Investigating the Effect of Fatigue on Fracturing

Oct. 2012, Volume 6, No. 10 (Serial No. 59), pp. 1310–1318 Journal of Civil Engineering and Architecture, ISSN 1934-7359, USA

Investigating the Effect of Fatigue on Fracturing

Resistance of Rocks

Nazife Erarslan and David John Williams

Geotechnical Engineering Centre, School of Civil Engineering, The University of Queensland, Brisbane 4072, Australia

Abstract: There is no doubt that an understanding of brittle rock fracturing is a key element in the solution of many engineering problems that involve rock structures. Some rock structures such as bridge and dam abutments and foundations, and tunnel walls, undergo both static and cyclic loading caused by drilling and blasting, and vehicle-induced vibrations. This type of loading often causes rock to fail at a lower than its static strength due to the effect of rock fatigue. A series of laboratory diametrical compression tests was performed on Brisbane tuff disc specimens to investigate their mode-I fracture toughness response to static and cyclic loading, as a function of the applied load. Both the static and cyclic loading tests were carried out on CCNBD (cracked chevron notched Brazilian disc) rock specimens. In the tests described herein, the reduction in fracture toughness under dynamic cyclic loading was found to be up to 48% of the static fracture toughness. Contrary to the static tests, the cyclic tests produced much more crushed material in front of the tip of the chevron notched crack. Key words: Fracture toughness, rock fatigue, CCNBD, SEM (scanning electron microscope).

1. Introduction

Rock masses normally consist of block of intact

rocks separated by joints, faults or interfaces. Even

intact rocks are also categorized as an inhomogeneous,

discontinuous material, on both small and large scales,

since they contain cracks, voids and pores, normally

induced by historical thermal, mechanical and/or

chemical actions and reactions. When rocks are loaded,

an internal stress flow is generated which travels

through the clear paths between several cracks with

potentials of jamming around crack tips causing

material failure. Research into the understanding of

rock crack, fracture and fatigue behaviour under

various loading conditions such as static, cyclic and

impact loading, has attracted many investigators in

recent years [1–4].

The use of underground facilities in rock for

purposes such as transportation tunnels, power station

caverns, radioactive waste repositories, and water and

Corresponding author: Nazife Erarslan, PhD, research

fields: rock mechanics, rock fracture mechanics, rock fatigue, microstructural features of rocks, and discrete fracture networks in rock masses. E-mail: [email protected].

gas storage is increasing. The excavation of such

spaces results in a change in the in situ stress

distribution; these changes alter the mechanical

parameters of the rock mass, including its strength,

deformability and, in particular, its permeability

through the network of stress-relief cracks that develop.

The EDZ (excavation damaged zone) is the disturbed

rock zone around an underground opening following

excavation. The occurrence of (macroscopic)

fracturing around the perimeter of a tunnel could be a

combination of damage caused by the excavation

process (e.g., dynamic forces during drilling and

blasting), and damage caused by stress concentrations

around the tunnel opening; in turn caused by seasonal

cyclic variations of temperature and traffic-induced

cyclic loading.

The mechanical behaviors of rock, and pre-existing

or newly formed cracks under static loading, have been

thoroughly investigated. However, the response of

rock to the cyclic, repetitive stresses resulting from

dynamic loading has been generally neglected, with the

exception of a few rather limited studies [4–9]. The

DAVID PUBLISHING

D

Investigating the Effect of Fatigue on Fracturing Resistance of Rocks

1311

effect of the fatigue on rock failure is still the subject of

much research in fracture mechanics [10, 11].

Rock fatigue has also been studied in the field of

rock cutting. An early attempt to assess the effect of

cyclic loading on rocks due to the action of mechanical

cutters using static and percussive tools was made by

Roxborough [12]. In the last decade, Hood and

Alehossein [13] described a novel method of rock

cutting using ODC (oscillating disc cutting)

technology. They found that the force required to cut

hard rock was reduced up to 60 to 70% using ODC

technology compared with that required using

conventional techniques.

For quasi-brittle materials such as concrete and rock,

cracking is the major cause of material failure in many

cases. The most fundamental parameter in fracture

mechanics is the fracture toughness, which describes

the resistance of a material to crack propagation.

Fracture toughness is an important material parameter

that corresponds to the critical state of the stress

intensity factor required for crack initiation and

subsequent propagation. As a result, assessment of the

resistance to crack propagation is crucial in

understanding the behavior of structures involving

brittle materials. In this paper, stress-induced micro

cracking under cyclic loading will be explained using

fracture toughness phenomena. The fundamental

outcomes described in the paper are believed to be

useful, especially for tunnels and other underground

facilities in rock subjected to both fatigue and creep

loading.

2. Rock Fatigue

It is well known that cyclic loading often causes a

material to fail at a stress level lower than its strength

under monotonic or static loading. This phenomenon is

commonly termed “fatigue”. A typical feature of

fatigue in experimental tests is that the repetition of

loading cycles produces a progressive accumulation of

permanent strain in the specimen.

The results of previous studies, expressed in terms of

the strength reduction of rock specimens subjected to

cyclic loading using the conventional S-N curve,

illustrative of the continuous weakening of rock with

the increase in number of cycles (N) required failing a

specimen loaded to a certain upper peak stress (S),

have demonstrated that brittle rocks can be strongly

affected by cyclic loading. However, most of the rock

fatigue research has been focused on the degradation of

the uniaxial compressive strength under cyclic loading.

There is very limited research on the degradation of the

tensile strength of rocks under cyclic loading.

Understanding of the dynamic tensile strength of rocks

is of considerable importance in assessing the stability

of rock structures under dynamic loads. It is also of

importance in determining rock breakage and

fragmentation.

Based on LEFM (linear elastic fracture mechanics),

two main explanations were proposed to explain why

rock fails under cyclic loading: (a) fracture toughness

decreases with time (stress corrosion), and failure

occurring when the stress intensity factor reaches its

maximum value for the applied load [14-16]; and (b)

the stress intensity factor increases even though the

applied load is kept constant, with failure taking place

when it reaches the fracture toughness [16]. The

physical processes occurring at the crack tip are

complex and probably both phenomena occur [17].

The generally accepted mechanism for

time-dependent weakening of rocks currently is

referred to as “stress corrosion”. Stress corrosion crack

growth occurs because the chemical action of an

environmental agent, such as water, or other

weakening mechanical actions, such as fatigue,

weakens the strained bonds at crack tips and so

facilitates crack propagation under lower stress levels.

Costin and Holcomb [9] indicated that decreasing the

amplitude means increasing the mean stress during

each cycle, which might increase the amount of stress

corrosion and decrease the amount of damage

produced by cycling. Stress corrosion is a

time-dependent mechanism that is most sensitive to the


1312

mean stress level, whereas cyclic fatigue is most

sensitive to the amplitude of the stress cycles.

The results of previous studies, either in terms of the

strength reduction of rock specimens subjected to

cyclic loading, revealed by the conventional S-N

approach, have demonstrated that brittle rocks can be

strongly affected by cyclic loading. However, most of

the rock fatigue researches have been focused on the

uniaxial compressive strength degradation under cyclic

loads. Information regarding the dynamic tensile

properties of rocks is of considerable importance in

assessing the stability of rock structures under dynamic

loads. It is also of importance in determining rock

breakage and fragmentation under explosive and

percussive excavation. On the other hand, there is very

limited research on the response of tensile strength of

rocks to cyclic loading (as opposed to dynamic loading,

such as explosive loads, impact loading). For

quasi-brittle materials such as concrete and rock,

cracking is the major cause of material failure in many

cases. The most fundamental parameter in fracture

mechanics is fracture toughness, which describes the

resistance of a material to crack propagation. Fracture

toughness is an important material property that

corresponds to the critical state of the stress intensity

factor required for crack initiation and the subsequent

propagation. As a result, assessment of the resistance to

crack propagation would be crucial in the

understanding of behaviour of structures involving

brittle materials. Corresponding to the crack

propagation modes, there are three kinds of fracture

toughness: mode-I (opening mode) with mode I

fracture toughness (KIC), mode-II (shearing mode) with

mode II fracture toughness (KIIC), and mode III (tearing

mode) with mode III fracture toughness (KIIIC) (Fig. 1).

3. Experiments and Results

In this study, CCNBD (cracked chevron notched

Brazilian disc) specimens have been used in the

standard testing method for the measurement of the

fracture toughness of rock recommended by the ISRM

(International Society of Rock Mechanics) [15], to

determine the mode-I fracture toughness under both

static and cyclic loading. The geometry of the CCNBD

specimen is illustrated in Fig. 2.

The tests were carried out on Brisbane tuff, which is

a host rock of Brisbane’s first motorway tunnel,

CLEM7, from which core samples were obtained. The

test specimens prepared were from standard Brazilian

discs with a diameter of 52 mm and thickness of 26 mm

(a diameter: thickness ratio of 0.5). The width of the

notches was 1.5 mm. The inner chevron notch crack

length was 7.5 mm and the outer chevron notch crack

length was 36 mm. All the dimensions of geometry

should be converted into dimensionless parameters

with respect to the specimen radius, R and diameter, D.

A circular 40 mm diamond saw was used to cut the

required notch. A special designed jig recommended

by ISRM was used to ensure that the chevron notches

are exactly in the center of the disc. Additionally, the

jig was controlled by an electronic alignment device

shows the displacement depending on x, y and z

Fig. 1 Three fracture modes and corresponding crack surface displacements.

Fig. 2 The CCNBD specimen geometry with recommended test fixture.

coordinates

penetration

shown in Fig

was used for

Instron 2670

was used to

displacemen

1 Hzfor all

expressed in

total range.

Two diffe

(a) cyclic

constant am

(Figs. 4a an

level and co

loading (Fig

Sinusoida

obtain an S

weakening o

cycles (N)

certain uppe

in tests to d

small, the d

However, th

causing failu

fatigue. A m

(from 1.12 t

In the dy

amplitudes

fatigue on th

Fig. 4 Incre

(a)

Inv

to control

of the saw.

g. 3. An Instr

r the dynami

0 series crack

measure the

nt). The cycli

l tests. The

n terms of an a

erent types of

loading with

mplitude, term

d 4b) cyclic

onstant ampli

g. 4b).

al cyclic load

S-N curve il

of the rock w

required to

er peak stress

determine th

data around h

he S-N curve

ure was reduc

maximum redu

o 0.82 MPa√

ynamic cyclic

were tested

he fracture to

asing mean lev

vestigating th

the center

Some prepa

on 6027 Rock

c compressiv

k opening dis

CMOD (crac

c loading fre

cyclic loadi

absolute (± va

f cyclic loadi

h constant m

med sinusoida

loading with

itude, termed

ding tests we

llustrative of

with increase

fail a specim

(S). Since the

he fracture to

high amplitu

e shows that t

ced from 4.5 t

uction in the

√m) was obtai

c loading test

to investiga

oughness of B

vel dynamic cy

he Effect of Fa

alignment

ared samples

k Testing Sys

ve testing, an

splacement ga

ck mouth open

quency used

ing amplitud

alue), equal to

ing were appl

mean level

al cyclic load

increasing m

d dynamic cy

ere carried ou

f the continu

in the numbe

men loaded

e load range u

oughness is v

udes is cluste

the ultimate

to 3.2 kN by r

static KIC of 2

ined (Fig. 5).

ts, four diffe

ate the effec

Brisbane tuff

yclic loading.

atigue on Fra

and

are

stem

d an

auge

ning

was

de is

o the

lied:

and

ding

mean

yclic

ut to

uous

er of

to a

used

very

ered.

load

rock

27%

erent

ct of

f: (a)

0.45

kN

and

T

und

√m

The

1.12

amp

resu

redu

cyc

rock

fati

betw

give

plot

Fig.

(b)

acturing Resi

5 kN (10% of

(20% of the

d (d) 1.8 kN (4

The mode-I fr

der static load

using the IS

e maximum re

2 to 0.51 MP

plitude tested

ults and detai

uction clearl

lic loading o

ks. For a cle

gue on the

ween static

en in followi

tted on the sa

. 3 Prepared

stance of Ro

f the SUL (sta

SUL); (c) 1.3

40% of the S

racture toughn

ding was calcu

SRM (ISRM,

eduction of th

Pa√m) was o

d (1.8 kN or

ils of tests ar

ly illustrates

on the fractur

ar understand

damage me

and dynamic

ing section, i

ame axes.

CCNBD specim

ocks

atic ultimate l

35 kN (30%

UL).

ness (KIC) of

ulated as 1.12

1978) sugge

he static KIC o

obtained with

r 40% of the

re given in T

the dramat

re resistance

ding of the e

echanism, a

c cyclic load

in which bot

mens.

1313

oad)); (b) 0.9

of the SUL),

Brisbane tuff

2 to 1.5 MPa

ested method.

of 46% (from

h the highest

e SUL). The

Table 1. This

tic effect of

of cracks in

effect of rock

comparison

ding tests is

th results are

3

9

,

f

a

.

m

t

e

s

f

n

k

n

s

e


1314

Fig. 5 S-N curve for CCNBD specimens.

4. Damage Mechanism of Rock Fatigue

A typical feature of fatigue in experimental tests is

that the repetition of loading cycles produces a

progressive accumulation of permanent strain in the

specimen, rather than any significant decay in the

material’s elastic modulus. In most research, acoustic

emission and specimen photomicrography suggest

microfracturing as the principal mechanism in the

fatigue failure of rock, with distinct differences

between cyclic compression and cyclic tension [8].

As seen in Fig. 6, both failure loads and damage

mechanisms are quite different under static and

dynamic cyclic loading. In both test types, stable and

unstable crack propagation stages are clear, however,

the resistance of crack propagation to cyclic loading

with accumulation of plastic deformation (0.8 mm) is

much more compared with the relative value (0.025

mm) under static loading before failure (Fig. 6). This

behaviour shows that development of a large number

of microcracks causing accumulation of irreversible

deformation is observed even prior to the appearance

of main cracks in a loaded specimen. This phenomenon

is similar to the subcritical failure of geomaterials

commonly known as subcritical crack propagation. A

load — CMOD plot further reveals that there is a clear

tensile softening behaviour with dynamic cyclic

loading graph. Because of the different postpeak

behaviour, the behaviour of the damage zone at the tip

of the chevron notch inside the sample is impressively

different. This may help to explain the fatigue

mechanism by using the FPZ (fracture process zone)

static loading tests given in the previous section (Fig.

6). These conclusions are quite impressive and helpful

Table 1 Results of Type I cyclic loading tests on CCNBD specimens.

Sample Amplitude % SUL Ultimate load (kN)Number of cycles up to failure

Mode-I Stress Intensity Factor (KI)

* Reduction of KIC (%)

CCNBD-Rp1 10 2.39 2453 0.62 35

CCNBD-Rp2 10 1.95 1829 0.50 45

CCNBD-Rp3 10 2.69 2261 0.69 26

Average 2.34 2181 0.61 35

CCNBD-Rp1 20 2.16 1553 0.55 41

CCNBD-Rp2 20 2.10 1501 0.53 42

CCNBD-Rp3 20 2.24 1630 0.57 38

Average 2.17 1561 0.55 40

CCNBD-Rp1 30 2.40 1218 0.62 34

CCNBD-Rp2 30 2.5 1702 0.64 32

CCNBD-Rp3 30 2.42 1501 0.62 33

Average 2.44 1473 0.63 33

CCNBD-Rp1 40 1.86 319 0.48 50

CCNBD-Rp2 40 2.17 446 0.55 41

CCNBD-Rp3 40 1.95 136 0.50 47

Average 1.99 300 0.51 46

* α is assumed at 0.5.

MPa m

to explain ro

front of the

behaviour p

important o

crack surfac

dynamic cyc

under dynam

including sm

chevron tip,

material is o

failed under

Rock fati

progressive

in the specim

decay in the

damage plot

degradation

irreversible

failure. Ac

responsible

increasing

influence th

mouth disp

irreversible

failure. At

develops fa

constant ra

begins to gro

In order t

damage pro

Fig. 8 CMO

Inv

ock fatigue me

cracks. In c

postpeak was

observation w

ces of failed

clic loading t

mic loading, t

mall particle

as shown in

observed on

static loading

igue can be

accumulation

men, rather th

e material’s e

ts (Fig. 8), cyc

of rock str

deformation

ccumulation

for the fatigu

trend of th

he cumulative

lacement res

deformation

the beginni

st, then defo

ate and fina

ow very fast u

to examine th

ocess at th

OD versus num

vestigating th

echanism in r

contrast, any

s not observ

was made by

d specimens

tests. For the

there is a clea

es and dust,

Fig. 4b. How

crack surfac

g, shown in F

e visualized

n of permanen

han observin

elastic modul

clic loading c

rength with

in front of th

of plastic

ue damage; th

he irreversib

e fatigue dam

sponse, it ca

increases co

ng, irreversi

ormation incr

ally cumulat

until failure.

he major char

he microscop

mber of cycles p

he Effect of Fa

rocks. Concep

tensile soften

ed with ano

y examining

after static

specimens fa

ar crushed reg

in front of

wever, no crus

ces of specim

Fig. 7.

by plotting

nt strain (CM

ng any signifi

lus. As show

caused signifi

accumulation

he crack tip u

deformation

he magnitude

ble deforma

mage. From cr

an be seen

ontinuously u

ible deforma

reases at a s

ive deforma

racteristics of

pic level, S

plots for dynam

atigue on Fra

pt in

ning

other

the

and

ailed

gion,

f the

shed

mens

the

MOD)

icant

wn in

icant

n of

up to

n is

and

ation

rack

that

up to

ation

slow

ation

f the

SEM

(sca

cha

by m

Fig.spec

Fig.chevload

mic cyclic loadi

acturing Resi

anning electro

aracteristics o

means of a JE

. 6 Comparcimens tested u

. 7 Failed spevron tip: (a) ding.

ing tests with a

stance of Ro

on microscop

of the fracture

EOL JMS-64

ison of load-Cunder static an

ecimens and daunder static

amplitude of 0.

ocks

pe) imaging w

e surfaces we

60 LA SEM.

CMOD curvend cyclic loadin

amaged zones loading; (b)

.45 kN and 1.8

1315

was used. The

ere examined

The JEOL

es of CCNBDng.

in front of theunder cyclic

8 kN.

5

e

d

D

e c


1316

JSM-6460 LA is a tungsten low-vacuum analytical

scanning electron microscope. In this study, all rock

fracture images were obtained under LV(low vacuum)

chamber pressures, i.e., 1–50 Pa (with adjustable

pressure between 10 Pa and 270 Pa). This allows

certain samples to be observed uncoated and reduces

damage to the specimens caused by the effects of high

vacuum.

The tips of the chevron notch crack in the CCNBD

specimens tested under both static and cyclic loading

were examined by SEM. Scanning electron

micrographs of fracture surfaces of Brisbane tuff

CCNBD specimens tested under static loading and

cyclic loading are shown in Figs. 9 and 10 respectively.

When compared with static rupture, the main

differences with the cyclically-loaded specimens are

two-fold: (a) the number of fragments produced is

much greater under cyclic loading than under static

loading; and (b) intergranular cracks are formed due to

particle breakage under cyclic loading (Fig. 10)

compared with smooth and bright cracks along

cleavage planes under static loading (Fig. 9).

SEM imaging revealed that the primary fatigue

damage mechanisms in front of a chevron notch crack

are grain decohesion and intergranular cracks. Debris

and dust are the results of fatigue damage in Brisbane

tuff cement and around loosened grains. The fatigue

cracks in the cement are restricted around the grains

and cannot grow through the grains. It is perhaps true

to say that those fatigue cracks are stable (subcritical)

cracks that coalescence to form macroscale fatigue

cracks resulting in failure. It is also possible to say that

each grain after decohesion may behave as an indenter

to indent the surface of the weaker cement material

under far field cyclic diametral compressive loading.

This could be an explanation for the mechanism of the

debris material around and in the corners of loosened

grains.

Fig. 9 SEM images of damaged region in front of chevron notch crack tip under static loading.


1317

Fig. 10 SEM images of damaged region in front of chevron notch crack tip under cyclic loading.

5. Discussion and Conclusions

The maximum reduction of the static KIC of 46%

was obtained for the highest amplitude dynamic cyclic

loading tested. For sinusoidal cyclic loading, a

maximum reduction of the static KIC of 27% was

obtained. These reductions clearly illustrate the

dramatic effect of cyclic loading on the fracture

resistance of cracks in rocks.

Damage was quantified as the accumulation of

permanent strain in front of the chevron notch crack tip

with each cycle of loading, since microfracturing

introduces nonlinearity into the theoretically elastic

behavior of the rock. A continuous irreversible

accumulation of damage was observed in dynamic

cyclic tests carried out at different amplitudes. After

the accumulation of irreversible damage and failure of

the specimen, clear tensile softening was observed in

cyclic loading tests carried out at different amplitudes

on vertically aligned chevron notch cracks (mode I).

However, no postpeak behaviour was observed in the

CCNBD specimens tested under static loading. This

may show that there is an extensive fracture process

zone in front of the chevron notch crack tip, which may

explain the large number of fragments produced under

cyclic loading.

The SEM results enable some of the qualitative

features of the fatigue damage process in Brisbane tuff

to be inferred. It was clearly understood after SEM

analysis that rock fracturing depends strongly on its

microstructures and loading situation. Because of the

delicate balance between the stress required to cause a

mineral grain to cleave and the stress required to cause

brittle grain boundary cracking it is not always an easy

matter to predict which will predominate under any

given set of conditions. SEM images showed that


1318

fatigue damage in Brisbane tuff is strongly influenced

by the failure of the matrix because of both

intergranular fracturing and transgranular fracturing.

The main characteristic is particle breakage under

cyclic loading, which probably starts at contacts

between particles and is accompanied by the

production of very small fragments, probably resulting

from frictional sliding within the weak matrix. This

stage can be correlated with a steady progression of

damage and produces a general “loosening” of the rock,

which is a precursor to the formation of intergranular

cracks.

Acknowledgments

Acknowledgement is made to Leighton Contractors

who provided core samples of Brisbane tuff from the

CLEM7 Project, and to Professor Ted Brown, Les

McQueen, Mark Funkhauser and Rob Morphet of

Golder Associates Pty Ltd for their assistance and

advice. The work described forms part of the first

author’s Ph.D. research carried out within the Golder

Geomechanics Centre at The University of Queensland.

The first author was supported by an Australian

Postgraduate Award/UQRS and the Golder

Geomechanics Centre.

References

[1] A. R. Ingraffea, Mixed mode fracture initiation in Indiana limestone and Westerly granite, in: Proc. 22nd US Symp. on Rock Mechanics, Cambridge, MA, 1981, pp. 186–191.

[2] Z. Tao and H. Mo, An experimental study and analysis of the behaviour of rock under cyclic loading, Int. J. Rock Mech, Min. Sci. Geomech, Abs. 27 (1990) 5–15.

[3] T. B. Celestino and A. A. Bortolucci, Determination of rock fracture toughness under creep and fatigue, in: The 35th U.S. Symposium on Rock Mechanics, Reno, Balkema Rotterdam, New York, 1995, pp. 147–152.

[4] V. Petros, M. N. Bagde, K. Holub and P. Michalcik,

Comparison of changes in the strength and the

deformation behaviour of rocks under static and dynamic

loading, in: 10th Congress of the ISRM — Technology

Roadmap for Rock Mechanics, Johannesburg, September,

2003, pp. 8–12.

[5] P. B. Attawel and I. W. Farmer, Fatigue behavior of rock,

Int. J. Rock Mech, Min. Sci. Geomech, Abs. 10 (1973)

1–9.

[6] M. N. Bagde and V. Pedros, Fatigue and dynamic energy

behaviour of rock subjected to cyclical loading, Int. J.

Rock Mech, Min. Sci. 46 (2009) 200–209.

[7] N. Gatelier, F. Pellet and B. Loret, Mechanical damage of

an anisotropic porous rock in cyclic triaxial tests, Int. J.

Rock Mech, Min. Sci. 39 (2002) 335–354.

[8] B. C. Haimson and C. M. Kim, Mechanical behaviour of

rock under cyclic fatigue, Rock Mechanics 3 (1971)

845–863.

[9] L. S. Costin and D. J. Holcomb, Time-dependent failure

of rock under cyclic loading, Tectonophys 79 (1981)

279–296.

[10] A. Lavrov, Kaiser effect observation in brittle rock

cyclically loaded with different loading rates, Mechanics

of Materials 33 (2001) 669–677.

[11] P. Zang, X. U. Jian-Guang and L. Ning, Fatigue

properties analysis of cracked rock based on fracture

evolution process, J. Cent. South Univ, Technol. 15 (2008)

95–99.

[12] F. F. Roxborough, Coal Ploughing, Colliery Engineering

12 (16) (1968) 66–71.

[13] M. Hood and H. A. Alehossein, Development in rock

cutting technology, Int. J. Rock Mech, Min. Sci. 37 (1-2)

(2000) 297–305.

[14] B. K. Atkinson, Subcritical crack growth in geological

materials, J. Geophys. Res. 89 (1984) 4077–4114.

[15] R. H. Dauskard, W. Yu and R. O. Ritchie, Fatigue crack

propagation in transformation-tougned ceramic, J. Am.

Ceram. Soc. 70 (1987) 248–252.

[16] R. H. Dauskardt, R. O. Marshal and R. O. Ritchie, Cyclic

fatigue crack propagation in magnesia-partially-stabilized

zirconia ceramics, J. Am. Ceram. Soc. 73 (1990) 893–903.

[17] T. B. Celestino and A. A. Bortolucci, Determination of

rock fracture toughness under creep and fatigue, in: The

35th U.S. Symposium on Rock Mechanics, Reno,

Balkema Rotterdam, New York, 1995, pp. 147–152.

Documents

Investigating the Effect of Fatigue on Fracturing