque material can then support more load and dissipate more energy when it is cleared from the area of contact. In such systems video records show no change in the size or shape of the transparent spots on the ascending side of sawteeth and more energy is probably dissipated in the removal of the opaque material during load drops (Gagnon and Molgaard, 1991 ).
398
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
5. Summary and conclusions The following observations have been made: 1. The frequency of the rapid load drops was a linear function of the actuator speed and most of the energy dissipated in the experiments ocduring the load drops. The top and bottom loads for any load drop in general are determined by a unique relationship. 2. The compliances of the testing apparatus and ice play an important role even in a stiff system. 3. The measured and calculated pressures, the trends in the temperature records and the thin section analysis of a transparent spot were consistent with the process of pressure melting and viscous flow of the melt introduced by Gagnon and Mzigaard ( 1991 ). The process was responsible for at least ~ 64% of the energy dissipated in these tests. A smaller central pressure transducer and a temperature sensor configuration with much less thermal inertia would greatly improve the capability of the apparatus to yield more detailed information about the temperature and pressure distribution within the high pressure transparent contact zones. A video system capable of 1000 frames/s, or faster, would provide extremely valuable information about the spalting process and the evolution of the transparent spots during the rapid load drops. Acknowledgements The author is grateful to Mr. Trent Slade, who operated the testing frame during the test program, and Mr. Douglas Maloney, who helped with the design and construction of the crushing apparatus. References Bowden, F.P. and Tabor, D., 1986. The Friction and Lubrication of Solids. Clarendon Press, Oxford, 274 pp.
Evans, A.G., Palmer, A.C., Goodman, D.J., Ashby, M.F., Hutchison, J.W., Ponter, A.R~S. and Williams, G.J., 1984. Indcntation spalling of edge-loaded ice sheets. In: IAHR Ice Symposium, Hamburg, pp. I 13-12 I. Fransson, L., Olofsson, T. and Sandkvist, J., 1991. Observations of the failure process in ice blocks crushed by a flat indentor. In: Proceedings of the I lth International Confcrence on Port and Ocean Engineering Under Arctic Conditions, St. John's, Vol. l, pp. 501-514. Frederking, R., Jordaan, I.J. and McCallum, J.S., 1990. Field tests of ice indentationat medium scale, Hobson's Choice Ice Island, 1989. In: Proceedings of the 10th International Symposium on Ice (IAHR 90), Espoo, Vol. 2, pp. 931944. Gagnon, R.E., 1992. Heat generation during crushing experiments on freshwater ice. In: N. Maeno and T. Hondoh (Editors), Physics and Chemistry of Ice. Hokkaido University Press, Sapporo, pp. 447-455. Gagnon, R.E. and Molgaard, J., 1991. Evidence for pressure melting and heat generation by viscous flow of liquid in indentation and impact cxpcriments on ice. In: Proceedings of the IGS Symposium on Ice-Ocean Dynamics and Mechanics, Hanover, NH, 1990. Ann. Glaciol., 15: 254260. Gagnon, R.E. and Sin.ha, N.K., 1991. Energy dissipation through melting in large scale indentation experiments on multi-year sea ice. In: Proceedings of the 10th International Conference on Offshore Mechanics and Arctic Engineering 1991, Vol. IV, pp. 157-161. Kheysin, D.E. and Cherepanov, N.V., 1970. Change of ice structure in the zone of impact of a solid body against the ice cover surface. Probl. Arkt. Antarkt., 34: 79-84. M~i~tfiinen, M., 1983. Dynamic ice-structure interaction during continuous crushing. CRREL Rep. 83-85. Meaney, R., Kenny, S. and Sinha, N.K., 1991. Medium scale ice-structure interaction: failure zone characterization. In: Proceedings of the 11th InternationalConference on Port and Ocean Engineering Under Arctic Conditions, St. John's, Nfld., pp. 126-140. Michel, B. and Blanchet, D., 1983. Indentation of an $2 floating ice sheet in the brittle range. Ann. Glaciol., 4:180187. Riska, K., Rantala, H. and Joensuu, A., 1990. Full scale observations of ship-ice contact. Laboratory of Naval Architecture and Marine Engineering, Helsinki University of Technology, Report M-97. Sodhi, D.S. and C.E. Morris. 1984. Ice forces on rigid, vertical, cylindrical structures. CRREL Rep. 84-33. Timco, G.W. and Jordaan, I.J., 1988. Time series variations in ice crushing. In: Proceedings of the 9th International Conference on Port and Ocean EngineeringUnder Arctic Conditions, Fairbanks, AL, pp. 13-20.
Cold Regions Science and Technology 22 (1994) 385-398
Generation of melt during crushing experiments on freshwater ice R.E. G a g n o n Institute for Marine Dynamics, National Research Council of Canada, St. John's, Nfld. A 1B 3T5, Canada (Received 22 October 1992; accepted after revision 18 June 1993)
Abstract
A stainless-steel platen, with arrays of pressure sensors and thermocouples on the front face, has been used to crush mono-crystaUine, bubble-free freshwater ice samples at - 10 oC 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.
1. Introduction In recent years the processes involved in ice impacts and crushing have been the focus of several investigations. These studies include visual observations of the contact zone between the crushing instrument and the ice (Riska et al., 1990; Gagnon and Molgaard, 1991; Fransson et al., 1991 ). In the recent work of Gagnon and Molgaard ( 1991 ) and Gagnon and Sinha ( 1991 ) it has been shown that pressure melting and generation of heat by viscous flow of the melt is an important mechanism. This paper reports resuits from experiments carefully designed to fur-
ther investigate this mechanism through visual records and measurements of pressure, load, and temperature at the ice/indentor interface. A preliminary report of these results has already been presented (Gagnon, 1992).
2. Apparatus Fig. 1 shows the ice specimen mounting holder. It consisted of a 5 cm X 13 cm X 17 cm plexiglas plate on which the ice samples sat. Confining plates for the sides of the specimen bolted to the plexiglas. The plexiglas plate was reinforced to
0165-232X/94/$07.00 © 1994 Elsevier Science B.V. All fights reserved SSDI O165-232X ( 93 )EOOI 7-D
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
386
MATING
,
PLATE
I ',
.
FOR
MTS
FRAME
MIRROR
J
.
.
.
.
.
.
PERIPHERAL REINFORCEMENT
l
! "
TRANSPARENT
'
PLEXIGLAS
PLATE
CONFINING
PLATE
~.
ICE
l INSTRUMENTED L
CRUSHING
-
PLATEN . . . .
ACTUATOR PISTON
Fig. 1. Crushing apparatus with mirror for viewing the contact zone during experiments.
minimize flexure by a 4 cm thick stainless steel rectangular backing structure which ran around the perimeter of the back face of the plexiglas plate. The reinforced plate was supported on opposite sides by two pillars of A1, 12.5 c m × 8 cm X 2.5 cm. A cross member attached to the base of the pillars and mated with the load cell of the testing frame. Between the pillars a mirror was situated at a 45 ° angle so that a video camera could view from the side through the plexiglas and ice to the region of contact between the ice and the steel platen that it was crushed against. A flood lamp was used to illuminate the ice and
platen along the same view path by placing it beside the video camera. The 4 cm × 20 cm X 20 cm platen which the ice was crushed against was made of stainless steel and instrumented with piston/diaphragm type pressure transducers (Fig. 2). Thermocouples (copper-constantan) were also installed in the platen by drilling and tapping small holes through the platen into which the thermocouples were inserted till they protruded slightly and filling the holes with 5 minute epoxy. When the epoxy had set the protruding portions were sanded off so the thermocouple tips were flush with the surface of the platen. An additional thermocouple was installed through the center of the central pressure transducer piston. This permitted direct measurement of temperature and pressure at one site. During tests the passive ends of the thermocouple wires were exposed to the ambient air temperature in the cold room, where they connected to the data acquisition system. Hence the temperature measured at the active ends of the thermocouples was relative to the ambient temperature of the cold room. The diameter of the four peripheral pressure transducers was 16 m m while the central one was 8 m m in diameter. Total load was monitored by a load cell attached to the crosshead of the loading frame. Data were acquired using a Data Translation analog to digital acquisition board with a throughput of 150,000 sampIes/s with 12 bit resolution. This was used in conjunction with an Empac 486 computer. The software package Viewdac (Keithley-Asyst) was used to control the acquisition board and to analyze the data. Typically 24,000 samples were acquired from each channel per test. All tests were run at fixed actuator speeds with durations ranging from 2 to 13 seconds, which allowed for a variety of sampling rates to be used, 2-18 kHz. The video recording system consisted of a Sony Hi8 camcorder capable of shutter speeds as high as 1/10,000 s at 30 frames/s and a Sony Hi8 VCR. During tests the VCR was connected to the camcorder so that two video records were obtained for each test. The shutter speed for all tests was 1/2000 s. In standard video format 60 video fields/s are acquired and in real-time playback
R.E. Gagnon / Cold Regions Science and Technology22 (1994) 385-398
STAINLESS
STEEL
387
PLATEN
PRESSURE
TRANSDUCER
THERMOCOUPLE
COMBINED AND
PRESSURE
SENSOR
THERMOCOUPLE
Fig. 2. Stainless steel crushing platen showing the configuration of pressure and temperature sensors.
two are interlaced to make up one frame to yield 30 frames/s. However, on still-frame playback only every second field is shown, with half the resolution of real-time playback. Connecting the VCR to the camcorder had the added advantage of sometimes gaining access to the full 60 fields/ s, that is, the camcorder video record, on stillframe playback, was shifted 1/60 s from the VCR record on still-frame playback. The video records were analyzed with the assistance of a frame grabber board (Targa M8 (Truevision)) and Java (Jandel) video analysis software, An LED was used to synchronize the video records with the data acquisition system. An elementary circuit caused the LED to start blinking at ~ 31 Hz, with a duty cycle of 50%, when activated by a 5 V signal from the data acquisition system at the start of a test. Because the LED blinked at a slightly different rate than the number of frames per second recorded by the video camera, subsequent video records would show
the LED on for several consecutive frames and then off for an equal number of consecutive frames, where the apparent on/off frequency was just the beat frequency of the LED/camcorder system i.e. Apparent Blink Rate =
( 1)
F(actual blink rate) -- Fframes/s
Synchronization was achieved by using the fraction of one full cycle of the apparent blink rate which appears on the video record at the beginning of a test to determine where in the first 1/30 s of the test that the first video frame was taken. This method yielded synchronization to within + 0.001 s.
3. Sample preparation The method of visual observation of the crushing process at the ice/indentor interface was
388
R.E. Gagnon /CoM Regions Science and Technology 22 (1994) 385-398
similar to that described by Gagnon and Molgaard (1991), that is, to make use of the transparency of the ice to view the process by looking through the ice specimen. In this case samples were cut from large single crystals of bubble-free freshwater ice with the c-axis vertical. The specimens were blocks initially 13 cm X 13 cm × 10 cm with the top portion trimmed to the shape of a truncated pyramid with a slope of ~ 40 °. Sharp edges and corners were rounded by melting and the very top of the peak was smoothed, by rubbing with a glove, to prevent premature cracking at low loads. Single crystal specimens were used to guarantee good visual observation by eliminating obscuring reflections off grain boundaries, and also crack formation associated with grain boundaries which would block the view. Specimens were mounted on the thick ( 5 cm) plexiglas plate by heating the plate's surface to just above 0 ° C and placing the sample (prewarmed to 0°C) onto it causing the ice to melt slightly and match the plate surface exactly. After wiping off excess water the plexiglas and ice were then put into the cold room at - 10 °C to freeze the melt layer. When the melt refroze the central annular region, comprising more that 50% of the bottom surface of the ice specimen was perfectly bonded to the plexiglas. The outer area had lifted slightly because of the expansion of the water on freezing. The gap between the ice and plexiglas in this region was very small, because Newton's interference rings were visible. The confining plates were then installed and a cclamp with a styrofoam pad was used to clamp the sample to the plexiglas to prevent separation when water, at 0°C, was poured in around the sides to fill the small gap between the confining walls and the ice, ~ 1-2 mm. These precautions were essential in preventing unwanted cracks in the bulk specimens during testing, due to improper bonding of ice to plexiglas, which would block the view of the ice/indentor interface. The large single crystals of freshwater ice were grown by placing a container with insulated sides and bottom filled partially with de-aired and deionised water in the cold room at - 10 ° C. The top of the container was covered with cardboard except for an opening at one end of the rectan-
gular container. Cold air blowing in through the opening at one end caused the growth of very long single crystal plates on the water surface. One of these continued to grow to take up the majority of the surface area, 20 cm × 60 cm. When a few centimeters thickness of this ice had grown it was removed from the container and the remaining water was dumped. In a room at 0 ° C, the ice plate was then placed in the bottom of the empty container and degassed water at 0 °C added through a small hose placed under the ice plate. As the water entered, the ice floated on the surface preventing air from saturating the liquid. When ~ 15 cm depth of water had been added, the container was put into the cold room at - 1 0 ° C which caused the gap between the ice edge and the sides of the container to quickly freeze sealing the water completely from the air. The ice plate behaved as a template and grew in thickness primarily as one large single crystal with no bubbles. When the ice had grown to the desired thickness it was removed from the container and a layer of a few centimeters thickness was cut from its top surface to serve as a template for the next refill of the ice growing container.
4. Data analysis Fig. 3 shows the pressure time series record from the central pressure/temperature sensor and the total load time series from the load celt for a typical run at - 10°C with an actuator speed of 1.5 cm/s. The total ice penetration was ~ 1 cm. The sampling rate was 18,5 kHz. Because of the symmetry of the confinement o f the ice and its pyramid shape most of the ice/platen contact occurred in the vicinity of the central pressure/ temperature sensor. The load and pressure records exhibit a sawtooth periodic breaking pattern often characteristic of ice crushing and indentation (Gagnon and Molgaard, 1991; Gagnon and Sinha, 1991; Michel and Blanchet, 1983; Evans et al., 1984; Frederking et al., 1990; Sodhi and Morris, 1984; Mii~ttiinen, 1983; Timco and Jordaan, 1988 ). The temperature sensor record (Fig. 4 ) shows that once the crushing process had gotten under way that the temperature at the in-
389
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398 70 60 5040
I
30 20 10 0 -10 50 4O
,-,
30
10 0 -10 0.0
L
I
J
I
0.2
0.4
0.6
0.8
~
1.0
(s)
Fig. 3. Pressure ( c e n t e r t r a n s d u c e r ) a n d load record for a test r u n at - l 0 °C with an a c t u a t o r speed o f 1.5 c m / s .
terface increased. The thermocouple temperature sensor had considerable thermal inertia because it was imbedded in epoxy which in turn was surrounded by metal and only the very tip of the sensor was at the platen's surface. For these reasons the temperature changes which registered were less than the actual changes in temperature at the platen's surface caused by its exposure to warm material produced in the ice crushing process. In other work on ice indentation (Gagnon and M~lgaard, 1991; Gagnon and Sinha, 1991 ), evidence has been presented that indicates that as a result of the indentation and crushing process liquid water is produced. To verify whether the thermocouple record from the
test indicated the presence of liquid and ice at 0°C the central transducer's response was recorded when a mass of fine wet snow was hand pressed against the center of the platen at - l 0 ° C. Fig. 4 shows the comparison of the thermocouple outputs from the test in Fig. 3 and the test with the wet snow. Clearly the trends and magnitude are very similar. While this is not an absolute calibration of the temperature sensor, it shows that it is very likely that liquid, produced by the ice crushing process, made contact with the sensor. The video records invariably showed the same characteristics for tests where specimens were confined properly and bonded well to the plex-
R.E. Gagnon / CoM Regions Science and Technology 22 (1994) 385-398
390
-0.20 > v
T E S T IN FIG.3
t~
m r.,o Z 0
-0.16
m
-0.12
m
m 0 0 0~
-0.08
-0.04
A M B I E N T T E M P E R A T U R E = -10oC
E-
0.00 0.00
I
I
0.22
0.44
I
0.66
0.88
1.10
T I M E (s) Fig. 4. Comparison of the response of the center temperature sensor during the test shown in Fig. 3 with its response when wet snow was hand pressed against the central region of the crushing platen.
iglas plate. The region of contact consisted of a central zone where the ice appeared to be undamaged, because the crushing platen was clearly visible through it, surrounded by a dense mixture of fine and coarse particles of ice that was opaque. This has also been observed by Gagnon and Molgaard ( 1991 ) using a different apparatus. As crushing occurred during a test the contact region would change in shape, size and position. Table 1 shows results from a number of tests from this test series where samples were well behaved because of proper confinement and good bonding to the plexiglas. Experiments were run at - 10°C and - 5 °C and for a range of actuator speeds, 0.15-2 cm/s. The table shows the maximum load for a penetration of 1 era, the ambient temperature, actuator speed, maximum pressure registered by the central pressure transducer for the whole test and the average sawtooth frequency for the whole test. There appeared to be no correlation between actuator speed and maximum load or maximum pressure at either temperature. In general higher maximum loads and maximum pressures were attained at the lower temperature. The mean maximum loads and
mean maximum pressures at - 10 oC and - 5 ° C were 28.7 kN and 22.1 kN respectively and 59.3 MPa and 47.4 MPa respectively. The sawtooth frequency of the load drops was strongly correlated with actuator speed at both temperatures, Fig. 5. The slope of the linear fit to the data at - 1 0 ° C implies an average actuator displacement of -,, 0.12 mm between sawteeth regardless of the actuator speed. It was noted in the slowest actuator speed tests at - 10 oC and occasionally in faster tests that in those instances where the time interval between load drops encompassed more than one video frame, i.e. longer than 1/30 see, that the size of the transparent area increased as the load increased. To cheek that in general for any test the size of the transparent contact spots correlated with load a series of contact areas were digitized from the video records (Table 2) from two tests run at - 10°C, one with an actuator speed of 1.5 c m / s and the other at 1.0 cm/s. A significant correlation was evident when the areas were measured and plotted against the corresixmding loads (Fig. 6). The slope of the linear fit was 0.126 eme/kN with a correlation coefficient of 0.86. One question arising from these experi-
391
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398 Table 1
Summary of results from tests at - 5°C and - 10°C Temperature (°C)
Actuator speed (cm/s)
Maximum pressure (MPa)
-
0.15 0.15 0.50 0.50 0.50 1.00 1.00 1.50 2.00 2.00 2.00 0.20 1.00 2.00
56.59 53.89 62.15 46.33 61.01 59.16 37.50 a 59.73 64.43 41.78 a 69.71 49.18 49.33 45.05
10 10 10 10 10 10 10 10 10 10 10 -5 - 5 - 5
Breaking frequency (Hz)
Maximum load to 1 cm (kN)
9 10 42 33 37 77 84 165 143 164 158 < 17 44 143
33.55 16.95 22.56 32.91 24.00 26.00 34.77 31.47 36.11 32.52 24.40 21.46 24.70 20.14
"Not used for average pressure calculation referred to in t e x t b e c a u s e of non-central contact and early cracking. 21111
Table 2
Transparent contact areas and corresponding loads from two
FIT FOR CIRCLES Y -1~7.5 + 82.81 X
t e s t s at - 10 ° C
=
O
Load (kN)
~120
Transparent contact area
Load (kN)
(cm2)
Transparent contact area
(cm2)
z
u.
41)
0.00
i
I
I
I
0.46
0.92
1-38
1.84
2.30
ACTUATOR SPEED (era/s) Fig. 5. Average frequency of the sawtooth load pattern versus
actuator speed for tests run at - 10°C and - 5°C.
ments and other ice crushing experiments is how the load is distributed relative to the transparent areas and the peripheral opaque snow-like material. The distribution of load was estimated in this ease by considering the measured pressure typical of the transparent spots, where the highest pressure measured during this test series by the center pressure transducer was 70 MPa at - 10*C. According to the slope of the line in Fig. 6, which yields a pressure of 79 MPa, this indi-
14.77 15.10 16.77 17.37 29.20 11.60 13.70 19.90 25.50 10.17 14.49 7.40 13.14 5.49 11.74 10.06 6.59 8.26 6.78 10.38
2.82 2.00 2.22 2.94 4.00 2.78 2.34 3.28 3.54 1.84 1.63 1.54 1.94 0.52 1.37 2.27 1.00 2.61 1.22 1.32
10.99 14.11 21.46 19.70 4.20 7.99 7.23 7.14 12.23 9.39 5.33 13.24 11.53 9.39 10.43 9.95 14.82 14.48 21.32 32.04
2.07 2.08 3.14 2.86 0.47 0.64 1.17 1.90 1.74 1.16 2.00 2.38 1.41 2.18 1.43 2.09 1.52 2.57 3.49 4.55
cates that in these experiments approximately 88% of the load is borne by the transparent spots, on the ascending side of the sawteeth at least. The
R.E. Gagnon / Cold Regions Scwnce and Technology. 22 (l 994) 385-398
392 6.0
IAREA = 0.449 + 0.126 x LOADI
4.8
t <
3.6
<
2.4
IPla,on.men,l\
8x104
D O I~
6x104
Z
4x10 ~
<
2x10 ~
t21 rn
1.2
J~'J D
Displacement Of Ice Against]
/
OxlO°
The Crushing Platen
/
J
0.0 0
8
16
24
32
40
LOAD (kN) Fig. 6. T r a n s p a r e n t contact area v e r s u s load for several video frames taken from two tests run at - l 0 ° C.
continuous wetting and softening of the opaque material by freshly produced liquid is probably responsible for the fact that the opaque material bears only 12% of the load. During the increase in load and the size of the hard spot the actual movement of the ice against the platen was ~ 0.3 × l0 -s m / N . This was determined by taking the difference between the apparent compliance of the ice/apparatus system as determined for ascending portions of the load record and the actual compliance as determined from elastic loading and unloading on previously damaged ice. Fig. 7 shows the true relative displacement of ice against the platen using the true compliance ( ~ 0.7× l0 -s m / N for the portion of the load record shown) of the ice/apparatus system. In general the compliance of the ice/apparatus system decreased as a sample was crushed. Fig. 8 illustrates the load, penetration and spot size relationships for the undamaged ice, assuming circular contact. The importance of the role of the transparent areas of contact has been noted and studied before (Gagnon and Melgaard, 1991; Gagnon and Sinha, 1991; Riska et al., 1990; Fransson et al., 1991 ). In particular Gagnon and Melgaard ( 1991 ) introduced the mechanism of pressure melting and heat generation by flow of melt during the rapid load drops as a means of explaining the visual and load and displacement data from ice crushing. In the present test results it is clear
_2xlO 4 0.00
0.01
0.02
0.03
...... 0.04
TIME (s) Fig. 7. Sections o f the t i m e series o f the c r u s h i n g platen disp l a c e m e n t a n d the relative d i s p l a c e m e n t o f the ice against the platen, d e t e r m i n e d using a c o m p l i a n c e o f 0 . 7 × 10 - 8 m / N, for the test s h o w n in Fig. 3.
that the same mechanism is also operating during the ascending portions of the load records. In this formulation the pressure is high enough on the transparent areas to initiate pressure melting Fig. 9. The thin layer of liquid which forms flows under the extreme pressure and generates heat from viscosity which goes into further melting. On moving towards the outer region of the high pressure zones the pressure is reduced and the melting temperature elevated so that refreezing occurs by dumping heat into the cold surrounding ice and metal. On leaving the high pressure zone the liquid has partially refrozen. This is consistent with several observations of refrozen liquid produced in indentation and impact on ice, e.g. (Gagnon and Molgaard, 1991; Gagnon and Sinha, 1991; Kheysin and Cherepanov, 1970). It is important to note that due to the size of the central pressure sensor, 0.5 cm 2, and the size and irregular shapes of the transparent contact spots (Fig. 10) that the sensor rarely, and then only marginally, was encompassed by the contact spot. The measured pressure was in fact an average pressure where the actual pressure was lower than average at the outer regions and higher than average at the center. This is why the pressure determined from the video and load records was
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
............... F .........
............ ~ ..........
393
F-16.7
..........
p t ~ R I M E T E R E X T E N T (era) Fig. 8. Surface characterization of the undamaged contact zone showing load, area and depth relationships, assuming circular contact.
Fig. 9. Schematic of the process of pressure melting and viscous flow of melt which occurs when the ice moves against the platen. The relative velocity of the ice towards the platen is ~ 0.5 c m / s on the ascending side of a sawtooth and ~ 18 cm/s on the descending side at a load drop. The fluid layer thickness is on the order of microns.
comparable to the highest measured by the transducer. A smaller pressure sensor would probably have recorded higher pressures when located in the center of a transparent contact spot. An average pressure of ~ 70 MPa is consistent with pressures required for pressure melting because a uniform layer of melt on a circular shaped transparent spot would imply a parabolic pressure distribution peaking to 140 MPa at the center (Bowden and Tabor, 1986, p. 274), which is adequate for melting at - 10 ° C .
The mechanism of pressure melting and viscous flow of melt, referred to above, implies a certain pattern of pressure and temperature across the transparent high pressure zones. The visual records and the configuration of sensors in the present experimental setup can, in principle, provide data on the distribution of pressure and temperature within these zones of contact. From the video records it was clear that whenever one of the transparent spots partially or completely (a very infrequent occurrence) covered the central pressure transducer that the pressure registered was very high. Because the frequency of the sawtooth breaks exceeded the rate at which video frames were captured and because of the thermal inertia of the temperature sensor most tests did not reveal any information about the temperature and pressure distribution within the hard spots. The experiments run at the lowest actuator speeds (0.2 c m / s ) and - 5 ° C did, however, provide some information. The time between the occurrence of large cracks was sometimes greater than 1 second and the behavior of a transparent spot as the actuator moved
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
394
^^^
2j ^ A A
^^
i 0
forward was easily captured in several video frames. The evolution of the spots at - 5 °C with an actuator speed of 0.2 c m / s seemed to be somewhat different from higher rate tests at the same temperature, and all tests at - 1 0 ° C . While the major drops in load governed the shape of the spots as before, more energy seemed to be consumed between major spalling events than for other tests. This was probably due to very tiny micro-spalls, evident in the video records, which continuously developed around the peripheries of the spots as the platen moved against the ice between major spalling events. Bearing this difference in mind, it is still reasonable to expect similar distributions of temperature and pressure across the transparent spots for all tests. Fig. 11 shows the pressure and therrnocouple readings for a segment of one of the tests at - 5 °C and 0.2 cm/s. As the crushing occurred the video record showed a transparent hard spot surrounded by opaque material. The size and position changed as the platen moved between major cracking events, such as at point A. In the figure points A, B, C, D corresponded exactly to the times when the hard spot had moved directly over the temperature and pressure transducer. Although the temperature record was not an absolute measurement of the actual temperature at the interface, for reasons discussed above, the trend in temperature from the outer to inner re-
u~-^
80
-5.5 A
C
60
:
D
-4.s
~-
-3,5 m
3
SCALE
cm
-2.5
:
0
J 2
3
' 4
~
-1,5
T I M E (s)
Fig. 10. Severalvideo framestaken at 1/60 s intervals showing the evolutionof the transparentcontactspotfromthe test in Fig. 3. The crosshatchedareas correspondto the opaque material surroundingthe hardspots.
Fig. 11. Comparisonof the trends in pressure and temperature at the centertransducersfor a test run at - 5°C with an actuator speed of 0.2 cm/s.
R.E. Gagnon I Cold Regions Science and Technology 22 (1994) 385-398
gion of the hard spot could be seen as the spot moved into position over the sensors, that is, higher at the outer regions and approaching the lower ambient temperature at the center. A similar inverse pattern of pressure was reflected in the pressure record. These observation are consistent with the mechanism of pressure melting described above. The video records and the sensor data revealed that the size, shape and position of the transparent spots were determined by two mechanisms, the pressure melting and extrusion of liquid process and the spalling process. This is best described by considering what happens in a typical test from a trough in the load record to the next trough (Fig. 12 ). T will denote the load at the top of the peak and, for convenience, B will be the load at the beginning of the section and the bottom of the load drop. On the ascending side the transparent spot area grew in size as the load increased according to the fit in Fig. 6. According to the values for the true and apparent compliance above, approximately 27% of the energy supplied by the actuator is associated with the growth of the transparent spot since 88% of the load is borne on it. 70% of the actuator energy goes into elastic energy of the ice/apparatus, given by C/2 × (T 2 - B 2) where the compliance, C, is 0.7× l0 -s m / N . Eventually, as the strain increased, the load on the ice reached a
395
point where a large crack(s) occurred and a spall(s) broke away from the area of contact (Fig. 13 ). This lead to a sudden rise in pressure on the remaining ice (Fig. 12) and rapid release of the built up elastic strain by movement of the ice against the platen. The load record and compliance indicate that even though the actuator was moving at a fixed rate of 1.5 cm/s, the relative displacement of the ice and platen towards one another occurred at ~ 18 cm/s until the consequent reduction in load and increase in hard spot area reduced the pressure on the ice to that which was present on the ascending portion of the sawtooth pattern and the cycle started again. It was clear from the results of the test program that more of the energy dissipated in the tests occurred during the rapid load drops than on the ascending sides of the sawteeth in the load records. A conservative estimate for the portion of that energy which is attributable to pressure melting and viscous flow of the melt can be obtained by determining the volume of hard spot ice removed by the process for a given load drop and multiplying it by the measured pressure obtained for the hard spots, ~ 70 MPa. This yields B
Ehardspot=70MPax
f
(Lx0.126+499)
2B-- T
X 10-7mE)<0.7X
lO-am/NdL
= 3.087 X 10-9 (4BT - 3B 2 - T 2) +2.2× 10-5(T-B) 411
(2)
3O
~1
The limits for the integration were established by recognizing that when a spall breaks away at the peak in the load the remaining hard spot area
Fig. 12. Sections of the pressure and load records, on an expanded scale, for the test shown in Fig. 3. The high frequency, low amplitude modulation in the load record corresponds to resonance in the apparatus. This corresponds to the same time segment shown in Fig. 7.
Fig. 13. Schematic of the spalling process that occurs at a load drop.
20
20
10
LOAD
SPALL E V E N T
0
10
-10 -20 0
~ 0.01
0.02
J 0.03
~ 0.04
0
TIME(s)
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
396
is small and grows to its eventual size at the bottom of the load drop as a result of the ice moving against the platen during the drop with a total displacement 0.7 X 10 - s ( T - B) m. This occurs according to the relationships of load, penetration and area illustrated in Fig. 8. This can be compared to the total energy expended by the apparatus/ice system according to
1.4 1.2 oe~ 1.0 u~ zm 0.8
[]
[-
o
/~../m
Y~= 0.134 + .423 X 1
c3D
/
/, /.-
/
cl
0.6 0.4
Etota,=(1/2)xO.7xIO-Sx(T2-B 2)
(3)
Table 3 and Fig. 14 show results of this comparison for several load drop events in the test shown in Fig. 3. In the mid-range the fit indicates that approximately 53% of the load drop energy was dissipated in the pressure melting and viscous flow of melt process. A percentage closer to 88% would be a reasonable expectation, however, due to the fraction of the load supported by the hard spots determined above for the ascending sides of the sawteeth. This implies that the pressure on the hard spot ice during the load drop was probably 66% greater than on the ascending portions of the load record, i.e. 116 MPa, Fig. 12 shows substantial rises in the pressure on the re-
Table 3 Calculated energies associated with the compliance of the ice and apparatus, and the transparent hard spots, for several load drops from the test in Fig. 3 Top load (kN)
Bottom load (kN)
Hard spot energy (J)
Compliant energy (J)
32.3 23.6 23.7 27.4 21.1 20.3 16.2 12.0 10.7 11.1 8.9 8.1 3.8 24.0 22.3
16.9 17.4 12.4 12.7 13.7 11.4 8.8 8.1 6.5 4.2 5.5 3.9 2.3 16.4 15.0
1.21 0.68 0.72 0.88 0.62 0.58 0.40 0.23 0.21 0.22 0.15 0.14 0.05 0.76 0.67
2.64 0.88 1.61 2.07 0.90 0.99 0.64 0.27 0.25 0.36 0.18 0.18 0.04 1.08 0.95
0.2 0.0 0.0
;
0.5
1
i
1.0 1.5 2.0 COMPLIANT ENERGY ( J )
2.5
3.0
Fig. 14. Energy associated with transparent contact areas versus energy calculated from the load data and compliance, Each point corresponds to a specific load drop event in the test shown in Fig. 3.
maining ice at load drops resulting from spalling which supports this conclusion, even though the central pressure transducer was not completely encompassed by the hard spots. We may conclude that since 88% of the energy dissipated on ascending portions of the load records and at least 53% on descending portions is associated with the hard spots that at least 6 4 % , i.e. 88% × 30% + 53% X 70%, of the total energy dissipated in the tests is attributable to the pressure melting process. The rest ofthe energy was probably dissipated as heat due to vibration in the apparatus and in the extrusion of the opaque material surrounding the spots. The goodness of the fit in Fig. 14 (the correlation factor was 0.95) implies that load drops occur in a manner such that the tops and bottoms of the drops closely satisfy the expression 0.13+0.21 X C( T2-B2)=Enardspot
(4)
where Ehardspot is given in Eq. (2). For a typical load drop from 22 kN to 15 kN the volume of ice removed by the melting process according to the expressions in Eq. (2) is 9.3 × 10 -9 m 3. The energy absorbed by the ice in the process is at least 0.65 J. This is sufficient to elevate the ice to 0°C and melt approximately
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
397
19% of it. Hence the ejecta that leaves the transparent high pressure zones is at least 19% liquid. A similar result was obtained by Gaguon and Molgaard ( 1991 ) based on data from tests using a different apparatus. We may also estimate the thickness of the liquid layer on both sides of the sawtooth using an expression from the theory of squeeze films (Bowden and Tabor, 1986, p. 274 ), assuming a circular contact area;
h= ( 3~lVR2/2P) i/3
(5)
where h is the layer thickness, q is the viscosity of water at 0°C ( 1750X 10 -6 Pa.s), Vis the velocity of the ice moving against the platen (0.005 and 0.18 m/s for the ascending and descending sides of the sawtooth respectively), P is the average pressure over the contact spot (70 MPa) and R is the radius of the spot (0.94X 10 -2 and 0.78× 10 -2 m on average for the ascending and descending sides of the sawtooth respectively). Using these values an average liquid layer thickheSS of 2.5 #m is obtained for the ascending side and 7.4 #In for the descending side. The evolution of the size and shape of a transparent contact spot is illustrated in Fig. 10 in a series of video frames, each separated by 1/60 s. These are from the test shown in Fig. 3 where the frequency of load drops was approximately 165 Hz. This implies that at least 2 spalling events occurred between each frame. Frame # 10 of Fig. 10 shows the last transparent zone created during the test. To demonstrate that during a test the ice in the high pressure zone was primarily removed by pressure melting and viscous flow of the thin layer of liquid, a thin section in the plane of the c-axis, was taken through the center of the spot in frame #10 (Fig. 15 ). Apart from a few cracks, some of which occurred during unloading at the end of the test, the figure clearly shows the ice through crossed polarized filters to be macroscopically undamaged in the zone, that is, no layer of crushed ice can be seen. Similar results have also been reported by Gagnon and Malgaard (1991 ) for crushing experiments on bubble-free freshwater ice. In the region of the high pressure zone it would be reasonable to expect densification and considerable cracking and recrystallization if the virgin ice has bubbles and/
Fig. 15. View through cross-polarized filters of a thin section (light area) taken through the last transparent spot in Fig. 10. Apart from a vertically oriented crack, which occurred during unloading, the ice is macroscopically undamaged in the central zone (A). The accumulation of dark material at the sides (B) corresponds to the opaque snow-like material surrounding the transparent spots in the video records. The unit on the scale is cm.
or brine channels, e.g. sea ice (Meaney et al., 1991). In the present setup the ice/(ice holder) system was not massive so that inertial effects did not play a large role during the sudden drops in load. However in the case of massive systems inertial effects lead to overshooting at the end of the load drops. Because of the overshoot in one cycle the pressure on the ice during load accumulation on the next cycle is not high enough for pressure melting and consequently the movement of the actuator results only in the build up of elastic strain in the system. This period of elastic build up when no fresh liquid is being produced by pressure melting provides time for refreezing of partially liquid opaque material extruded from the high pressure zone previously. Hence the opaque material can then support more load and dissipate more energy when it is cleared from the area of contact. In such systems video records show no change in the size or shape of the transparent spots on the ascending side of sawteeth and more energy is probably dissipated in the removal of the opaque material during load drops (Gagnon and Molgaard, 1991 ).
398
R.E. Gagnon / Cold Regions Science and Technology 22 (1994) 385-398
5. Summary and conclusions The following observations have been made: 1. The frequency of the rapid load drops was a linear function of the actuator speed and most of the energy dissipated in the experiments ocduring the load drops. The top and bottom loads for any load drop in general are determined by a unique relationship. 2. The compliances of the testing apparatus and ice play an important role even in a stiff system. 3. The measured and calculated pressures, the trends in the temperature records and the thin section analysis of a transparent spot were consistent with the process of pressure melting and viscous flow of the melt introduced by Gagnon and Mzigaard ( 1991 ). The process was responsible for at least ~ 64% of the energy dissipated in these tests. A smaller central pressure transducer and a temperature sensor configuration with much less thermal inertia would greatly improve the capability of the apparatus to yield more detailed information about the temperature and pressure distribution within the high pressure transparent contact zones. A video system capable of 1000 frames/s, or faster, would provide extremely valuable information about the spalting process and the evolution of the transparent spots during the rapid load drops. Acknowledgements The author is grateful to Mr. Trent Slade, who operated the testing frame during the test program, and Mr. Douglas Maloney, who helped with the design and construction of the crushing apparatus. References Bowden, F.P. and Tabor, D., 1986. The Friction and Lubrication of Solids. Clarendon Press, Oxford, 274 pp.
Evans, A.G., Palmer, A.C., Goodman, D.J., Ashby, M.F., Hutchison, J.W., Ponter, A.R~S. and Williams, G.J., 1984. Indcntation spalling of edge-loaded ice sheets. In: IAHR Ice Symposium, Hamburg, pp. I 13-12 I. Fransson, L., Olofsson, T. and Sandkvist, J., 1991. Observations of the failure process in ice blocks crushed by a flat indentor. In: Proceedings of the I lth International Confcrence on Port and Ocean Engineering Under Arctic Conditions, St. John's, Vol. l, pp. 501-514. Frederking, R., Jordaan, I.J. and McCallum, J.S., 1990. Field tests of ice indentationat medium scale, Hobson's Choice Ice Island, 1989. In: Proceedings of the 10th International Symposium on Ice (IAHR 90), Espoo, Vol. 2, pp. 931944. Gagnon, R.E., 1992. Heat generation during crushing experiments on freshwater ice. In: N. Maeno and T. Hondoh (Editors), Physics and Chemistry of Ice. Hokkaido University Press, Sapporo, pp. 447-455. Gagnon, R.E. and Molgaard, J., 1991. Evidence for pressure melting and heat generation by viscous flow of liquid in indentation and impact cxpcriments on ice. In: Proceedings of the IGS Symposium on Ice-Ocean Dynamics and Mechanics, Hanover, NH, 1990. Ann. Glaciol., 15: 254260. Gagnon, R.E. and Sin.ha, N.K., 1991. Energy dissipation through melting in large scale indentation experiments on multi-year sea ice. In: Proceedings of the 10th International Conference on Offshore Mechanics and Arctic Engineering 1991, Vol. IV, pp. 157-161. Kheysin, D.E. and Cherepanov, N.V., 1970. Change of ice structure in the zone of impact of a solid body against the ice cover surface. Probl. Arkt. Antarkt., 34: 79-84. M~i~tfiinen, M., 1983. Dynamic ice-structure interaction during continuous crushing. CRREL Rep. 83-85. Meaney, R., Kenny, S. and Sinha, N.K., 1991. Medium scale ice-structure interaction: failure zone characterization. In: Proceedings of the 11th InternationalConference on Port and Ocean Engineering Under Arctic Conditions, St. John's, Nfld., pp. 126-140. Michel, B. and Blanchet, D., 1983. Indentation of an $2 floating ice sheet in the brittle range. Ann. Glaciol., 4:180187. Riska, K., Rantala, H. and Joensuu, A., 1990. Full scale observations of ship-ice contact. Laboratory of Naval Architecture and Marine Engineering, Helsinki University of Technology, Report M-97. Sodhi, D.S. and C.E. Morris. 1984. Ice forces on rigid, vertical, cylindrical structures. CRREL Rep. 84-33. Timco, G.W. and Jordaan, I.J., 1988. Time series variations in ice crushing. In: Proceedings of the 9th International Conference on Port and Ocean EngineeringUnder Arctic Conditions, Fairbanks, AL, pp. 13-20.