The effect of non-coaxial strain paths on crystallographic preferred orientation development in the experimental deformation of a marble

73

THE EFFECT OF NON-COAXIAL STRAIN PATHS ON CRYSTALLOGRAPHIC PREFERRED ORIENTATION DEVELOPMENT IN THE EXPERIMENTAL DEFORMATION OF A MARBLE

E.

H.

RUTTER

Department of Geology, Imperial College, London (Great Britain) M. RUSBRIDGE Department of Geology, South London College, London (Great Britain)

ABSTRACT

In order to understand development necessary complex

by intracrystalline to perform

are described

the principal

the principal concentrations defined

anisotropy

tectonites,

compression.

it is

history

Some simple

of finite strain do not coincide In the more successful

The development

oblique

with

experiments

to the foliation

of such fabrics was studied

stage methods

technique,

is more

strain paths in a marble

of calcite c axes were produced

universal

orientation

the deformation

by axisymmetric

directions

by grain shape.

susceptibility

in which

aimed at producing

stress directions.

using both standard

orientation

preferred

glide in natural

experiments

than that produced

experiments in which

crystallographic

and a magnetic

which detects

calcite preferred

directly.

INTRODUCTION

In

most experimental studies of rock deformation, rock

cylinders are subjected to axial compression, which results in a simple strain path with applied stress, incremental elastic and plastic strains and finite strain all coaxial. This coaxiality is usually reflected in the axial symmetry of the pattern of preferred crystallographic orientation (optical fabric) which may be produced under favourable conditions.

Only after very large shortenings (-50%)

will

significant

heterogeneous

the superposition total

symmetry

of non-axial

For example,

punching

action

expanded

specimen

results fabric

produces shape

in the corners

in an apparent

to the

clusters section,

of

the

into a laterally of the foliation of the specimen.

in an optical

departure

to

from axial

analysis

symmetry

in the

diagram.

as described

finite

of incremental

with

between

the orientation

stress,

To complement

deformed

the petrofabric

and theoretical

necessary

to study along

incremental (non-coaxial

fabric

strain

strain

of naturally

of fabric

development

paths which

strain

(Fig. 1).

of such

geologists. deformed

development,

in rocks

result

axes

strains,

fabric

to structural

study

of

of the distorted

of the optical

studies

and finite

strain

deformation

and incremental

interest

(e.g.,

the directions

of the boundaries

are of considerable

zones

from the principal

progressive finite

shear

1970)

diverge

and the characteristics

material

ductile

and Graham,

strains

strain

The relationships

region

occurring

by Ramsay

the principal

experimentally

in separation

principal

it is

of the

directions

paths).

DIRECTION OF

1

L INCREMENTAL Fig. 1.

pistons

grains

contributions

cut thin

deflections

of such rotated

leading

of localised

seen in an axial

In some naturally

zones

fabric

of the loading

by grain

Inclusion

intervene,

symmetric

of the optical

grains.

defined

deformation

SHEAR

FINITE EXTENSION

SHORTENING STRAIN

Schematic diagram showing relative orientations incremental permanent strains in a shear zone.

of finite and

75 In this study an attempt has been made to devise simple experiments which result in non-coaxial deformation paths.

We

will show that the optical fabric of a calcite marble deformed by intracrystalline glide responds rapidly to changes in either applied stress or incremental strain directions.

Also,

the optical fabric may become oblique to the grain shape fabric, which reflects finite strain if the strain is homogeneous between the microscopic and mesoscopic scales. The conclusions may be broadly applicable to aggregates of minerals such as quartz and olivine, which normally crystallise in equidimensional habit. EXPERIMENTS In all of the experiments to be described, cylindrical specimens of Carrara marble, 9 mm diameter and 20 mm long, were deformed at 400°C in a fluid medium testing machine under conditions of confining pressure ranging between 1.5 -1 and 3.0 kb at strain rates of about 10s5sec . Under these conditions it had been previously established (Rutter, 1974) that this rock deforms by intracrystalline glide and that the initially equidimensional, crystallographically randomly oriented grains develop a flattened shape fabric which corresponds closely with the bulk strain imposed on the aggregate.

The grain size is about 200 pm, which is well

suited to optical orientation measurements.

Forty experiments

were performed in total. Axial symmetric compression to high strains results in the development of a preferred orientation of e {Oli2) planes , which in turn means 1 that c {OOOl}axes lie on a small circle girdle oriented at

normal to the compression direction, d 26O to ol .

Fig. 2 shows a c axis pole figure for a sample

shortened 50%.

The slight orthorhombic symmetry superposed

on the axial symmetry is attributed to the effects of some heterogeneous deformation.

This type of preferred orientation

for calcite aggregates has been predicted qualitatively using a simple theoretical model (Wenk et al, 1973) and.assuming that r {lOil} glide is the dominant slip process.

COMPRESSION DIRECTION 1

PRINCIPAL AXES

Fig. 2. Equal area projection of crystallographic c axes (158 grains) in Carrara marble experimentally shortened by 50%. The c axis distribution before deformation was random. Contours are at 2.5% concentration intervals. The small squares represent calculated principal axes of the distribution of data points.

Owens

and Rutter

development magnetic

methods.

and it has been susceptibility orientation using

Using

principal

data

2 are plotted

optical

data,

determined

by direct

crystals

and

tensor

susceptibilities

may be

measured

of calcite, in

of the fabric

from

standard

'magnetic'

due to individual

grains

terms (Owens,

can be described

kI% = 300 (kll-k33)/(kll+k22+k331 susceptibilities.

principal

and these

can be measured

the directions

can be expressed

kii are the principal

On Fig.

that the

from preferred

susceptibility

intensity

parameter,

authors

and

mineral

in an aggregate Thus

single

the contributions

by the single

the progressive

by both optical

resulting

grains

deformed

The relative

1974).

by the above

magnetometer.

orientation

by summing

studied

is a diamagnetic

of the resultant

experimentally

where

shown

of calcite

determined.

optical

Calcite

anisotropy

a torque

magnitudes

(1976) have

of this type of fabric

axes

correspond

measurement.

calculated

closely Fig.

from the

with magnetic

3 shows

axes

the development

11

of fabric both

intensity

optical

and magnetic

are clearly small

circle

girdle

within

girdle

used

of fabric

measurements

fabric,

the limits

fabric

are shown.

The data

and magnetic

line representing

to trace

data

a perfect

are

26' small

technique

rapidly

deformation

a

For

error.

This magnetic

study

from

line representing

and optical

in non-coaxial

Data

strain.

of experimental

is shown.

in the present maxima

progressive

to a horizontal

a horizontal

reference,

been

asymptotic

circle

identical

(H%) with

has

the rotation

experiments.

'PERFECT' SINGLE CRYSTAL

'*[ IO i

DEFORMED

8

6

f I

I

a

26' GIRDLE ------------

&

0

SINGLE CRYSTAL

X

I__-)+--

R----

0

MAGNETIC DETERMINATION OPTICAL DETERMINATION

I

I

0.1

I

0.2

0.3

I

1

L

0.5 0.4 log (I+r)

I

I

0.7

0.6

0.8

Fig. 3. Variation of fabric intensity (H%) in Carrara marble with progressive strain. Data points obtained from magnetometer measurements and calculated from optical measurements are shown. Also shown are calculated H% for a perfect 26O small circle girdle of c axes and measured H% for 'perfect' (undeformed)and experimentally deformed single crystals of calcite.

Several in order

arrangements shear)

kinds

were

aimed

jacket

non-coaxial

configuration deformation

at producing

simple

were

paths.

devised TWO

shear directly

(direct

tried:

(a) A conventional steel

of experimental

to produce

over

a cut was made

cylindrical the standard

through

specimen thin

the steel

was encased

copper

jacket

sleeve,

in a thick except

that

at 45O to the axis of

the cylindrical

specimen

within

shear band

a narrow

(b) An annular punch

through

shear

to constrain

shaped

sample

and backed

by a steel

deformation

in the specimen.

zone was produced

a disc

a standard

metal

in order

to 3 mm thickness, die

by forcing

specimen,

(compare

a steel

formed

by cutting

down

jacketed

in thick

copper

deep drawing

of cup-shaped

parts).

In both

cases

the shear

zones

produced

were

only

a few grains

wide. Alternatively, of material

were

The sequence First,

It will

preferred

as strong

develops

into

long) whose

axes were

at angles

inclined

strain

whose

superposed

principal

directions

------Q (I)

This

with

4. strain

strain

a fabric

were

to the initial

almost

and 7 mm

compression

The new cylinders

amounts

results

in

then

(6.3 mm diameter

axes are always of stress

in Fig.

(a natural

produces

60° and 70'.

by various

test conditions.

amounts

experiments.

3 that crystallographic rapidly

Specimens

cylinders

between

then re-shortened

the same

very

30% shortening

smaller

in larger

out is shown

be seen from Fig.

and that

paths

of two stage

30% axially

as it can ever become.

re-machined

were

carried

shortened

orientation

this marble,

direction

were

strain

in a series

of operations

specimens

of 0.35).

non-coaxial produced

up to 30% under

in a state inclined

and incremental

of finite

to the strain.

(2)

(3)

(4)

ROTATE

RE-CUT SPECIMEN

RE-DEFORM

1

r

DEFORM

Fig. 4. Schematic diagram showing the sequence of operations carried out in the two stage deformation experiments.

79 RESULTS

Direct shear tests

In these experiments the strain in the deformed zone was highly heterogeneous, with local apparent shear strains ranging between 0 and 5.

Because of the geometry of the

experimental setups only a small number of grains were deformed compared to the total number in the sample.

Fig. 5

shows the results of an optical analysis of one such specimen. These results are typical of the several experiments carried out in the punching and constrained shearing configurations described above.

The figure shows the relationship between

the azimuth of grain elongation and the azimuth of c axes (c axes were always found to lie very close to the plane of thin sections cut along the applied compression axis). Clearly, there is a tendency for c to lie at a high angle to the grain elongation direction.

That is, the optical fabric

is geometrically related to the finite strain.

However,

optical evidence for the passive bending or rotation of many grains leads us to treat these data with scepticism.

There

is little to suggest that, in our attempts to produce direct shear, any significant component of strain by simple shear occurred!

J. Tullis (this volume) has obtained similar

results from the fabric study of sheared grains adjacent to the loading piston in an experimentally deformed quartzite. Perhaps the only satisfactory way to produce simple shear may lie in the torsional testing mode.

This we were unable

to do in the present study.

TL)O stage

tests

The results of the two stage tests were much more satisfactory and most of each specimen was apparently deformed homogeneously in the second stage.

Fig. 6 shows the final preferred orientation of c axes and twin lamellae in a sample recut 60° to the original compression direction and redeformed by 20%.

For homogeneous deformation in the second stage, the

90

70

50

AZ C

30

IO

AXES

Fig. 5. Results of optical measurements on a specimen deformed using the punch technique. Right hand diagram shows sense of measured angles of azimuth (AZ) of c crystal axes and grain long axes relative to the direction of applied shear.

FOLIATION SECOND 'APPLIED COMPRESSION

t SECOND APPLIED COMPRESSION

Fig. 6. Results of an optical analysis of a specimen deformed using the two stage technique (equal area projection). c axis (left) and e twin lamellae (right) pole figures are shown. On each diagram the rotation of foliation defined by grain shape in the second stage compression is also shown (188 grains). Contours are at 2.5% concentration intervals.

81 grain long axes and grain shapes change in orientation and magnitude respectively.

It is a simple matter to compute these

changes (Ramsay, 1967, p.61).

The computations were borne out

well by observations on the deformed samples. It must be borne in mind that during the second deformation the 'foliation' due to the alignment of elongate grains produced during the first deformation is oriented in a plane of high resolved shear stress.

In addition to the rotation of

grain elongation directions which occurs as a result of homogeneous shortening, any sliding which may occur on surfaces parallel to the foliation will lead to a passive rotation of grains (i.e. without concomitant intergranular strain) because the ends of the specimen are constrained against moving sideways by the rigid loading pistons.

If the

foliation originally makes an angle 6 with the compression direction, then the final orientation, B', is given by cos 8' = JA cos

e

where JA is the component of quadratic extension in the axial direction which is due to sliding on the foliation. Computed grain long axis rotations due to these two effects are shown in Fig. 7 for an initial foliation attitude of 25O to the second stage compression direction.

For the first 35% shortening these curves lie very close together. If all of the shortening was accumulated by sliding on surfaces parallel to the foliation there would be little or no intracrystalline strain in the second stage and the pre-existing optical fabric would be simply passively rotated with the sliding grains. The maximum of the optical fabric would then plot along the dashed curve in Fig. 7 with progressive strain. It is evident from Fig. 6 that the symmetry of the optical fabric is lowered in the second stage of straining.

Therefore the vector mean axis is used below in order to describe the rotation of the preferred orientation pattern.

Fig. 7 shows the orientation of the vector mean axis of the resultant fabric for several runs to different strains, determined from

both optical and magnetic measurements. Clearly, the crystallographic fabric rotates faster than the grain shape fabric, so that in the range 0 to 30% shortening the optical

82

F

80-

P z

70-

POLES

TO

GRAIN

LONG

FLATTENING,

_HOMOCENEOUS ALONG

AXES NO

FOLIATION

SLIDING ALONG

u ?

SLIDING

FOLIATION

40-

0

oz 20 -

z F z = E 0

0

Cl

0

IO-

0

I

I

1

I

I

I

I

S

IO

15

20

25

30

35

%

1 40

SHORTENING

Fig. 7. Relative changes of orientation of grain shape fabric and vector mean orientation of optical fabric ( o ) maximum (determined both optically and magnetically) during the second stage of two stage experiments in which the recut orientation was 65O. Continuous and dashed lines show rotations of grain shape fabric asswing homogeneous deformation without sliding along the foliation and deformation entirely by sliding along the foliation without intergranular strain, respectively.

fabric shown

is oblique clearly

observed

spread

fabrics

principal

of the specimens,

experiments

parallel

to the foliation

inference

lower envelope deformation

suggests

direction,

grain

Part

of Fig.

by sliding

that

35% shortening

coincides

with

size

indicates

that

on surfaces The

importance.

out by optical

parallel

physical

probably

was of variable

of the crystallographic

fabric

is

in the location

of the small

rotation

sliding

This of the

7 representing

to the data may represent

that by about

the optical

pole.

6 and 7.

the remainder

was borne

without

Extrapolation

foliation

is due to uncertainty

axes because

whilst

in these

latter

of Figs.

in the data

crystallographic of magnetic

to the resultant

in the data

The

observations. homogeneous

to the foliation. data

trend

the vector

the newly

is, the rock has largely

in Fig. mean

imposed

'forgotten'

7

axis of

shortening its

83 earlier deformation history, at least as far as the vector mean axis of the optical fabric is concerned. Skewing of the optical fabric pattern may, however, persist as an indicator of the complex deformation path. The simple, quantitative description of the development of optical fabric along various kinds of strain path which is afforded by the magnetic method, will provide constraints for checking the validity of theoretical studies of fabric development using techniques such as the Taylor-Bishop-Hill analysis.

Using this analysis for quartz, Lister and Hobbs

(1976) have made theoretical predictions that support the results of the experiments reported here, namely, that crystallographic fabrics show an ability to forget the orientation of the earlier elements of the deformation history, because according to the above analysis, crystallographic axes rotate rapidly with respect to grain shape into specific orientations with respect to the incremental strain axes.

DISCUSSION AND CONCLUSIONS

In our direct shear experiments it was theoretically impossible to produce separations of finite and incremental strain directions of more than about 15O, and then only if the displacements had been of precisely the simple shear type. In contrast, in the two stage experiments, clear separations of at least 40° were obtained.

The development of oblique

optical fabrics shows that, whereas grain shape orientation reflected finite strain, crystallographic preferred orientation responds rapidly to variations in the orientation of either stress

or incremental strain.

Patterns of preferred orientation in which the optical fabric symmetry is oblique to grain shape fabric symmetry are not uncommon in natural tectonites.

Fig. 8 reproduces examples for calcite rocks given by Wenk et al.(1968) and Wenk and

Shore (1975), and examples for quartz tectonites are given by Eisbacher

(1970).

We can conclude that such fabric asymmetry

could result from either polyphase deformation or from a non-coaxial deformation involving a large strain, for example,

Fig. 8. Examples of oblique crystallographic c axis fabrics in natural calcite tectonites. S = foliation, 1 = lineation. Contours are times random. Left, Calcite marble, Val Prato, Ticino, Switzerland (after Wenk et al, 1968). Right, calcite mylonite, Ticino, Switzerland (after Wenk and Shore, 1975). Reproduced with permission.

by

simple

shear.

This simple picture may be severely modified through the effects of sliding on grain boundaries, resulting in passive grain rotations, and which is particularly liable to occur after an initial grain flattening has developed.

Sliding,

accommodated by diffusive mass transfer processes, is particularly likely if fine grained recrystallised material develops in grain boundaries.

The approximately lenticular

shape of flattened grains may also mean that sliding cannot be considered to occur on a single family of parallel oriented planar discontinuities, but effectively on a conjugate pair of orientations.

This will probably invalidate the idea that

grain shape reflects finite strain, and the possible effects of grain boundary sliding should always be considered in studies of fabric development, particularly in shear zones. In plastically or elastically anisotropic continuous materials, principal axes of stress and incremental strain do not coincide except when the principal directions of the elasticity or plasticity tensor coincide with those of stress

85 or incremental strain.

We can write (using summation

convention), for elastic distortions 6

ij

=c.

rjkl apk aqlepq

is the elastic strain where 6. . is the stress tensor, e pq 13 * is the effective stiffness tensor and a tensor, c. pk rs rjkl to c the array of direction cosines linking e ijkl' Pq A corresponding relation exists relating Stress to incremental becomes a plasticity tensor, plastic strain, where the c.. rjkl whose representation surface is the yield surface. The for either the elastic or plastic cases components of c ijkl can probably only be determined satisfactorily by direct experiment, requiring various types of loading geometry. During the first part of the second stage of our two stage experiments, when the optical fabric is oblique to the cylinder axis, it is therefore likely that shear stresses develop parallel to the faces of the loading, pistons.

Thus

the second stage applied compression probably corresponds neither to a principal stress nor to a principal incremental strain direction.

The discrepancy is probably not large,

however, for the cylindrical specimens were not found to be visibly sheared to one side, though sections cut normal to the loading direction were found to be elliptical.

Clearly,

caution must be exercised in discussing relationships between finite strain, stress, elastic strain and incremental plastic strain in anisotropic granular materials, especially in the absence of relevant experimental data.

ACKNOWLEDGEMENTS This work forms part of an experimental investigation of rock deformation processes financed by the Natural Environment Research Council.

The writers are grateful to experimental

officer Mr. R. F. Holloway for assistance with theexperimental programme and to Dr. W. H. Owens, through whose courtesy the magnetic determinations reported here were performed.

We have benefitted greatly from discussions with and constructive criticism from Dr. G. Lister, of the Rijksuniversiteit,Leiden.

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J. G., 1967. Folding

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