Mechanisms of fracture propagation in experimentally extended Sioux quartzite

259

Tectonophysics, 182 (1990) 259-218

Elsevier Science Publishers B.V.. Amsterdam

Mechanisms of fracture propagation in experimentally Sioux quartzite

extended

Duncan Mardon *, Andreas K. Kronenberg, John Handin, Melvin Friedman and James E. Russell Centerfor Tectonophysics, Texas A&M University, College Station, TX 77843 (U.S.A.) (Received November 30,1989; accepted February 14,199O)

ABSTRACT Mardon, B., Kronenberg, A.K., Handin, .I., Friedman, M. and Russell, J.E., 1990. Mechanisms of fracture propagation in experimentally extended Sioux quartzite. Tectonophysics, 182: 259-278. Notched samples of Sioux quart&e have been extended to faihtre at temperatures 7’ between 25 o and 710 o C, strain rates i from 5.2 x 1Om6 to 6.7 x 10W4 s-i, and 100 MPa confining pressure, and fracture morphologies examined by optical and scanning electron microscopy. In all the extension tests performed, sample failure occurred by the formation of a tensile fracture in or near the notch mid-plane. Differential stress magnitudes at failure are insensitive to variations in T and < and calculated tensile strengths are comparable to previously reported values for unconfined tests at room temperature. Force-displacement records show a change in mechanical response, from linear elastic behavior at temperatures between 2S0 and 412*C to significant yielding in compression prior to failure in the 500° to 71O*C tests. In all cases, fractures consist almost entirely of intragranular cracks (IGC) which exhibit characteristic surface features which can be used to infer local crack propagation directions. In one test in which fracturing was initiated at an edge flaw, IGC propagation directions show no overall trend. The observations indicate that the mechanism of fracture propagation involves nucleation, growth and coalescence of IGC which are themselves propagating in all directions in the plane of the main fracture. The onset of inelastic yielding prior to failure at elevated temperatures is attributed to the formation of thermally induced GBC which act as nucleation sites for IGC during extension.

Introduction The rich variety of features developed on the surfaces of fractures in brittle solids provides a record of the variations in stress and velocity at the tips of propagating cracks. Detailed observation and interpretation of such features is thus a potentially powerful tool for studying the fracture process, especially when combined with information on bulk mechanical behavior. Microscopic features observed on fracture surfaces have been used to infer the locations and dimensions of fracture-initiating flaws, the direction and velocity of crack propagation and details of the mechanisms of crack nucleation and growth in metals,

* Now at Exxon Production Research Company, P.O. Box 2189, Houston, TX 77252, U.S.A. HO-1951/90/$03.50

0 1990 - Elsevier Science Publishers B.V.

glass, ceramics and polymers (e.g., Strauss and Cullen, 1978) and has served to guide theoretical work on fracturing in these materials (e.g., Broek, 1974; Lawn and Wilshaw, 1975). Although significant advances have been made towards understanding fracturing in rocks and minerals (e.g., Atkinson, 1984) relatively few studies have reported detailed observations of fracture surface features. Ryan and Sammis (1978) studied the mechanics of columnar jointing of basalt, driven by thermal stresses during cooling from a melt. Combining evidence from seismic surveys of crystallizing basalt flows with an analogy to fracture surface features produced in cyclic-loading experiments in alu~num and polymers, they interpreted the parallel, evenly spaced markings on joint surfaces as fatigue striations, each corresponding to a discrete episode of crack extension. Smooth and rough bands within each striation

260

D. MARDON

were associated tion,

with elastic and inelastic

respectively,

deforma-

of the host rock at crack

Using similar surface features,

DeGraff

(1987) were able to infer directions

tips.

and Aydin

of joint growth

a canonical are

ensemble

disposed

mediately

upon

gion has been named ing the mirror

plumose joints

Engelder

markings

cutting

episodic

(1984)

on the surfaces

interbedded

siltstones

attributed

logic materials

which report

mineral

as

a

rockforming

and its similarity

ing has been studied

in geo-

and

roscopic

of fine radial

with to its

intensity including tions

industrial

In fact, fracture

as hackle,

crack branching

A variety

observations

to glass in which fractur-

extensively.

mirror.

Border-

roughening,

as mist. This in turn gives way to a zone of larger

of fracture surfaces have been conducted quartz single crystals. This is due mainly importance

the fracture

re-

usually

of fracturing detailed

featureless.

of cross-fold

scale ridges known studies

Im-

this smooth

is a zone of incipient

consisting

origin.

and shales to

crack growth.

Most experimental

and almost

its high reflectivity,

larly,

and

regions which

the

the site of crack nucleation,

are smooth

and determine the sequence of fracture events leading to polygonization of cooling basalts. SimiBahat

about

surrounding

crack surfaces Based

of four textural

radially

ET AL.

beyond

is observed

of factors

may influence

of development microstructure,

in macroscopic

ridges, referred

to

which macto occur. the relative

of these textural zones, specimen size and variastresses.

For

example,

all

four zones are often well developed and mutually distinct on fracture surfaces in glass, owing to its

surface features produced in tensile tests on quartz are highly similar to those in glass (Norton and

homogeneity and ceramics, however,

Atkinson, 1981). Unlike glass, however, quartz has a weak cleavage on its rhombohedral planes which

or even absent,

isotropy. In polycrystalline some zones may be indistinct

especially

in coarse-grained

porous

contributes to the formation of stepped fracture surfaces (Martin and Durham, 1975; Ball and

materials. The development of zones of increasing surface roughness in the direction of crack propagation is

Payne, 1976) the form of which provides further information on the details of fracture behavior.

a dynamic effect in which breakdown crack front into numerous secondary

The primary purpose of this study has been to investigate the mechanism of tensile fracture prop-

curs (e.g., Shand,

1954; Mecholsky

The mirror

corresponds

agation bulk

in polycrystalline mechanical

behavior

quartz

by examining

the

and

morphologies

of

fractures produced in extension experiments performed on Sioux quartzite. The fractures in our experimental samples show many of the characteristic surface features seen on fractures in quartz single crystals. Detailed observations and mapping of crack propagation directions inferred from these surface features provides substantial insight into the fracture propagation process quartzite constitution responsible yielding elevated

prior to failure temperatures.

and changes in for the onset of

in samples

extended

at

Fracture surface features Glass and ceramics Experimental work on tensile crack propagation in glass and ceramics (e.g., Henderson, 1975; Rice, 1984) has established the existence of

region

of a single, from

primary

the initiating

crack

of a single cracks ocet al., 1978).

to the propagation

that

accelerates

flaw. As the velocity

away of the

crack tip nears the terminal velocity for crack propagation of the medium, sufficient energy becomes available to nucleate secondary microcracks about

the primary

propagation ing in the Rayleigh upper

surface

bound

crack tip, but not for extensive

of these secondary cracks, thus resultformation of mist. The velocity of waves

is usually

for the terminal

taken

crack velocity

as an (e.g.

Field, 1971) and velocities of 0.6 u, are typically observed in experiments where v, is the shear wave velocity

(Mecholsky

et al., 1978). The larger

energy release rate associated with a longer overall crack cannot effect further acceleration of the primary crack but instead produces increasingly extensive propagation of secondary cracks leading to hackle formation and, ultimately, crack branching. The presence of flaws in polycrystals tends to hasten the onset of breakdown of the accelerating primary crack front.

FRACTURE

PROPAGATION

Several

IN EXPERIMENTALLY

characteristic

have been identified

fracture

ceramics

whose

of crack propagation.

form

can

cate crack growth parallel this configuration area, change patterns vidual trolled. gation

and

therefore

The

gence of cleavage

to a line bisecting

toward

The concavity

the fracture

origin,

the angle of

of cleavage

especially

suggests

that their formation

teraction

with elastic stress waves (McColm,

the increase associated

with

surface.

steps (Friedel,

a

by in1983).

of crack

Experimental

methods

River of indi-

is cleavage-con-

in the direction

is influenced

in surface

on the surfaces

direction

steps

those on m,

to the step lines because

in which fracturing inferred

was parallel

step intersection.

steps indi-

of the fracture

is down-stream,

the

261

QUARTZITE

gation

features

to infer

Straight

energy,

are often formed

SIOUX

with glass and

be used

minimizes

in elevation grains

surface

in experiments

direction

EXTENDED

propa-

of conver-

1964).

The fractures duced

examined

in this study were pro-

in a suite of extension

dry (no pore pressure)

tests on nominally

Sioux quartzite

at tempera-

tures T from 25 o to 710 o C and strain

rates i of

5.2 X 10m6 to 6.7 x 10e4 s-‘. A lateral confining pressure PC of 100 MPa was applied in all the

Quartz single crystals

experiments.

Essentially all the fracture surface features described above have been produced in tensile frac-

Starting

ture experiments on quartz single crystals, in addition to features associated with its cleavage on the rhombohedral planes r{lOil} and z{Olil}

The texture and composition of Sioux quartzite makes it well suited to the purposes of this study.

(Ball and Payne, 1976; Norton and Atkinson, 1981). A mirror region is generally present about the fracture-initiating flaw. However, for most crystallographic orientations, mist and hackle features are replaced by cleavage steps which are concave toward the fracture origin and increase in size in the direction of crack propagation. Macroscopic crack branching occurs on r and z. Ball and Payne (1976) made a comprehensive study of tensile crack growth in quartz from an edge slit in thin, single crystal slabs of five different orientations in a variety of chemical environments and at temperatures ranging from 77 to 800 K. Arcuate cleavage steps were produced on fracture surfaces of all orientations except for fracture on the (ll!?O) plane in the [liOO] direction. This last orientation exhibited mirror and hackle zones similar to glass. Norton and Atkinson (1981) studied crack propagation from a surface flaw in synthetic and natural Brazilian quartz crystal rods in bending and found that arcuate cleavage steps on basal fracture surfaces exhibited angular, saw-tooth profiles with characteristic hexagonal symmetry. Two intersecting sets of arcuate steps with a gentler, low-amplitude form were produced on m-fractures. In both cases the direction of crack propa-

material

and sample preparation

It is a well indurated, sedimentary orthoquartzite consisting of 99% equigranular quartz and minor amounts of hematite, magnetite, zircon and rutile. The mean quartz grain size, determined by the linear intercept method, is 160 pm. The bulk density

of Sioux

quartzite

is 2.64 g/cm3,

com-

pared to 2.651 g/cm3 for crystalline alpha-quartz (Sosman, 1965), indicating it has extremely low porosity. Krech et al. (1974) have reported a variety of physical properties for Sioux quartzite, including unconfined

tensile

at room temperature.

and compressive Critical

tors for mode I crack propagation zite have been .determined (1982).

strengths

stress intensity

fac-

in Sioux quart-

by Peck and

Gordon

The sample geometry used in the extension tests is shown in Fig. 1. Cylindrical samples with diameters of 18.30( +0.05) mm were cored from a single block of Sioux quartzite. Each core was then cut and ground perpendicular to its axis to a length of 39.8( f 0.9) mm. A circular notch with a radius of curvature of 11.07( + 0.04) mm was machined midway along the length of each core to generate a stress concentration in the sample during extension and thereby localize fracturing. The circular notches were fabricated by turning the samples on a lathe against a cylindrical diamond grinding tool that was held in a controlled feed

D. MARDON

load piston. determined perature

Based using

on axial a hollow

accuracy

ET AL

temperature

profiles

test sample,

the tem-

was taken to be +5”C.

Raw load records (e.g., Fig. 3) show an initial rise as confining pressure is increased, followed by measurements

of

constant-load

packing

segment

friction,

corresponding

and

LOADIN

Fig. 1. Geometry cular

notch

mid-way

Sioux quartzite

of 11.07( +0.04)

along the sample length.

the notch shown

of notched

with a radius is 15.45( +0.05)

with Cu jacket

while jacket

mm.

samples.

sample

-SPECIMEN

sample

Sq-8 is shown

area a at Sq-24

is

with

its

RESISTANCE

removed.

’ Cu

and turned on an axis oriented normal to that of the sample. The diameter of each sample at the notch

mid-plane

was machined

IG PISTON

mm is machined

The cross-sectional Extended

A cir-

a

to free-travel

-

OR

Pb

LUCALOX

FURNACE

JACKET

SPACER

to 15.45( kO.05)

mm. EXTENSION

FITTING

Test apparatus The design of the sample column used are illustrated

assembly and loading in Fig. 2. Notched

samples of Sioux quartzite were sealed in Cu and Pb jackets and extended by retracting an axial loading piston while maintaining a lateral (argon) confining pressure PC of 100 MPa. The loading column incorporates a gun-lock fitting between the lower piston

and closure

of the pressure

vessel OSURE

which allows an interval of free-travel displacement. This permits packing friction to be measured for each test, prior to extending the sample, by measuring the load while advancing and retracting the load piston. Axial loads were measured using a BLH load cell calibrated against a 133 kN (30,000 lb) Tinius Olsen proving ring and confining pressures were read on a Heise gauge. Given the sample dimensions, axial and lateral stresses applied to the sample are resolvable to within kO.7 MPa. An internal resistance furnace with nichrome wire windings was used to achieve elevated temperatures which were monitored using a chromel-alumel thermocouple entering the pressure vessel through a port along the axis of the top

50 mm Fig. 2. Sample

and piston

used for extension were prepared ends.

The

hardened fitting, assembly

with

lower

circular

piston

steel tube allowed

assembly

tests at pressure. notches

assembly,

threaded

of triaxial mid-way

to the endplug

friction

prior to loading

the sample.

their

of a hollow, and a bayonet

piston

measurements

samples

between

consisting

for free travel of the upper

so that packing

gas apparatus

Sioux quartrite

and sample

could be made

FRACTURE

PROPAGATION

IN EXPERIMENTALLY

EXTENDED

SIOUX

sq-2 T = 25’C

263

QUARTZITE

corrected

for the effects of packing

strength,

and for the stress concentration

ated with the notch. conveniently

made

tests on precut

samples

axial force supported mid-plane

measured

load

total

the results as follows.

by an intact at failure

a simple

are

of extension Let F, be the sample

across

and let Fp’ be the

for a precut

displacement.

positive,

jacket associ-

The first two corrections using

the notch

friction,

sample

at the same

Taking

compression

force balance

yields:

to

F,=F,-P,(A-a)+C

IO

05 DISPLACEMENT

Fig.

3. Raw

load-displacement

Following

pressurization

advanced

and then retracted

friction ment

(measured

was then performed

constant

displacement

15

for experiment

in order

to measure

= 2f).

by retracting

corresponds

to the lower

hollow

steel tube.

portion

of the sample

Nominally

A is the cross-sectional

tensile

are obtained

deflection stresses

at a

in the force

engaging

with

the

at the notched

at a load Pc(A - CI) where

area of the load piston

cross-sectional

experi-

the load piston

piston

was

the packing

The extension

rate. The negative

record

Sq-2.

to PC = 100 MPa, the load piston

load difference

and

n is the

area at the notch.

displacement. Once the gun-lock fitting has engaged and contact with the sample is made, the measured deviator+

load drops reflecting stress to the sample.

(1)

where A and a are the cross-sectional areas of the piston and notch mid-plane, respectively, and C is the correction for packing friction and jacket

(mm1

record

be

the application

of

Extension tests on samples containing a precut through the notch were performed at conditions identical to those used in the tests on intact samples to determine jacket strength corrections. Pb

strength. For a precut sample, which can support no tensile axial force, we have: O=Fp’-P,(A-a)+C

(2)

Assuming C is a constant perature, displacement rate, F, is found

by subtracting

age axial stress at failure

for a particular temand jacket material,

(2) from (1). The avera,, is then given by:

u, = F,/a The correction for the stress concentration sociated with the notch is made using an propriate extension, developed

(3) asap-

concentration factor K. During an annular zone of tensile stress is first at the periphery of the notch and then

Stress

expands radially inward, displacing the zone of compression, toward the axis of the sample. The maximum periphery %l,X =

tensile stress a,,,,,, which occurs at the of the notch at failure, is given by:

KU,,

jackets, used only in room temperature tests, were significantly weaker and have smaller strains to failure than Cu jackets. In some tests in which Pb jackets were used, Pb appears to have entered microcracks in the specimen surface, suggesting

our sample geometry. As expected, relatively weak stress concentrator.

these samples could have failed by hydraulic fracture and that the results obtained using Cu jackets

Here, the maximum compressive stress u, is equal to the confining pressure P,; the minimum

may be more

compressive displacements

reliable.

However,

after

correcting

for jacket strength, the load supported by samples extended at the same conditions are the same for both jacket materials, within measurement error. Analysis

of mechanical

data

To determine the failure stress for each test specimen, the measured load at failure Fp must be

(4)

and is taken as the failure stress. Based on results given by Peterson (1974, we estimate K = 1.27 for

stress and

the notch

u3 is the axial nominal strains,

initial sample lengths, were corrected distortions of the apparatus. Observational

is a

stress. Axial dividing by for elastic

methods

Fracture traces were studied in thin sections under plane light and crossed polarizing filters in

D. MAROON

264

......== ’ 4====....._

ET AL

FRACTURE

PROPAGATION

experimentally

IN EXPERIMENTALLY

extended

sure-impregnated surfaces

were

quently

examined

samples

with coated

blue

epoxy.

with

SIOUX

carbon

going, tensile fracture

35 scanning

a narrow

subse-

The measured

Results

tensile Table

TABLE

occurred

stresses

at failure

behavior

In all the extension failure

zone about

tests

performed,

by the formation

the main fracture

differential

stresses

1. In ten of the eighteen samples

within (Fig. 4). of high

u, - a,, axial

a, and amax, and nominal

ple to be discussed

of a through-

in orientations

for all the extension

on notched

sample

consist of

the notch mid-plane

Few cracks are observed resolved shear stress.

elec-

(SEM).

Bulk mechanical

(Fig. 1). Fractures

many cracks that parallel

Fracture and

265

QUARTZITE

that were pres-

using a JEOL

tron microscope

EXTENDED

strains

tests are given extension

tests run

(one test on a modified later),

the average

Comments

c in

sam-

axial stress

1

Sioux quartzite

extension

tests *

T

.

PCa

0,

(“C)

;s-t)

(MPa)

(MPa)

b

-03

Jacket

0” ’

mate-

(MPa)

d enlmax (MPa)

rial

Strain at

W ’

Exp.

failure

(J)

No.

e (W)

25

5.4 x 10-6

100

116.2

cu

-0.3

-0.4

0.42

25

5.4 x 10-6

100

119.1

cu

- 3.2

-4.1

0.35

25

1.2 x 10-s

100

93.1

Pb

_

25

5.5 x 1om5

100

124.5

cu

- 8.6

25

5.6

1O-5

100

112.8

Pb

- 12.2

25

5.7 x 10-s

100

105.6

Pb

- 5.0

25

6.0 x 1O-4

100

96.4

Pb

Sq-4 sq-5

0.31

0.08 _

- 10.9

0.35

0.21

sq-1

- 15.5

0.35

0.34

sq-2

-6.4

0.26

_

0.43

0.12 _

Sq-6

sq-13

Shallow sawcut at notch used to initiate

x

fracture

sq-3 Apparently

did not enter

tensile field 25

6.7

x

1O-4

79.2

100

0.23

Pb

Sq-8

Apparently

did not enter

tensile field 412

1.7 x 10-s

100

500

5.2 x 1O-6

100

108

CU

77.9

-6.1

-7.7

cu

0.42 0.32

0.10 _

sq-15 sq-22

Apparently

did not enter

tensile field 500

8.7 x 1O-6

100

108.0

cu

500

1.1 x 10-5

100

89.2

cu

-3.9 _

-5.0

0.84 0.95

0.78 _

sq-24 sq-23

Apparently

did not enter

tensile field 500

1.7 x 10-s

100

107.5

cu

- 3.4

-4.3

0.75

1.36

Sq-16

500

1.7 x 10-s

100

107.9

cu

- 3.8

-4.8

0.67

0.94

sq-17

500

1.7 x 10-s

100

101.9

cu

-0

-0

0.53

Sq-18

8.4 x 1O-6

100

105.5

cu

-0

-0

0.78

sq-30

251

from

25 o to 500’ C and back to

500/ 25 600

Cycled at pressure

25 o C prior to extension 6.8 x 10-6

99.8

100

cu

0.74

Sq-28

Apparently

did not enter

tensile field 600

8.1 x 1O-6

80.9

100

cu

-

0.43

sq-27

Apparently

did not enter

tensile field 710

6.6 x 10-6

100

104.0

T = temperature;

i = extensional

stress

a,,,

at failure;

no. = experiment

cu

strain

= maximum

PC= confining

rate;

tensile

- 2.0

stress

-2.5 pressure;

at failure;

compressive

Nominal

value at notch (uncorrected

Nominal

value at notch corrected

Corrected

for stress concentration

See text for method

stress). for jacket for friction

of determination.

at notch,

strength). and jacket

friction,

strength.

and jacket

strength.

0.76

(I, - us = differential

W= estimate

number.

PC= q (the maximum

0.68

of mechanical

Sq-26 stress at failure; work

o, = average

in extension

to failure;

tensile Exp.

266

D. MARDON

was tensile

when sample

failure

tests, a,, was approximately six tests, failure

while axial stresses

However,

fractures

these tests have the same location as those

produced

In two

in tests

as tensile

fractures

generated failure

perature,

unrelated

1). As discussed

above,

material

tensile

stresses

temperature

1). This

Given tensile

to variations

room

average

- 11 MPa) reported

ocinter-

stress a,,,

in the tem-

within

used (Table

1). However,

the loading

column

and flaws in the sample

increase

such

tensile

tic behavior

could

stress

deformed

Samples

was generally

con-

insensi-

and strain investigated

rate, (Table

difference

be-

records

at low and high tempera-

extended (Figs.

is in

the maximum

the form of the load-displacement

tures.

at

(- 10 to

is apparently

there is a significant

25 o and 412’ C exhibit

substantially

strengths

in temperature

Bending

of

- 10.9 MPa,

tensile

in the data,

for samples

due to small misalignments

strength

value,

at failure

ated in the sample at the periphery of the notch before the average axial stress becomes tensile. moments

tensile

we esti-

the three largest values

the range of conditions

tween

are gener-

Thus,

by Krech et al. (1974).

the scatter

tive to variations

axial stress at failure

strain rate or jacket

for Sioux quartzite.

the range of unconfined

and orientation

in which

the

(Table

in

as well.

The sign of the measured is apparently

mate

stress

PC= 100 MPa by averaging

were

curred in the tensile field; they are therefore preted

fracture

zero and in the other

occurred

still compressive.

occurred.

ET AL.

at temperatures nearly

5a and

marked

between

perfect

linear

5b). Specimen

by a peak

elasfailure

in differential

centrations and thereby induce fracturing prior to achieving a net tensile stress. Because such imper-

stress and a small, inaudible stress drop to values supported by the metal jacket. In contrast, sam-

fections

ples extended at temperatures undergo significant inelastic

all act

to reduce

stress magnitude (most negative)

the measured

tensile

at failure, we regard the largest values as closest to the “true”

failure

(Fig.

5~). The onset

of 500’ yielding of yielding

0.2

06

04

DISPLACEMENT

P,(=u,

AXIAL

T = 25 o C in Cu and Pb jackets, exhibiting

a similar

mechanical

T = 500 ’ C. d. Sample

(shown

response

as samples

deformed

at T = 25 o C following

correspond

to changes

at

I%)

DISPLACEMENT

Sioux

with arbitrary

Sq-2 deformed

, I0

05 STRAIN

(mm)

for extended

respectively

Sq-30 extended

Displacements

records

TESTS

)=lCOMPo

0

DISPLACEMENT

(mm)

OUARTZITE

EXTENSION

stress-displacement

at

06

04

DISPLACEMENT

(mm) SIOUX

Fig. 5. Differential

occurs

b

cl 02

to 710°C prior to

quartzite

specimens.

offset in displacement). at room

temperature.

heat treatment

lmml

a. Samples b. Sample c. Samples

Sq-1 and

Sq-15 extended Sq-16

at T = 500 o C at hydrostatic

in length of entire samples,

corrected

for apparatus

and

Sq-17

pressure distortion,

at T = 412 o C, extended

at

PC= 100 MPa.

FRACTURE

PROPAGATION

differential sure.

IN EXPERIMENTALLY

stresses well below the confining

Nominal

strains

at failure

temperatures.

mechanical tween 412”

100 MPa (Sosman, Inelastic

nonlinear

behavior

to

the areas

under

at in

static conditions.

which occurs somewhere

be-

this

500 o to 710” C extension

to an elastic

was tensile.

temperatures

similar

and

by finding

subtracting return

in Table

For

between

the

to hydro-

1 for all the

tests for which the measured

at failure

1965).

yielding

determined

for W are given

Values extension

which occurs near 600 o C at

were

their curves

change

twice those obtained

and 500” C, is not due to the alpha-

beta quartz transition

267

QUARTZITE

pres-

in the 500”

Evidently,

behavior,

SIOUX

area corresponding

710° C tests are typically lower

EXTENDED

samples

axial stress extended

25O and 412”C,

at

W varies

in the

from 0.08 to 0.34 J and has a mean value of 0.17 J.

tests (e.g., Fig. 5c) was

For the 500 o to 710 o C tests, W ranges from 0.76

to that observed

also seen in one test (Sq-30) in which the sample

to 1.36 J, with

was extended hydrostatically This indicates

approximately five times larger than that for the lower temperature tests. This effect is illustrated in

at 25’C after first being annealed at 500 ’ C and 100 MPa (Fig. 5d). that the change in mechanical be-

mated

the mechanical

W is approximated under each curve.

and contain

where F, and AL are the force drop and change in axial length at failure, respectively. Values of W for samples which exhibited yielding followed by

low-relief

steps of widely varying

20

-J" QO 5 J

;

IO ..

k!E k u. 0

:

W=O.94

J

0 -R-;

0

DISPLACEMENT

Fig. 6. Estimates respectively.

of inelastic

Substantial

work

differences

of nonlinear

in W are apparent,

behavior

0.6

02

(mm)

W done in extension and increased

re-

I

I3

i 0.4

sizes

"C

A

0.2

area

mist and hackle

sq-2 25'C

w = 0.34

(Sq-17).

the shaded

Thin section examination shows that fractures occupy a narrow zone, generally less than two grain-diameters wide, about the notch mid-plane (e.g., Fig. 4). Fractures consist of many smaller cracks, most of which are linked, that parallel the

(5)

T=

is

fracture surfaces protests are relatively flat

and shapes. Distinct mirror, gions are not developed.

that the sample

“O7

as one-half

Macroscopically, the duced in all the extension

in mechanical we have esti-

w = ;F,AL

J, that

Fracture surface morphology

work W done in extending

the samples to failure. Assuming behaves as a linear elastic solid:

0.96

sion test (Sq-2) and a test run at 500°C

some permanent constituat elevated temperature. In the paper, we argue that thermally-induced micro-

To further illustrate this change behavior at elevated temperatures,

value,

Fig. 6 which shows differential load versus displacement records for a room temperature exten-

havior, from a linear elastic response at low temperature to significant inelastic yielding at high temperatures, is due to tive change that occurs subsequent sections of this change is due to cracking.

a mean

DISPLACEMENT

for experiments associated

0.4 (mm)

Sq-2 (a) and Sq-17 (b) performed

with the lack of yielding

strain to failure exhibited

0.6

at T= 25’

and 5OO”C,

prior to failure at T = 25 o C and the onset

by Sioux quartzite

at T = 500 o C.

D. MARDON

268

Fig. 7. Optical Fracture those

of fractures developed photc nnicrographs co1nsist largely of IGC at all conditions

in samples

surfaces developed

at low temperatures.

c. Fracture

step

ET AL.

Sq-5 (a) and Sq-18 (b) at T = 25 o C and T = iOO”C, rc:spectively. as ctre not as smooth fractures formed at high temperatures

tested. However, at grain

micrographs

boundary

in sample

taken in plane light).

Sq-18

shown

at hig h magnifi cation

(all

FRACTURE

PROPAGATION

main fracture.

IN EXPERIMENTALLY

Individual

one grain diameter

EXTENDED

crack lengths

SIOUX

range from

of fractures

to more than 10 mm. Fractures

formed at all temperatures

consist mainly

which

grains

269

QUARTZITE

412°C quartz

of cracks

grains

4 and 7)

boundaries

i.e., intragranular cracks (IGC). In all cases, grain boundary cracks (GBC) make up a small fraction

to 710°C commonly

of the fracture

7~). Thus,

cut through

quartz

surface.

In thin sections,

Fig. 8. SEM micrographs

of fracture

primarily

and stepped

of IGC (smooth

used to nucleate exhibits

fracture

a river pattern

(Figs.

surface

of sample

surfaces)

in this sample of coalescing

the traces

and promote

cleavage

Sq-13 extended

with isolated fracture

propagation

with respect

its growth

surface

at temperatures typically

without

cutting

of 25’

and

across many

deflections

(Fig. 7a). Fractures

at

produced

grain at 500”

have more jagged traces (Fig. 7b) and show steps at grain boundaries (Fig. IGC

at T= 25’C

GBC (pitted

steps from which

formed

are straight,

which

and i = 1.2

make

x

in top right corner).

from left to right. direction

to each other by 90 o ).

10V5 s-‘. Shallow

b. At higher

has been inferred

up these

a. Fracture

consists

saw cut (at left) was

magnification,

(images

fractures

an IGC

a and b are rotated

D. MARDON

270

SEM examination reveals the form and 1~ )cation of individual IGC and GBC. GBC are irn :gular in shape and appear as pitted patches on the fracture surface with widely ranging orientati !ons relative to the fracture plane (e.g., Figs. 8a and 9a). IGC surfaces are much smoother and are oriented sub-parallel to the main fracture surl!ace (Figs. 8, 9 and 10). Some IGC surfaces are feat1ure-

have a wider range of orientations than those form Led at lower temperatures. In plane polarized light , grain boundaries throughout the samples show a exter rded at the higher temperatures notic ;eably higher relief than in the lower temperature specimens. This suggests that pervasive cracking (2f grain boundaries has occurred at elevated temr jeratures.

Fig. 9. SEM micrographs

of fracture

from GBC step. b. Two well-developed

surface

(sample

Sq-13).

sets of intersecting

ET AL.

a. Arcuate

arcuate

propagation

cleavage

steps of IGC suggest

steps on IGC provide direction.

a high-confidence

crack

growth

indicator

directio n out of local crack

FRACTURE

PROPAGATION

IN EXPERIMENTALLY

EXTENDED

SIOUX

less or show broad undulations. However, many IGC exhibit diagnostic surface features, like those seen on crack surfaces in experimentally deformed quartz single crystals, which can be used to infer IGC propagation directions. Examples include river patterns (Fig. 8) and concentric, arcuate cleavage steps (Fig. 9a). In some cases, intersect-

Fig. 10. SEM micrographs parallel

cleavage

possibly

across a subgrain

of complex

steps to coalescing

within a single quartz these features

cleavage

wall. b. Multiple

grain (small arrows). within individual

ing sets of arcuate cleavage steps are observed (Fig. 9h). Often, the direction of IGC propagation inferred from these features is away from an adjacent GBC (Figs. 8 and 9a). This suggests GBC form pre-existing flaws which act as nucleation sites for IGC. The inferred direction of IGC propagation is often different for adjacent quartz grains

steps on IGC surfaces

river pattern

within

sets of arcuate Patterns

suggest

of fracture

an individual cleavage multiple

grains yield low-confidence

271

QUARTZITE

in sample

IGC suggesting

Sq-13. a. Transition a change

in growth

steps indicating

strongly

crack nucleation

sites along grain boundaries.

indicators

varying

of crack propagation

direction

directions

from closely-spaced direction

by

- 45O,

of crack propagation Visual averages

(large arrows).

of

272

D. MARDON

and, in some cases, varies within individual grains (Figs. 10a and lob). In the example shown in Fig. lob, IGC appear to have nucleated at several places on a single quartz grain boundary. These observations indicate that the grain-scale mechanism of fracture formation is complex, involving simultaneous propagation of many cracks in different directions within the fracture plane.

Fig. 11. SEM micrographs

of fracture

exhibit many of the features

observed

patterns.

b. In addition

surface

of sample

for IGC of fractures

to these features,

fracture

surfaces

Fractures in samples extended at 500 o to 710” C show the same surface features as those developed in the lower temperature tests, induding river patterns and arcuate cleavage steps (Fig. lla). In addition, the surfaces of these frac:tures show traces of IGC, intersecting the main fralcture at high angles (Fig. lla). This observation indicates that IGC formed in samples extendced at

Sq-26 extended generated

at T= 710°C

at room temperature,

of high temperature

small flake-like

ET AL.

steps.

samples

and

(= 6.6

including

X

10m6 s-i.

arcuate

a. IGC s urfaces

cleavage

show IGC which intersect

steps an id river at high ang les and

FRACTURE

PROPAGATION

elevated

temperatures

orientations, from

IN EXPERIMENTALLY

thin

have

consistent section

EXTENDED

a broader

observations.

Unique

fractures produced at high temperatures flake-like steps, up to a few micrometers ter (Fig. lib).

range

with the conclusions

The origin

SIOUX

of

the saw cut. Together,

drawn

the direction

to the

from the saw cut.

are small in diame-

of these features

is not

known. Crack propagation

213

QUARTZITE

where en echelon

cracks overlap

The variability inferred

served

in SEM,

in the directions from

IGC

suggests

of crack propa-

surface that

the

features direction

obof

motion of a macroscopic fracture front may have little or no influence on the propagation direction of individual cracks nucleating within the fracture tip process

zone.

To test for a relationship

be-

tween crack (grain-scale) and fracture (macroscopic) propagation directions, an extension test was performed at room temperature using a modified notched sample (Sq-13) in which a shallow saw cut was placed in one side of the notch mid-plane to initiate fracturing. Surface features on the fracture produced in this test were mapped at two scales of observation, on a close-up photo-

that

was away

(Fig. 12b). Nearly

all steps

on the fracture

surface

vergence.

On the close-up

photograph

crack

tips just

Viewed

along

below

have

the same (Fig. 12a),

in color than the surround-

ing surface due to scattering gation,

indicate

propagation

Fractures consist of en echelon cracks, most of which are linked. Steps on fracture surfaces occur

these steps are lighter

directions

these features

of fracture

of light by en echelon

the main

the fracture

fracture

plane,

surface.

away from

the

saw cut, these steps would appear as en echelon cracks rotated clockwise relative to the main fracture plane. Presumably, these are secondary cracks which formed by breakdown of the primary crack front as it accelerated away from the saw-cut. Directions of crack propagation at the grainscale were inferred from surface features mapped on IGC surfaces in a traverse of contiguous SEM photographs taken along a chord oriented normal to the saw cut (Figs. 12b and 13). Like the fractures produced in tests using standard notched samples, the fracture surface of Sq-13 consists

graph and in a traverse of SEM photographs. Based on the radius of curvature of the tip of the

almost entirely of IGC, oriented sub-parallel to the fracture plane, linked by GBC, at high angles to the fracture plane, which form steps in the

saw cut, about 0.2 mm, the stress concentration the deepest part of the saw cut is estimated

the total fracture

have

been

about

ten

times

stronger

than

at to that

associated with the notch. As expected, the nominal stress across the notch at failure was small and did not appear to reach the tensile field (Table 1). In a close-up photograph (Fig. 12a), the fracture surface can be separated into two regions of distinctly different surface roughnesses. Surrounding the saw cut is a relatively smooth zone containing a few small steps that is interpreted as a fracture mirror. The remainder of the fracture surface contains steps interpreted

much larger and more numerous as hackle. The boundary between

these regions is symmetric and concave toward the saw cut. The distance between this boundary and the leading edge saw cut measured along a diameter bisecting the saw cut is 3.2 mm (Fig. 12b), about one fifth the diameter of the notch midplane. Many steps on the fracture surface have raised, straight edges that trend nearly normal to

fracture

surface.

GBC comprise surface.

tion, there is no roughness between

a small fraction

of

At this scale of observa-

marked difference in surface the mirror and hackle regions,

Determinations of local crack propagation direction were assigned either high-confidence (solid arrow, Fig. 13) or low-confidence (open arrows) ratings. These ratings were subjective and reflect possible ambiguity in inferring crack propagation directions. High-confidence ratings were reserved for those features judged tors of local propagation tinct

river

patterns

and

as unambiguous indicadirection, including disarcuate

cleavage

steps

(Figs. 8 and 9), whereas low-confidence ratings were awarded in situations where an interpretation other than the one given was possible (Fig. 10) but still less likely. No determination of crack propagation was made in cases where two or more alternative interpretations appeared equally likely. In contrast to the direction of fracture growth, i.e., away from the saw cut, indicated by macro-

D. MARDON

274

I........&A -4,..m..............e.....w.....v

%. ... ... ...L&&p? . . . . . .

I

. . . . . . . . . . .

p’.]

ET AL.

from SEM traverse across sample Sq-13. Grain boundaries are shown as solid lines and GBC at the surface are shown stippled. Local

P_= lOOMPa

Tz25C

crack propagation directions are indicated for IGC, based upon cleavage steps and river patterns. The overall fracture extension direction is vertical, away from the saw cut.

Fig. 13. Map of fracture surface constructed

iJ

SQ-13

High Confidence LOW Condidence

I

Local Crack Propagation Direction

Grain Boundary

400pm

276

scopic surface features (Fig. 12), there is no overall trend in local crack propagation directions indicated by IGC surface features (Fig. 13). This indicates that microstructural heterogeneities, especially grain boundaries and cleavage, are the dominant controls on the direction of crack propagation at the grain-scale. Figure 8 shows a striking illustration of this effect. In this example, a prominent river pattern provides a ‘high-confidence indicator of IGC propagation direction (large arrow, Fig. X), away from an adjacent GBC, that is at least 100” oblique (clockwise) to the overall direction of fracture propagation (small arrow, Fig. 8). Note that this location is less than 0.5 mm away from the saw cut at which the fracture initiated and that the GBC is oriented parallel to the fracture plane. Opening displacements across the GBC in this example apparently resulted in tensile stress concentrations along its perimeter that were substantially stronger than that associated with the nearby saw cut and thereby initiated crack growth in the adjacent quartz grain. Discussion

Detailed examination of the fractures produced in our experiments has established that, over the range of conditions investigated, failure of Sioux quartzite occurs by tensile fracturing. Fractures consist almost entirely of ICC which exhibit characteristic surface features like those seen on fractures in quartz single crystals extended under conditions which ensured brittle behavior (Ball and Payne, 1976; Norton and Atkinson, 1981). In addition, our results indicate that catastrophic fracturing of quartzite involves localized nucleation, propagation, and coalescence of microcracks about the primary fracture front. This is essentially the same mechanism that has been inferred for stable fracture growth in quartz-bearing crystalline rocks from both field (e.g., Segall and Pollard, 1983) and experimentai studies (Hoagland et al., 1973; Peck and Gordon, 1982). While a consistent direction of fracture propagation at the macroscopic scale can sometimes be identified, crack propagation at the grain-scale has no such preferred direction. This implies that the tip of a propagating fracture

Il. MARDON

ET AL,

consists of a zone of microcracks which are themselves propagating in various directions in the plane of the main fracture. Evidently, the macroscopic stress field associated with the main fracture confines IGC formation within a narrow zone, up to a few grain-diameters wide, about the fracture plane while heterogeneities in stress intensity at the grain-scale, associated with the rock grain structure, control IGC nucleation and propagation. Because sample failure occurred by brittle fracturing in all the extension tests performed, the transition in mechanical behavior, from a linear elastic response at low temperature to significant inelastic yielding prior to failure at high temperatures, cannot be due to a change in deformation mechanism. Instead, this transition, which occurs between 412” and 500°C appears to be due to thermally induced microcracking of quartzite grain boundaries which act to increase the density of critical flaws for IGC nucleation during extension. This interpretation is supported by the mechanical response observed in extension test Sq-13, run at 25” C after first annealing the sample at 500°C which shows inelastic yielding like that observed in the extension tests run at 500 o to 710 o C. Thin section observations suggest that grain boundaries in samples heated to at least 500” C may be extensively cracked. However, many of these samples have non-zero tensile strengths, indicating that not all grain boundaries are cracked. Thin section and SEM observations also indicate that IGC in test specimens which exhibited yielding prior to failure have a broader range of orientations than in specimens for which such yielding was not observed. A microcrack population having a broad range of orientations could accommodate the bulk shear deformation associated with yielding in compression prior to failure. Thermally induced microcracking of Sioux quartzite subjected to slow, uniform heating has been investigated by several methods, including measurements of acoustic emissions and P-wave velocities (Johnson et al., 1978). and by pointcounting in thin sections (Friedman and Johnson, 1978). Johnson et al. (1978) found that the onset of microcracking associated with the thermal expansion anisotropy of quartz in unconfined speci-

FRACTURE

PROPAGATION

IN EXPERIMENTALLY

EXTENDED

SIOUX

OUARTZITE

211

the thermal aa

coefficients

(Y, - (Y,, varies

from 0.6 X 10e5 to 1 X 10m5 “C’

in the temper-

ature range 20” to 500 o C (Birch, 1966; Skinner, 1966). Using these values and assuming a tensile

E =;+uAT

strength

Et = E2

ture dl

z

(Y= 10 MPa yields

for microcracking

ture change quartz interface

grains

thermal

expansion

AT at confining of similar

dimension

(c, = e2). Expansion

ferences in expansion

anisotropy

neighboring

(d, = d2), bonded

anisotropy

coefficients

for tempera-

PC between

pressure

depends

a and Young’s

the a and c crystallographic

at their upon

moduli

a threshold

tempera-

PC= 100 MPa in the

at

range 304” to 490 o C. Given the highly idealized nature of the bi-crystal model and assumptions

d2

involved, Fig. 14. Maximum

expansion

dif-

atures

the range of estimated

is in surprisingly

temperature experiments cracking

interval

412”

indicate

has begun

threshold

good agreement

temperwith the

to 500 o C in which our

thermally

induced

micro-

to occur.

E for

axes.

Conclusions (1) Notched samples tended at temperatures

of

Sioux quartzite between 25”

exand

mens occurs at a threshold temperature of 200°C and that thermal cracking continues as the temperature is increased beyond 200” C. This threshold temperature can be expected to increase with increasing confining pressure. To estimate the temperature increase AT re-

710°C strain rates i from 5.2 X 10e6 to 6.7 x lop4 s-l, and 100 MPa confining pressure fail by brittle, tensile fracturing. Failure occurs at differential stresses that are insensitive to variations

quired

in T and

for thermal

cracking

of quartzite

at 100

i and

calculated

tensile

strains model,

(2) The fractures produced in all extension tests consist mainly of intragranular cracks (IGC) which closely parallel the main fracture. Grain boundary

sions are bonded across a planar interface. The a and c crystallographic axes in one of the crystals are, respectively, parallel and normal to this interface; in the other crystal these orientations are reversed. Because the principal directions of thermal expansion anisotropy in the adjoining crystals are orthogonal, this model yields a minimum estimate for AT. Assuming the strains in both halves of the bi-crystal are equal, we find: AT=

a[l+

E,/E,.] +2P, E,(a,-a,.)

for un-

tests at room temperature.

cracks (GBC) make up a small fracture surface area in all cases.

fraction

of the

(3) IGC exhibit characteristic surface features, like those developed on experimentally produced tensile fractures in quartz single crystals, which can be used to infer IGC propagation directions. (4) Two scales of crack propagation are defined. At the sample scale, fracture propagation is directional, whereas microcracks at the grain scale grow in all directions within the fracture plane. This conclusion suggests that the tip of a propa-

(6)

where E, and EC are the effective Young’s

values

are

MPa confining pressure, we have used a simple model for linear, one-dimensional thermoelastic in a quartz bi-crystal (Fig. 14). In this a pair of quartz crystals of equal dimen-

reported

strengths

comparable confined

to previously

T

moduli

in the a and c directions, (Y, and (Y, are the corresponding coefficients of thermal expansion, and (Yis the uniaxial tensile strength of quartz. At temperatures below the alpha-beta transition, the elastic moduli for quartz are insensitive to variations in the temperature (Johnson et al., 1978) so we have used the room temperature values E, = 78 GPa and EC = 103 GPa. The difference between

gating fracture consists of a zone of microcracks. The macroscopic stress field associated with the main fracture restricts IGC formation within a narrow zone about the fracture plane while microstructural heterogeneities, principally grain boundaries and cleavage, are the dominant controls on IGC nucleation and propagation. The mechanism of catastrophic fracture propagation in Sioux quartzite thus involves localized nucleation,

D. MARDON

278

growth,

and

essentially

coalescence

the same

of microcracks

as that

and

for stable

is

Friedman,

M. and Johnson,

fined Sioux quartzite.

fracture

B., 1978. Thermal

ET AL.

cracks in uncon-

Proc. 19th Symp.

Rock Mech., 423-

430.

growth.

Hendersen,

(5) The change linear

elastic

in mechanical

behavior

temperatures

yielding

to 710°C

tests,

quartzite

in extension

between

cant inelastic

from

tests run

at

R.,

1975.

SEM/TEM

Metals and Ceramics Hoagland,

R.G.,

Hahn,

fluence

prior to failure

boundaries.

GBC act as nucleation

in the 500 o cracking

Thermally

of

induced

sites for IGC during

Johnson,

of microstructure B.. Gangi,

Krech,

Cambridge Martin,

for their

study,

fabricating

forming

invaluable

extension

and R. Gott-

contributions

to this

specimens

and per-

pressure

(of more

the notched tests under

than one form). Many thanks are extended to B. Johnson for helpful discussions and to J. Ehrman for his assistance with the scanning electron microscope.

We thank

preparation

C. Littleton

of multiple

for her flawless

manuscripts

in varying

forms of revision. Support from the U.S. Department of Energy (grant DE-FGO584ER13228) is gratefully

in rock.

temperature

F.A. and Hjelmstad,

crackchanges.

acknowledged.

R.J.

McColm,

T.R., 1975. Fracture

University III, and

crack growth

Durham,

W.B.,

of Brittle Solids,

1975.

J. Geophys.

I.J., 1983. Ceramic

Mecholsky,

U.S. Bur.

Press, Cambridge.

in quartz.

gists. Leonard

K.E., 1974. A

research,

7865.

Lawn, B.R. and Wilshaw,

Acknowledgements

schalk

propagation

rock suite for rapid excavation

Mines, Rep. Invest.,

J. Magouirk

1973. In-

J., 1978. Thermal

to slow, uniform

W.W., Henderson,

standard

B. Turk,

Ohio.

A.R.,

Proc. 19th Symp. Rock Mech., 259-267.

exten-

sion.

We thank

on fracture

A.F. and Handin,

ing of rock subjected

Handbook.

Batelle. Columbus,

G.T. and Rosenfield,

Rock Mech., 5: 77-106.

to thermal

Fractography

Info. Center,

25 o and 412 o C to signifi-

is due

grain

response,

Science

Mechanisms

of

Res.. 80: 4837-4844. for Material

Technolo-

Hill, Glasgow.

J.J., Frieman,

S.W. and Rice, R.W., 1978. Fracto-

graphic

analysis

of ceramics.

Cullen

(Editors),

Fractography

In: B.M. Strauss in Failure

and

Analysis.

W.H. ASTM

STP 645: 363-379. Norton,

M.G. and Atkinson

phological

features

Tectonophysics,

B.K., 1981. Stress-dependent

on fracture

surfaces

of quartz

mor-

and glass.

77: 283-295.

Peck, L. and Gordon,

R.B., 1982. The effect

stress on the fracture

energy

of compressive

of Sioux quartzite.

Geophys.

Res. Lett., 9: 186-189. Peterson,

R.E.,

1974.

Stress

Concentration

Factors.

Wiley,

New York.

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