Higgins R.A. Engineering Metallurgy: Applied Physical Metallurgy
Подождите немного. Документ загружается.
Fig.
4.9 The movement of a screw dislocation.
4.17 A brief mention of experimental evidence supporting the oper-
ation of slip in a polycrystalline mass of metal was made earlier in this
chapter (4.11), but so far we have been dealing mainly with the methods
by which slip can take place in individual crystals. If slip occurred com-
STRESS
STRESS
STRESS
STRESS
Fig.
4.11 The operation of a Frank-Read source.
The original source is visualised as a dislocation line anchored at its ends, possibly by other
faults.
The action of a suitable shear stress causes the line to bow outwards, ultimately
turning upon itself (iii), and eventually forming a complete dislocation loop (v). Since the
original dislocation line still remains, the process can repeat ad lib producing a series of
dislocation loops or ripples flowing out from the original source.
pletely over a whole plane, as was assumed above, the dislocation would
pass right out of the crystal and there would be no reason for any change
in mechanical properties. Yet, as we know, metals, which have solidified
under ordinary conditions and which consist of a mass of individual
crystals, become harder and stronger as the amount of cold work to which
they are subjected increases, until a point is reached where they ultimately
fracture.
Fig.
4.10 The combination of a screw dislocation with an edge dislocation.
EDGE
DISLOCATION
SCREW
DISLOCATION
RESULTANT CURVED
DISLOCATION
ELONGATION
PER
CENT
Fig.
4.12
Differences
in
tensile properties between
a
single copper 'whisker'
and
ordinary
polycrystalline copper.
Consequently,
it is
assumed that many dislocations remain
in
every
crystal
and
that increase
in
hardness results from their mutual interference
and
the
building
up of a
transcrystalline 'traffic
jam'.
Increase
in
hardness
and strength
is due to the
greater difficulty
in
moving
new
dislocations
against
the
jammed ones, whilst
a
'pile
up' of
jammed dislocations
may
propagate
a
fracture. Dislocations will
be
unable
to
escape
at
crystal boun-
daries
by
forming steps because
of the
adherence
of
crystals
in
terms
of
the amorphous film (3.11). Moreover,
the
amorphous film will
act as an
effective barrier preventing dislocations from passing from
one
crystal
to
another, even supposing that
the
lattice structures
of two
neighbouring
crystals were suitably aligned
to
make this possible. Since individual
crystals develop
at
random
in a
polycrystalline mass, this will rarely
be so.
Individual crystals
in a
polycrystalline metal deform
by the
same mechan-
isms
as do
single crystals,
but
since they
are
orientated
at
random, shear
stress
on
slip planes will attain
the
critical value
in
different crystals
at
different loads (acting
on the
metal
as a
whole). Thus there
is
considerable
difference between
the
deformation
of a
single crystal
and
that
of a
polycry-
stalline mass.
The
yield stress
of the
latter
is
generally higher
and
glide
occurs almost simultaneously
on
several different systems
of
slip planes.
Dislocations cannot escape from individual crystals
and so
they
jam. A
'pile
up' on one
slip plane will prevent dislocations
in
intersecting planes
from moving, producing
a
situation
not
uncommon
in the
case
of
motor-
traffic conditions
at
most crossroads near
the
South Coast
on
almost
any
Sunday
in the
summer.
For these reasons, strain-hardening proceeds much more rapidly
in a
polycrystalline metal than
it
does
in a
single crystal.
A
decrease
in
crystal
size leads
to
strain-hardening taking place more quickly
so
that, though
the material
is
stronger,
it is
less ductile. Strain-hardening, however,
is
supremely important.
If a
metal
did not
strain-harden
but
continued
to
slip,
as
would
any
perfectly plastic material
(Fig.
4.5A), failure would
be
inevitable, immediately
it
were loaded above
its
yield point.
STRESS(N/-""
2
)
STRESS-STRAIN CURVE
FOR A
SINGLE COPPER 'WHISKER
-STRESSED PARALLEL
TO
ClItJ DIRECTION. WHISKER
YIELDED SUDDENLY
AT E
A
ND
LOAD
WAS
RELAXED.
LOAD
WAS
RE-APPLIED
AT Y-
ORDINARY POLY-CRYSTALLINE COPPER
4.18 In addition to deformation by slip, some metals, notably zinc, tin
and iron, deform by a process known as 'twinning'. The mechanism of this
process is illustrated in Fig. 4.13. In deformation by slip all atoms in one
block move the same distance, but in deformation by twinning, atoms in
each successive plane within a block will move different distances, with
the effect of altering the direction of the lattice so that each half of the
crystal becomes a mirror image of the other half along a twinning plane.
It is thought that twinning also proceeds by the movement of dislocations.
Twins thus formed are called 'mechanical twins' to distinguish them from
the 'annealing twins' which are developed in some alloys—notably those
of copper—during an annealing operation which follows mechanical defor-
mation. The mechanical twins formed in iron by shock loading are known
as 'Neumann bands'. Twin formation in a bar of tin can actually be heard
as the bar is bent and used to be called 'The Cry of Tin'.
Fig.
4.13 The formation of 'mechanical twins' (i) before stressing, (ii) after stressing under
shearing force P.
Energy of Mechanical Deformation
4.19 As deformation proceeds the metal becomes progressively harder
and stronger and, whether by slip or by twinning, a point is reached when
no more deformation can be produced. Any further increase in the applied
force will lead only to fracture. In this condition, when tensile strength and
hardness have reached a maximum and ductility a minimum, the material is
said to be work hardened. As deformation proceeds the capacity for further
deformation decreases and the force necessary to produce it must increase.
All dislocations present at the start of stress application have moved into
'jammed' positions, as have all new dislocations generated by the progress-
ive increase in stress, until no further slip by movement of dislocations is
possible. At this point of maximum resistance to slip (maximum strength
and hardness) further increase in stress would give rise to fracture. The
material must then be annealed if further cold work is to be carried out
on it.
During a cold-working process approximately 90% of the mechanical
energy employed is converted to heat as internal forces acting within the
TWIN
TWINNING
PLANES
metal are overcome. The remaining 10% of mechanical energy used is
stored in the material as a form of potential energy. The bulk of this—
about 9% of the energy originally used—is that associated with the number
of dislocations generated. These have energy because they result in distor-
tion of the lattice and cause atoms to occupy positions of higher-than-
minimum energy. The remaining potential energy (1% of the energy
originally used) exists as locked-up residual stresses arising from elastic
strains internally balanced.
The increased-energy state of a cold-worked metal makes it more chemi-
cally active and consequently less resistant to corrosion. It was suggested
earlier in this chapter that as deformation proceeds dislocations will tend
to pile up at crystal boundaries. Consequently these crystal boundaries will
be regions of increased potential energy due to the extra micro-stresses
present there. For this reason the grain-boundary areas will corrode more
quickly than the remainder of the material so that intercrystalline failure
will be accelerated.
This stored potential energy is also the principal driving force of recovery
and recrystallisation during an annealing process.
Annealing and Recrystallisation
4.20 A cold-worked metal is in a state of considerable mechanical stress,
resulting from elastic strains internally balanced. These elastic strains are
due to the jamming of dislocations which occurred during cold defor-
mation. If the cold-worked metal is heated to a sufficiently high tempera-
ture then the total energy available to the distorted regions will make
possible the movement of atoms into positions of equilibrium so that the
elastic strains diminish and the 'locked-up' energy associated with them
'escapes'. Since dislocations will once more be in positions of minimum
energy from which they can be moved relatively easily, tensile strength
and hardness will have fallen to approximately their original values and
the capacity for cold-work will have returned. This form of heat-treatment
is known as annealing, and is made use of when the metal is required for
use in a soft but tough state or, alternatively, when it is to undergo further
cold deformation. Annealing may proceed in three separate stages
depending upon the extent of the required treatment.
4.30 Stage I—The Relief of Stress This occurs at relatively low tem-
peratures at which atoms, none the less, are able to move to positions
nearer to equilibrium in the crystal lattice. Such small movements reduce
local strain and therefore the mechanical stress associated with it, without,
however, producing any visible alteration in the distorted shape of the
cold-worked crystals. Moreover, hardness and tensile strength will remain
at the high value produced by cold-work, and may even increase as shown
in the curve for cold-worked 70-30 brass (Fig. 4.14). It is found that a
controlled low-temperature anneal at, say, 250
0
C applied to hard-drawn
70-30 brass tube will effectively reduce its tendency to 'season-crack'
(16.33) without reducing strength or hardness.
ANNEALING TEMPERATURE (
0
C)
Fig.
4.14 The relationship between hardness and annealing temperature (cartridge brass).
4.40 Stage II—Recrystallisation Although a low-temperature
annealing process intended to relieve 'locked-up' stresses may sometimes
be used, annealing generally involves a definite and observable alteration
in the microstructure of the metal or alloy. If the annealing temperature
is increased a point is reached when new crystals begin to grow from nuclei
produced in the deformed metal. These nuclei are formed at points of
high potential energy such as crystal boundaries and other regions where
dislocations have become entangled. The crystals so formed are at first
HARDNESS(BRINELL)
"AS-CAST"
STRUCTURE
RE-CRYSTALLISED
REGION
REGION COVERED
BY MfCROGRAPH.
ORIGINAL
CRYSTALS.
CORED
RE-CRYSTALLISATION
AT FORMER GRAIN
BOUNDARIES.
Plate 4.2 A cast 70-30 brass slab (38mm thick) was being cold-rolled when the mill was
stopped.
The partly rolled slab was then annealed at 600
0
C.
The photomicrograph (A) reveals two regions: (1) the coarse-grained region which suffered
no cold-work and consequently did not recrystallise on annealing (hence it shows the original
coarse as-cast structure); (2) the heavily cold-worked part of the slab which has recrystallised
on annealing so that the crystals are much too small to be visible in the photomicrograph.
The photomicrograph (x 100) (B) is taken from a region which suffered very little cold work.
On annealing, recrystallisation has just begun at points on the original crystal boundaries
where,
presumably, a pile-up of dislocations had just commenced. Small twinned crystals
have been formed at these points, whilst the remainder of the structure is still the original
as-cast.
small, but grow gradually until they absorb the entire distorted structure
produced originally by cold-work (Fig. 4.15). The new crystals are equi-
axed in form, that is, they do not show any directional elongation, as did
the distorted cold-worked crystals which they replace. They are, in fact,
of equal axes.
This phenomenon is known as recrystallisation, and it is the principal
method employed, in conjunction with cold-work, of course, to produce a
fine-grained structure in non-ferrous metals and alloys. Only in rare cases
—notably in steels and aluminium bronze, where certain structural changes
take place in the solid state—is it possible to refine the grain size solely by
heat-treatment.
Fig.
4.15 Stages in the recrystallisation of a metal.
(A) Represents the metal in its cold-rolled state. At (B) recrystallisation had commenced with
the formation of new crystal nuclei. These grow at the expense of the old crystals until at (F)
recrystallisation is complete.
4.41 The minimum temperature at which recrystallisation will take
place is called the recrystallisation temperature. This temperature is lowest
for pure metals, and is generally raised by the presence of other elements.
Thus,
pure copper recrystallises at 200
0
C, whilst the addition of 0.5%
arsenic will raise the recrystallisation temperature to well above 500
0
C; a
useful feature when copper is to be used at high temperatures and must
still retain its mechanical strength. Arsenical copper of this type was widely
used in the boiler tubes and fire-boxes of the steam locomotives of former
years.
Similarly, whilst cold-worked commercial-grade aluminium recrys-
tallises in the region of 150
0
C, that of 'six nines' purity (99.999 9% pure)
appears to recrystallise below room temperature and, consequently, does
not cold-work.
Other metals,
for
example lead
and tin,
recrystallise below room
tem-
perature,
so
that
it is
virtually impossible
to
cold-work them, since they
recrystallise even whilst mechanical work
is
taking place. Thus, they
can
never
be
work-hardened
at
normal temperatures
of
operation. Most engin-
eering metals have recrystallisation temperatures which
are
well above
ambient temperatures,
and are
therefore hot-worked
at
some temperature
above their recrystallisation temperature.
4.42
The
recrystallisation temperature
is
dependent largely
on the
degree
of
cold-work which
the
material
had
previously received,
and
severe
cold-work will generally result
in a
lower recrystallisation temperature,
since
the
greater
the
degree
of
cold-work
the
greater
the
amount
of
locked-
up potential energy available
for
recrystallisation.
It is
therefore
not
poss-
ible accurately
to
quote
a
recrystallisation temperature
for a
metal
to the
extent that
it is for, say, its
melting point.
For
most metals, however,
the recrystallisation temperature
is
between one-third
and
one-half
of the
melting point temperature,
T
m
. (T
m
being measured
on the
absolute scale,
K.) Thus
the
mobilities
of all
metallic atoms
are
approximately equal
at
the same fraction
of
their melting point
(K).
4.50 Stage III—Grain Growth
If the
annealing temperature
is
above
the recrystallisation temperature
of the
metal,
the
newly formed crystals
will continue
to
grow
by
absorbing each other cannibal-fashion, until
the
structure
is
relatively coarse-grained,
as
shown
in Fig. 4.15.
Since
the
crystal boundaries have higher energies than
the
interiors
of the
crystals,
a polycrystalline mass will reduce
its
energy
if
some
of the
grain boundaries
disappear. Consequently,
at
temperatures above that
of
recrystallisation
large crystals grow
by
absorbing small ones.
As
indicated
in Fig. 4.16, a
crystal boundary tends
to
move towards
its
centre
of
curvature
in
order
to
shorten
its
length.
To
facilitate this, atoms move across
the
boundary
to positions
of
greater stability where they will
be
surrounded
by
more
DIRECTION OF MOVEMENT
OF CRYSTAL BOUNDARY
CRYSTAL
GROWING
DIRECTION OF MOVEMENT
OF CRYSTAL BOUNDARY
CRYSTALS BEING ABSORBED
Fig.
4.16 The
'cannibalising'
of
small crystals
by
larger ones.
neighbours in the concave crystal face of the growing crystal. Thus the
large grow larger and the small grow smaller. The same type of mechanism
(in this case surface tension along a liquid film) causes small bubbles to be
absorbed by the larger ones in the froth in a glass of beer. The extent of
grain growth is dependent to a large degree on the following factors:
(a) The annealing temperature used—as temperature increases, so grain
size increases (Fig. 4.17).
(Jb)
The duration of the annealing process—grains grow rapidly at first
and then more slowly (Fig. 4.17).
(c) The degree of previous cold-work. In general, heavy deformation
will lead to the formation of a large number of regions of high energy
within the crystals. These will give rise to the production of many nuclei
on recrystallisation and consequently the grain size will be small. Con-
versely, light deformation will give rise to few nuclei and the resulting
grain size will be large (Fig. 4.18). What is generally referred to as the
critical
amount of cold-work is that which is just necessary to initiate recrys-
tallisation and so give rise to extremely coarse grain. This is likely to occur
at lightly-worked regions in a deep-drawn component which is subse-
quently annealed (Fig. 4.19).
(d) The use of certain additives in a metal or alloy. Thus the presence
of nickel in alloy steels limits grain growth during heat-treatment processes.
Nickel is in fact the universal grain refiner and does much to increase the
toughness of many alloys by limiting grain growth.
Insoluble particles are also thought to act as barriers to grain growth in
some cases. For example small amounts of thoria (thorium oxide) are
added to the tungsten used for electric lamp filaments. Here the films or
particles of thoria prevent excessive grain growth which would otherwise
result from maintaining the filament for long periods at temperatures well
above that of recrystallisation for tungsten.
4.51 Of these factors the one requiring the most accurate control, in
normal conditions, is the annealing temperature. Some alloys, particularly
the brasses, are exceptionally sensitive to variations in the annealing tem-
perature and an error of 100
0
C, on the high side, may increase crystal size
GRAIN
SIZE
GRAIN SIZE
ANNEALING TIME
Fig.
4.17 The relationship between grain
size and annealing time.
DEFORMATION (<Vo)
Fig.
4.18 The relationship between grain
size and the degree of original deformation.
Fig.
4.19 Grain size in a deep-drawn component which has subsequently been annealed.
The grain size at the base of the cup (A) will be that of the original material since there has
been no cold-work, and consequently no recrystallisation during the annealing process. In
the side walls of the cup (B) grain size is small since heavy cold-work during the drawing
process has resulted in the formation of many nuclei during recrystallisation. In the region
(C) cold-work has been slight—-the 'critical' amount—so that, during annealing, few nuclei
formed and the resultant grain is very coarse.
five-fold for a given annealing time. This coarse grain will, in turn, lead to
loss in ductility and the formation of a rough, rumpled surface (known as
'orange peel') during a subsequent forming operation. When coarse grain
has been thus produced in material of finished size, it cannot be refined,
as is possible with steel, by heat treatment. The only remedy would be to
remelt the brass and go through the complete stages of rolling and
annealing, until once more the finished size was reached.
4.52 It follows that a reasonably accurate assessment of grain size is
necessary when a material is destined for a pressing or deep-drawing pro-
cess (6.43). Grain size is usually determined by counting the number of
crystals in a known area during the microexamination of a prepared speci-
men. The result is expressed as the number of grains per mm
2
. In the USA
the ASTM index is often used and this is obtained by counting the number
of grains per in
2
when viewed at a magnification of x 100. The ASTM
index, G, is then given by:
N = 2
(G
~
1}
where N is the number of grains per square inch at x 100.
Values of G between 1 and 8 cover normal grain size ranges.
A further method of estimating grain size involves measuring the Aver-
age Grain Diameter (mm). Here an image of the prepared surface is pro-
jected on to the reflex screen of a microscope at a magnification of XlOO.
A line AB, 100 mm long is previously drawn randomly on the screen and
the number of crystals cut by the line counted. The 100 mm line on the
screen represents a 1 mm line on the surface of the specimen, hence:
Average Grain Diameter = mm
Number of crystals cut by line
In Fig 4.20, 13 crystals have been intersected by the line AB, therefore
the Average Grain Diameter = Vi
3
mm = 0.08 mm. (The optimum grain