Table Of ContentPergamon Titles of Related Interest
Carlsson MECHANICAL BEHAVIOR OF MATERIALS IV
Hearn MECHANICS OF MATERIALS
Kachaniwsky IMPACT ON PRODUCTIVITY OF NON-FERROUS
METALLURGICAL PROCESSES
Macmillan QUALITY AND PROCESS CONTROL IN REDUCTION AND
CASTING OF ALUMINIUM AND OTHER LIGHT METALS
Rigaud ADVANCES IN REFRACTORIES FOR THE METALLURGICAL
INDUSTRIES
Ruddle ACCELERATED COOLING OF ROLLED STEEL
Salter GOLD METALLURGY
Smith FATIGUE CRACK GROWTH — 30 YEARS PROGRESS
Tait FRACTURE & FRACTURE MECHANICS, CASE STUDIES
Valluri ADVANCES IN FRACTURE RESEARCH
Related Journals
(Free sample copies available upon request)
ACTA METALLURGICA
CANADIAN METALLURGICAL QUARTERLY
SCRIPTA METALLURGICA
Proceedings of the International Symposium on
FRACTURE MECHANICS
Winnipeg, Canada
August 23-26, 1987
Co-Sponsored by
the Basic Sciences and Materials
Engineering Sections of METSOC and
the Canadian Committee for Research
on the Strength and Fracture of Materials
Vol. 6 Proceedings of the Metallurgical Society
of the Canadian Institute of Mining and Metallurgy
Edited by
w. R. TYSON
PMRL/CANMET, Ottawa, Ontario, Canada
B. MUKHERJEE
Ontario Hydro Research, Toronto, Canada
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Copyright © 1988 Canadian Institute of Mining and
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First edition 1988
Library of Congress Cataloging in Publication Data
International Symposium on Fracture Mechanics (1987:
Winnipeg, Man.)
Proceedings of the International Symposium on
Fracture Mechanics, Winnipeg, Canada, August 23-26,
1987 edited by W. R. Tyson, B. Mukherjee.
p. cm. — (Proceedings of the Metallurgical Society of
the Canadian Institute of Mining and Metallurgy; vol. 6)
"Co-sponsored by the Basic Sciences and Materials
Engineering Sections of METSOC and the Canadian
Committee for Research on the Strength and Fracture of
Materials."
Includes index.
I. Fracture mechanics — Congresses. I. Tyson, W. R.
II. Mukherjee, B. III. Metallurgical Society of CIM. Basic
Sciences Section. IV. Metallurgical Society of CIM.
Materials Engineering Section. V. Canadian
Committee for Research on the Strength and Fracture of
Materials. VI. Title. VII. Series.
TA409.I56 1987 620.1Ί26—dc19 88-2504
British Library Cataloguing in Publication Data
International Symposium on Fracture Mechanics
(1987: Winnipeg, Man.)
Proceedings of the International Symposium
on Fracture Mechanics, Winnipeg, Canada,
August 23-26 1987.
1. Materials. Fracture. Mechanics
I. Title II. Tyson, W. R. III. Mukherjee, B.
IV. Series
620.1Ί26
ISBN 0-08-035764-4
Printed in Great Britain by A. Wheaton & Co. Ltd., Exeter
INTRODUCTION
This volume contains the proceedings of a Symposium held as a part of
the 26th Annual Conference of Metallurgists held in Winnipeg, Manitoba, 23-26
August 1987. The Symposium was jointly sponsored by the Basic Sciences and
Materials Engineering Sections of the Metallurgical Society of the Canadian Insti
tute of Mining and Metallurgy, and the Canadian Committee for Research on the
Strength and Fracture of Materials.
The Symposium, patterned after the Conference on "Fracture Control in
Engineering Structures" (Can. Met. Quart. _19 #1, Jan. - Mar. 1980) held at a pre
vious Conference of Metallurgists in Sudbury, Ontario, in August 1979, was opened
with a tutorial session of invited reviews of the state of the art in key areas of
fracture research followed by four sessions of presentations of current work. The
topics covered a broad range of materials and methods of evaluation, reflecting the
pervasive interest in avoiding fracture and fatigue in traditional and novel
materials.
We would like to thank the sponsoring organizations for making this
Symposium possible, and our employers and colleagues at Ontario Hydro and CANMET
for invaluable support, both administrative and technical, in preparing for the
Symposium and for processing the manuscripts. Finally, we would like to thank the
participants, and organizers of the individual sessions - Graham Bellamy, Bob
Coote, Jacques Masounave, and Pat Nicholson - for making the Symposium a success.
W.R. Tyson B. Mukherjee
PMRL/CAtfMET Ontario Hydro Research
Ottawa Toronto
Symposium Co-chairmen
v
MICROMECHANISMS OF FRACTURE
J.D. Embury and F. Zok
Materials Science and Engineering
McMaster University, JHE-358
Hamilton, Ontario L8S 4L7
CANADA
ABSTRACT
Various forms of damage may accumulate in engineering materials during monotonic
deformation. The fracture mode is governed by which form of damage first
reaches a critical level. Here, the various types of damage and fracture are
reviewed. Metallographic evidence of the damage in a range of ferrous and non-
ferrous materials under various stress states is presented and related to the
fracture modes. Fracture mechanism maps are used to show the competition
between failure modes, particularly for tests performed under superimposed
pressure.
KEYWORDS
Fracture mechanism maps; damage accumulation; microcracks; ductile fracture;
localized shear failure; delamination.
INTRODUCTION
When stresses are applied to a material it is essential to be able to predict
whether the response will involve elastic or plastic flow or some form of
fracture. However, such predictions are difficult because the competition
between these modes of response depends on the detailed microstructure, the
prevailing state of stress and the thermal-mechanical history of the material.
Thus in the past decades material scientists have pursued two well defined
approaches to the description of fracture processes which can be approximated as
macroscopic and microscopic in concept. The macroscopic approach, termed
fracture mechanics, asks what the resistance to fracture is if the material or
structure contains a pre-existing flaw of known size. In this approach we can
characterize resistance to failure in a quantitative manner by designating a
critical value of a parameter such as stress intensity factor or energy release
rate.
1
2 FRACTURE MECHANICS
In addition, a microstructural approach can be pursued which asks what processes
can become locally favorable relative to continued elastic or plastic flow.
These processes can include a wide variety of failure mechanisms such as brittle
fracture or cleavage, decohesion of grain boundaries, ductile failure by void
growth, delamination, or localized shear.
The description of the competition between these local events, and continued
plastic flow involves a complex array of factors such as the scale of the
microstructure, local chemistry of interfaces, stress state and strain path.
These descriptions are essentially empirical and depend on the use of continuum
descriptions to indicate the levels of stress and strain in the material or the
growth of voids, and the use of criteria such as critical stress levels which
are difficult to verify or to calculate from first principles.
Despite these shortcomings the microscopic approach allows a new dimension of
the fracture process to be explored, mainly the concept of damage accumulation
prior to failure. This is a concept of wide applicability including compressive
failure of granular materials, ductile failure in metals, wear processes,
failure in forming operations and the degradation of composites. Thus the
approach taken in the current work will be to consider damage processes in terms
of nucleation and growth events, and to consider both the stress state and
microstructural dependence of these events. It is important to emphasize the
link between damage accumulation and fracture mechanics in that in many
situations failure occurs by the local accumulation of damage into a critical
sized flaw which initiates failure rather than by growth of a pre-existing
defect.
At this point it is of value to put the damage accumulation process into a
practical engineering context. Consider first the classical situation of the
increase in fracture resistance of structural steels with temperature as shown
by the K data in Fig. 1. A consideration of the stresses at the crack tip
lc
indicates that the local stresses to cause cleavage failure are of the order of
2,000 to 2,500 MPa. However, the event which nucleates cleavage appears to be
heterogenous, and involves the injection of cracks from carbides as shown in
Fig. 2 (a). Thus the control of the ductile brittle transition involves both
Experimental K0 values
Including plastic zone
correction
-125 -100 -75
Temperature (°C)
Fig. 1 Variation in fracture toughness with temperature for a high nitrogen
steel (after Knott, 1973).
FRACTURE MECHANICS 3
i 1 ii i i 1 i
(a) (b)
Fig.2 (a) Optical micrograph of a stable microcrack in the ferrite matrix
originating from a grain boundary carbide (after Timbres, 1970). (b)
The effect of grain size, d and carbide size (inym) on the cleavage
r
fracture strength of steel (after Petch, 1986).
the control of grain size, and the scale of the carbides which inject cleavage
nuclei as shown in Figure 2 (b). In the above case damage is in the form of
microcracks and their spatial organization into a cleavage front. This process
can be observed directly by conducting bend tests in the SEM to determine
whether macroscopic crack growth occurs by cleavage events or by void growth
(Luo et al., 1985). It is worth noting that current models of heterogenous
cleavage are static in form. It is possible that the condition is a dynamic one
which involves the velocity of the crack which can be injected from the carbide
into the ferrite. Kinetic criteria of this type are now being developed by
Hack et al. (1987).
A second important aspect to consider in the use of structural materials is that
as the flow stress of a material is increased, the range of failure modes which
can occur increases rapidly due both to the high local stresses which can result
in decohesion events, and to the occurrence of localized strain due to the
difficulty of maintaining work hardening capacity at high stress levels. These
are shown schematically in Fig. 3. It can be seen that the higher the level of
the flow stress the lower the useful strains which can be imposed prior to the
attainment of a failure mode. However, in terms of materials development, it
may be possible to avoid some failure modes by the use of nanometer scale
materials, amorphous solids and ceramics.
4 FRACTURE MECHANICS
10
10 Lattice decohesion or dislocation nucleation
Shear Localization in cold worked materials
jr
s ·»-"
Cleavage by heterogeneous events or grain boundary failure
Flow stress for structural materials.
10
10
Fig. 3 Schematic drawing showing the increase in available fracture
modes at high stress levels.
MODES OF FAILURE
For clarity let us consider specific modes of failure and proceed to indicate
how they relate to damage accumulation processes. In order to accomplish this
let us consider the pressure dependence of flow and fracture which can be
explored using axisymmetric stress states of the type illustrated in Fig. 4. By
varying the superimposed pressure, or by introducing notches in the tensile
samples, we can attain a wide range of stress states over which fracture can be
studied.
The major failure modes found in monotonic loading are cleavage fracture,
ductile fracture by void growth, brittle intergranular fracture and localized
shear. Examples of these modes for a variety of materials are shown in the
fractographic evidence in Fig. 5.
♦ σ
7
-|σζ= <Τ-ρ
L_2a-J σΓ = σ€ — - σΓ = σθ·- -ρ
-1 0 1
t*
az = ff-p»CTt(r)
ar:-P'at(r)
(b)
Fig. 4. Schematic drawings showing tensile tests under superimposed
hydrostatic pressure, p, and the corresponding stress distributions
(a) prior to necking and (b) after necking (or in pre-notched
samples). Note the additional hydrostatic tension, σ , which results
from the necked (or notched) geometry.
FRACTURE MECHANICS 5
INTER-
DUCTILE SHEAR 1 mm GRANULAR
FRACTURE FRACTURE FRACTURE
Fig. 5. Schematic drawings and fractographic evidence of various fracture
modes at room temperature. Examples are (from left to right):
fracture surface of a 4340 quenched and tempered steel,
macrophotograph of a directionally solidified Al-Ni eutectic alloy,
and the fracture surface of a brittle Cu-0.02% Bi alloy.
♦ Davidson etal, C33 0.40 %C Sphersteel
o ; French #/ Ol, C7] 0.5I %C Spher steel
v : Yojimo et at, C63 Pur« Cu
* Port Ft
o 0.49 %C steel
o » 0.27 7.C steel
/ / /
500 1000
IEAN STRSE S(MoP
Hydrostatic pressure (MPa)
(b)
(a)
Fig. 6. Diagrams showing the effects of superimposed pressure on (a) the ratio
of the fracture strain under pressure, ερ (Ρ), to the fracture strain
at atmospheric pressure, ερ(0), for a variety of materials, and (b)
the void nucleation strain ε^ in a spheroidized steel. Extrapolation
of the data in (b) to ε = 0 gives an estimate of the interfacial
Ν
strength (after Brownrigg et al., 1983).
6 FRACTURE MECHANICS
By conducting a series of tests at different imposed pressures, we can determine
both the pressure dependence of the overall ductility and the pressure
dependence of damage initiation and growth processes as illustrated in Fig. 6
and 7. These types of diagrams are of commercial relevance because in a number
of materials containing high volume fractions of second phase particles the
nucleation event determines the ductility. Thus measurement of the pressure
dependence of the nucleation event yields an approximate value for the critical
stress for interfacial decohesion for various types of particles as shown in
Fig. 6 (b). This type of data may be of value in optimizing features such as
particle size and distribution, interfacial chemistry and particle volume
fraction in both conventional materials and materials fabricated by techniques
such as powder compaction.
By considering the pressure dependence of various events, a map or diagram of
the competitive fracture processes can be developed. These are termed fracture
or failure mechanism maps, and the quantitative description of their development
is given in abbreviated form in the Appendix. We now consider how damage
processes lead to fracture in various materials and how fracture maps can be
used to depict the competition between these processes.
Cleavage and Brittle Intergranular Fracture
At low temperatures and high hydrostatic tensile stresses, many crystalline
solids fail in a brittle manner. Cracks may nucleate through a slip or twinning
process or by injection from second phases, and propagate either by
transgranular cleavage or by an intergranular path.
Fig. 7. SEM micrographs showing the damage due to void growth in a 1045
spheroidized steel at (a) atmospheric pressure and (b) a superimposed
pressure of 1100 MPa. (c) A diagram showing the effect of pressure on
the development of void damage with plastic strain (after Brownrigg et
al., 1983).
