experimental deformation of polycrystalline h20 ice at...

PROCEEDINGS OF THE FOURTEENTH LUNAR AND PLANETARY SCIENCE CONFERENCE, PART 1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 88, SUPPLEMENT, PAGES B377-B392, NOVEMBER 15, 1983

Experimental Deformation of Polycrystalline H20 Ice at High Pressure and Low Temperature' Preliminary Results

W. B. DURHAM AND H. C. HEARD

Lawrence Livermore National Laboratory

S. H. KIRBY

U.S. Geological Survey, Menlo Park

Interest in the mechanical properties of water ice under the conditions in which it exists in the outer solar system has motivated the development and use of a new high-pressure, low-temperature triaxial deformation apparatus. Constant displacement rate tests on 70 samples of pure polycrystalline water ice have been performed at temperatures 77 _< T • 258 K, confining pressures 0.1 • P • 350 MPa, and strain rates 3.5 x 10 -6 • g • 3.5 X 10 -4 S-•. In most cases, the ice polymorph tested was ice I•,. Both brittle and ductile behavior have been observed. Brittle behavior of ice, promoted by lower pressure, lower temperature, and higher strain rate, is analogous to that in rocks, with the important exception that brittle fracture strength becomes independent of confining pressure above 50 MPa pressure and the fracture angle is approximately 45 ø to the loading direction (i.e., the coefficient of internal friction is approximately zero). Ductile flow, the predominant behavior in our tests at T • 195 K, follows a law of form g = Aa n exp (-H*/RT) (a is stress; R is the gas constant; A, n, H* are material constants). Three sets of material constants are required to fit the data, with changes in sets (or mechanisms) occurring near 243 K and 195 K. The value of n remains near 4 throughout the measured ductile field, but H* drops from 91 to 61 to 31 k J/mole as temperature decreases. The maximum brittle strength measured was 171 MPa; the maximum ductile strength measured was 91 MPa. At confining pressures near the phase transition pressure of ice I•,--, ice II, the ductile strength is observed to drop dramatically. Some overlap with previous work occurs at higher temperatures and lower pressures. Agreement with present work is generally good, both quantitatively in the values of n and H*, and qualitatively in the mechanism of deformation. Although the ductile strengths measured here are somewhat higher than expected on the basis of extrapolations of previous work, the low value of H* at T < 195 K indicates that the ice I•, layer on icy bodies in the solar system is much weaker than has generally been predicted.

INTRODUCTION

Ice Is is the stable crystalline phase of H20 under conditions found on the earth's surface (T = 220 to 273 K, P = 0.1 to 20 MPa). Over this range of environmental conditions, its rheology and general physical properties are better known than for any other rock type (see recent reviews by Weertman [1983], Mellor [1980], Weeks and Mellor [1983], Duval et al. [1983], and Poirier [1982]).

Interest in the rheological properties of ice under more ex- treme conditions of pressure and temperature has an extrater- restrial background. It has long been recognized that H20 is an important component of some of the outer planets and their moons. Ice in these bodies exists at temperatures as low as 100 K and pressures as high as several gigapascals. Of particular interest are Jupiter's two largest moons, Ganymede and Callisto, whose H20 mass fraction is very large (approximately 50%), and whose evolutionary processes and current tectonic activity are controlled in great measure by the rheological properties of H20 ice (see reviews by Poirier, [1982], and Consolma•;no, [1983]). Ice must exist in several of its polymorphs within these moons (Figure 1).

Modeling of the physical processes, past and present, within these bodies requires an understanding of the rheological properties of ice Is and of the higher pressure polymorphs. Such an understanding is the goal of a laboratory research

Copyright 1983 by the American Geophysical Union.

Paper number 3B5125. 0148-0227/83/003 B- 5125 $05.00

program we have recently undertaken, whose preliminary results on ice Is are reported here.

SAMPLE PREPARATION

Polycrystalline ice samples are molded using standard techniques adapted to our requirements (see review by Cole, [-1979•). Ice seeds are produced by crushing in a blender clear ice taken from a vat of partially frozen distilled water. The crushed ice is sieved at 248 to 253 K between 1 mm and 0.4

mm Nalgene sieves. The seed ice is packed into stainless steel tube molds with double O-ring-sealed stainless steel end plugs. The tubes are inserted into a vacuum manifold, evacuated to about 5 x 10-3 mm mercury for about 30 min. at 248 K. The manifold, still under vacuum, is then immersed in an ice/water bath for about 15 minutes. Distilled water at 273 K, degasscd by boiling and then cooling under its own vacuum, is admit- ted to the evacuated molds and allowed to saturate them for

about 5 to 10 min. The molds are then inserted into vertical

holes in a large styrofoam block such that the mold bottoms rest on a copper plate at the bottom of a deep freezer. Freez- ing thus proceeds upwards from the bottom of the molds and concentrates freezing strains into a seed-free upper chamber of the mold. The samples are removed by gently warming the tubes and pushing the samples out.

The as-molded diameter of the ice cylinders is 25.4 mm. The ends of the cylinders are shaved flat and perpendicular to the cylinder axes to a length (in most cases) of 63.5 +_ 0.3 mm. To deny entry of the confining fluid into the samples during a deformation test, they are sealed in 0.5-mm wall indium tub•s capped at each end by 19-mm long, indium-coatcd stainless

B377

B378 DURHAM ET AL.' DEFORMATION OF ICE

280

260

240

220

180

160,

140

120

LIQUID

Tr (I.17)

(I.23) I (I.31)

(specific gravities at I atmosphere and 9•K)

Fig. 1. Phase diagram for H20. Dashed lines are extrapolations. Numbers in parentheses represent relative density of the phases pro- jected to 0.1 MPa and 98 K (from Flecther [1970]). The dotted curve is a possible temperature profile for Ganymede and Callisto. The shading indicates the region explored experimentally in this study.

steel discs. The sealing weld is made with a soldering iron with all constituent parts (ice, tube, and end caps) held at 195 K in a dry ice/alcohol bath. Prior to sample 51, little care was taken to avoid thermal shock to the ice samples and some fracturing may have occurred. Based on observations of shocked and more gently treated samples, those made prior to 51 probably contained a few (3-8) large horizontal and vertical fractures prior to testing. Samples 51 and later contained no fractures prior to experimentation. The results presented below show no sign of an influence from the thermal fractures.

The initial sample length, lo in the notation used below, was determined from the length of the entire sample assembly at 195 K. The ends of the assembly were usually parallel to within +__ 0.05 mm.

APPARATUS AND TECHNIQUES

Deformation Apparatus

The experimental apparatus is described in detail by H. C. Heard et al. (unpublished data, 1983). At the heart of the apparatus is a conventional 600-MPa triaxial pressure vessel (Figure 2). The tensile reaction frame connects the vessel to a screw-loading mechanism below the vessel. Welded to the tensile reaction frame is a cryostatic tank surrounding the vessel. The confining medium is helium, nitrogen, or argon, depending on temperature and pressure. Confining pressure is gener- ated by a conventional separator/intensifier system and is measured with a heise bourdon tube gauge.

Cooling of the vessel to 195 K and below is achieved by

filling the cryostat level with the top of the vessel with approximately 30 1 of cold liquid or liquid/solid mix. Temper- ature stability is achieved by using mixtures thermally buffered by the latent heats of phase change (Table 1). Thermo- couples in the top of the aluminum safety ring and inside the moving piston, roughly 12 mm from the sample assembly, revealed that significant temperature gradients exist in the buffer mixtures when they are not agitated (liquid nitrogen is self-agitating). Hence the accuracy of sample temperatures prior to run 63 is given as _+ 3 K in Table 1. The situation improved beginning with run 63. An agitator was added and temperature control for T > 195 K was made more conventional' the cryostat is filled with alcohol and a cooling coil is immersed in the alcohol. A separate cold alcohol system circu- lating through the coil adds or removes heat in response to the vessel thermocouples. With agitation, temperature variations are less than _ 0.5 K.

A load is applied to a test sample by means of a moving piston that enters from the bottom of the vessel. The load is measured with an internal force gauge that has a sensitivity well below _0.1 MPa. Calibration runs using an external force gauge revealed that the gain of the internal gauge is linear and not a function of pressure or temperature. The zero point of the gauge is, however, very sensitive to pressure and temperature. Load determinations are therefore made at the beginning and end of a run (or the end of a step within a run) when the zero point of the gauge can be quickly checked by unloading the sample.

Prior to the start of a test, sample length (lo) is measured to

CLOSURE NUT

.... '•'•' BATH

ß

ß PRESSURE

• :,: VESSEL. ß . .

ß • i,,,,•-. PACKING

• GAS InAlut .,

ß

';; INTERNAL. ß . • -'-. FORCE

•!/.. : GAU• •.! '• ..

• i'i. • 'ß"11 4. • "-" IDIU¾ JAC•E? ..

ß

ß . ..•- .: ß

ß .' .i • ",:i¾ _ --

":'; I •'E . HOLE .

...

..

ß • .... LOADIN6 ß. ß PISTON ß

ß

- '• = ALU¾1NU¾

.

ß

.... . •.. ½LOSURI: NUT/ .... ...... .-• i.: 17. :•i•:•:.i. ß TEnSiLe YOKe

Fig. 2. Scale drawing of the 0.6 GPa triaxial testing apparatus. Force on the sample is determined by measuring the elastic distortion of the force gauge' the measurement is not influenced by friction on moving seals. The apparatus resides inside a cryostatic tank and is in direct contact with the cold, temperature-controlling fluid.

DURHAM ET AL.' DEFORMATION OF ICE B379

TABLE 1. Cooling Mixtures Used

Nominal T(K) Mixture T Accuracy

77

113

143

158

195 (Run 62 and earlier) > 195 (After run 62)

gas/liquid N 2 _+ < 1 K (self agitating) liquid/solid isopentane liquid/solid pentane _+ 3 K liquid/solid ethanol gas/solid/CO 2 in alcohol cool alcohol (agitated) _+ 1 K

--+0.02 mm using vernier calipers at a fixed reference temperature of 195 K. This temperature was chosen primarily out of convenience, being the warmest of our temperature-buffered mixes (Table 1). Access to the chamber is gained through the top of the assembly by unscrewing the top nut and extracting the top plug/force gauge, allowing the sample to be lowered onto the bottom (moving) piston. A guide pin protruding from

the bottom end cap of the sample fits a matching hole on the upper surface of the piston to assure good column alignment. After redosing and pressurizing the vessel, the sample is left to equilibrate at temperature, usually at least an hour. In most cases, the vessel is chilled to test temperature before the sample is introduced into the chamber.

The position of the lower piston at the start of a run is

TABLE 2a. Brittle and Transitional Runs

P, {•ult, Fracture Run* MPa T, K /• •, s-• MPa Angle,• deg Failureõ Comments

2 30.0 77 0.003 3.50e-04 24.7 B 3 0.1 77 0.022 3.50e-04 20.7 B 4 29.2 77 0.019 3.50e-04 50.5 B 5 100.0 195 3.50e-04 12.2 B 6 0.1 195 0.021 3.50e-04 7.7 B 7 100.0 195 0.011 3.50e-04 39.3 B 8 130.0 195 0.050 3.50e-04 22.2 B 9 0.1 195 0.013 3.50e-04 41.2 B

10 0.1 195 0.015 3.50e-04 33.1 B 13 0.1 195 0.043 3.50e-06 16.2 B-D 15 0.1 77 0.008 3.50e-06 48.3 B 17 0.1 113 0.007 3.50e-06 29.5 B 18 0.1 113 0.001 3.50e-06 36.8 B 19 100.0 113 0.015 3.50e-06 140.3 B 20 0.1 113 0.017 3.50e-04 31.2 B 21 170.0 113 0.021 3.50e-06 117.2 B 22 230.0 113 0.011 3.50e-06 145.3 B 26 222.0 158 0.132 3.50e-04 89.7 B-D 27 250.0 158 0.038 3.50e-04 85.4 B 28 350.0 158 0.144 3.50e-04 156.0 B 32 180.0 77 0.027 3.50e-06 171.4 47 B

33 350.0 77 0.012 3.50e-04 91.5 fill B 34 300.0 77 0.011 3.50e-06 139.1 48 B 35 0.1 77 0.001 3.50e-06 46.8 vf B 36 50.0 77 0.025 3.50e-06 162.4 44 B 45 25.0 195 0.033 3.50e-04 75.3 46 B-D 47 100.0 141 0.011 3.50e-06 125.7 44 B-D 48 150.0 139 0.019 3.50e-06 135.9 46 B-D 49 200.0 143 0.012 3.50e-06 136.2 52 B-D 50 250.0 141 0.0i4 3.50e-06 128.3 49 B-D 51 182.0 77 0.011 3.50e-04 59.5 vf B 52 182.0 77 0.023 3.50e-06 166.4 45 B 53 100.0 77 0.024 3.50e-04 119.6 43 B 54 100.0 77 3.50e-06 163.7 44 B 55-2 50.0 159 0.074 3.50e-05 121.7 40 B-D 56 10.0 158 0.023 3.50e-06 99.6 45 B 57 80.0 160 0.013 3.50e-04 105.4 44 B 58 80.0 159 0.020 3.50e-05 119.3 46 B-D 59 182.0 157 0.011 3.50e-05 121.5 45 B-D 60 0.1 161 0.014 3.50e-04 32.2 vf B 61 80.0 193 0.018 3.50e-05 60.7 vf B-D

nnô an

an

an

an

nn

an

JJ JJ JJ

JJ full strength after failure

full strength after failure

new phase

an-anomalous {•ult

nn--jj

nn--jj 2 pieces-can't measure/final

nn--jj

nn--jj

*Runs 1, 16, 46 not reported. •'Constant displacement rate runs, g strictly accurate only at start of run. $With respect to load axis. õB = brittle; B-D = transitional. II vf (from 'vertical fractures') - crushing; no distinct failure plane. ônn = not plotted in figures. **jj = jacket leak.


TABLE 2b. Ductile Runs

Run P, MPa T, K lgrec O'ult• O'ss• u• t •,'{' s- • MPa MPa Comments

11 100.0 195 0.058 12 5.0 195 0.055 14 50.0 195 0.066 23 180.0 158 0.050 24 120.0 158 0.046 25 90.0 158 0.053 29 60.0 158 0.035 30 200.0 195 0.029 31 200.0 195 0.013 37 100.0 195 0.158 38 50.0 195 0.140 39 150.0 195 0.196 40 200.0 195 0.170 41 225.0 195 0.241 42 200.0 195 0.146 43 200.0 195 0.395 44-1 100.0 195 0.045 44-2 100.0 195 0.065 44-3 100.0 195 0.110 44-4 100.0 195 0.138 44-5 100.0 195 0.422 55-1 38.8 158 0.067 62-1 80.0 193 0.095 62-2 80.0 193 0.129 62-3 80.0 194 0.158 62-4 80.0 195 0.214 62-5 80.0 195 0.257 63-1 125.0 195 0.083 63-2 125.0 196 0.095 63-3 125.0 194 0.134 63-4 125.0 194 0.156 63-5 125.0 195 0.166 63-6 125.0 197 0.202 63-7 125.0 197 0.252 64-1 50.0 192 0.055 64-2 125.0 193 0.079 64-3 100.0 194 0.097

64-4 24.8. 195 0.129 64-5 25.0 196 0.152 64-6 50.0 195 0.176 64-7 75.0 197 0.194 64-8 100.0 196 0.211 64-9 150.0 195 0.242 64-10 175.0 195 0.266 65-1 100.0 233 0.072 65-2 100.0 233 0.105 65-3 50.1 233 0.143 65-4 25.1 233 0.176 65-5 99.5 233 0.210 65-6 50.0 233 0.259 65-7 50.0 233 0.292 66-1 10.0 232 0.005 66-2 10.0 233 0.066 66-3 50.0 232 0.200 66-4 49.4 232 0.285 67-1 50.4 243 0.099 67-2 99.5 243 0.159 67-3 50.0 244 0.190 67-4 50.5 244 0.265 67-5 50.0 244 0.279 67-6 50.0 244 0.305 68-1 100.0 224 0.065 68-2 99.8 223 0.100 68-3 50.1 223 0.158 69-1 49.7 212 0.096 69-2 49.5 212 0.123 69-3 50.4 212 0.130 69-4 50.5 213 0.174 69-5 50.4 213 0.223 69-6 51.0 213 0.257 69-7 51.0 213 0.284 70-1 49.6 258 0.135

0.598 3.50e-06 25.0 0.941 3.50e-06 22.9 0.930 3.50e-06 24.4 0.495 3.50e-06 67.1 0.785 3.50e-06 87.2 0.872 3.50e-06 93.9 0.825 3.50e-06 99.4 0.256 3.50e-04 51.2 0.300 3.50e-06 10.7 1.013 3.50e-04 65.5 0.921 3.50e-04 63.7 0.953 3.50e-04 58.6 0.743 3.50e-04 48.8 0.892 3.50e-04 25.6

3.50e-04 45.1 0.892 3.50e-04 51.8

3.50e-04 75.6 3.50e-06 3.50e-04 3.50e-06

0.967 3.50e-04 3.50e-06 104.9 3.50e-05 65.9

3.50e-06 3.50e-05 3.50e-04

0.993 3.50e-05 3.50e-05 55.9 3.50e-06 3.50e-05 3.50e-04 3.50e-06 3.50e-05

0.951 3.50e-04 3.50e-05 67.5 3.50e-05 3.50e-05 3.50e-05 3.50e-05 3.50e-05 3.50e-05

3.50e-05 3.50e-05

0.929 3.50e-05 3.50e-04 27.3 3.50e-04 3.50e-04

3.50e-04 3.50e-04 3.50e-04

1.025 3.50e-04 3.50e-05 16.5 3.50e-05 3.50e-05

1.007 3.50e-04 3.50e-04 23.2 3.50e-04

3.50e-06 3.50e-04 3.50e-05

1.031 3.50e-05 3.50e-04 35.4 3.50e-04

1.054 3.50e-04 3.50e-04 59.9 3.50e-05 3.50e-06 3.50e-04 3.50e-04 3.50e-05

1.037 3.50e-04 3.50e-04 14.4

14.6

20.0

56+_8 72.6 78.1 91.1

31.2 <1.0

52.7 49.2 49.2

31.7

1o.4

32.3 60.2 22.4

57.6 21.0

66.4

86.7 47.5

29.8 46.4

69.9 48.6 39.7 21.6 41.0 64.1

25.5 40.4 61.0

49.0 44.3

45.3 41.2 44.0

47.6 47.2

46.5 45.2

40.9

17.5

18.3

17.6 17.5

18.8 19.2

9.0

11.4

18.7 12.8 11.9

4.1 12.9

6.6 7.1

24.8 23.1 39.0 22.1

11.5

35.2 34.2

20.7

34.8 7.0

nn•:--jjõ after yield jj near end of run ass varied up and down

nn--jj after yield

%• = 21.9 MPa, aco II %• = 54.8 MPa, aco trs• = 19.7 MPa, aco tr• = 50.4 MPa, aco

%• = 28.4 MPa, aco a.,• = 43.7 MPa, aco %• = 64.8 MPa, aco %s = 41.7 MPa, aco

%• = 21.1 MPa, aco %• = 38.8 MPa, aco a•s = 61.0 MPa, aco %• = 22.0 MPa, aco %• = 35.3 MPa, aco a.,s = 53.8 MPa, aco

tr• = 43.3 MPa, aco tr, = 43.5 MPa, aco %• = 38.1 MPa, aco a•., = 39.9 MPa, aco %• = 42.5 MPa, aco t% = 41.3 MPa, aco %• = 39.9 MPa, aco trs• = 37.3 MPa, aco t% = 31.9 MPa, aco ssô not reached

ss not reached

ss not reached

DURHAM ET AL.: DEFORMATION OF ICE B381

TABLE 2b. (continued)

Urec (/ult, Run P, MPa T, K e* ua• t •,'[' s-• MPa MPa Comments

70-2 49.6 258 0.159 3.50e-04 6.5

70-3 50.2 258 0.188 3.50e-05 3.7 70-4 50.1 258 0.235 3.50e-04 6.9 70-5 50.0 258 0.354 0.999 3.50e-04 5.8

*For multiple-step runs e is the cumulative shortening. ?Constant displacement rate runs; g strictly accurate only at start of run. $nn = not plotted in figures. •j = jacket leak. Ilaco - area correction only. At 195 K in the multiple-step runs, a second correction (in addition to the

correction for base area widening) to ass was necessary to compensate for an apparent strain softening. The correction was linear in e.

ôss = steady state level of stress.

always such that a small gap exists between the top of the sample and the force gauge. Since the force gauge is internal to the vessel and since there is no preload, friction along sliding seals does not introduce an error in the force gauge read- ing. The run is started by switching on an electric motor to drive the piston upwards at a constant rate, compressing the sample against the force gauge. At the end of the run the motor is reversed and the piston is driven back down to its starting position by the pressure in the sample chamber. After pressure is released, the vessel is quickly opened up and the sample removed and immersed in 195 K alcohol. A minimum delay is important in cases where a jacket leak is suspected (say, because of an anomalously low strength). Pinhole leaks in the jacket, even those too small to be observed by the eye, are plainly visible by the bubbles they produce in alcohol as residual pressure fluid leaks out of the alepressurized sample. The sample is left in the 195 K bath until temperature equilibrium is assured, and the sample length is again measured with vernier calipers.

During a run, load is monitored as a function of time on a strip chart recorder. Earlier runs took place under constant conditions of pressure, temperature, and strain rate and produced essentially one strength measurement each. In later runs, pressure and/or displacement rate were stepped, produc- ing multiple data. The force gauge was usually rezeroed (as discussed above) between steps.

Thin Section Techniques

The standard techniques for making ice thin sections is to secure a microtomed or polished surface to a glass slide by melting and quickly refreezing. This technique is not appropriate for samples that are deformed at lo•w temperatures where the internal energy due to dislocations, faults, and fractures is likely to be large and thus the driving potentials for grain boundary motion, grain growth, and recrystallization are large. Accordingly, we have developed a new method for making thin sections at 247 to 254 K (Daley and Kirby, unpublished data, 1983). The samples are first band-sawed and then microtomed to a flat and smooth finish. They are then glued to glass slides using a commercial cyanoacrylate glue with a chemical activator. Finally, the ice is thinned to about 250 microns by microtoming and then covered with another glass slide using cyanoacrylate glue.

RESULTS--MECHANICAL TESTS

Seventy samples have been tested to date in constant displacement rate compression tests. The data are summarized in

Table 2. The experimental range of confining pressure (P) and temperature (T) is illustrated in Figure 1. P, T, and strain rate (g) have ranged as follows: 0.1 < P < 350 MPa, 77 K<T<258 K, 3.5 x 10 -• s-a<g<3.5 x 10 -4 s-a. The samples have displayed two basic types of macroscopic inelas- tic behavior, brittle and ductile: (1) Brittle fracture, characterized by an initially linear stress-strain curve punctu- ated by one or more stress drops often accompanied by a loud report (Figure 3a). The deformed samples display one or more macroscopic faults or a complex crush zone and do not devel- op significant radial strains or barreling (Figure 4a). (2) Duc- tile flow, characterized by a stress-strain curve lacking a dis- continuous stress drop but showing a stress maximum after initial yield followed by a smooth decrease in stress with increasing strain (Figure 3b). Beyond a few percent permanent strain, the stress supported by the samples usually stablized to a nearly steady value. Ductile samples show a relatively uniform radial expansion along their central two-thirds and show tapering near their ends. Surface irregularities on the scale of a few millimeters are typical (Figure 4b). As explained in more detail below, ductile flow can apparently be either volume conserving, the traditional plastic flow behavior, or it can be volume nonconserving, wherein phase transformation plays an essential role.

T<143K

The behavior encountered at the two lowest temperatures (77, 113 K) was entirely brittle (Figures 5a, b). In each sample deformed at elevated pressure, one or two macroscopic fractures formed and the magnitude of the stress drop at failure was a significant portion (--• 1/5 to > 1/2) of O'ul t. The angle of the primary fracture was close to 45 ø from the direction of loading. The angle was recorded photographically beginning with sample 32 and is reported in Table 2. In samples deformed at room pressure, a number of smaller stress dis- continuities usually replaced the single event, giving the force- time record a stair-step appearance. These samples usually showed a crushed look, with the crushing often localized near one end. The dependence of strength upon pressure was strongly positive for 0.1 MPa < P < 50 MPa. The fracture strength at 50 MPa and above did not show a pressure dependence. Four samples were tested at 143 K at high pressures and the slowest displacement rate in an attempt to bridge the brittle-to-ductile transition (Figure 5c). All four showed a hint of curvature in their load-displacement records prior to failure, and hence were designated B-D in Table 2. The four were run at P > 50 MPa and, as at lower temperatures, strength


BRITTLE

Run 52

T=77K P=I82.0MPa

150-

z I00-

50-

i

(a)

CTult •

.•1 -- I • I

cd I New time cale ,, w ß = displacement rate

SOs I • -I I

DUCTILE

60-

Run 64, step I T--195 K P=50MPa

CTul t

(b)

Crss

fi: 2.2 x IO'$m rn/s

At:600s 1

2.1%

Fig. 3. Individual run records selected to illustrate the definitions of (a) brittle, and (b) ductile behavior as used in this study. The symbol ti means displacement rate of the piston.

did not show a pressure dependence. Fracture strength at T < 143 K and P > 50 MPa showed a weak, negative temperature dependence. Fracture strength in this temperature range at P = 0.1 MPa did not show a significant strain rate dependence over the two orders of magnitude explored. Strain rate dependence at P > 0.1 MPa has not yet been investigated.

143_< T= 158K

The brittle-to-ductile transition was bridged at 158 K

(Figure 5d). At the two higher strain rates, brittle or transitional behavior was encountered, with the same characteristics as at lower temperatures, in particular the pressure independence of strength above P - 50 MPa. At the lowest strain rate, ductile behavior was observed above P = 10 MPa. The ductile

strength was lower than the brittle strength and tended toward a negative dependence on confining pressure. The ductile strength at P = 180 MPa was unmistakably lower than that of the lower pressure runs. Run 28 was anomalous, being the only sample that underwent a phase transition at the start of a run. In run 28 a pressure drop occurred near P = 330 MPa during initial pressurization, but the pressure recovered as pumping continued. The moving piston did not encounter any resistance until it had traveled several millimeters beyond its usual position at the start of a run. The sample failed at a much higher load than did any of the other samples at 158 K, indicating, remarkably, that the jacket withstood the high strains of phase transition without rupturing. Upon removal of the sample from the apparatus, the diameter was 4.5% smaller than before the run and the length shortening (14.4%) was exactly twice what the piston displacement alone could have caused.

At all temperatures, the large and sudden displacement that accompanied brittle failure usually caused the indium jacket to rupture. It was convenient in the higher strain rate runs to allow the piston to continue its upward travel following failure, and in most cases, the resultant strength was observed to drop, in small but discreet steps, to lower and lower values. In two of the runs so tested (21 and 26), the downward stepping did not occur and we inferred that the jackets had not rup- tured. As the piston movement continued, both samples re- loaded up to their original strength before failing abruptly once again. In the case of run 26, three nearly identical events occurred, and following the third event the sample regained its original strength once again, which it then retained for several percent further shortening. Sample 21 had a single fracture; sample 26 had an indistinct fracture or fractures but did show the same barreling seen in ductile samples.

T> 195 K

Two sets of data with a nominal T = 195 K are shown. The

first, shown in Figure 5e, are 20 to 30% weaker than the second, shown in Figure 6. The break between sets corre- sponds to a temporal break of more than two months and correlates almost perfectly (run 62 being the only exception) with the apparatus change involving the agitators and separate cooling system. For reasons discussed in the Discussion section, the second set is favored. The first is retained because it spans a wider pressure range and shows the anomalous weaking at P _> 200 MPa (see below).

The behavior at 195 K and above was almost entirely ductile (Figures 5e, 6), the only brittle behavior occurring at low confining pressures at 195 K. The ductile flow strength (ass in Table 2) was distinctly higher at higher displacement rates. The ductile flow strength also showed a negative temperature dependence. The pressure dependence was complex and showed similarities to that at 158 K. The data show the

strength rising with pressure between 0 and 50 MPa, then falling thereafter. Pressures in the neighborhood of the ice I•,--} II phase transition (see Figure 1) were explored only at 195 K, where the negative pressure dependence became very strong (Figure 5e), an effect almost certainly due to the phase transformation taking place (see Discussion). At t•= 3.5


Fig. 4a Fig. 4b

Fig. 4. Typical morphologies of brittle and ductile samples. (a) Run 58, brittle. The single fracture plane is inclined 44 ø with respect to horizontal. (b) Run 38, ductile. Both samples are shown with end caps, encapsulated in their indium jackets. Both started with the same height and diameter.

x 10 -4 s-• the strength was a factor of five lower at P = 225 MPa than at P < 150 MPa. At g = 3.5 x 10 -6 s -x and P = 200 MPa, the flow strength was too low to be resolved, yet there was no evidence, such as a discontinuity in the load- displacement record or bubbles in the alcohol bath, to indicate a jacket leak. An additional anomaly in these weakened runs was that the total recorded displacement and actual length change of the sample were in serious disagreement. Whereas

the ratio U•,ct/Ure c Was usually close to 1.0, in the weakened runs it fell as low as 0.256 (Table 2b). There is a weak negative correlation between P and u•,ct/ure• at fixed g.

RESULTS--THIN SECTION PETRoGRAPHY

Most of our samples have been deformed at temperatures much less than 248 K. We cannot be certain that important changes in the textures and structures have not occurred

,eo (a) 160

140 -

120 -

lO0 -

80-

a. 60-

(n 4

n- 20

0

z

w 140-

u. 120

60-

T--77K - ß

T=IISK

?

T=I58K

o

o

New phase

T=I95K (d)

I I I

200 $00 moo 300

PRESSURE(MPA)

(b)

(e)

T=I43K --

Brittle

i

(c)

?

I00 200 300

PRESSURE (MPA)

SYMBOLS

Ductile

o • = •.5 • •½•s"

,, • = •.5 x ,d•s"

o • = •.5 •, ,6e½ '

Brittle- Ductile transition

Fig. 5. Run data plotted as O'ul t (brittle runs) or ass (ductile runs) versus P for the five coldest temperatures used in this study: (a) 77 K, (b) 113 K, (c) 143 K, (d) 158 K, and (e) 195 K. The data in (e) are for runs 46 and earlier and for reasons discussed in the text are segregated from later data at 195 K. Half-solid points represent transitional behavior between brittle and ductile. The approximate location of the brittle-to-ductile transition is shown by lines labeled B-D. In most cases a single run produced a single data point. Differential stress in the ductile run at P = 180 MPa in (d), open square with vertical bars, showed anomalous up and down variations over the range indicated.

flo

6O

40-

• 20-

,• 0

z ,,• 20 -

I0-

5-

0 6 -

T= 195 K T=213K

150 0

I I

T = 233 K

0 (33

0

I

T=243K

, I

T = 22:5 K

•:3 5 x 10-5s -I

T=258K

Fig. 6. Run data plotted as ass versus P for the warmer temperatures used, 195 K to 258 K. All runs were ductile. Most runs involved stepping of P and/or i, so produced multiple data points. V* is in units of cm3/mole.

I I I i I I i i 50 I00 50 I00 150 0 50 I00 150

PRESSURE (MPo)

DURHAM ET AL.: DEFORMATION OF ICE B385

i 1

10 mm

Starting Material Run 58 Run 38

1;0 rnm

Fig. 7. Thin-section photomicrographs of ice specimens. Top row (a-c): low magnification; bottom row (d-f): high magnification. Micrographs made in transmitted light between crossed polarizing filters. (a and d) Starting material. Note polygonal grains and equigranular texture. (b and e) Run 58, deformed at 158 K and 80 MPa. Note inclined fault and lack of textural modification outside recrystallized fault zone. The fault angle is 46ø; (c and f) Run 38, deformed at 195 K and 50 MPa. Partial recrystallization is evident from the smaller grain size.

during storage and thin section making at about 250 K. We do know, however, that significant optical-scale changes in structures and textures have not occurred after thin section

making. Thin sections of the starting material indicate that it has an

equigranular texture with polygonal grain shapes and an average grain size of 1 to 2 mm (Figures 7a, d). Individual grains show uniform optical orientation and the samples lack significant quarter-wave plate effects, suggesting that the grains do not have preferred orientation. Although the whole specimens are clear, grain boundaries observed in thin sections are slightly cloudy and are decorated by arrays of small bubbles.

We have examined four deformed samples in thin section: runs 11, 29, 38, and 58. Sample 58 (T = 158 K, brittle-ductile) developed a single through-going fault inclined at about 46 ø to the load axis. In thin section, the fault zone is revealed as a complex structure involving microfracturing and fine recrystallized grains (Figures 7b, e). Cohesion was not lost on the fault surface, but we cannot be certain that this is not a postdeformation annealing phenomenon. Sample 38 (195 K,

ductile) showed textural modification from the starting material (Figures 7a, d). It was partially recrystallized to smaller grain size and the grain shapes were more irregular than the original polygonal grains (Figures 7c, f). This high- temperature recrystallization texture is typical of rocks and ceramics deformed at temperatures above half the absolute melting temperature. Sample 29 (158 K, ductile) was not recrystallized. Individual grains showed very irregular grain shape and undulatory extinction.

DISCUSSION

It is convenient to discuss our test results within the frame-

work of four categories of behavior encountered to date. Using the symbol Pc to indicate the ice I•,-• II phase transition pressure (Figure 1), the categories are as follows: (1) Brit- tle, all P; (2) ductile, volume conserving, P << P•; (3) ductile, nonvolume conserving, P-,• P•; and (4) spontaneous phase change, P >> Pc.

1. Brittle, all P (Figures 5a-5d). While similar in some respects, the brittle behavior of ice also contrasts strikingly with the brittle behavior of most silicate rocks. Like other


2O0

•100

m 50

,• io

MI•C

(I (383)

ICE I h This P=50MPo Study.

0 E=3.5 xld4• '1

• • = 3.5 x I0'% '• /

I- "• I • I I I j 4 5 6 7

I x10 s T(K}

Fi•. 8. Ductile flow data plotted as 1o• c versus 1IT at a fixed pressure of 50 •Pa. Constant strain rate flow conformin• to (•) plots as a straight line with slope •*/Z3nE, so that a break in slope is often indicative of a chan•c •*, i.e., a chan•c in mechanism. Simple open fi•urcs represent actual data from Figure 6 and Fisurc 5•. The solid represent data (interpolated in strain mtc) from Mdlor • Col• [1983]. The solid lines (broken where thc• approach data points) arc least-squares fits of (•) to the above mentioned points, with a boundary at •43 K between two such curve fits. The dashed curve is defined to pass from the data point at T = 158 K to point at 195 K on the solid linc appropriate to • = 3.5 x 10 -• s-•. Also shown in error bars on the fiSurc, but not included in the fits, arc estimates based on extrapolations of the 195 K data in Figure 6 of where the • = 3.5 x 10 -• s- • and • = 3.5 x 10 -• s- • points should bc at 50 •Pa.

rocks, ice has a brittle strength that is only weakly strain rate dependent but strongly pressure dependent at low confining pressure. Unlike most other rocks, however, the brittle strength of ice becomes pressure independent above P-.. 50 MPa.

The Mohr-Coulomb theory, backed by a large volume of data, states that the resistance z to shear failure on a single inclined fault is given by

T •- T o + an• o

where T o is the cohesive strength, a-• is the normal stress across the fault, and #o is the coefficient of internal friction, analogous to the coefficient of sliding friction (see Handin l'1966-1). If T is independent of pressure, as in our tests at P > 50 MPa, then #o = 0 (since an is directly proportional to pressure). The fault angle, 0, is given in the Mohr-Coulomb theory by

0 = +4• o -T- &/2

where •b=arctan #o. If #o=0, then •b=0 and the fault should be inclined at an angle of about 45 ø to the compression direction, as we observe (Table 2a). Basic physical laws, in fact, argue that a process that is not influenced by confining pressure cannot require a change of volume. The failure plane occuring at the angle of maximum shear stress is consistent with the failure mechanism being fundamentally a shearing process, i.e., without volume change. Any dilation of the microfractures seen in sample 58 must have either been ex- ceedingly small or unimportant to the fracture process. The

observation that many of the faults did not intersect the speci- men ends and were inclined at a constant angle of 45 ø + 6 ø indicates that the observed fracture strength and mechanism are intrinsic to polycrystalline ice and do not depend on end conditions or upon initial fractures in the samples due to thermal shock.

Another unusual feature of the high-pressure fracture behavior of ice is that the fracture strength is recoverable after initial failure. Jacket failure did not accompany faulting in two tests (21 and 26). After the first stress drop, the stress resumed increasing and the samples failed at about the same fracture strengths as in the initial cycle, indicating a remarkable heal- ing process has taken place after the initial faulting. This heal- ing may be related to the zone of recrystallization observed in a thin section of another faulted sample (Figures 7b, e). Since only one fault was observed in sample 21 (sample 26 is un- clear), the fault formed by the initial fracture event also nu- cleated subsequent events but did not reduce the fracture strength.

2. Ductile, volume conserving, P << P•. Data taken at P< 175 MPa and T=195 K, and at P< 100 MPa and T = 158 K are free of phase change effects (see paragraph 3, below). This includes all of the data in Figure 6 (T > 195 K) and three of the ductile points in Figure 5d (T = 158 K). The steady-state ductile flow of most materials can be described emperically by a relationship of the form

g = Aa" exp (_E* + P V• (1)


TABLE 3. Steady-State Flow Parameters for Ice I h

268>T>243K 243K>T> 195K 195K>T> 158K

log A, MPa-" s-• 11.8 +_ 0.4•' n 4.0 +_ 0.6 H*, kJ/mole 91 +_ 2

5.1 +___ 0.03 - 3.1:!: 4.0 +_ 0.1 --4.0 61 + 2 31/;

•'One standard deviation. ,Based on dashed line in Figure 8.

where A, n, E*, and V* are material parameters and R the gas constant. On a plot of log a versus l/T, (1) is a straight line at constant P and g. Figure 8 is such a plot using data obtained at P - 50 MPa. For the purposes of fitting to these data, the flow law may be simplified to the form

• = Ao 'n exp -- • (2) where H*, called the activation enthalpy, differs from the activation energy (E*) by a constant value (= 50 MPa. V*).

It is apparent from Figure 8 that a single set of material parameters (A, n, H*) does not describe the data. At least three sets are needed, which implies that at least three different mechanisms have controlled flow between 158 K and 268 K.

Note that the data in Figure 8 include points at 268 K from Mellor and Cole [1983]. Least squares fits of the data in Figure 8 to (2) give the three sets of constants given in Table 3. The greatest uncertainty applies to the set appropriate to 158 K < T < 195 K where there is, in fact, insufficient information to determine A, n, and H*. We have therefore arbitrarily taken n = 4 (the value appropriate to the higher temperatures) in order to calculate A and H* in Table 3.

Regarding the pressure dependence of ductile flow in ice, it has already been pointed out that there does not appear to be a linear, nor even a monotonic, relationship between a and P at 'fixed g and T. In terms of (1) this means that the effective value of V* is a function of pressure. Straight lines in the 195 K portion of Figure 6 are meant to demonstrate that for 0<P<50 MPa, V*..•20x 10 -6 m3/mole and for 50 MPa<P<175 MPa, V*..•-10x 10 -6 m3/mole. We cannot be certain that the positive pressure dependence of

strength at P < 50 MPa is not due, in part, to distributed microfracturing occurring in these tests. Thin section work should help resolve this uncertainty. In any case, the maximum effect of the PV* term in (1) within the pressure stability field of ice In can only be about -1.50 kJ/mole, i.e., less than the error bounds of our determination of H*.

Results for the ductile flow of ice show appreciable scatter, and the causes ,are not well understood. Certainly the most troublesome observation is the apparent change in flow properties at 195 K between early experiments (through run 45) and more recent experiments (run 62 and beyond). The second set must be assumed more reliable since most of them

(all but 62) were tested after the fluid agitator was added to the apparatus. However, the temperature of the first set would have to have been over 8 K too warm, given Figure 8, to have produced the observed results. Such an error is sufficiently beyond the estimated error (Table 1) to be eliminated as the probable cause. If the difference were real (i.e., if the samples themselves were different), then we are justified in using the second 195 K set in Figure 8, since all data in Figure 8 between 258 and 213 K are taken on more recent samples.

3. Ductile, nonvolume conserving, P ..• P•. There is com- pelling evidence in Table 2 and Figures 5d, e, and 9 that as confining pressure approaches (and passes) the ice ln• II phase transition pressure, the apparent strength of ice I• samples is increasingly affected by the gradual transformation of ice lh into ice II. When plotted as a function of confining pressure at T = 158 K (Figure 5d) and T --• 195 K (Figure 5e), the ductile strength of ice is approximately pressure- independent below approximately 100 MPa. At higher pressures, the strength of the samples shows a dramatic negative

ioo

• 75

• 5o

POLYCRYSTALLINE ICE

T ß 195 K

• - $.5x1(•4S -I

/-P=25 MPa -• •-100 MPa •• -

........ _/i• • •

-

•/-- 225 MPo 0 • I I I I I I .... I

IO 20 30 40

s HORTE N ING (%)

Fig. 9. Tracings of records of most of the g = 3.5 x 10 -'• s-• runs shown in Figure 3e, illustrating the effects of the ice I h • II phase transition at higher confining pressures (see text). Run 44 (P -- 100 MPa) is shown with dashed interpola- tions through two portions of the run where g was stepped down to 3.5 x 10 -6 s-•


pressure dependence. The following evidence suggests that a phase transformation is occurring. Firstly, in the anomalously weak samples, there is consistently poor agreement between sample shortening as measured directly on the specimens after the runs and as calculated from the known displacement of the piston (see Uact/Ure c in Table 2b). The discrepancy is generally so large that it can only be explained by accepting that the sample grew in length between the time the piston stopped and the time the sample length was measured directly. Ice II is metastable at atmospheric pressure only below 170 K [Bertie et al., 1963] and post-test length measurements were made at one atmosphere and 195 K. Secondly, the two anomalously weak samples strained > 20% encountered a rapid hardening at high strain (Figure 9). If the anomalous weakness was caused by phase transformation, then the anomaly would dis- appear when the entire volume of samples had transformed. The strength of those two samples following the hardening phase is approximately the same as that of normal samples under the same conditions and may be characteristic of ice II.

There is a third observation which, although it does not directly imply phase transformation, does imply important structural differences in the weak samples. Viewed with the indium jacket still on, anomalously weak samples invariably have a finer surface texture than the heavily rumpled surfaces of the normal samples.

It cannot be determined at this point whether the predominant cause of the weakening is an intrinsic weakness of a transforming ice/h/ice II mix or direct accommodation of the piston displacement by the volume reduction during progres- sive transformation. The latter effect surely occurred to some extent. If the former effect did not occur, the results of the two high-strain runs where weakening occurred (Figure 9) mean that the volume strain of transformation under load is aniso-

tropic. In the isotropic case, complete transformation and strength recovery should have occurred at roughly 8% shortening instead of the 20 to 30% shortening indicated in Figure 9.

4. Spontaneous phase change, P>> P•,. Bridgman [1911] noted that the kinetics of the transformation lh-• II are ex- ceedingly slow at the transformation pressure and T < 225 K. This sluggishness has allowed us to do tests on ice lh at pressures well outside its stability field (Figures 1, 5), especially at cooler temperatures. Sufficient overpressurization, however, will result in spontaneous phase change, as evidenced by run 28 (Figure 5d), whose shortened initial length indicated the sample had entirely transformed before the initial piston contact.

COMPARISON WITH PREVIOUS WORK

Brittle Fracture

Very little work has been done on the brittle failure of ice in the low strain rate range covered in this study because, as pointed out by Parameswaran and Jones [1975], there is little terrestrial interest in the subject. Those authors, in fact, did a number of unconfined compression tests on polycrystalline ice at 77 K and found failure occurred at a differential stress of

approximately 50 MPa, in excellent agreement with our two tests done under the same conditions (Figure 5a). Quoting several pieces of unpublished work, Parmeswaran and Jones [1975] also concluded that the unconfined brittle strength de- creased with increasing temperature, a trend with which our unconfined data are in rough agreement.

Transient Flow

We observed peaked stress-strain curves in all of our constant strain rate tests that were conducted in the ductile

regime within the stability field of ice Ih. Such curves are also characteristic of constant strain rate tests on polycrystalline ice at atmospheric pressure and high temperature (see reviews by Weertman [1973, 1983] and Glen [1975]). Although acoustic emissions caused by microfracturing occur in the atmospheric pressure tests, the peak in emissions occurs before the yield drop and thus microfracturing is probably not the funda- mental cause of the yield drop [St. Lawrence and Cole, 1982; Cole and St. Lawrence, 1983; Mellor and Cole, 1983]. Mellor and Cole [1982, 1983] have also shown that creep tests on polycrystalline ice often display high initial creep rates followed by strain rate reduction to a minimum followed by strain softening to a steady-state rate at strains approaching 10%. These features are the counterparts of the initial yield- ing, strength maximum, and yield drop to steady state stress in the constant strain rate tests and the rheological relationships between stress, strain rate, strain, and time are completely derivable from one type of test to the other [Mellor and Cole, 1982; Cole, 1983a, b].

Weertman [1973, 1983] points out that polycrystalline materials that exhibit strain softening have small initial dislocation densities and that dislocation glide motion in them is inhibited by various drag mechanisms. The physics of the yield drop phenomenon is then controlled by the glide velocity and the nature of dislocation multiplication (see Gilman [1969] and Alexander and Haasen [1968]). Steinemann [1958], Kamb [1972], and Duval [1979, 1981] observed strain softening in torsion tests on polycrystalline ice at atmospheric pressure, a phenomenon they attributed, in part, to the development of preferred orientations favoring basal slip, the easy glide system for ice. For geometrical reasons, this softening cannot operate in our tests. The softening effects of the growth of new strain-free grains may also be important in ice. Strain softening occurred in our tests in the samples deformed at 158 K in the ductile regime where, as noted above, a thin section showed no textural evidence of recrystallization. This suggests that strain softening at 158 K does not require recrystallization, but rather stems from dislocation multiplication and velocity-limited dislocation glide [Weertman, 1973, 1983].

Steady-State Flow

Whatever the source of the initial transient flow, subsequent deformation above 5 to 10% strain is essentially steady-state out to strains where the calculated strengths begin to lose validity because of strain heterogeneity.

We observed three different values of H* depending on temperature. At intermediate temperatures (•-195 to •-243 K), H*= 61 _+ 2 kJ mole, which compares very well with H* values at atmospheric pressure and temperatures between 223 and 263 K(•-60 kJ/mole) [Weertman, 1983] and with the activation energies for self-diffusion [Weertman, 1983] and recovery by dislocation climb [Duval and Le Gac, 1983], suggesting relationships among these processes. Weertman [1983] cautions against strict adherence to this conclusion because various dislocation glide-controlled mechanisms, also influenced by self-diffusion, could also apply.

The creep experiments of Barnes et al. [1971] at T < 263 K indicate a power law relationship with n = 3.05 for a _< 3.8 MPa and an exponential law above 3.8 MPa. Their results conflict seriously with our finding that flow conforms to a


200

ioo

5o

• 2o b

ICE I h P= 50 MPo

/ /

/ /

/ /

/

," • /,,,

"iF' // /'•' • /x x/ // •o //

//// / /// /

/ • 2432 •223 /

7

/ /

(frocture)-•1

113 T(K)

• 9 I0 II 12 -• x •0 •

Fie. 10. Summary of our understanding of the isobaric (P = 50 MPa) flow of ice I h, plotted on the same axes as Figure 8. S•id lines represeht observed behavior. Dashed lines represent extrapolations based, for the most part, on the information in Table 3. It is assumed in this plot that fracture strength is independent of strain rate.

power law with n = 4 for stresses at least as high as 70 MPa. Jones [1978, 1982] has done constant strain rate triaxial tests at T = 262 K and confining pressures to 85 MPa. His work is difficult to compare directly with our results because his samples were not jacketed and because the confining pressure increased with piston displacement in his experiments. The effective least principal stress was therefore not fixed during his experiments. Nonetheless, his strength data compare favor- ably with the atmospheric pressure tests of Mellor and Cole [1983] and his results on peak stresses versus nominal confining pressure show broad maxima at confining pressures of 10 to 30 MPa. Lastly, he determined the parameter n = 3.95 of (2) from the peak stress versus strain rate data. All of these results compare well with those of the present study.

The increase of H* to 91 -t- 2 kJ/mole, which we observe above about 243 K at P = 50 MPa, compares well to a similar effect observed by others above about 263 K at atmospheric pressure [Mellor and Testa, 1969' Barnes et al., 1971]. This higher temperature sensitivity does not occur in single crystal ice above 263 K, so it is clearly associated with grain boundaries [Mellor and Testa, 1969' Homer and Glen, 1978; Jones and Brunet, 1978]. Weertman [1983] attributes the effect to the onset of recrystallization and grain growth. This sugges- tion does not appear to apply to our results in a straightfor- ward way because even a sample deformed at 195 K was partially recrystallized (Figure 7c, f). 195 K is well below the mechanism change at about 243 K. Mellor and Testa [1969], Barnes et al. [1971], Duval [1977], and Baker and Gerberich [1979] all attribute the softening they observed at T > 263 K to the presence of liquid water at grain boundaries, for which there is independent evidence from nuclear magnetic reso- nance and electrical conductivity measurements and optical observations [Mellor and Testa, 1969' additional references in Barnes et al., 1971 and Baker and Gerberich, 1979]. The way in which grain bondary water facilitates creep is under debate. Barnes et al. [1971] suggest that water at grain boundaries and triple junctions can promote grain boundary sliding. Duval [1977] and Ohtomo and Wakahama [1983] propose that water at grain boundaries might facilitate grain boundary

motion and dynamic recrystallization. Duval et al. [1983] ad- vance the idea that grain boundary water relaxes the con- straints to slip that apply to individual grains because of their neighbors. The stress exponent n in this high-temperature regime is 4.0 + 0.6 (Table 3)' Mellor and Cole [1983] find 4.0 + 0.1 in their room pressure tests at 268 K. Since the value of n - 4 is the same as at intermediate temperatures (Table 3), the same basic physical mechanism may be operating, en- hanced by grain boundary relaxation. Duval [1977] and Duval et al. [1983] have made similar arguments.

The transition between the high-temperature ductile regime and the one at intermediate temperatures is at 243 + 5 K at P = 50 MPa in our tests (Figure 8). This is 20 K below the transition temperature observed in room pressure tests [Melior and Testa, 1969' Barnes et al., 1971]. The discrepancy may be partly due to the depression of the melting point of pure ice by the larger mean stress in our experiments. With a macroscopic least principal stress of 50 MPa and a maximum stress difference of 15 MPa, the upper limit of the mean stress is 55 MPa. The average (•?T/•?P) for H20 at the univariant equilibrium boundary for ice lh and melt is about 0.135 K/MPa, which gives a reduction of 7.4 K, about one third the observed displacement of the transition. We do not understand this discrepancy. It is important to understand this pressure effect on the transition temperature in order to estimate how the transition varies with depth in the icy satellites.

The low-temperature (T < 195 K) ductile regime has not been adequately characterized because the onset of fracture makes the T and e ductility range rather narrow (Figure 10). The stress-strain curves, sample shapes, and thin section observations at T -- 158 K and • = 3.5 x 10 -6 s-• clearly show ductile behavior at P > 39 MPa and the ductile strength under these conditions is only about one third that expected from extrapolation from the intermediate temperature ductile regime, indicating that the temperature or strain rate sensiti- vities (or both) are different in this regime. The lack of recrystallized grains and recovery features in the sample of run 29 deformed at 158 K suggests that the low temperature regime may be a consequence of low self-diffusion rates or low grain

B390 DURHAM ET AL..' DEFORMATION OF ICE

IOO

2o

0.5

0.2

o.I

..%

o 50 I

*",Ooß*****.Ooooooo o o .../o/e '. ß

ß

ß

ß

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CALLISTO I00 150kin

I

5'0 IOO GANYMEDE

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T{K) 120140 160 180 200 220 227

Ill I. I [ ) • I I I • I IOO 200

PRESSURE (MPa)

Fig. 11. Implications of our work for Ganymede and Callisto, calculated from Figure 10 (i.e., Table 3), using the temperature- pressure profile in Figure 1. Ganymede and Callisto have approximately the same temperature-pressure profile, but not the same pressure-depth profile, so individual horizontal scales are given in the figure. Given any two of the set of (a, g, depth), the third can be determined from the figure. Also shown are values of effective vicosity,

boundary mobility. Without question, additional tests are needed in order to establish the rheology of ice in this regime.

IMPLICATIONS FOR THE ICY PLANETS

The temperature profile in Figure 1 is generally consistent with the present-day profiles of most thermal evolutionary models of Ganymede and Callisto [Consolmagno and Lewis, 1976; Parmentier and Head, 1979] and allows us to illustrate the implications of our data for present-day processes within the ice lh layer of those bodies. Figure 10 illustrates the extrapolation of the data in Figure 8 to lower strain rates using (2) and the flow parameters in Table 3. Figure 11 is construc- ted from the flow results in Figure 10, the temperature- pressure profile of the moons (Figure 1) and the pressure- depth profiles of the moons [Parmentier and Head, 1979].

Lines of constant effective viscosity, r/= a/3• [Griqqs, 1939; Praqer and Hodge, 1951], are also shown. One can read from Figure 11, for instance, the strain rate versus depth relationship required to maintain a constant differential stress through the ice I h layer, or the stress versus depth relationship required to maintain a constant effective viscosity.

Predicted viscosities at very low temperatures in Figure 11 are many orders of magnitude lower than those predicted on the basis of previous work (see, for example, Croft [1983]). A direct result of our finding a rather weak temperature sensitivity of flow (H* = 31 kJ/mole in equation 2) below 195 K is that ice can be expected to be easily deformable over geologic periods under near surface conditions on Ganymede and Cal- listo. It should be pointed out that the low value of H* is the result of our somewhat arbitrary assumption that n = 4 at T < 195 K. The slopes of the curves in the ductile portion of Figure 10 are proportional to H*/n, hence H* will be re- defined higher or lower if n is found to be higher or lower than 4. Viscous relaxation apparently has occurred to an appreciable extent on the surfaces of both Ganymede and Callisto [Parmentier and Head, 1981; Parmentier et al., 1982; Passey and Shoemaker, 1982], although the near-surface viscosities required to explain the observed features are a few orders of magnitude higher than those predicted in Figure 11 [Parmen- tier and Head, 1981; Passey and Shoemaker, 1982]. Further calculations and a more sound determination of H* are neces-

sary to determine whether or not the discrepancy requires that the upper layers of the icy moons be something other than pure H20.

Nonimpact fracture on Ganymede and Callisto must be restricted to depths of a few kilometers. Figure 11 indicates that a relatively rapid strain rate (• 10 -9 s-•) is required to maintain a stress difference above a = 50 MPa (the lowest brittle strength of pure, intact ice as measured in this study) at a depth of 10 km on Callisto. Given the increasing temperature and confining pressure below 10 km, it seems unlikely that anything but a meteoritic impact could produce brittle failure (moonquakes) below that depth. If the rift pattern on Ganymede is suggestive of deeper faulting [Parmentier et al., 1982], then perhaps the crust of that body is a more rigid material, for example, a rock-ice mix, than we have been measuring here. If interior temperatures were cooler that at present [Consolmaqno and Lewis, 1976], deep faults could have formed earlier in the evolution of the moons.

If the temperature-pressure profile in Figure 1 is reasonably accurate, then Figure 11 indicates that present-day large scale convection involving any of the ice I h layer requires the presence of stresses of the order of 1 MPa at depths of 100 to 200 km. A lithosphere, roughly defined by the point of strongest curvature in the lines of constant t•, has a thickness of 20 to 30 km. The latter conclusion hinges rather strongly on the arbitrary curvature of the T-P profile in Figure 1 and on our experimental results below 195 K. Even if the extrapolation of our results (Figure 10) is valid, this estimate of lithospheric thickness could easily be altered by a factor of two or three.

CONCLUSIONS

A preliminary study involving 70 constant strain deformation tests on pure polycrystalline H20 ice conducted under conditions covering most of the stability field of ice I h (Figure 1) leads us to the following conclusions:

1. Brittle failure of I h is promoted by lower P, lower T,


and higher g; ductile flow is promoted by higher P, higher T, and lower g.

2. The character of brittle failure of ice lh is most unusual. Fracture strength is a positive function of P only below P = 50 MPa. At P •_ 50 MPa fracture strength is independent of P and the fracture plane lies approximately 45 ø from the load axis. Fracture strength also shows a weak negative temperature dependence at a strain rate of 3.5 x 10 -6 s-l, falling from about 170 MPa at 77 K to about 120 MPa at 158 K.

3. In the ductile field, ice flows according to a law of the form given by (2) and the constants in Table 3. There are at least three different regimes of flow in which different mechanisms control flow. Agreement with existing work on ice, most of that work conducted at high temperature and low pressure, is generally good.

4. Existing extrapolations (based on existing experimental data) to Ganymede and Callisto may be badly in error. Near the base of the ice lh layer in those moons (at P ~ 175 MPa and T ~ 200 K) ice is slightly stronger (a factor of 2 to 3) than previously expected. At near-surface temperatures (100 to 120 K), however, ice is vastly softer than previously predicted.

NOTATION

P confining pressure (minimum principal stress in triaxial compression), MPa.

e sample shortening (engineering strain) computed by e -- 1 - I/lo, dimensionless.

g strain rate, s-1 10 initial sample length at 195 K, mm. l instantaneous sample length during a run, mm.

Urec displacement recorded during a run, mm. u,ct displacement as measured directly on the sample, mm,

l•act "- lo -/final- ty differential stress (maximum principal stress minus mini-

mum principal stress), MPa. %•t maximum ty measured, MPa. tyss steady level of ty reached in a ductile run, MPa.

Acknowledgments. The authors gratefully acknowledge NASA support under order number W-15,070. Pegi Daley and Carl Boro furnished invaluable technical assistance. This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract W-7405-ENG-48.

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(Received May 31, 1983; revised September 9, 1983;

accepted September 9, 1983.)

experimental deformation of polycrystalline h20 ice at...

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