Deformation partitioning, shear zone development ... - Science Direct

Tectonophysics, 158 (1989) 163-171

163

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

Deformation

partitioning, shear zone development and the role of undeformable objects T.H. BELL ’ Department ’ Department

I, A.C. DUNCAN

’ and J.V. SIMMONS

2

of Geology, James Cook University, TownsviNe, Qld. 481 I (Australia)

of Civil and Systems Engineering, James Cook University, Townsville, Qld, 4811 (Australia) (Received February 16,1987;

accepted July 27.1987)

Abstract Bell, T.H., Duncan, A.C. and Simmons, J.V., 1989. Deformation undeformable objects. In: A. Ord (Editor), Deformation

partitioning, shear zone development and the role of

of Crustal Rocks. Tectonophysics,

158: 163-171.

The formation of a mylonite zone by homogeneous progressive simple shear is highly unlikely because heterogeneous strain of grains with different compositions causes deformation partitioning and results in progressive inhomogeneous simple shear or non-coaxial progressive bulk inhomogeneous shortening. However the presence of rigid bodies in a zone of rock undergoing bulk simple shear spreads and homogenizes the stress field such that the instantaneous displacement field is essentially homogeneous at a scale up to at least four times the diameter of the rigid object. That is, the portion of rock surrounding the rigid body deforms by homogeneous progressive simple shear and the rigid object is forced to rotate. This has considerable implications for the rotation or lack thereof of unstrained porphyroclasts and hence the information Geometric

relationships

between porphyroclasts

or porphyroblasts

and the surrounding matrix that arc superficially

similar can indicate exactly the opposite sense of shear depending on whether the porphyroclasts have or have not rotated leading to considerable problems in interpretation Resolution

of these relationships

bulk inhomogeneous

and porphyroblasts,

such grains preserve about the sense of shear on their margins or through inclusion trails.

enables ready distinction

or porphyroblasts

of the bulk movement in a shear zone.

of whether the deformation

history involved progressive

shortening or progressive simple shear.

In particular these results have considerable implications

for the origin of blueschist minerals preserved in garnet

porphyroblasts

via the roles of strain softening and hardening during mylonitization due to the destruction of feldspar

porphyroclasts

and growth of garnet porphyroblasts

respectively.

Recent work on the role of deformation partitioning during foliation development has considerably advanced our understanding of the micro-

deformation history is very unusual because most rocks deform heterogeneously due to the role of phyllosilicates and graphite versus other minerals (Bell et al., 1986). This is because phyllosilicates and graphite, unlike most other minerals, localize

structural processes associated with deformation. Of particular significance is the concept that porphyroblasts do not rotate if deformation partitioning occurs and, indeed, can only rotate if the deformation involves homogeneous progressive simple shear alone (Bell, 1985). The latter type of

progressive shearing causing deformation partitioning and hence progressive inhomogeneous simple shear or even progressive bulk inhomogeneous shortening. Hence we decided to investigate deformation partitioning in a bulk shear environment in order

Introduction

0040-1951/89/$03.50

0 1989 Elsevier Science Publishers B.V.

164

to determine progressive

how zones of strictly homogenous simple shear alone could form or if

element

analysis using a simple Mohr-Coulomb

criterion

as this involved the fewest assumptions

apparent

terms

of

stresses

in naturally

occurred. Potentially to occur with the het-

in nature but not allowed

values of the function imply no yielding and positive values define stress states that the material cannot

attain without modification

function by elastoplastic

of the yield

response. A value of the

yield function can be assigned to any point of a body. Mathematically

using a viscous or v&co-elastic approach.

the function may be visual-

ized as a surface in suitable stress-space Mohr-Coulomb

non-associated

and

state of stress at which yielding occurs. Negative

rocks. The approach

erogeneity

in

was finite

formed

it also allows deformation

formulation

material strength parameters that defines a current

this was even possible

about how the deformation

matical

is a mathe-

de-

indeed

chosen

The Mohr Coulomb yiefd function

which only elastic

elastoplasticity

behaviour

occurs

within

but along

tool

which elastoplastic (which in this case is dominantly plastic with up to 5% elastic) behaviour

as it contains only two assumptions, and the flow rule used can be adjusted to simulate a large range

occurs (Simmons, 1981). The primary purpose of the yield function is to define permissible stress

of material properties. It is based on a simple Mohr-Coulomb material (Fig. 1; Davis, 1968)

increments when yield occurs.

This is a simple and effective elastoplastic

to complex behaviour

The flow rule is used to predict the plastic strain increment components associated with an increment of plastic flow at a given yielding stress

(1) the current directions of principal stresses control, and are coaxial with, the strain incre-

hardening or softening respectively. Mathematically, hardening is associated with expansion of

which is readily adaptable (Simmons, 1981). The assumptions are:

state. Strength gain or loss during yielding is called

ments;

the yield surface and softening with contraction.

(2) that there is a definite relationship between increments of volume strain and shear strain. Until failure occurs we are saying the material is isotropic and elastic. Whether the failure occurs

The yield function, flow rule and hardening (or softening) law provide a self-contained means of predicting plastic strains associated with known stress changes during yielding, or vice versa.

along grain boundaries or by intragranular glide is not specified and the deformation is treated as a continuum; i.e., we are looking at the sum of discrete slips on grain boundaries or slip surfaces within a crystal. This is in fact a good approach to modelling plastic deformation of rock in a structural/metamorphic environment as it allows us to deform a body of rock without assuming anything

An increment of yielding strain probably involves components of elastic and plastic behaviour, thus:

about the role of grain-boundary sliding versus intra-granular slip. Since microstructurally all dissolution and solution transfer appears to be controlled by progressive shearing strain (Bell et al., 1986) the model also allows us to take into account the bulk effects of this mode of deformation as we can simply input into the program dissolution as a function of shearing strain (using assumption 2 above). Assumption 1 is just as applicable to deformation in natural rocks as it is only reasonable to expect that the local stresses directly control the resultant strain increments.

E=EE+EP

(1)

where E is a vector of strain increment components and the E, P superscripts denote elastic and plastic components respectively. Nonassociated Elastoplasticity

Mohr-Coulomb consists of a

material that has a fixed yield function and constant plastic dilatancy rate. A linear MohrCoulomb strength relationship is used as a strength criterion (Fig. 1). The dilatancy rate D (or ratio of increments of plastic volumetric strain and plastic shear strain) is a material constant which may assume any reasonable value. The yield function is: fl=r-C,-a

tan+,

(2)

where r = us (the shear stress), u = uN (the normal stress), C, is the Mohr-Coulomb cohesion

165

Material

Fig. 1. Shows schematically

the intended

model. The values of the material the Mohr-Coulomb

cohesion

:

Properties

material

properties

intercept,

Cp , +p , D

,

model hehaviour.

(elastic

K,G)

This modei is called the constant

used are shown in Fig. 2. o is the normal

+ the Friction

angle for peak strength,

rate of dilation

Mohr-Coulomb

stress, r the shear stress, y the shear strain,

D the dilatancy

rate, G the rigidity

modulus,

C,

and K is

the bulk modulus.

(or a constant known as the cohesion or shear strength) and c&, is the friction angle (or angle of internal friction) for peak strength. The coefficient of internal friction (p), is related to +r by the equation: intercept

j.t = tan &

(3)

The yield function must remain equal to zero for sustained yielding. The dilatancy rate D at peak

that they would tend not to deform (Fig. 2b). We deformed these meshes under bulk simple shear conditions. No internal constraints were imposed and the only external constraints were the pinning of the element nodes around the edge to maintain a simple shear geometry on the boundaries. The results for the mesh without the central stiff elements are shown in the upper part of Fig.

D, = Ch,kx

3. This mesh deformed heterogeneously as one would expect for an inhomogeneous rock body, and the deformation progressively migrated its way outwards across the mesh from the centre. In other words, with no constraints except bulk sim-

This is a natural physical property of the Mohr circle.

ple shear of the boundaries, deformation partitioning occurred within the deforming mesh and some

yield strength is constant and is the ratio of volumetric ( Er!) to maximum shear strain (y’) plastic increments (Simmons, 1981).

The deformation

experiments

portions took up shearing strain before others resulting in a deformation history of progressive inhomogeneous simple shear.

We established a mesh with a random distribution of elements whose stiffness and strength properties varied ten percent either side of a mean (Table 1, Fig. 2a). We then made an identical mesh except that we gave the central four elements strength and stiffness characteristics an order of magnitude greater than the average so

Deformation of the mesh with the four strong elements in its centre produced markedly different results that are shown in the lower part of Fig. 3. Even though the mesh used in these experimental runs had four essentially undeformable elements in its centre, the deformation proceeded homogeneously on the scale of the mesh by homogeneous

-

-. x

x

Fig. 2. Element

meshes. Numbers

refer to material

properties

defined

2a except for four extremely

a

b

LO

Fig. 3. Comparison

of strain

fields resulting

from varying

stiff elements

c

8O

degrees

and for the mesh in Fig. 2b (along the bottom)

in Table 1. Note that the mesh in Fig. 2b is identical

to that in

in the centre.

d

12"

160

of bulk simple shear of the mesh shown in Fig. 2a (along for the equivalent

amounts

of angular

shear.

the top)

167

TABLE

1

Material

properties

*

M 1

0.0

0.0

26.67

40.0

80.0

0.0

0.0

-0.2

2

0.0

0.0

28.33

42.5

85.0

0.0

0.0

-0.2

0.0

3

0.0

0.0

30.00

45.0

90.0

0.0

0.0

- 0.2

0.0

4

0.0

0.0

31.67

47.5

95.0

0.0

0.0

- 0.2

0.0

5

0.0

0.0

33.33

50.0

100.0

0.0

0.0

-0.2

0.0

6

0.0

0.0

35.00

52.5

105.0

0.0

0.0

-0.2

0.0

7

0.0

0.0

36.61

55.0

110.0

0.0

0.0

-0.2

0.0

8

0.0

0.0

38.33

51.5

115.0

0.0

0.0

-0.2

0.0

9

0.0

0.0

40.00

60.0

120.0

0.0

0.0

-0.2

0.0

10

0.0

0.0

41.67

62.5

125.0

0.0

0.0

- 0.2

0.0

11

0.0

0.0

333.33

500.0

1000.0

0.0

0.0

- 0.2

0.0

+ 28)] = bulk Modulus;

G = E/[2(1

* M = material = rigidity

number

Modulus;

(peak) strength;

in the mesh; Y = Poissons

y,, u,, = body forces per unit volume; ratio;

I = tensile strength;

E = Youngs

D,, = dilatancy

modulus; rate;

K = E/[3(1

Cr, = Mohr-Coulomb

a = coefficient

of thermal

cohesion volumetric

intercept;

0.0

et, = friction

+ 28)]

angle

for

strain

progressive simple shear. It is also evident that the

The stress fields generated by these experiments

block of central strong elements rotated without undergoing significant internal plastic deformation.

Figure 4 shows plots of the stress fields that resulted in the strain field diagrams described

a

40

b

c

12O

d

16O

168

above.

The stress

field for the mesh without

central

strong elements

was initially

and these inhomogeneities the deforming widening

centre

strain

mencement

However,

mesh

containing

ments,

the stress

was

obtained. regard

of the

homogeneous

strong

inhomogeneous

ele-

in the immediate

vicin-

neous

stress

field.

When

However, under

all portions

that

is

be deformed plastically is included mesh, the block does not undergo stress change

of the

the same set of rules.

a very strong block of elements

after deformation

rigid

and

useful

pear to indicate

putty.

towards

had

experiments

been in

and Ramberg

inclusions

are present,

the inclusion

is remarkably the shear

on

in a viscous

that when a rigid inclusion

from

this

(1976)

Some of their results

of rigid inclusions)

well away

results

the same experiments

non-rigid

of silicon

zone

edges,

ap(or a

the strain

(e.g., at twice

homogeneous,

and

formerly

lines tend to remain straight after However, when non-rigid inclusions

its that

straight

deformation. are present,

bowing of formerly straight lines tends to occur towards the shear zone edges (e.g., cf. Ghosh and Ramberg,

1976, figs. 35b and 38b with 20b, 22a,

that cannot

29b, 31b and 33b). effects operate during

within the any further

of deformation minishes.

has begun.

this strong block acts as an internal condition where very little is happening

both

diameter)

(which is like a statisti-

most

as they had performed

number

cally homogeneous sample) and impose a set of simple boundary conditions such as bulk simple shear, it does not lead to a statistically homogemesh are deforming

The

similar

were those of Ghosh

matrix

throughout

ity of the strong central core. It appears that when we take a mesh randomly

from

from the com-

the central

from some variation

to see whether

heterogeneous

of the mesh in front

effects.

shear

outwards

of bulk simple shear of the boundaries

of the apart

migrated

the

This suggests that similar viscous flow where the role

partitioning

presumably

di-

Hence

boundary and where

in fact there is very great resistance to anything happening. However, the boundaries between elements remain interconnected, and therefore the rigid block influences the stress field over a wide area. Statistically the bulk of the material still yields, but it is forced to do so under a different

Significance

These results have considerable significance to both structural and metamorphic geology. They resolve the problem which caused us initially to undertake the investigation; that is whether it is possible or not to develop a deformation history of homogeneous progressive simple shear in rocks.

set of displacement conditions, which result in a more homogeneous style of deformation. That is, the rigid block of elements stiffens up the whole structure.

We have found that deformation partitioning will always occur during bulk simple shear of a rock body resulting in progressive inhomogeneous sim-

The distance over which the very strong block of elements effects the stress field, and hence the

inhomogeneous shortening. However, if large (relative to the matrix) rigid objects are present, they

strain field, appears to be about 4 x its width. Outside of this zone, the stress field and the resultant strain field would return to the situation

deformation by homogeneous shear. This was an unexpected

shown in the upper row of strain and stress fields in Figs. 3 and 4 respectively, and deformation partitioning would result in progressive inhomogeneous simple shear.

ple shear,

cause

or even

the stress

non-coaxial

progressive

field to homogenize

resulting

bulk

in

progressive simple potential solution

to the problem of a being able to explain those few garnet porphyroblasts that contain genuinely spiral-shaped inclusion trails (Bell, 1985). Porphyroblust

rotation

Discussion

Because of the unexpected homogenizing effects of the rigid inclusion we investigated work done on experimental modelling of bulk simple

Microstructural examination of many porphyroblasts led Bell (1985) to suggest that they would not rotate relative to geographic coordinates during a general ductile deformation history unless

169

they deformed internally. special

conditions

of

He proposed that the

homogeneous

progressive

dergoing

bulk simple shear will actually

deformation

partitioning

simple shear were necessary before porphyrobiasts

sult in a deformation

would rotate

progressive

during

ductile

deformation.

This

means that there could be no deformation tioning

in the matrix

porphyroblasts

and the rotation

parti-

cause

to locally cease and rehistory

of homogeneous

simple shear rather than progressive

inhomogeneous simple shear!

of the

was driven not by shear on their

Blueschist

inclusion trails

rims, as previously supposed, but instead by shear In a number

on the foliation planes that actually contained, or were truncated locally by, the porphyroblast. However, in general, deformation partition

will always

in rocks due to heterogeneities

world garnet

of mylonitic

porphyroblasts

zones around contain

the

blueschist

minerals as inclusion trails that are not present in

in shear

the matrix of the rock. A possible solution to this

strength on the grain and larger scales even when

is that prior to garnet porphyroblast growth the deformation had localized within a zone of rock undergoing bulk simple shear, as shown in the

a bulk simple shear is imposed with no shortening component. The environments in which bulk simwith no shortening component possible are limited

upper part of Fig. 4, resulting in extremely high strain rates in this zone. Blueschist minerals ini-

to mylonitic zones associated with vertical trans-

tially form in zones of high shearing strain across

current faults. Possibly ductily deforming rocks on some portions of thrusts or detachments may also

a

ple shear can occur during ductile deformation

have no shortening component across them. Genuine spiral shaped inclusion trails in garnet porphyroblasts could possibly be explained in this way (e.g., Rosenfeld, 1968; Powell and Vernon, 1979; Bell and Brothers, 1985). However, Bell and Johnson (1989) have recently demonstrated that classic examples of spiral-shaped inclusion trails in garnet

porphyroblasts

from

thrust

environ-

ments did not form by rotation of the porphyroblast. These experiments indicate that it is unreasonable to expect a deformation history of homogeneous progressive simple shear in a zone of rock undergoing bulk simple shear. However, if strong objects that remain rigid are present, or grow

grade

transition

(e.g.,

New

Caledonia,

N.

Brothers, pers. commun., 1985) and it is conceptually possible that localization of intense strain energy could explain this. If this explanation

is

correct then the presence of blueschist minerals within garnet porphyroblasts, but not in the matrix, could have resulted from the growth of the porphyroblast in a zone of localized high strain rate where previously blueschist minerals were forming. The growth of the porphyroblast caused the stress field, and thus the instantaneous strain field, to homogenize resulting in a decrease in the local strain rate and the development of nonblueschist minerals in the matrix. Sense of shear in mylonite zones

during deformation, they will force the stress field in their vicinity to homogenize. This results in a

Feldspar porphyroclasts can be used in different ways to obtain opposite senses of shear in a

deformation

zone of mylonitic rock. Yet, both senses of shear can be correct in certain circumstances. Mylonitic

history in the matrix,

from half a

diameter through to at least four diameters away from the rigid block, of homogeneous progressive

rocks can form in deformation

simple shear. That is, deformation petitioning wifI occur in a zone undergoing bulk simple shear, except locally where undeformable objects (at the T-P conditions operating) have grown or are present, such as garnets and feldspar megacrysts respectively. Hence the growth of garnet porphyroblasts during mylonitic deformation in an environment un-

bulk simple shear, or coaxial or non-coaxial progressive bulk inhomogeneous shortening (Bell, 1981). If feldspar porphyroclasts are present, and do not strain internally, in a rock undergoing bulk simple shear, they will cause the stress and instantaneous strain fields to homogenize and the rigid porphyroclast will be forced to rotate resulting in a strain shadow geometry similar to that

histories involving

170

and the resulting

theoretical

1968, Ghosh and Ramberg, not be representative

models (e.g., Gay, 1976) may therefore

of deformation

rock. They certainly

in natural

do not predict to relation-

ships obtained herein.

Strain

a

hardening

us. strain

softening

The growth of garnet porphyroblasts in a zone of rock undergoing bulk simple shear should result in strain hardening and the deformation will spread more uniformly across the body of rock. The destruction of feldspar porphyroclasts in zones of high strain in a mylonite zone undergoing such a deformation will however have exactly the opposite effect and will lead to strain localization

b Fig. 5. Schematic feldspar

diagrams

porphyroclasts

showing

on their rims for (a) rotation zone

undergoing

deformation

of a feldspar

bulk simple

shear;

on the porphyroclast geometries

the relationship

and strain shadows

yet opposite

between

or tails of feldspar porphyroclasts

(b) S and C plane

rim. Note

in a style

tion.

well the similar

senses of shear.

shown in Fig. 5a. However, if they are present in a rock undergoing coaxial or non-coaxial progressive bulk inhomogeneous shortening they will not rotate if they do not internally

and possibly rupture as the strain rate becomes too high to be accommodated by plastic deforma-

deform and the

resulting geometry will be that shown in Fig. 5b. It is readily apparent that these geometries are superficially similar and give the opposite sense of shear. Hence extreme care must be taken when using rigid objects for a sense of shear criteria, both in the field and the laboratory.

Acknowledgements This project was funded by the Australian Research Grants Scheme. Scott Johnson read the manuscript and his comments and those of two anonymous reviewers were greatly appreciated. References Bell,

T.H.,

1981.

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1985.

rotation

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modelling

using jluid j7ow analogies

Metamorph.

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blueschist

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