Table Of ContentINTERNATIONAL SERIES ON THE
STRENGTH AND FRACTURE OF MATERIALS AND STRUCTURES
General Editor: D M R Taplin, DSc, DPhil, FIM
OTHER TITLES IN THE SERIES
CARLSSON & OHLSON Mechanical Behaviour of Materials (ICM 4) (2 Volumes)
EASTERLING Mechanisms of Deformation and Fracture
FRANCOIS Advances in Fracture Research (ICF 5) (6 Volumes)
GARRETT & MARRIOTT Engineering Applications of Fracture Analysis
GIFKINS Strength of Metals and Alloys (ICSMA 6)
HAASEN, GEROLD
& KOSTORZ Strength of Metals and Alloys (ICSMA 5) (3 Volumes)
MILLER & SMITH Mechanical Behaviour of Materials (ICM 3)
OSGOOD Fatigue Design, 2nd Edition
PIGGOTT Load Bearing Fibre Composites
RADON Fracture and Fatigue: Elasto-Plasticity, Thin Sheet and
Micromechanisms
SIH & FRANCOIS Progress in Fracture Mechanics
SMITH Fracture Mechanics: Current Status, Future Prospects
TAPLIN Advances in Research on the Strength and Fracture of
Materials (ICF 4) (6 Volumes)
VALLURI Advances in Fracture Research (ICF 6) (6 Volumes)
RELATED PERGAMON JOURNALS
(free specimen copies gladly sent on request)
Acta Metallurgica
Canadian Metallurgical Quarterly
Computers and Structures
Corrosion Science
Engineering Fracture Mechanics
Fatigue and Fracture of Engineering Materials and Structures
International Journal of Solids and Structures
Journal of the Mechanics and Physics of Solids
Materials Research Bulletin
Metals Forum
Physics of Metals and Metallography
Scripta Metallurgica
FRACTURE
AND
FRACTURE MECHANICS
Case Studies
Proceedings of the Second National Conference on Fracture,
University of the Witwatersrand, Johannesburg,
26-27 November 1984
Edited by
R. B. TAIT
Leader, Fracture Research Programme,
University of the Witwatersrand, Johannesburg, Republic of South Africa
and
G. G. GARRETT
Professor and Head of the Department of Metallurgy,
University of the Witwatersrand, Johannesburg, Republic of South Africa
PERGAMON PRESS
OXFORD · NEW YORK · TORONTO · SYDNEY · FRANKFURT
U.K. Pergamon Press Ltd., Headington Hill Hall,
Oxford 0X3 OBW, England
U.S.A. Pergamon Press Inc., Maxwell House, Fairview Park,
Elmsford, New York 10523, U.S.A.
CANADA Pergamon Press Canada Ltd., Suite 104,
150 Consumers Road, Willowdale, Ontario M2J 1P9, Canada
AUSTRALIA Pergamon Press (Aust.) Pry. Ltd., P.O. Box 544,
Potts Point, N.S.W. 2011, Australia
FEDERAL REPUBLIC Pergamon Press GmbH, Hammerweg 6,
OF GERMANY D-6242 Kronberg-Taunus, Federal Republic of Germany
Copyright © 1985 Pergamon Press Ltd.
All Rights Reserved. No part of this publication may be re
produced, stored in a retrieval system or transmitted in any
form or by any means: electronic, electrostatic, magnetic
tape, mechanical, photocopying, recording or otherwise,
without permission in writing from the publishers.
First edition 1985
Library of Congress Cataloging in Publication Data
National Conference on Fracture (2nd : 1984 :
University of the Witwatersrand)
Fracture and fracture mechanics, case studies.
(International series on the strength and fracture of
materials and structures)
Includes index.
1. Fracture mechanics — Case studies — Congresses.
2. Structural failures — Case studies — Congresses.
I. Tait, R. B. II. Garrett, G. G. III. Title.
IV. Series.
TS409.N37 1984 620.1'126 85-9293
British Library Cataloguing in Publication Data
National Conference on Fracture
{2nd : 1984 : University of the Witwatersrand)
Fracture and fracture mechanics : case studies. —
(International series on the strength and fracture
of materials and structures)
1. Fracture mechanics
I. Title II. Tait, R. B. III. Garrett, G. G.
IV. Series
620.1Ί26 TA409
ISBN 0-08-031659-X
Printed in Great Britain by A. Wheaton & Co. Ltd., Exeter
ORGANISING COMMITTEE
Prof G G Garrett Department of Metallurgy
Chairman University of the Witwatersrand
DrRBTait Department of Metallurgy
Principal Conference Organiser University of the Witwatersrand
Metallurgy Department
Dr M F Ball
SASOL
Licensing Branch
Dr K D Bogie Atomic Energy Corporation
Department of Metallurgy
Mr C A Boothroyd University of the Witwatersrand
Department of Metallurgy
Mr M B Cortie
University of the Witwatersrand
Mr P J Eccleston Department of Mechanical Engineering
University of the Witwatersrand
Mr P R Fry Mechanical Services Division
Anglo American Corporation
Mr J D'A Kirkman Middleburg Steel and Alloys
Prof G C Klintworth Department of Mechanical Engineering
University of Pretoria
Dr S L Luyckx Department of Physics
University of the Witwatersrand
Mr D P Spencer Materials Test and Research
ESCOM, Rosherville
Mrs I Clark Department of Metallurgy
Conference Secretary University of the Witwatersrand
v
NOMENCLATURE
A Area of cross-section of a specimen
AQ Area of cross-section of a specimen at the start of testing
Af Area of cross-section of a specimen at fracture
a Crack length - one half the total length of an internal
crack or depth of a surface crack
a Original crack length - one-half of total length of an
0
internal crack at the start of a fracture toughness test,
or depth of a surface crack at the start of a fracture
toughness test
ap Measured crack length - one-half the effective total length
of an internal crack or effective depth of a surface crack
as measured by physical methods
a Effective crack length - one-half the effective total length
e
of an internal crack or effective depth of a surface crack
(adjusted for the influences of a crack-tip plastic zone)
Aa, Aa , . . Crack growth increment
p
da/dN Rate of fatigue crack propagation
B Test piece thickness
b Atomic interval (Burgers vector magnitude)
d Average grain diameter
D^ Lattice diffusion rate
Dg Grain boundary diffusion rate
Dg Surface diffusion rate
E Young's modulus of elasticity
exp Exponential base of natural logarithms
G Strain energy release rate with crack extension per unit
length of crack border or crack extension force
Gj GJJ G Crack extension forces for various modes of crack opening
TTT
h Planck's constant
I Moment of inertia
J Path-independent integral characterising elastic/plastic
deformation field intensity at crack tip; also, energy
release rate for non-linear elastic material
Xll Nomenclature
K Stress-intensity factor - a measure of the stress-field
intensity near the tip of a perfect crack in a linear
elastic solid
K Fracture toughness - the largest value of the stress-
c
intensity factor that exists prior to the onset of rapid
fracture
K Maximum stress-intensity factor
max
K £ Minimum stress-intensity factor
m n
K h Threshold stress intensity factor below which fatigue
t
crack growth will not occur
Kj Opening mode stress-intensity factor
K Plane-strain fracture toughness
IC
Kj£ Elastic stress-intensity factor at the start of a
sustained-load flaw-growth test
Κ Plane-strain K-r threshold above which sustained-load
τςΓρ
flaw-growth occurs
KJJ Edge-sliding mode stress-itensity factor
Km Tearing mode stress-intensity factor
K Rate of change of stress-intensity factor with time
ΔΚ Stress intensity range
k Boltzmann constant
k^ Parameter that determines grain-size dependence
of yield strength
1 Gauge length
0
In Natural logarithm
log Common logarithm
m Strain-rate sensitivity exponent
Nf Number of cycles to failure
n Strain hardening exponent
P Force
P Maximum force
mx
Q Activation energy
Nomenclature xiii
Q Activation energy for crack growth
a
Q Activation energy for creep
c
Qjj Activation energy for self diffusion
T Temperature
T Absolute melting temperature
M
Tp Ductile-brittle transformation temperature
t Time
t Time at the onset of a test
tf Fracture time
U Potential energy
Y True surface energy
s
Yg Grain boundary surface energy
Yp Effective surface energy of plastic layer
6 Value of crack opening displacement
6 Critical crack opening displacement, being one
C
of the following:
(1) Crack opening displacement at fracture
(2) Crack opening displacement at first instability
or discontinuity
(3) Crack opening displacement at which an amount
of crack growth commences
6 Crack opening displacement at first attainment of
m
maximum force
6 Thickness of grain boundary layer
Z
ε Normal strain
ε Normal strain, elastic
β
ε Normal strain, plastic
ρ
ε^ Normal strain, total
e Normal strain at maximum tensile load
max
ε Engineering normal strain
ρ
Nomenclature
Normal strain, critical value at failure
Principal strains (i = 1, 2, 3)
Principal strains, plastic
Cartesian strain components
Strain tensor
Strain rate
Strain rate, elastic
Strain rate, plastic
Strain rate, initial value
Strain range
Plastic strain range
Poisson's ratio
Normal stress
Yield stress under uniaxial tension
Principal normal stresses
Fatigue strength, endurance limit
Fracture stress
Maximum stress
Cartesian components of normal stress
Stress rate
Stress range
Shear stress
Critical shear stress
Principal shear stresses
Shear stress, maximum value
Atomic volume
CONVERSION UNITS
To convert from to multiply by
inch metre (m) ! 2.54 x 10"2
pound force newton (N) 4.448
kilogram force newton (N) 9.807
1 t *y
kilogram force/metre pascal (Pa) 9.807
pound mass kilogram mass (kg) 4.536 x 10""1
ksi pascal (Pa) 6.895 x 106
ksi /in MN m"3/2 1.099
torr pascal (Pa) 1.333 x 102
bar pascal (Pa) 1 x 105
angstrom metre (m) 1 x IO"10
calorie joule (J) 4.184
foot-pound joule (J) 1.356
degree Celsius kelvin (K) T = T + 273.15
K c
IMPORTANT MULTIPLES
I Multiplication factor Prefix Symbol
10-12 pico P !
, -9
1Λ0 nano n
IO"6 micro y
IO"3 milli m
103 kilo k
106 mega I
1θ9 giga MG I
XV
INTRODUCTION
J. P. Hugo
Nuclear Development Corporation of South Africa, Pelindaba,
Republic of South Africa
Materials fracture and degradation in service represents one of the major
technological factors which limits the efficiency and adaptability of industry
today. The National Bureau of Standards in the USA published a report in March
1983 in which it was estimated that fracture related failures represents some 4%
of the USA GNP ($120 Billion per year) of which $40 billion per year could have
been saved by the application of presently available knowledge on Fracture. In
the South African context a pro rata figure would be 1 billion Rand, based on
the 1982 GNP. How then does one go about decreasing this loss? Certainly it
needs a determined effort from government, industry and the educational
institutions in respect of education, establishment of mechanical data banks,
and improved codes, standards and regulations.
Having just referred to education, in this context we refer not only to formal
education but also to "awareness". It is essential that all levels of industry
are educated to the awareness of what fracture related problems could be costing
an industrial company.
It is with these thoughts in mind that this conference's aim was to bring
together engineers and scientists with a central interest in the problems
associated with fracture, failure analysis, and safe design in industries as
diverse as mining, power generation, transport, petrochemical and
manufacturing. Furthermore, the emphasis in this conference, as reported in
this volume, was that based on a "case study approach" deriving important
"lessons to be learnt" from such cases to help prevent similar failures in other
circumstances. Of particular importance in such studies is the application of
fracture mechanics assessment procedures in relation to both "fitness for
purpose" with its economic implications and "residual life evaluation" with its
safety implications. In safety critical engineering applications, in
particular, where the design against fracture is now commonly based on the so-
called defect tolerant approach, the widespread application of this approach
over the last decade has provided invaluable information in respect of safety
prediction and the associated cost savings.
For this Conference, we were particularly pleased to have present some
distinguished speakers from Europe and the U.S.A. Such international
interactions in the fracture field are particularly important since in many
cases the problems encountered are very similar. A two-way interchange of such
experiences in the fracture field should continue to be actively fostered since
xvii
