Higgins R.A. Engineering Metallurgy: Applied Physical Metallurgy
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Fig.
5.5 The
nucleation
and
development
of a
crack
in a
ductile material.
itself
is
strong
and
does
not
shear,
a
minute fissure will develop
at the
interface
(Fig. 5.6). Of
course,
the
development
of the
fissure will also
depend upon
the
degree
of
adhesion between
the
surface
of the
inclusion
and that
of the
metal. Thus,
if
there
is
little adhesion
as, for
example,
at
the interface between copper
and
cuprous oxide particles, then fissures will
form easily,
but if
adhesion
is
high then
the
particles
may
indeed have
a
strengthening effect. Thus sintered aluminium powder (SAP), which
con-
tains
a
high proportion
of
aluminium oxide particles,
is
stronger than pure
aluminium because
of the
high adhesion
at the
Al/Al
2
O
3
interface.
5.41 Other barriers
to the
movement
of
dislocations
can
also initiate
micro-cracks
in a
similar manner. Thus
Fig. 5.7
suggests
how a
grain boun-
Fig.
5.6 A
pile-up
of
dislocations
at
some obstacle leading
to the
formation
of a
crack which
will
be
propagated
if the
stress,
a, is
increased.
EMBRYO
CRACK
OBSTACLE
(SEPARATE
PHASE)
STRESS
STRESS
O"
crack
nucleus
Fig.
5.7 The nucleation of a grain-boundary fissure.
dary can act as a barrier to the movement of dislocations so that a pile-up
occurs and nucleates a micro-crack. Such a crack continues to grow as
further dislocations, possibly generated from the same Frank-Read
source, move to join it. Dislocations will not cross grain boundaries since
lack of alignment and some disorder will always be present there.
Crack initiation can also be caused by movement of dislocations along
close-packed or other planes within a crystal (Fig. 5.8(i)). These dislo-
cations then pile up at the intersections of the slip planes and so form a
crack (Fig. 5.8(ii)).
5.42 It was shown earlier (5.22) that, arising from Griffith's Crack
Theory, at the tip of the crack:
/ Crack length
Stress concentration oc
J——-—
:
—
v
Crack-tip radius
Thus the spread of a crack in a plate glass window is arrested by drilling
a hole in front of the tip of the advancing crack. Similarly, catastrophic
brittle fracture in welded-steel ships (5.50) was prevented by including
dummy rivet holes to arrest the progress of cracks already initiated at
structural faults in the steel.
Fig.
5.8 The initiation of a micro-crack by a running together of dislocations (after A. H.
Cottrell).
plane
plane
plane
cleavage
plane
micro-crack
EDGE DISLOCATIONS
SLIP PLANE
MICRO-CRACK
Ductile-Brittle Transition in Steels
5.50 There have been many instances in the past of failure of metals by
unexpected brittleness at low temperatures. That is, metals which suffered
normal ductile fracture at ambient temperatures would fail at low tempera-
tures by sudden cleavage fracture and at comparatively low stresses. The
failure of the motor sledges during the very early stages of the British
South Pole Expedition of 1912-13 may well have been due to fracture of
this type and contributed towards the final disaster which overtook the
Polar party. In more recent years similar failure was experienced in the
welded 'liberty ships' manufactured during the Second World War for
carrying supplies from America to Europe and was unexpected and
dangerous.
Under normal conditions the stress required to cause cleavage is higher
than that necessary to cause slip, but if, by some circumstances, slip is
suppressed, brittle fracture will occur when the internal tensile stress
increases to the value necessary to cause failure. This situation can arise
under the action of bi-axial or tri-axial stresses within the material. Such
stresses may be residual from some previous treatment, and the presence
of points of stress concentration may aggravate the situation. The liberty
ships mentioned above were fabricated by welding plates together to form
a continuous body. Cracks usually started at sharp corners or arc-weld
spots and propagated right round the hull, so that, finally, the ship broke
in
half.
Had the hull been riveted, the crack would have been arrested at
the first rivet hole it encountered. Some riveted joints are now in fact
incorporated in such structures to act as crack arresters.
5.51 The relationship between mechanical properties and the method
of stress application has already been mentioned (2.52) with particular
reference to the impact test. Plastic flow depends upon the movement of
dislocations and this occurs in some finite time. If the load is applied very
rapidly it is possible for stress to increase so quickly that it cannot be
relieved by slip. A momentary increase of stress to a value above the yield
stress will produce fracture.
5.52 As temperature decreases, the movement of dislocations becomes
more difficult and this increases the possibility of internal stress exceeding
the yield stress at some instant. Brittle fracture is therefore more common
at low temperatures. This is supported by the fact that the liberty ships
were in service in the cold North Atlantic.
5.53 Those metals with a FCC structure maintain ductility at low tem-
peratures, whilst some metals with structures other than FCC tend to
exhibit brittleness. BCC ferrite is particularly susceptible to brittle fracture,
which follows a transcrystalline path along the (100) planes (see 4.12). This
occurs at low temperatures as indicated in Fig. 5.9 and the temperature at
which brittleness suddenly increases is known as the transition temperature.
Other things being equal, as the carbon content of a steel increases so
does the transition temperature, making steel more liable to brittle fracture
near ambient temperatures. Phosphorus has an even stronger effect in
Fig.
5.9 The relationship between brittle fracture and temperature for ferritic and austenitic
steels.
raising the transition temperature in steel and this is one reason why phos-
phorus is one of the least desirable impurities in ordinary carbon steels.
Some elements, notably manganese and nickel, have the reverse effect in
that they depress the transition temperature. Thus, for applications involv-
ing atmospheric temperatures the transition temperature can be reduced
to safe limits by increasing the manganese-carbon ratio of the steel, whilst
at the same time controlling the grain size by small additions of aluminium.
A suitable steel contains 0.14% carbon and 1.3% manganese. Where lower
temperatures are involved it is necessary to use low-nickel steels.
Fatigue
5.60 Engineers have long been aware that either 'live' loads or alternating
stresses of relatively small magnitude can cause fracture in a metallic struc-
ture which could carry a much greater static or 'dead' load. Under the
action of repeated or fluctuating stresses a metal may become fatigued.
Some of the earliest quantitative research into metal fatigue was carried
out in 1861 by Sir William Fairbairn. He found that raising and lowering
a 3-tonne mass onto a wrought iron girder some 3 x 10
6
times would cause
the girder to break, yet a static load of 12 tonnes was necessary to cause
failure of a similar girder. From further investigations he concluded that
there was some load below 3 tonnes which could be raised and lowered an
infinite number of times without causing failure. Some ten years later
Wohler did further work in this direction and developed the fatigue-testing
machine which bears his name.
Many engineering metals are subjected to fluctuating stresses during
service. Thus the connecting rods in a piston engine are successively pushed
IMPACT
VALUE
(j)
AUSTENITIC (F.C.C.) STEEL
FERRITIC
(B(ZC.)
STEEL
DUCTILE
FRACTURE
8O%
BRITTLE
WITH DUCTILE
FRACTURE
AT
RIM
BRITTLE
FRACTURE
TEMPERATURE
(
0
C)
and pulled; contact springs in electrical switch gear are bent to and fro;
rotating axles suffer a reversal of stress direction through every 180° of
rotation; and aircraft wings are continually bent back and forth as they
pass through turbulent air. Often a structure will vibrate in sympathy with
some external vibration emanating from equipment such as an air com-
pressor. This too may initiate fatigue failure so that fracture by fatigue is
probably the most common cause of
engineering
failure in metals.
5.61 The yield strength of a material is a measure of the static stress it
can withstand without permanent deformation, and is applicable only to
components which operate under static loading. Metals subjected to fluc-
tuating or repeated forces fail at lower stresses than do similar metals
under the action of 'dead' or steady loads. A typical relationship between
the number of cycles of stress (N) and the stress range (S) for a steel is
shown in the S-N curve (Fig. 5.10 (H)). This indicates that if the stress in
the steel is reduced then it will endure a greater number of stress cycles.
The curve eventually becomes almost horizontal indicating that, for the
corresponding stress, the member will endure an infinite number of cycles.
The stress born under these conditions is called the fatigue limit, 5
D
. For
many steels the fatigue limit is approximately one half of the tensile
strength as measured in a 'static' test.
5.62 Most non-ferrous metals and alloys and also some steels operating
under conditions of corrosion, give S-N curves of the type shown in Fig.
5.10(iii). Here there is no fatigue limit as such and a member will fail
ultimately if subjected to the appropriate number of stress reversals even
at extremely small stresses. With such materials which show no fatigue
Stress
(S)
Stress
(S)
Fig.
5.10 (i) Represents a test piece suffering alternating stress of range S about a mean
value of zero; (ii) a typical S-N curve for steel; (iii) an S-N curve typical of many non-ferrous
alloys and some steels, particularly those operating under conditions promoting corrosion.
No.
of Stress Cycles (N)
Na of Stress Cycles (N)
fatigue limit(%)
endurance
limit i\)
cantilever
test-piece
No.
of Stress Cycles (N)
limit
an
endurance limit, SN,
is
used instead. This
is the
maximum stress
which
can be
sustained
for a
stated number,
N, of
cycles
of
stress.
Components made from materials
of
this type must therefore
be
designed
with some specific life
(in
terms
of
stress cycles)
in
mind
and
then 'junked'
—as
our
American friends
put
it—after
an
appropriate working life, that
is,
before
the
number
of
cycles
(N) for the
corresponding stress
(S) has
been reached.
It should
be
noted that many authorities
now use the
terms 'fatigue limit'
and 'endurance limit'
to
mean
the
same,
but the
above distinction still
seems valid
in
differentiating between
the two
classes
of S-N
curve
obtained
for
different materials.
5.63 Fatigue-testing machines vary
in
design
but
many
are
based
on
the original Wohler concept
(Fig.
5.11). Here
the
test piece
is in the
form
of
a
cantilever which rotates
in a
chuck,
the
load,
W,
being applied
at the
'free'
end. For
every rotation
of 180° the
stress will change from
W in one
direction
to W in the
opposite direction. Thus
the
stress-range will
be 2W
with
a
mean value
of
zero.
To
determine
the
fatigue limit
(or
endurance
limit)
a
number
of
test pieces
are
tested
in
this
way,
each
at a
different
value
of W,
until failure occurs,
or
alternatively, until
an
infinite number
of stress reversals have been endured—since
it is
somewhat impracticable
to apply
an
infinite number
of
reversals,
a
large number
(say 20 x 10
6
) is
used instead.
STRESs(S)
Fig.
5.11 The
principles
of a
simple fatigue-testing machine
in
which
the
stress range,
S
=
2W.
NUMBER
OF
REVERSALS
OF
STRESS
(N)
FATIGUE
LIMIT
S/N CURVE
EQUIVALENT
CANTILEVER
EFFECT
FINAL TEAR
(CRYSTALLINE)
FATIGUE CRACK
(BURNISHED)
REVOLUTION
COUNTER
BALL
RACE
TEST
PIECE
CHUCK
LOADING
SYSTEM
5.64 The Mechanism of Fatigue Failure Fatigue failure begins quite
early in the service life of the member by the formation of a small crack,
generally at some point on the external surface. This crack then develops
slowly into the material in a direction roughly perpendicular to the main
tensile axis. Ultimately the cross-sectional area of the member will have
been so reduced that it can no longer withstand the applied load and
ordinary tensile fracture will result. A fatigue crack 'front' advances a very
small amount during each stress cycle and each increment of advance is
shown on the fracture surface as a minute ripple line. These ripple lines
radiate out from the origin of fracture as a series of approximately concen-
tric arcs. The individual ripples are far too small to be visible on the
fractured surface except by using very high-powered metallographic
methods, but under practical conditions a few ripples much larger than the
rest, probably corresponding to peak stress conditions, are produced and
these are visible on the fractured surface showing the general path which
the crack has followed (Fig. 5.12).
Fig.
5.12 The progress of fatigue failure.
A fatigue fracture is often easy to identify because the crack-growth region is burnished by
the mating surfaces rubbing together as stresses alternate. The ultimate fracture is strongly
'crystalline' in appearance.
A fatigue fracture thus develops in three stages—nucleation, crack
growth and final catastrophic failure. Since the crack propagates slowly
from the source, the fractured surfaces rub together due to the pulsating
nature of the stress and so the surfaces become burnished whilst still
exhibiting the conchoidal markings representing the large ripples. Final
fracture, when the residual cross section of the member is no longer able
to carry the load, is typically crystalline in appearance. Fatigue failures in
metals are therefore generally very easy to identify.
Fatigue cracks are not the result of brittle fracture but of plastic slip.
During cyclic stressing, at stresses above the fatigue limit, plastic defor-
mation is produced continuously and alternately positive and negative. It
is this continuous to-and-fro plastic deformation in localised regions which
ultimately propagates and spreads a fatigue crack. The continual plastic
oscillation of metal layers along slip planes in and out of the surface causes
burnished
crystalline
FRACTURE
CRACK
GROWTH
NUCLEATION
some of the metal to produce ridges as work hardening sets in to resist
'back slip'. These ridges are forced up at the surface and are termed
extrusions (Fig. 5.13). Narrow fissures or intrusions are formed in a similar
manner. Several of these intrusions may then interconnect to initiate the
start of a fatigue crack.
Fig.
5.13 (i) Stages in the formation of an extrusion by movements of blocks of atoms
along slip planes; (ii) the nature of extrusions and intrusions.
5.65 Some Causes of Fatigue Failure Since the fatigue character-
istics of metals can be measured accurately, it seems reasonable to suppose
that fatigue failure due to a lack of appropriate allowances in design should
not occur. This is of course true, yet fatigue failure does continue to happen
even in the most sophisticated items of engineering equipment. The cata-
strophic fatigue failure in Comet airliners some years ago is a case in point.
In many such instances a member may be designed to carry a static load
(well above
5
D
or
S
N
),
yet it may be suffering undetected vibrations which
give rise to reversal of stress at a value above S
D
(or
S
N
).
Such vibrations
are often sympathetic.
Other design faults include the presence of such stress raisers as a sharp-
cornered key way in a shaft or an unduly sharp radius in an in-cut corner.
Poor workmanship in the shape of surface roughness, scratches or careless
toolmarks can also cause stress concentrations. Minute quench cracks in
heat-treated steels are also a source of fatigue failure as are the presence
of small cavities, inclusions or other discontinuities just below the surface
of the material. A surface weakened by decarburisation or other types of
deterioration which have led to the softening and weakening of the surface
layers also favours the initiation of micro-cracks via the formation of
intrusions.
Corrosive conditions in the environment can also provide stress-raisers
in the form of etch-pits and other surface intrusions such as grain boundary
attack. Ordinary surface oxidation may have a similar effect and conse-
quently nucleate a fatigue crack.
5.66 Methods of Improving Fatigue Strength In order to maintain
fatigue strength it follows from the above that surface finish should always
slip
plane
EXTRUSION
INTRUSION
slip
planes
be good. Engineer craftsmen of the past were not wasting their time when
producing a high surface polish on many of their items of equipment.
Since the fatigue strength of a metal is approximately proportional to its
tensile strength, any method used to increase the tensile strength of the
material will correspondingly improve the fatigue strength. As fatigue fail-
ure nearly always commences at the surface, methods of surface hardening
will be most effective in limiting the initiation of fatigue cracks. Thus,
work-hardening of the surface by shot-peening is beneficial, whilst the
carburising and nitriding (19.10) of steels will improve fatigue strength. A
case-hardened axle provides a good all-round combination of core tough-
ness,
surface wear-resistance and fatigue resistance.
Creep
5.70 So far in this description of plastic deformation and ultimate failure
of metals little mention has been made of the part played by time. Never-
theless, metals in service are often required to withstand steady stresses
over long periods of time and it has been shown that under these conditions
gradual deformation of the metal may occur at all temperatures and
stresses. Metals can therefore fail in this way at a stress well below the
tensile strength at that particular temperature. This phenomenon of con-
tinuous gradual extension under a steady force is known as creep.
The effects of creep in most engineering metals are not serious at ambi-
ent temperatures though some metals of low melting point (T
m
) such as
lead exhibit noticeable creep under these conditions. Lead sheeting which
may have been protecting a church roof for centuries is sometimes found
to be slightly thicker near the eaves than at the ridge. The lead has 'crept'
under its own weight over the centuries.
Creep becomes very serious with many metals at temperatures above
0.4r
m
where T
m
, as noted previously (4.42) is measured on the Kelvin (or
'absolute') scale. Thus T
m
for lead is equivalent to 327 + 273 or 600 K.
Hence 0.4 T
m
(for lead) is 240 K or -33°C. This explains why lead sheeting
on a church roof will be likely to creep appreciably at ambient temperatures
between, say,
—
10
0
C and 30
0
C. Similarly the effects of creep must be very
seriously considered in the design of gas and steam turbines, steam and
chemical plant and furnace equipment. Creep is thus associated in practical
terms with both time and temperature and is basically due to slip by the
movement of dislocations.
5.71 Fig. 5.14 shows the type of creep curve obtained when a metal is
suitably stressed. This curve indicates that, following the initial elastic
strain, the plastic strain associated with creep occurs in three stages:
(i) Primary, or transient creep, EP, beginning at a fairly rapid rate
which then decreases with time because work-hardening sets in.
(ii) Secondary, or steady-rate creep, PS, in which the rate of strain is
uniform and at its lowest value.
(iii) Tertiary creep, SX, in which the rate of strain increases rapidly
TIME
Fig.
5.14 A typical creep curve, showing three stages of creep during a long-time, high
temperature creep test.
until fracture occurs at X. This stage coincides with necking of the test
piece.
The form of relationship which exists between stress, temperature and
the resultant creep rate is shown in Fig. 5.15. At a low stress and/or a low
temperature (curve A) some primary creep occurs but this falls to a neglig-
ible value as strain-hardening prevents further slip from taking place. With
increased stress and/or temperature (curves B and C) the rate of secondary
creep also increases leading to tertiary creep and ultimate failure.
STRAIN
STRAIN
primary
" creep
secondary
creep
tertiary
creep
initial elastic strain
low temperature
and/or low stress
high temperature
and/or high stress
TIME
Fig.
5.15 Variations of creep rate with stress and temperature.
In curve A the creep rate soon becomes negligible as work-hardening sets in. In curve C
the creep rate is higher than in curve B because of the use of either higher stress or higher
temperature.