THE MECHANICAL PROPERTIES OF SINGLE CRYSTALSOF ICE AT LOW TEMPERATURES

S.J. JONES and J.W. GLENDepartment of Physics, University of Birmingham,

Birmingham 15, England.

ABSTRACT

The mechanical properties of single crystals of ice have been investigated at varioustemperatures down to — 90 °C. Two methods have been used: creep tests in tension andconstant strain-rate tests in compression. Results show that the activation energy forcreep varies with temperature from 0.41 -_t 0.03 eV between — 50 °C and — 90 °C to0.68 ± 0.04 eV between -50°C and -10°C. The glide direction in ice is confirmedto be the <(ll20)> crystallographic direction. The yield point phenomenon observedin the constant strain-rate tests is discussed in terms of the theory of the multiplicationof dislocations, and experimental curves are compared with computed curves.

Evidence is produced which shows that small amounts of H F dissolved in ice causea pronounced softening.

RÉSUMÉ

Les propriétés mécaniques de simples cristaux de glace ont été étudiées à différentestempératures jusqu'à — 90 "C. Deux méthodes ont été utilisées: des tests de fluage soustension et des tests à vitesse constante sous compression. Les résultats montrent quel'énergie d'activation pour le fluage varie avec la température de 0,41 ± 0.03 eV entre- 50 °C et - 90 °C à 0,68 ± 0,04 eV entre - 50 °C et - 10 °C. La direction de glissementdans la glace a été confirmée d'être < 1l20> de direction cristallographique. Le phéno-mène du point critique de fluage observé dans les tests à vitesse constante est discuté entermes de la théorie de la multiplication des dislocations, et les courbes expérimentalessont comparées aux courbes calculées.

Il est mis en évidence que de très faibles quantités de HF dissous dans la glacecausent un amolissèment prononcé.

1. INTRODUCTION

A number of workers have investigated the mechanical properties of single crystalsof ice close to the melting point. Two groups, Readey and Kingery ( 1964) and Higashi,Koinuma and Mae ( 1965) have made studies at various temperatures down to — 42 °C.One of the objects of the present work was to continue these investigations to evenlower temperatures, and to do this two types of test were employed: tensile creeptests under a constant load and compressive tests at a constant strain-rate.

Preliminary results from the tensile creep tests were presented by Glen and Jones(1967) at the International Conference on Low Temperature Science held in Sapporo.This paper gives further results from this experiment at somewhat lower temperaturesas well as giving results from the constant strain-rate tests. Experimental stress-straincurves are compared with curves computed from Johnston's (1962) theory of disloca-tion multiplication derived for LiF. This gives an initial density of mobile dislocationsof about 105 cm"2 and dislocation velocities of the order of 50 Â s-1.

It was discovered that doping the ice crystals with small quantities of H F had apronounced softening effect, and the evidence obtained from both types of test is pre-sented in this paper. Results for other dopings are briefly mentioned.

2. THE TENSILE CREEP TESTS: APPARATUS AND SPECIMENS

The technique used to grow the crystals and the tensile creep apparatus are bothdescribed in Glen and Jones (1967) and so will not be discussed here.

326

3. TENSILE CREEP: RESULTS

3.1 Mechanical Tests

Preliminary results obtained at -50°C have been presented in Glen and Jones(1967) and so this paper will concentrate on tests at lower temperatures. Creep curvesobtained at -60°C are shown in figure 1, in which the shear strain resolved on the

4—1

SHEARSTRAIN

«XDO•IVTa

XXIXVIXXIXVIXVIXVIX I IXVIVI

BB2AA 1CBlEA 2B

IOO .TIME (HOURS)

Fig. 1 — Creep curves of ice crystals deformed at -60"C.

I5O

ÎI O -

SHEAR

STRAIN

o i-

- 6 O C

II O IOO

TIME (HOURS)

Fig. 2 — The creep curves of figure 1 plotted logarithmically.

327

basal plane, defined by Schmid and Boas (1950, p. 58), is plotted as a function of time.The creep curves have the same shape as those found at higher temperatures, i.e. acontinually increasing creep rate is observed with no apparent strain hardening. Theshape of the curves was found by plotting the logarithm of the strain, e, against thelogarithm of the time, l, as shown in figure 2. In all cases the result was a straight lineshowing that

E oc T (1)

where m = 1.4±0.2 for strains between 0.2% and 5%.Since e oc t1A, it follows that è op /°-4 and hence £ oc £o.286 This being so, È/s0-280

should be a constant for each crystal, the value of which depends on the resolved shearstress, T, acting on the crystal. This was found to be the case and since it was expectedthat the dependence of strain-rate on stress would be a power law type of relationship,a graph of the logarithm of è/s0-286 was plotted against the logarithm oft, as shown infigure 3. A straight line was fitted to these data by the method of least squares. Thisshows that

„0.286OC T" (2)

with n = 2.6 ± 0.4. However, it was possible that the data might be better fitted by anon-linear curve and, to test for this, a least squares determination was made of theconstants in the simple parabolic type of equation

log (e/e0286) = a + b log T + C (log r)2 (3)

Once this had been done the Gauss criterion (see Worthing and Geffner(1943) pp. 260-62) was used to determine whether the linear or non-linear function was the betterfit to the experimental data. For the data of figure 3, the non-linear curve, equation 3,

2-

1 : 105 10

Log T >

Fig. 3 — The stress dependence of the strain-rate of the crystals deformed at -60°C.

328

gave the better fit, and this curve is also drawn on figure 3. It is possible that the datawere also better fitted by other non-linear equations, for example a circle or cubicparabola, but these were not tested since the object was primarily to show whether thedata constituted a random distribution about a straight line or whether there was asignificant curvature to the line. Since the shape of the curve is a function of stress thismeans that in the power law expression, equation 2 above, n varies with stress from1.0 at 2.5 kg cm-2 to 4.2 at 6.3 kg cm"2.

A similar analysis has been carried out of the creep curves obtained at —50 °C and-70°C. The value of n = 4-h 1 at -50°C reported by Glen and Jones (1967) wasobtained over a small range of comparatively high stresses and when a larger range ofstress was used it was found, as at — 60 °C, that n depended slightly on stress.

An attempt was made to obtain creep curves at —90 °C, but on all occasions thecrystal fractured before any significant strain could be detected. One crystal remainedunder a resolved shear stress of 13.8 bar (nominal stress = 27.6 bar) for 200 h at— 90 eC. The maximum strain that could have occurred was 0.07% and it is possiblethat, over this long period, thermal effects causing differential expansion in the appara-tus could have caused this apparent strain. It was impossible to raise the stress abovethis value without the occurrence of fracture within, at most, 48 h of the start of the testas happened with three other crystals. Calculation from data at — 70 °C shows thatwith a shear stress of 13.8 bar and an activation energy of 0.41 eV (9.5 kcal/mol), astrain of 2-3% should have developed in 200 h at — 90 °C; this would have been easilyobserved. From this it would appear that at — 90 °C ice crystals arc brittle. Nevertheless,if a crystal is first deformed at a higher temperature and thereby softened, it is possibleto obtain a measurable strain-rate when the crystal has cooled to — 90 °C. More as-growncrystals need to be tested at — 90 °C over very long periods of time before it is possibleto say categorically whether or not they are brittle at -90°C.

The effect on the creep curve of annealing a specimen close to the melting point wasinvestigated by straining a specimen for a certain time, removing and storing it in aparaffin bath in a cold room at — 6 °C, and then re-straining it under the same conditionsas initially. The result for two crystals which were annealed for 240 h and 160 h res-pectively showed that annealing has little effect in that the initial strain-rate afterannealing is nearly equal to, or slightly less than, the final strain-rate before annealing.

I5O

IOO

5O

- ÎSTRAIN

xio4

- 7 O " -8O"

50TIME .HOURS

IOO

Fig. 4 — The method used to compare the strain-rate of a crystal at various temper-atures.

329

3.2 The Activation Energy Analysis

In order to determine the activation energy of the creep process a number of crystalswere deformed at various temperatures, as shown, for example, in figure 4. Betweentemperature changes the load was removed, and after the new temperature was reachedthe same load was re-applied to the crystal. The final strain-rate before the temperaturewas changed and the initial strain-rate after the temperature was changed were bothmeasured. Assuming that the strain-rate, é depends on absolute temperature, T,according to an Arrhenius relation

ê ocexp(-E/fcT) (4)

a plot of In £ against 1/r should be a straight line of slope —Elk. If there is more thanone creep process operating, each of which has a different activation energy, a plot ofIn £ against 1/7" will have a slope that varies with temperature. Such a plot is shown infigure 5, in which the data are fitted with two straight lines of different slopes dependingon the temperature. Between — 50 °C and — 10°C, the slope gives an activation energyof 0.68±0.04 eV (15.6±0.8 kcal/mol) and between -50°C and -90°C an energy of0.41 ±0.03 eV (9.5 ±0.6 kcal/mol).

X

o•aaaV

XCXIXXIXXIIXIIX BXII

BABC

A

Fig. 5 — A plot of the natural logarithm of the strain-rate against reciprocal absolutetemperature, the slope of which gives the activation energy.

3.3 The Glide Direction in Ice

No further evidence has been obtained regarding the glide direction in ice that wasnot presented in Glen and Jones (1967). The conclusion reached then was that <1120>is the glide direction in ice, a result which confirms the X-ray topographical work ofHayes and Webb (1965).

330

4. CONSTANT STRAIN-RATE TESTS: APPARATUS AND SPECIMENS

4.1 Specimen Preparation

The crystals were grown in the same manner as those which were used for thetensile creep tests and described by Glen and Jones (1967). Since the constant strain-ratetests were to be in compression, however, crystals of a larger diameter than those used inthe tensile creep tests were required and so glass tubes of 1.5 cm internal diameter wereused. The tubes having been warmed gently, the crystals were removed and cut toapproximately 3 cm in length; a warm piece of metal was then used to melt flat theends of the crystal and one end was then frozen to a ceramic plate.

4.2 The Constant Strain-rate Machine

A schematic diagram of the constant strain-rate machine is shown in figure 6.The central compression rod, A, was driven downwards at a constant velocity by an

Fig. 6 — Schematic diagram of the compression machine.

331

electric motor. The load applied to the crystal was mesurcd by a transducer, B, whichgave an output voltage, continuously monitored on a pen recorder, that was directlyproportional to the applied load. The crystal, c, was frozen to the bottom ceramic endplate which fitted into a brass holder fixed to the bottom of the copper cell, D. A coppertube, K, fitted around the brass holder and a similar ceramic end plate and holder, F,was placed on top of the crystal. The object of the copper tube, E, was to prevent anysideways movement of the holder, F, when the compressive load was applied. A de-scription of the method of cooling, i.e. by liquid nitrogen, and that of controlling thetemperature is given by Glen and Jones (1967), and will not be repeated here. The loadwas measured with two transducers, one used for loads of 0-200 lb (0-90 kg, 0-890 N)and the other for the range 0-1 000 lb (0-450 kg, 0-4448 N). They had elastic constantsof 4.19 x 10"5 cm/kg and 0.538 x 10"5 cm/kg, and gave output voltages of 1 mV/7.5 kgand 1 mV/36 kg respectively. This output voltage was continuously recorded as a func-tion of time, and since at a constant strain-rate time is directly proportional to strainthe load-time curve could be re-plotted as a stress-strain curve.

4.3 Experimental Method

The crystals were grown and orientated and the compression apparatus was cooledto - 10°C. The crystal was taken to the machine in a cold paraffin bath and then quicklytransferred to the brass holder in the copper cell of the apparatus. A copper tube wasthen placed around the brass holder and crystal, and the top ceramic end plate and hol-der were put in the tube. The cell was then filled with cold toluene, to prevent evapora-tion of the crystal, and the cooling process was continued until the desired temperaturewas reached. The compression rod and transducer were then screwed down manuallyuntil contact with the crystal was obtained. The electric motor was then switched onand the drive was connected to the compression rod.

5. CONSTANT STRAIN-RATE TESTS: RESULTS

5.1 Experimental Stress-Strain Curves

Typical stress-strain curves obtained in the compression tests at a nominal strain-rate of 1.6 x 10"5 min"1 are shown in figure 7. From this figure it can be seen that ini-tially the stress rises linearly with strain until it reaches the upper yield stress, Tmax,when it drops owing to the rapid yielding of the crystal. The stress continues to drop ata decreasing rate even to the quite large strains (resolved shear strains of 10%) observedin the experiment. Thus, in general, no work hardening was observed.

The effect of temperature on the stress-strain curve can also be seen from figure 7.At lower temperatures rmox is increased and so is the yield drop. To determine theeffect of temperature more precisely, a graph of In Tmax against (1/7") was drawn, asshown in figure 8. If the strain-rate of the crystal depends on temperature accordingto an Arrhenius expression Iikeequation4, then the stress should depend on temperatureas

Tmilx = é 1 " I exp(E 'MT) (5)

and a plot of In rmax against (1/7") should be a straight line of slope E'/nk. A leastsquares straight line was fitted to the data which gave a slope of 3.12i0.15. Two leastsquares straight lines were also fitted to the data, one from - 10°C to -50°Cand onefrom -55°C to -80°C. These had slopes of 3.66 and 2.15 respectively. Using theGauss criterion it was shown that the two straight lines were a better fit to the experi-mental data than just the one line. All these lines are drawn on figure 8.

332

t 30HSHEARSTRESS

20H

kg cm

0-

-70"

-20"I I I

0 2 4 6SHEAR STRAIN lo

I8

Fig. 7 — Stress-strain curves of pure ice single crystals obtained at a strain-rateof 16 x lO'^min"1, and at various temperatures.

LnTmax

2 -

1 -

o-/&/ o o

//-30 -50Ao i i

I I

-70°

I

/

0

-90

I f36 40 44 O48 52 56

103/T >

Fig. 8 — The logarithm of the yield stress plotted as a function of temperature.

In the region -55 to -80°C, the slope of 2.15 gives E'/n = 0.19 eV (4.30 kcal/mol).From the tensile creep experiment the value of n in this temperature range varieswith stress but has a mean value of 2.4. This value gives

£ ' = 0.45 ± 0.03 eV (10.3+ 0.6 kcal/mol) ( - 55 °C to -80°C) (6)

333

which agrees well with the value of 0.41 ±0.03 eV from the creep experiment. In the ran-ge - 10 °C to -50°C, the value of E'jn is 7.32 which, with n = 2.4, gives

E' = 0.79 + 0.04 eV (18 + 1 kcal/mol) (-10°C to -50°C) (7)

This is slightly higher than the value of 0.68 ±0.04 eV found in the tensile creep tests.On the other hand, it is quite possible that, on analogy with other materials, the valueof n has decreased in this higher temperature range giving £' a smaller value.

The effect of interrupting the stress-strain curve was investigated, as is shown infigure 9. This crystal was deformed at — 60 °C to the point A of the stress-strain curve

Shear Strain

Fig. 9 — The effect on the stress-strain curve of a crystal deformed at — 60 °C ofinterrupting the test for different lengths of time.

when the load was removed and immediately re-applied. This was repeated at B. At cthe load was removed and the crystal kept at — 6 °C for six weeks before being returnedto the testing machine, cooled to - 60 °C, and the load re-applied. As can be seen fromfigure 9, at A and B the load rose to the value it had before interrupting the test, whileat c it rose, after annealing, to a value a little higher than that which it had before thetest was interrupted.

After testing, the crystals were usually barrel-shaped with, at the lower temperatures,a number of cracks mostly running vertically, but occasionally there were shear crackslying in the basal plane of the crystal.

5.2 Computed Stress-strain Curves

It was decided to analyse the stress-strain curves obtained in this experimentaccording to Johnston's (1962) theory developed for LiF. This theory uses the equation

è = b N(e) K(T) (8)

334

which gives a value for the shear strain-rate È in terms of the Burgers vector b of thedislocations, the density of dislocation, N(e), and the dislocation velocity, V(r). InLiF, the dislocation density increases linearly with strain so that

N(e) = ae (9)

with a = 109 dislocations/cm2, and the dislocation velocity is given by

V = (t/D)" (10)

where D = 540 g/mm2 and n = 16.5. These two functions arc derived from etch-pitmeasurements on LiF. Johnston (1962) then shows that these three equations can becombined to give

dy(ID

where x is the resolved shear stress, y is the crosshcad displacement and C and B areconstants of the testing machine and crystal. For an initial pair of values (to, yo),which is equivalent to specifying (TO, NO), the differential equation can, in principle,be integrated to obtain the stress-strain curve that the testing machine should produceunder the same initial conditions. This is what Johnston did and he obtained goodagreement with LiF stress-strain curves.

Unfortunately, we do not know how the individual dislocations in ice respond tostress, as no suitable etchant has been discovered which will show the basal disloca-tions. Assuming equations 9 and 10 hold for ice stress-strain curves were computedfrom equation 11 and various parameters were varied until good agreement was obtainedwith experimental curves. Such a fit is shown in figure 10 in which the solid line is thecomputed curve and the open circles are experimental points for two crystals deformedat -50°C. The parameters used to fit the curve were n = 3.0, D = 1 000 kg cm"2 andNo = 5x 105 dislocations/cm2. The value of n is in reasonable agreement with the

m 3-OD lOOOk^cmN„ 5 x l O 5 cm2

o Exp. points IICHI A

Fig. 10 — A stress-strain curve computed as described in the text (solid line) com-pared with the experimental points for two crystals deformed at — 50 °C.

335

value expected-from the stress dependence of the strain-rate of the tensile creep experi-ment, equation 2 above. The number of initial mobile dislocations is much higher thanthat found by Johnston in LiF (~ 102), but may be a reasonable value for the methodused to grow the crystals. The value of D gives a dislocation velocity of 172 As"1 atthe upper yield point, dropping to 21 As"1 by the time the stress has fallen to 6 kg cm"2.

6. TESTS ON HF DOPED CRYSTALS

In the course of these experiments it was decided to investigate the effect of dopingthe crystals with hydrogen fluoride, and the preliminary results of this work have beenpublished by Jones (1967). The crystals were grown as above, but from de-ionizedwater to which had been added some hydrofluoric acid, instead of from pure water.It was found that if the water had a concentration of about 400 p.p.m. HF the icecrystals contained about 5 p.p.m. HF, as determined by melting the crystal after it hadbeen mechanically tested and analysing the melt water by a standard Alizarin-Zirconiumcolorimetric technique.

Creep curves obtained at — 70 °C for HF doped crystals are shown, compared withtwo pure crystals, in figure 11. The resolved shear stresses and HF concentrations arcmarked on the curves. From this it can be seen that for a given stress, the doping hasconsiderably increased the strain-rate of the crystals.

4-1

Î 3-

SHEAR2-

STRAIN

6-7 kg cm'5 ppm

.-2

20 40TIME hours

60

Fig. 11 — Creep curves of HF-doped ice single crystals deformed at -70°C, com-pared with pure specimens.

Figure 12 shows the results obtained in the constant strain-rate tests at — 70 °C.Here the stress required to maintain the strain-rate of 1.6 x ]0~5 min"1 has been greatlyreduced by the H F doping—in agreement with the creep results of figure 11. Similarresults have been obtained at — 60 C.

In order to show that the effect was due to the presence of HF in the crystal ratherthan to an effect associated with the growth of the crystals from an impure melt, ice

336

crystals were compressed at -70°C at a constant strain-rate for some time and thenremoved from the apparatus, immersed in dilute hydrofluoric acid for 10 min andstored in a paraffin bath at — 6°C for 24 h. They were then returned to the machineand the compression continued at the same temperature and strain-rate as initially.

Î 30-ShearStress

-2kg cm

20-

10-

3ppm

2 4 6Shear Strain L

8

Fig. 12 — Stress-strain curves obtained at — 70 "C for ice crystals doped with variousconcentrations of HF, compared with a pure ice crystal.

30-

20-

10-

Shear Strain /.

Fig. 13 — Stress-strain curves obtained at — 70 °C. The as-grown crystals were de-formed, doped with-H F by diffusion, and returned to the machine.

337

The result for two crystals is shown in figure 13 which shows that, after diffusion of HFinto the ice, the crystals required a much smaller stress to maintain the same strain-rate.The effect is not due to any annealing process during the 24 h that the crystal was at— 6 °C since a pure crystal can be held at this temperature for many days and on returnto the testing machine the stress will rise to at least the value it had before the crystalwas removed, as was shown in figure 9.

This softening has also been found at — 20 °C but at this temperature it is a lesspronounced effect. Results obtained from doping ice with NH4OH and NH4F indicatethat, at -70 °C, NH4OH has a slight hardening effect while NH4F has no observableeffect. These doped results will be published in greater detail later, together with apossible theoretical explanation.

7. DISCUSSION

7.1 The Tensile Creep Tests

The tensile creep tests have shown that ice is still plastic in the temperature range-50°Cto - 70 °C and that it deforms by basal (0001) slip in a <ll20> glide direction.There is not a temperature at which it suddenly becomes brittle. At — 90 "C, although acreep curve was not obtained, it is still possible that, using a more sensitive strain gaugeand waiting for very long times, of the order of months, creep curves would be obtainedat -90°C and lower temperatures. Between -50°C and -70°C, the ice crystalsexhibited accelerating creep with no apparent occurrence of strain hardening beforefracture. The only other workers to have done creep tests on ice at low temperaturesare Higashi, Koinuma and Mae (1965), who have conducted three point bending testsdown to - 44 °C. Their curves are characterised by a gradual increase in slope followedby a constant slope; the constant slope occurring at a strain of about 30%, much largerthan the strains observed in the present experiments. The stress dependence of theircreep curves gave n = 1.58, a value somewhat lower than that found in the presentwork. Their activation energy of 0.69 eV agrees well with the value of 0.68 eV foundin these creep tests in the range - 10°C to — 50 °C.

Readey and Kingery (1964) found from their constant strain-rate tests at varioustemperatures down to — 40 °C that « = 2.5 for low strains and that n decreased withstrain giving an average value of 2.0 for nominal strains less than 25%. This value of nis similar to that found in this work.

The time dependence of the creep curves has been found to give m = 1.4^0.2 at— 60°C. This differs from Readey and Kingery's results which implied an exponentialcreep curve. At higher temperatures, however, other workers have found " power-law"type creep curves: at -5°C Jellinck and Brill (1956) found m = 2 in tension, as didGriggs and Coles (1954) in their comprcssive creep tests. If m varies with temperatureit must decrease with decreasing temperature, since if it were to increase it would meanthat, given sufficient time, a low temperature would eventually give a faster strain-ratethan a high temperature test. So a value of m — 2 at — 5°C is not inconsistent with thevalue of 1.4 found in this work at — 60 °C.

The fact that accelerating creep is observed is explained in a manner similar to thatused to explain the same phenomenon in LiF. An initial low density of mobile disloca-tions is present in the crystal and, under stress, these move at a velocity governed by thestress. Since there are only a few of them present, they can only give rise to a smallstrain-rate as observed in the initial part of the creep curve. However, while moving, thedislocations can multiply by some such means as Koehler's (1952) double cross-slipmechanism. As more dislocations are generated, the strain-rate will increase giving riseto the accelerating creep curve. In the case of ice, cross-glide could occur by movement

338

of a screw dislocation (0001) on to either the (lOlO) or (lOTl ) planes and then back on toanother (0001) plane. Hayes and Webb (1965) have shown that there is a strong pre-ference for dislocations of pure screw orientation in the basal plane of ice crystals andhave observed slip of dislocations on both the basal (0001) plane and on pyramidalplanes, probably (lTOl).

The effect of annealing a specimen in the middle of a creep test has been shown tohave little effect but, if anything, it causes a slight hardening. In the light of the disloca-tion multiplication theory this is explained by saying that during the annealing periodthe number of mobile dislocations is reduced and so, on return to the testing machine,the strain-rate is reduced. This reduction in the number of mobile dislocations could becaused either by pinning of the dislocations by point defects, vacancies, intentitials,etc., due to the interaction between the elastic stress fields of a dislocation and a pointdefect; by the annihilation of similar dislocations ofopposite sign: or by the movementof the dislocations into relatively stable configurations, such as low angle boundaries,from which they would be difficult to move.

7.2 The Constant Strain-rate Tests

The present work used a compressive strain-rate of 1.6 x 10~5 min"1 and obtainedplastic deformation at temperatures as low as — 80 °C, with nominal stresses of about70 kg cm"2—a value which could not be approached with tensile tests without fracture.If a smaller strain-rate was to be used it is problable that plastic deformation in icesingle crystals would occur at still lower temperatures.

Unfortunately, owing to lack of time, it was not possible to conduct these tests at anumber of strain-rates and so no information regarding the value of n (equation 2)could be obtained directly from this experiment. However, assuming the value of nobtained from the creep experiment, values of the activation energy of the strain-ratewere obtained which agreed well with the activation energies obtained directly fromthe creep tests. It is reasonable to suppose, therefore, that the stress dependence of thestrain-rate would be the same in these compressive strain-rate tests as in the creep tests.This was also found by Higashi, Koinuma and Mae (1964) and 1965 who obtainedn = 1.53 from tensile constant strain-rate tests and n = 1.58 from bending creep tests.

The explanation of the large yield drop observed in the stress-strain curves is thesame as that of the accelerating creep curve; indeed, they are both the same phenomenonobserved under different experimental conditions. The initial rise in stress of the stress-strain curve corresponds to the very small initial strain-rate of the creep curve and theyield drop corresponds to the faster, accelerating part of the creep curve.

In general, no strain hardening was observed in these compressive tests. This mustbe because the density of dislocations had not increased to the point where the inter-action between dislocations became more important than their multiplication.

The computed curves of section 5.2 were based on Johnston's (1962) calculationsfor lithium fluoride and involved a number of assumptions which may or may not betrue for ice. The exact form of the dependence of the density of dislocations on strainand the dependence of dislocation velocity on stress are unknown for ice and are likelyto remain so until a suitable etchant is discovered that will reveal the basal dislocationsin ice or until the X-ray topographical method of Hayes and Webb (1965) is used.Assuming that equations 9 and 10 do hold for ice, the number of initial mobile dislo-cations needed to make the computed curve fit the experimental data was 5 x 105 cm"2.This is large compared to well annealed LiF, although smaller than typical metals,~ 107 — 108cm~2, and is not unreasonable considering the method used to grow thecrystals. Ice grown by another method, for example Czochralski's method, whichwould avoid the pressure build up on freezing, would probably have fewer initialdislocations and therefore would show a larger yield stress and yield drop. Higashi,

339

Koinuma and Mac (1964) found an etch pit density of non-basal dislocations of-— 105

cm"2 in their natural, glacier ice single crystals. The basal dislocation density, providedthe ice had not been recently deformed, was probably of the same order of magnitudeand this fact lends support to the computed value.

The dislocation velocities derived from the computed curves were of the order of50 As"1. These are very small velocities, which is not altogether surprising since accel-erating creep was still present after many days at — 70 CC.

A possible reason for. this slow dislocation velocity is given by Glen (1968) andthis, together with full details of the doped ice results and their interpretation, will bediscussed in a later paper.

8. ACKNOWLEDGEMENTS

We should like to express our thanks to the Royal Society for the provision of thecold laboratory used in the preparation and handling of specimens, and to the ScienceResearch Council for the research studentship held by one of us (S.J.J.).

REFERENCES

(*) GLEN, J.W., (1968): The effect of hydrogen disorder on dislocation movementand plastic deformation of ice. Physik der Kondensierten Materie, Bd. 7, pp. 43-51.See also paper by J.W. Glen in this conference.

(2) GLEN, J.W. and JONES, S.J., (1967): The deformation of ice single crystals at lowtemperatures. Proc. Int. Conf Low Temperature Science, Sapporo 1966, Vol. 1,Pt. 1, pp. 267-75.

(3) GRIGOS, D.T. and COLES, N.E., (1954): Creep of single crystals of ice. S.I. P. R.E.Report 11.

(4) HAYES, C.E. and WEBB, W.W., (1965): Dislocations in ice. Science, Vol. 147,pp. 44-45.

(5) HIGASHI, A., KOINUMA, S. and MAE, S., ( 1964): Plastic yielding in ice single crystals.Jap. J. Appl. Phys., Vol. 3, No. 10, pp. 610-6.

(6) HIGASHI, A., KOINUMA, S and MAE, S (1965): Bending creep of ice single crystals.Jap. J. Appl. Phys., Vol. 4, No 8, pp. 575-82.

(7) JOHNSTON, W.G., (1962): Yield points and delay times in single crystals. / . Appl.Phys., Vol. 33, pp. 2716-30.

(s) JONES, S.J., (1967): Softening of ice crystals by dissolved fluoride ions. PhysicsLetters, Vol. 25A, No. 5, pp. 366-67.

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(10) READEY, D.W. and KINGERY, W.D., (1964): Plastic deformation of single crystalsof ice. Ada Metall., Vol. 12, pp. 171-8.

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DISCUSSION

C.JACCARD

How did you determine the concentration of the doping agents, and when?

S.J. JONES

The concentration of the doping agents was determined by a colormetric method onthe melted ice crystal after the mechanical test had been conducted.

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