The experimental deformation of dunite

Tectonophysics,

Elsevier

78 (1981)

Scientific

Publishing

THE EXPERIMENTAL

P.N. CHOPRA

Company,

Amsterdam

DEFORMATION

- Printed

in The Netherlands

OF DUNITE

and M.S. PATERSON

Research School (Australia)

(Received

453

453-473

January

of Earth Sciences,

Australian

National

University,

Canberra

A.C.T.

2600

26,198l)

ABSTRACT Chopra, P.N. and Paterson, M.S., 1981. The experimental Lister, H.-J. Behr, K. Weber and H.J. Zwart (Editors), Rocks. Tectonophysics, 78: 453-473.

deformation The Effect

of dunite. In: G.S. of Deformation on

Deformation experiments have been carried out on two dunites (Anita Bay, of 100 pm grain size, and aheim, of 900 pm grain size) at strain rates from 10e3 to 10m6 s-l and temperatures from 1OOO’C to 13OO’C in a gas-medium deformation apparatus at 300 MPa defined by the presconfining pressure. Most of the tests were under “wet” conditions ence of small amounts of water from hydrous minerals initially present. Constant strain rate and relaxation experiments, covering ranges of flow stress down to about 70 MPa and 7 MPa, respectively, show that there is a change in flow law in going below about 100 MPa differential stress, and that the coarser-grained rock is stronger than the finer-grained one. Power law parameters above the transition are n = 4.48 f 0.31 and Q = 498 It 38 kJ mol-’ for Aheim dunite and n = 3.35 * 0.17 and Q = 444 + 24 kJ mol-’ for Anita Bay dunite, while below the transition relaxation tests on Anita Bay dunite give n = 2.44 xk 0.18 and Q = 386 * 27 kJ mol-‘. It is concluded that there is a weakening effect of water, that this effect is mainly in the grain boundaries and that grain boundary sliding is probably a significant deformation mechanism at the lower stresses under wet conditions.

INTRODUCTION

The general acceptance in recent years that olivine is the dominant mineral in the upper mantle has led to a strong interest in its flow properties, both in single crystal and polycrystalline form. As a result there have been a number of experimental studies in this field. On the one hand, there are experiments at high pressure on dunite and peridotite by Carter and Ave Lallemant (1970), Raleigh and Kirby (1970), Blacic (1972), Kirby and Raleigh (1973), Post (1977) and Ross et al. (1979), and on single crystals of olivine by Phakey et al. (1972). On the other hand, there have been a number of studies on single crystals of olivine at atmospheric pressure (Kohlstedt and Goetze, 1974; Durham and Goetze, 1977a, b; Durham et al., 1977, 1979; Jaoul et al., 1980; Kohlstedt and Hornack, 1981; Darot and Gueguen, 1981; Poumel-

0040-1951/81/0000-0000/$02.50

@ 1981 Elsevier Scientific

Publishing

Company

let et al., 1981). Creep observations on polycrystalline specimens at atmospheric pressure have also been published by Murrell and Chakravarty (1973) and by Berckhemer et al. (1979). However, there are a number of limitations inherent in these studies, as follows: (1) The high-pressure studies have been carried out in solid medium apparatus at temperatures not exceeding 1300°C. They therefore only cover a regime of relatively high flow stress, above about 100 MPa (1 kbar). They are also subject to limitations in accuracy due to the corrections for friction and the finite strength of the pressure medium and to the existence of substantial temperature gradients in the specimens (a revision of the results of Carter and A& Lallemant in the light of further consideration of some of these factors is given by Carter, 1976). The stress range covered is therefore considerably above the range l-10 MPa (10-100 bar) often estimated for upper mantle flow (e.g. Goetze, 1978). Since it is known that the flow law can change at lower stresses in other materials (for example in marble and limestone: Schmid et al., 1977, 1980), extrapolation of the high-stress results to geological conditions cannot be done confidently without further justification from lower stress studies. (2) The single crystal studies at atmospheric pressure are free from the above limitations and are better controlled with respect to oxygen fugacity and temperature uniformity, and they afford the opportunity of reaching low flow stresses through the use of temperatures up to 1600°C. There is, however, a serious question as to how far these single crystal results are applicable to polycrystalline material, firstly because of the requirements of multiple slip for intergranular compatibility in polycrystals, and secondly because of possible contributions to the strain from the relative movement of grains. (3) Attempts to determine the creep properties of polycrystalline specimens at atmospheric pressure are subject to uncertainties about the role of cracking on the scale of the grains. From the foregoing it is clear that further observations on polycrystalline specimens deformed under a confining pressure are still required, with an emphasis on the achievement of lower stress levels than hereto available. Such is the aim of the present work using a gas-medium deformation apparatus equipped with an internal load cell which eliminates inaccuracies associated with friction and provides a high sensitivity in load measurement (< 1 MPa). EXPERIMENTAL

The deformation apparatus is basically the same as described earlier by Paterson (1970). It uses argon gas as the confining medium and is fitted with an internal furnace and an internal load cell. However, the furnace has been redesigned to reduce convective heat losses and can now reach temperatures of at least 1450°C. It has been found that both the jacketing of the specimens and the choice

455

of material for the loading pistons present severe problems at temperatures above 1000°C. Considerable development has therefore been needed in this connection. Initially an attempt was made to adapt the previously used arrangement of push-fitted sealing rings located in the high-temperature zone (Paterson, 1970) by using sintered aluminium-oxide pistons and rings of various designs. With the aid of a special device for circumferentially loading the rings while pushing them on, in order to reduce the circumferential tensile stress induced in them, and with careful polishing of the mating surfaces of both jacket and piston, successful jacket sealing was achieved in a number of runs, as judged by the absence of gas leakage up the hollow loading piston, the absence of brittle shear failures in the specimens and a general consistency in results. However, the degree of reliability was very unsatisfactory. Therefore, in the latter part of the study a new method of jacketing was adopted in which the seal was made with O-rings at low temperature outside the fur-

-O-ring

O-ring

Fig. 1. Methods of jacketing and mounting specimens. The earlier procedure on the left has been used with nickel and copper jackets and the other with iron jackets.

456

nace itself. This procedure requires the fabrication of a special longer jacket of stepped diameter which covers both the specimen and the larger diameter pistons (Fig. 1). At the same time a change was made from nickel to iron for the jacket material because of the higher melting point of iron and some difficulties experienced with embrittlement of the nickel. All experiments have been done in compression at 300 MPa confining pressure. The specimens were mostly 10 mm in diameter and 20 mm long (in a few high-stress experiments 7 mm diameter specimens were used). Aluminium oxide spacers of 4 mm thickness with an axial hole of 0.8 mm diameter were inserted between the specimen and the piston, with a platinum foil of 0.2 mm thickness separating the specimen from the aluminium oxide to avoid reaction. A sheathed Pt-Pt/l3% Rh thermocouple was introduced through a hollow in the piston to measure the temperature near the end face of the specimen. The temperature gradient in the specimen was controlled by periodic calibrations in which the temperature profile was measured over the length of a hollow, dummy, aluminium oxide specimen and related to the temperature gradient in the piston adjacent to the specimen; the latter could be adjusted during each run by proportioning the power to the two furnace zones. The temperature gradient over the length of the specimen is less than 10°C in most cases. The use of a hollow piston for thermocouple access also provides that the centre of one end of the specimen is directly vented to atmosphere. The differential stresses have been calculated using a cross-sectional area calculated on the assumption that the specimen deforms with constant volume as a right circular cylinder. The load borne by the jacket has not been corrected for since it is equivalent to only about 1 MPa in flow stress on the specimen at lob4 s-’ strain rate in the most extreme case of 1300°C. Uncertainty in load calibration is less than 5% and therefore negligible in comparison with the effects of specimen variability. SPECIMEN

MATERIAL

AND

CHEMICAL

CONDITIONS

Two dunites have been studied, one from Anita Bay, New Zealand, and one from Aheim, Norway. Electron microprobe analyses are given in Table I, each analysis representing an average for 12 olivine grains. Anita Bay dunite (olivine 94%, pyroxenes 5%, chromite 1%) has an average olivine grainsize of about 100 pm but some olivine porphyroclasts of size up to several millimeters occur randomly; it is compositionally layered and foliated and has a lineation defined by trace chromite in the foliation (grain size has been measured by a method of linear intercepts and corrected for sectioning effects by using a multiplying factor of 1.5; Exner, 1972). Aheim dunite (olivine 96%, pyroxenes 2%, secondary alteration products 2%, spinels
451 TABLE I Chemical analyses Anita Bay dunite

heim

SiOz Fe0 NiO MnO MgO

41.31 7.11 0.18 51.47

41.31 6.92 0.17 0.03 51.68

Total

100.07

100.11

92.8

93.0

MUI%

+ Fe)

dunite

case and oven dried at 110°C before testing. Both rocks contain traces of layer silicate minerals which dehydrate during the test so that water is present during the deformation. The amount of water can be quite substantial, as indicated by the observation of 0.6% weight loss during the high-temperature drying of the specimen of Aheim dunite considered later. Some of the water is evidently lost through the ends of the specimens during the test since condensate is observed within the bore of the non-vented lower piston (Fig. l), but the permeability is evidently low enough to retain part of the water within the jacketed specimen since the deformed specimens show an amount of infrared absorbance in the 3 pm region that would correspond to the presence of about 0.1 weight percent of water (using the calibration discussed by Paterson, 1981). The effective oxygen fugacity in the experiments is determined by the intrinsic oxygen fugacity of the specimen itself and the presence of the nickel or iron jacket. The intrinsic oxygen fugacities for the two rocks concerned are not known individually but it is known that for similar rocks of upper mantle origin the intrinsic oxygen fugacities are relatively low in the olivine stability field, generally in the neighbourhood of the iron-wustite buffer line (Nitsan, 1974; Sato, 1978; Arculus and Delano, 1981). In the present experiments with iron jackets, if the intrinsic oxygen fugacity of the dunite is below the iron-wustite line, the oxygen fugacity prevailing in the experiments can be expected to remain at this point in the presence of the iron unless the latter has a substantial coating of oxide. If the intrinsic oxygen fugacity is somewhat above the iron-wustite line, however, the oxygen fugacity in the experiments is likely to decrease towards it with the formation of oxide on the inside of the jacket. Visual examination did not reveal any obvious oxidation on the inside of the iron jackets, although this may not be a very sensitive indicator for change in the olivine. In either case, the oxygen fugacity in the experiments with iron jackets is likely to be close to that thought to be characteristic of lower crust or upper mantle conditions. The same conclusion applies in the case of nickel jackets. The Ni-NiO equilibrium

458

oxygen fugacity line is higher than the iron-wustite line and probably therefore higher than the intrinsic oxygen fugacity of the rocks. The specimens are therefore likely to be always effectively self-buffered in the presence of the nickel since the jackets were pre-polished on the inside and the amount of NiO available for oxidation of the olivine would be very small. Extensive oxidation of olivine would be revealed optically by a red-brown discolouration and might be expected adjacent to the vent hole at the top end face of the specimen where there is exposure to the atmosphere (Fig. 1). However, no discolouration at this point has been observed except in the single experiment using a copper jacket (4409) in which a red-brown region about 1 mm diameter and 0.3 mm deep appeared.

RHEOLOGICAL

RESULTS

Tables II and III list the experiments. Most were carried out at constant strain rate over the range of conditions from 1000°C to 1300°C and 10e3 to 10m6 s-i strain rate. Typical stress-strain curves are shown in Figs. 2 and 3, plotting differential stress versus shortening strain. A constant flow stress is in general reached after 5-10s strain (or 2% strain in creep) and so the final flow stresses listed in the tables can be taken as approximating rheologically steady state values. It should be emphasized that except for 4392 the results refer to specimens that are in the as-received state apart from oven-drying at 110°C. Since, as discussed earlier, the water of decomposition of hydrous phases is still present to some degree during the deformation, these results will be referred to as being for “wet” conditions. Logarithmic plots of the final flow stresses against the strain rates are shown in Figs. 4 and 5. Where the data at one temperature cover a range sufficient to define a trend (mainly at 1200°C) it is seen that there is for each rock an approximately linear relationship between log flow stress and log strain rate, that is, a power relationship between flow stress and strain rate. However, the lowest final flow stresses in the constant strain rate experiments are all still above 60 MPa, and experimental difficulties and limitations in operator endurance make it impracticable at this time to carry out constant strain rate experiments at lower strength levels. In order to explore the rheological behaviour at lower stresses, stress relaxation tests have therefore been carried out on the Anita Bay dunite at the end of some of the constant strain rate experiments. In these tests, the straining motor is turned off at the end of the constant strain rate run and the external load on the piston is reduced slightly and maintained at a level such that the loading piston is locked by friction where it enters the pressure vessel, ensuring that only the loading assembly inside the pressure vessel takes part in the relaxation. The load is then recorded as a function of time. Using the known elasticity of the loading assembly, the strain rate can be

II

1300 1300

1200 1200 1200 1200 1200 1200 I 1200 1215 1200 1195

1100 1100 1100 i 1100 1100 1110 1095

x x x x

1O-4 10-4 10-s 10-s

x x x x x x x x x x

10-a 10-a 10-4 10-4 10-s 10-s lo-” 10-S 10-6 10-6

1.15 x 10-4 1.15 x 10-s

1.11 1.10 1.13 1.12 5.03 1.12 1.45 1.04 4.5 1.13

1.11 x 10-s 0.96 x lo-’ 1.15 x 10-6

0.87 0.99 1.09 1.07

15.4 16.7

16.3 14.0 14.7 11.7 14.8 6.5 8.6 9.2 8.9 11.5

13.6 4.3 8.7

11.6 10.2 10.0 16.4

11.2 6.5 7.0

(%)

(s-l )

1.10 x 10-s 0.75 x 10-s 0.60 x lo-’

Final strain ’

where indicated)

Strain rate

strain rate except

* Includes elastic strain. 2 Indicates that a relaxation test was done at the end of the constant strain rate test. 3 Indicates that a steady state flow stress was not achieved in the test.

Ni Ni

’ 2

4306 4299

Fe Fe Ni Fe Fe Ni

Fe Ni Ni

Ni Fe Ni

Ni Fe Ni

2

2 2

’

2 2

4265 4419 4272

4434 4438 4307 4371 4417 4141

4372 4262 4271

4313 4374 4201

1000 1000 1000

cu cu cu

4409 2706 2711

2

(“C)

Temperature

(constant

Jacket

on Anita Bay dunite

Run number

Experiments

TABLE

118 65

445 3 395 3 212 211 142 99 106’ 88 69 63

376 513 3 259 260 ’ 246 204 146 3

501 3 508 492

(MPa)

Final flow stress

Creep test

Interrupted at 6.5% for relaxation test

Interrupted at 10% for relaxation test

Test by I. van der Molen Test by I. van der Moien

Remarks

III

2

2

4392

x x x x x x x x x x x x

x x x x x x x 1O-3 10-4 1O-4 10-4 lo-’ 10-s lo+ 10-s 10-s 10-s 10-4 10-6

10-4 10-4 10-4 10-4 10-s lO+ lo-’

14.5

9.6 -12

13.2 5.3 13.5 10.3 7.9 8.6 16.7 16.0 19.7

8.3 11.8 5.4 8.5 9.5 9.0 8.7

4.9 12.7

(%I

Final strain

’

’ Includes elastic strain. 2 Indicates that a relaxation test was done at the end of the constant strain rate test. 3 Indicates that a steady state flow stress was not achieved in the test.

Fe Fe

Fe Fe Fe Fe Fe Fe Fe Ni

4436 4398 4378 4370 4390 4395 4380 4267

4396

1.18 1.30 1.16 1.12 1.25 1.13 1.16 0.86 1.12 1.11 1.34 1.09

1200 1200 1200 1200 1200 1200 1210 1200 1200 1200 1190 1190

Ni Fe Fe

4275 4401 4439

2

1.07 1.05 1.10 1.10 1.79 1.42 1.42

1100 1100 1100 ’ 1085 1100 1100 1100

Fe Fe Fe

.

where indicated)

1.01 x 10-s 0.96 x lo-’

(s-l 1

4403 4440 4381

(“C)

Strain rate

strain rate except

Temperature

(constant

1000 1000

Dunite

Fe Fe

Jacket

on Aheim

4391 4402

Run number

Experiments

TABLE

479 268 301 300 207 189 144 3 172 174 294 3 360 112 I

652 3 511 566 3 707 318 331 403

735 740

W’a)

stress

flow

Final

Interrupted at 16% for relaxation test Furnace dried (see text) Strained at 10d4 s-’ to approx. 12%’

Creep test

Creep test

Remarks

0

g

461

I

0

Anita

Bay

strain

4

2

Dunite 16’

6

6 Strain

rate

Se’

10

percent

Fig. 2. Typical stress-strain curves for Anita Bay dunite at lo-’ the influence of temperature. Wet conditions (see text).

4275

him

4265

llOO°C

Anita

Say

strain rate

105 s-’

12OO’C

5

10 Strain

s-l strain rate, showing

15

percent

Fig. 3. Comparison of stress-strain curves of Anita Bay dunite and Aheim dunite s-l strain rate, at 1lOO’C and 12OO’C. Wet conditions.

at

10m5

462 ANITA

BAY

DUNITE

7Oc-

.

500“0

400I?? = 300-

;:

.

t ; 200x E

.

f = 6 loo-

A = 9550

s-‘Mf$ -1

0 =444

70

KJmol

n = 3.35 -\ I -3

I

I 10-4

10

Strain

s-l

d

Id5

Rate

Fig. 4. Plot of final flow stress versus strain rate at various temperatures for Anita Bay dunite. Wet conditions. The open symbols represent stepping tests, In three cases the flow stresses have been adjusted to correspond to the nearest hundred-degree temperature using the value of Q shown.

calculated ship : de dt=-idt

at any value of flow stress during the relaxation

IL*

(h, + h,)

hIElM

DUNITE

700

y

.

.

‘*ooo c

_?oO _ ooc

-2.8

-.-

“000c

. .

400d = 300-

.

.

- 2.6 -

.’

m

.

I ?! -2.4

B g, ?I 200-

z s F

+, -.

.

Yi z e 2 z 0 loo-

I

I

I

500-

using the relation-

-2.2

g 0

A=420

.w

&'a-"

-2.0

$ 2

0 = 498 KJmol-’ n = 4.48

70-

I

-1.8

I

-3 10

I

I

I

I

-4 10 Strain

-5 10 Rate

I

1

-6 10

6’

Fig. 5. Plot of final flow stress versus strain rate at various temperatures for aheim dunite. Wet conditions. Other details as for Fig. 4.

463

ANITA

BAY

DUNITE

- RELAXATIONS

7QOL soo-

.

;_,oc ‘70 0 .a*.

‘-.,o‘Do

.

0 - 2.6

l*

:

70-

f m

50-

I 5

30-

A = 7600

20-

Q= 386

t

z’ ii

.

0

z B

s’ MP;” KJmol-’

4

n =2.44 lo7-

I

I

I

-4 10

-5 10 Strain

-6 10 Rate

-7 10

S’

Fig. 6. Plot of flow stress versus strain rate during relaxation tests for Anita Bay dunite. Wet conditions.

where de/dt is the strain rate, dL/dt the rate of change of load, k, and k, are the spring constants for the loading assembly and the specimen (k, = l/AE where 1 is the length, A the cross sectional area and E the Young’s modulus of the specimen). The results for six specimens at various temperatures are

4392

pre-dried

at 1000~c

aheim strain

”

0 0

”

”

“1

1 10

5 Strain

’

Unite rate

“1

12DO°C 65k

1 15

percent

Fig. 7. Stress-strain curve for keim dunite after drying at 1OOO’C (see text) compared with the behaviour under wet conditions.

shown in Fig. 6. The scatter reflects errors in the reading of values for the slope dL/dt (especially at the lower strain rates) together with the effects of small fluctuations in temperature and pressure during the relaxation. The amount of permanent strain introduced into the specimen during the relaxation test is approximately one percent. Finally, a constant strain rate experiment (4392) was carried out on an Aheim dunite specimen that was first dried at 1000°C in a 92% C02, 8% CO gas atmosphere for 22 hours at an oxygen fugacity of 10T7 Pa (lo-” atmospheres) within the olivine stability field (Nitsan, 1974). The resulting stressstrain curve is shown in Fig. 7, together with a result for the standard wet conditions described earlier. OPTICAL

MICROSTRUCTURE

The optical microstructures of the Anita Bay dunite and Aheim dunite starting materials are shown in Figs. 8a and b. .These microstructures are extensively modified by the experimentally imposed deformations. In Anita Bay dunite deformed at 1000°C and a strain rate of lo-’ s-l, kinks, deformation bands and deformation lamellae are the main optical features observed. As the temperature of the deformation is increased at this strain rate, deformation lamellae cease to be observed, and the kinks and deformation bands become less prevalent; the deformation bands that do

Fig. 8. a. Initial optical microstructure optical microstructure of aheim dunite.

of Anita Bay dunite. Scale bar 100 pm.

Scale

bar 50 pm.

b.

Initial

465

Fig. 9. Optical microstructures of deformed specimens. The maximum compressive stress was aligned north-south in each case. a. Anita Bay dunite Run 4201 at llOO’C, lo-’ s-r, 16.2% strain. Wet conditions (see text). Scale bar 50 pm. b. Anita Bay dunite Run 4306 at 1300°C, lo-’ s-l, 15.4% strain. Wet conditions. Scale bar 50 pm. c. aheim dunite Run 4267 at 1200°C, 10m5 s-l, 19.7% strain. Wet conditions. Scale bar 50 pm. d. aheim dunite Run 4392 at 1200°C, lo-’ s9.6% strain. Dry conditions (see text). Scale bar 100 pm.

r,

366

appear become progressively wider and their boundaries more diffuse. At 1000°C and 1100°C the strain is clearly reflected in a strong flattening of the olivine grains, while the grain boundaries take on a serrate appearance indicative of the initial stages of grain boundary mobility (Fig. 9a). At higher temperatures and/or lower strain rates, most grains exhibit only a general undulatory extinction and some subgrain development. The grain boundaries now show signs of greatly increased mobility and act as sites for recrystallization. Such a microstructure is shown in Fig. 9b from experiment 4306 at 13OO”C, lo-’ s-l. Even though the final strain achieved in this specimen is of the same order as that in Fig. 9a, there is no obvious grain flattening; indeed the grain morphology is essentially similar to that of the starting material. The same progression in microstructural features is found in the Aheim dunite over the experimental range of conditions, when it is deformed wet, with kinks, deformation bands and deformation lamellae giving way to undulatory extinction, subgrain development and recrystallization along grain boundaries at the higher temperatures and slower strain rates (Fig. 9c). The recrystallization observed in this rock seems to be promoted by proximity to dehydrating layer silicate minerals which is probably a reflection of enhanced diffusion of the olivine’s constituent chemical species in a waterrich fluid phase. Recrystallization in this rock at 1200°C seems to be more common than in wet Anita Bay dunite, although the difficulty of positively identifying recrystallization in the latter may be a factor. The predried Aheim dunite specimen from experiment 4392 deformed at 1200°C and lo-’ s-’ shows the same type of optical microstructure within the grains as wet specimens deformed at similar stresses (i.e. experiments at 12OO”C, 10m4 s-l and llOO”C, lo-’ s-l). The main features observed, kinks, deformation bands and undulatory extinction, are shown in Fig. 9d. The principal effect of the predrying treatment has been to repress the recrystallization along the grain boundaries in the deforming rock; the other microstructural differences between wet and dry specimens deformed at the same temperature and strain rate can probably be ascribed purely to the higher stress level prevailing in the latter. DISCUSSION

Analysis of results

The two dunites show distinctly different rheological behaviour, the finergrained Anita Bay dunite being weaker than the Aheim material at all strain rates and temperatures over the range investigated. In each case, the dependence of the final or steady state flow stress on strain rate and temperature in the constant strain rate tests can be described satisfactorily, within the limits set by scatter, by an empirical flow law of the power law form: 6 = Au” exp(-Q/RT)

(1)

461

where & is the strain rate, u the differential stress, T the absolute temperature, R the gas constant, and A, rz, Q are adjustable constants. The best fits to this expression by multilinear regression analysis are represented by the straight lines in Figs. 4 and 5. It is seen that the higher strength of the Aheim dunite is associated with higher values of both the stress exponent n and the apparent activation energy Q. The relaxation data for Anita Bay dunite cannot be adequately represented over the whole range by a single power law. To demonstrate this, a selective fit to part of the data shown in Fig. 6 has been made and is represented by the straight lines. In making this fit, the parameters of which are given in Table IV, the slope has been constrained by the 1300°C points, while the spacing of the isotherms was determined by taking into account only the lower stress data at the other temperatures which give a similar slope. When the other data that are obviously discordant to the slope of the fit in Fig. 6 are independently fitted by expression (l), they give the following parameters: log,4 = 3.6 f. 0.4 s-l MPa-“, IZ= 3.11 f 0.25 and Q = 417 + 27 kJ mol-‘, values which conform within the 95% confidence limits to the constant strain rate values. Taking the latter observation to indicate that the relaxation data give a reliable guide to the nature of the steady-state behaviour, it therefore appears that there is a change in stress exponent in passing from flow stresses above about 100 MPa to lower values. Preliminary relaxation experiments on Aheim dunite show a similar effect. The value of 386 kJ mol-’ for the apparent activation energy in the low IZ regime explored by the relaxation tests may be an overestimate since the 1200°C data points tend to fall below the fitted line in Fig. 6. Thus there seems also to be a decrease in apparent activation energy in going from flow stresses above 100 MPa to lower stresses in the relaxation experiments. Such a trend is possibly also evident in the constant strain rate experiments since the two low stress points available at 1300” fall somewhat above the fitted line in Fig. 4, but more experiments would be needed to confirm that this was not just a result of scatter.

TABLE IV Power law parameters

log, o-4

n

(s-l MPa-“) aheim dunite, constant 6 Anita Bay dunite, constant =$ (a > -100 MPa) Anita Bay dunite, relaxation (u < -100 MPa)

mole1 )

2.62 + 0.18

4.48 f 0.31

498 f 38

3.98 * 0.17

3.35 f 0.17

444 + 24

3.88 + 0.43

2.44 f 0.18

386 + 27

Note: The errors given are at the 95% confidence level (two standard deviations).

468

Comparison

with previous

work

In view of the difference in strength between the Aheim and Anita Bay dunites, it is of interest to make a comparison with the flow stress levels observed in previous work on dunites and on single crystals of olivine. For this purpose, the lines that best describe the trends in the present data in Figs. 4, 5 and 6 for 1100°C to 1300°C are reproduced in Fig. 10. Additional flow stress values for more or less comparable rheological steady-state conditions from other work are indicated by the various symbols. These data may be considered in three categories: (1) Mt. Burnet dunite (grain size about 1 mm) has been studied by Carter and Ave Lallemant (1970) and Post (1977) in solid-medium apparatus under “wet” conditions provided by the water of decomposition of the surrounding talc pressure-medium and by any water from hydrous alteration minerals within the dunite itself. Average data points for constant strain rate tests taken from the plot of results given by Carter and Ave Lallemant are reproduced in Fig. 10; their results for 1100°C agree fairly well with those of Post for the same temperature. It is seen that these flow stresses correspond in level to those of the finer-grained Anita Bay dunite and fall below the results for the Aheim dunite of nearly equal grain size; moreover, if allowance is made for the marked barrelling, the Mt. Burnet values would be moved downward and to the left in the plot (Carter, 1976, reassesses their results to allow for this effect but does not give the actual revised data). (2) The flow strengths at 1200°C and atmospheric pressure of single crystals of olivine of two orientations favourable to slip have been reported by Durham and Goetze (1977a, fig. 5) and are represented in Fig. 10 by the triangular symbols. Crystals of the softest orientation, [ 1101 E, are seen to have a strength between that of the Anita Bay and Aheim trends while those of the [Oil], orientation are stronger than both rocks. Since single crystals of other orientations are known to be still stronger, the strength of a polycrystal made up of grains of many orientations can be expected to be substantially above the single crystal points shown. As the single crystal experiments were done under dry conditions, these results suggest that the strength of dry polycrystalline olivine must be substantially higher than the strength observed here for wet Aheim dunite. This conclusion is consistent with the present observation on furnace-dried Aheim (Fig. 7), also indicated in Fig. 10, and with earlier observations by Carter and AvQ Lallemant (1970), Kirby and Raleigh (1973) and Post (1977) on Mt. Bumet dunite. (3) The flow properties of another dunite from the aheim district, of finer grain size than the one studied here, have been measured at atmospheric pressure by Berckhemer and co-workers (results given at the present conference). The creep rate which they observe at 1200°C and 30 MPa stress falls approximately on the Anita Bay 1200°C relaxation line. However, the probable loss of water from the unjacketed specimens would have led one to expect, from the discussion in the previous paragraph, a flow stress of perhaps

469

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700-

- 2.6

200- 2.2

-

t -1.6 ’ 1

1

g

ii t - 1.4 5 20-

_

10-

-

4 1.0

75

I lO+

I

I lo-4

I

I -5 10 Strain Rate

1

I -6 10

1

.

0.6

lo-7

P

Fig. 10. Comparison with results of previous workers. Solid lines represent the present results under wet conditions, taken from Figs. 4-6. The cross represents the final flow stress for Aheim dunite pre-dried at 1OOO’C (from Fig. 7), the circles represent average data points for constant strain rate tests under wet conditions on Mt. Burnet dunite as given by Carter and Avb Lallemant (1970), and the triangles represent average data points for olivine single crystals of the orientations shown, as given by Durham and Goetze (1977a). In each case the test temperature is shown.

an order of magnitude higher than is reported. While there may be some effects attributable to the finer grain size and the higher oxygen fugacity in the argon atmosphere used, and some water may be retained in the rock (see observations at slightly lower temperatures by Murrell and Chakravarty, 1973) it is also possible that this relatively low strength reflects the occurrence of microcracking in the absence of a confining pressure. Mechanistic aspects From the present results and from the discussion in the previous section it is evident that the dunites are weaker under wet conditions than in the absence of water; this effect has, of course, been reported previously (Carter and Ave Lallemant, 1970; Blacic, 1972; Post, 1977) but there have been possible complicating factors in the solid medium experiments (Paterson, 1979). The present results also show that under the same conditions the finer-grained

470

Anita Bay dunite is weaker than the Aheim dunite indicating that the water weakening effect is more prominent when grain boundaries are more abundant. The olivine grains themselves are of very similar composition in the two rocks (Table I), so, unless there are some subtle differences affecting the strengths, it would appear that the water weakening is to be associated primarily with the grain boundaries and not with hydrolytic weakening within the grains. This conclusion is strongly supported by the observation that the microstructures within the deformed grains in the .&heim dunite are very similar under wet and pre-dried conditions if comparison is made at the same flow stress level. The weakening effect is more marked at lower strain rates, as indicated by the lower stress exponent n in the Anita Bay dunite, and is associated with a lower apparent activation energy Q. Thus, although changes in grain shape show that over much of the range of conditions explored in the constant strain rate experiments the main part of the strain is achieved by slip within the grains, accommodation processes at grain boundaries apparently have an important influence on the strength of the rock in the presence of water and lead to the lower values of IZand Q. The amount of water present, of the order of 0.1 weight percent, is probably much greater than could be accommodated in solid solution in the grains under the present conditions (the solubility of water in quartz is less than 0.01 weight percent under comparable conditions, Kekulawala et al., 1981). The water is therefore likely to form a fluid phase at the grain boundaries. This would result in a loss of grain boundary cohesion and introduce the possibility of enhanced diffusion along the grain boundaries, thereby facilitating a certain amount of grain boundary sliding. The latter could be expected to be especially effective in lowering the flow stress in polycrystalline olivine because of the problem of inter-granular strain compatibility associated with the relatively small number of slip systems in olivine vis a vis the von Mises criterion (Groves and Kelly, 1963; Paterson, 1969). The observation that the values of Q in wet dunite can be lower than in single crystal experiments (Durham and Goetze, 1977a) points to different controlling factors in the two cases. This in itself does not necessarily mean that the main control may not be still within the grains of the dunite, perhaps associated with intergranular compatibility requirements not seen in the single crystal experiments. However, it seems more likely that the low values of Q reflect an influence of diffusion in water-rich grain boundary films. The actual value of Q may well represent a combination of factors, including a change in the volume of the grain boundary film with temperature. The lower value of n may also be explained by a characteristically higher strain rate sensitivity of diffusion-dominated grain boundary sliding processes, approaching more nearly the Newtonian sensitivity of diffusion-controlled viscosity in fluids, but again the actual value may represent a combination of influences. Seen in this context, the close correspondence between the value of Q for the relaxation experiments on Anita Bay dunite and that for self-diffusion of 8i in forsterite (Poumellec et al., 1981) may be a chance coincidence.

471

The change in deformation structures within the grains from sharply defined deformation bands to a more general undulatory extinction on going to lower flow stresses suggests a change in the relative resistance to various deformation mechanisms within the grains, probably involving an increasing role for dislocation climb. This progression eventually leads to some recrystallization at grain boundaries, and in the finer-grained dunite at the higher temperatures and lowest strain rates it is striking that the grain shape no longer reflects the total strain. The latter effect probably represents a transition to relative grain movement as a major mechanism of deformation, reflected in the lower values of it in the relaxation experiments at the lower stresses (cf. Schmid et al., 1977). At the upper limit of stress, the occurrence of some microcracking has to be borne in mind where the value of the flow stress substantially exceeds that of the confining pressure (cf. experience in marble, Edmond and Paterson, 1972). In this case, the flow stresses at the highest levels in Figs. 4 and 5 might be found to be a little higher at confining pressures sufficient to suppress all cracking. Microcracking during deformation has been recognized by Boland and Hobbs (1973) in a peridotite deformed at lower temperatures, using detailed transmission electron microscopy; such a study has not been undertaken on the present specimens but axial microcracks have been observed optically in a specimen at 1000°C. Geophysical

implications

Direct extrapolation of the present results to predict the flow behaviour of dunite under geophysical conditions would be premature at this stage, for several reasons. Firstly, since the presence of water and presumably its quantity influence the flow law, this dependence needs to be further quantified and the water contents in the natural situations decided (in fact, the water content of around 0.1% in the present specimens may be fairly representative of the upper mantle: Ring-wood, 1975, p. 150). Secondly, the grain size has now been established as another important variable that needs similar study. Finally, even for a given water content, grain size and oxygen fugacity there are changes in the flow law (at least if expressed as a power law) in passing from one regime of flow stress and strain rate to another. This is presumably due to changes in the mechanism of deformation, so a prior decision has to be made as to which regime is relevant to a given natural situation. The importance of this can be demonstrated by considering an extrapolation in strain rate from a typical flow stress of 100 MPa at 12OO”C, lo-’ s-l strain rate, ignoring the additional extrapolation in pressure that is needed in application to the earth; a power law extrapolation with n = 3.5 would predict a stress of 0.3 MPa (3 bar) at 12OO”C, lo-l4 s-’ strain rate whereas with n = 2.5 the predicted stress under these conditions would be 0.03 MPa (0.3 bar), an order of magnitude less. A further conclusion from the present study is that due to the apparent

importance of grain boundary processes it is inappropriate to extrapolate from single crystal studies to predict the flow behaviour of olivine aggregates under high-temperature conditions, whether laboratory or natural. ACKNOWLEDGEMENTS

We thank Dr. J.N. Boland for the specimen of Anita Bay dunite, and the A/S Olivin Company of Aheim, Norway for the Wheim specimen, Dr. I. van der Molen for kind permission to quote his unpublished data at lOOO”C, D.H. Mainprice for the supply of the computer program used for the multilinear regression analyses, and those authors who have allowed us to quote material not yet published. We also wish to thank P. Percival for his technical assistance and the drafting of the figures, P. Willis for his technical advice and photographic expertise and C. Neagle for the typing of the manuscript. G. Horwood and T. White provided excellent technical backup in maintaining the apparatus and K. Morris did all the difficult precision grinding required during the course of the work. REFERENCES Arculus, R.J. and Delano, J.W., 1981. Intrinsic oxygen fugacity measurements: techniques and results for spinels from upper mantle peridotites and megacryst assemblages. Geochim. Cosmochim. Acta, in press. Berckhemer, H., Auer, F. and Drisler, J., 1979. High-temperature anelasticity and elasticity of mantle peridotite. Phys. Earth Planet. Inter., 20: 48-59. Blacic, J.D., 1972. Effect of water on the experimental deformation of olivine. In: H.C. Heard, I.Y. Borg, N.L. Carter and C.B. Raleigh (Editors), Flow and Fracture of Rocks. Am. Geophys. Union, Geophys. Monogr. Series, 16: 109-115. Boland, J.N. and Hobbs, B.E., 1973. Microfracturing processes in experimentally deformed peridotite. Int. J. Rock Mech. Min. Sci., 10: 623-626. Carter, N.L., 1976. Steady state flow of rocks. Rev. Geophys. Space Phys., 14: 301-360. Carter, N.L., and Ave Lallemant, H.G., 1970. High temperature flow of dunite and peridotite. Geol. Sot. Am. Bull., 81: 2181-2202. Darot, M. and Gueguen, Y., 1981. High temperature creep of forsterite single crystals. Durham, W.B., Froidevaux, C. and Jaoul, O., 1979. Transient and steady-state creep of pure forsterite at low stress. Phys. Earth Planet. Inter., 19: 263-274. Durham, W.B. and Goetze, C., 1977a. Plastic flow of oriented single crystals of olivine. 1. Mechanical data. J. Geophys. Res., 82: 5737-5753. Durham, W.B. and Goetze, C., 197713. A comparison of the creep properties of pure forsterite and iron-bearing olivine. Tectonophysics, 40: T15-T18. Durham, W.B., Goetze, C. and Blake, B., 1977. Plastic flow of oriented single crystals of olivine. 2. Observations and interpretations of the dislocation structures. J. Geophys. Res., 82: 5755-5770. Edmond, J.M. and Paterson, M.S., 1972. Volume changes during the deformation of rocks at high pressures. Int. J. Rock Mech. Min. Sci., 9: 161-182. Exner, H.E., 1972. Analysis of grain- and particle-size distributions in metallic materials. Int. Metall. Rev., 17: 25-42. Goetze, C., 1978. The mechanisms of creep in olivine. Philos. Trans. R. SOC. London, Ser. A, 288: 999119.

413 Groves, G.W. and Kelly, A., 1963. Independent slip systems in crystals. Philos. Msg., 8: 877-2381. Jaoul, O., Froidevaux, C., Durham, W.B. and Michaut, M., 1980. Oxygen self diffusion in forsterite: implications for the high temperature creep mechanism. Earth Planet. Sci. Lett., 47: 391-397. Kekulawala, K.R.S.S., Paterson, MS. and Boland, J.N., 1981. An experimental study of the role of water in quartz deformation. In: N.L. Carter et al. (Editors), Handin Vol. Am. Geophys. Union, Geophys. Monogr. Series, in press. Kirby, S.H. and Raleigh, C.B., 1973. Mechanisms of high-temperature solid-state flow in minerals and ceramics and their bearing on the creep behaviour of the mantle. Tectonophysics, 19: 165-194. Kohlstedt, D.L. and Goetze, C., 1974. Low-stress high-temperature creep in olivine single crystals. J. Geophys. Res., 79: 2045-2051. Kohlstedt, D.L. and Hornack, P., 1980. Effect of oxygen partial pressure on the creep of olivine. Paper presented to Symposium on Anelastic Properties and Related Processes in the Earth’s Mantle, XVII General Assembly, Int. Union Geod. Geophys., December 1979 (in press). Murrell, S.A.F. and Chakravarty, S., 1973. Some new rheological experiments in igneous rocks at temperatures up to 112O’C. Geophys. J.R. Astron. SOC., 34: 211-250. Nitsan, U., 1974. The stability field of olivine with respect to oxidation and reduction. J. Geophys. Res., 79: 706-711. Paterson, MS., 1969. The ductility of rocks. In: A.S. Argon (Editor), Physics of Strength and Plasticity. M.I.T. Cambridge, Mass., pp. 377-392. Paterson, M.S., 1970. A high-pressure high-temperature apparatus for rock deformation. Int. J. Rock Mech. Min. Sci., 7: 517-526. Paterson, M.S., 1979. The mechanical behaviour of rock under crustal and mantle conditions. In: M.W. McElhinny (Editor), The Earth: Its Origin, Structure and Evolution. Academic Press, London, pp. 469-489. Paterson, MS., 1981. The deformation of hydroxyl by infrared absorption in quartz, silicate glasses and similar materials. Submitted for publ. Phakey, P., Dollinger, G. and Christie, J., 1972. Transmission electron microscopy of experimentally deformed olivine crystals. In: H.C. Heard, I.Y. Borg, N.L. Carter and C.B. Raleigh (Editors), Flow and Fracture of Rocks. Am. Geophys. Union, Geophys. Monogr. Series, 16: 117-138. Post, R.L., 1977. High-temperature creep of Mt. Burnet dunite. Tectonophysics, 42: 75110. Poumellec, M., Jaoul, O., Froidevaux, C. and Havette, A,, 1981. Silicon diffusion in forsterite: a new constraint for understanding mantle deformation. Paper presented to Symposium on Anelastic Properties and Related Processes in the Earth’s Mantle, XVII General Assembly, Int. Union. Geod. Geophys., December 1979 (in press). Raleigh, C.B. and Kirby, S.H., 1970: Creep in the upper mantle. Mineral. Sot. Am., Spec. Paper, 3: 113-121. Ringwood, A.E., 1975. Composition and Petrology of the Earth’s Mantle. McGraw Hill, New York, N.Y., 618 pp. Ross, J.V., Ave Lallemant, H.G. and Carter, N.L., 1979. Activation volume for creep in the upper mantle. Science, 203: 261-263. Sato, M., 1978. Oxygen fugacity of basaltic magmas and the role of gas-forming elements. Geophys. Res. Lett., 5: 447-449. Schmid, S.M., Boland, J.N. and Paterson, M.S., 1977. Superplastic flow in finegrained limestone. Tectonophysics, 43: 257-291. Schmid, S.M., Paterson, M.S. and Boland, J.N., 1980. High temperature flow and dynamic recrystallization in Carrara marble. Tectonophysics, 65: 245-280.