Higgins R.A. Engineering Metallurgy: Applied Physical Metallurgy
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Fig.
3.16 The
imperfect nature
of a
metallic crystal.
that some solid substance
has
been dissolved
by a
liquid,
but in
science
a
solution
is a
homogeneous mixture
of two (or
more) substances
in
which
the atoms
or
molecules
of the
substances
are
completely dispersed—
whether
in the
gaseous, liquid
or
solid states. Thus
in
metals
a
solid solution
(8.20) consists
of a
crystal structure
in
which 'stranger' atoms take
up
positions within
the
lattice
of the
parent metal.
In
a
substitutional solid solution (8.21) some lattice sites
are
occupied
by
'stranger' atoms
(Fig.
3.16), that
is,
they
are
substituted
for
some
of the
atoms
of the
parent metal. Such stranger atoms
are
generally
of a
similar
size—either larger
or
smaller—to those
of the
parent metal.
If the
stranger
atoms
are
smaller than those
of the
parent metal they
are
quite likely
to
dissolve
interstitially,
that
is
they
fit
into
the
spaces
(or
interstices) between
the parent atoms forming
an
interstitial
solid solution.
The
very small atoms
of hydrogen, carbon
and
nitrogen
are
able
to
dissolve interstitially even
in
solid y-iron,
the
latter
two
elements making
the
processes
of
carburising
and nitriding possible.
3.63 Whatever
the
nature
of a
points defect
it is
likely
to
stop
or at
least impede
the
smooth movement
of
dislocations through
a
crystal
so
that
a
greater force must
be
used
to
produce
a new
movement
of
dislo-
cations.
For
this reason solid solutions
are
stronger than pure metals.
Exercises
1.
Compare
and
contrast:
(i)
the
properties
of
covalent
and
metallic bonding;
(ii) atomic packing
in FCC and HCP
structures.
(3.11 and 3.14)
2.
What
is
meant
by
'polymorphism'? Discuss
the
term with particular reference
to iron, showing
the
connection which this property
has
with
the
engineering
uses
of the
metal.
interstitial
solute atom
several vacancies
have diffused to
form a void which
has collapsed'
Simple edge
dislocation
large
substitutional
solute atom
'vacancy'
Frenkel
defect
small substitutional
J solute atom
How could one of the manifestations of polymorphism be demonstrated in
the laboratory? (3.14)
3.
Sketch the three most important types of spatial arrangement encountered in
the lattice structures of metals.
Show how the density of packing of the atoms in each case affects volume
changes in those metals which, like iron, are polymorphic. (3.14)
4.
Derive Miller indices to represent the plane shown in Fig. 3.17. (3.15)
Fig.
3.17.
5.
Why do metallic crystals generally have irregular boundaries? (3.16)
6. Explain the term 'dendritic solidification'. Show how certain mechanical proper-
ties of cast metals can be explained by reference to this type of crystal structure.
(3.16)
7.
Fig. 3.18 illustrates cross-sections of three castings of similar shape and compo-
sition but which have been cast under different conditions of pouring tempera-
ture and mould material.
Account for the different structures produced. (3.18)
Fig.
3.18.
8. Discuss the formation and distribution of gas porosity in
(i) cast steels;
(ii) cast aluminium alloys.
Show in each case how this form of defect may be minimised. (3.20)
9. Show how a 'pipe' tends to form during the solidification of a large ingot.What
methods may be used to minimise the pipe?
Why do impurities generally tend to segregate in the pipe? (3.30 and 3.42)
Bibliography
Barratt, C. S. and Massalski, T. B., Structures of
Metals,
Pergamon Press, 1980.
Brown, P. J. and Forsyth, J. B., The Crystal Structure of Solids, Arnold, 1973.
Cahn, R. W., Physical Metallurgy, North Holland, 1980.
Chadwick, C. A. and Smith, D. A., Grain Boundary Structures and Properties,
Academic Press, 1976.
Hume-Rothery, W., Smallman, R. E. and Howarth, C. W., The Structure of
Metals
and Alloys, Institute of Metals, 1988.
Kennon, N. F., Patterns in Crystals, John Wiley, 1978.
Smallman, R. E., Modern Physical Metallurgy, Butterworths, 1985.
Woolfson, M. M., An Introduction to X-ray
Crystallography,
Cambridge University
Press,
1978.
4
Mechanical Deformation
and Recovery
4.10 Deformation in metals can occur either by elastic movement or by
plastic flow (2.30). In elastic deformation a limited distortion of the crystal
lattice is produced, but the atoms do not move permanently from their
ordered positions, and as soon as the stress is removed the distortion
disappears. When a metal is stressed beyond the elastic limit plastic defor-
mation takes place and there must, clearly, be some movement of the
atoms into new positions, since considerable permanent distortion is pro-
duced. We must therefore consider ways in which this extensive rearrange-
ment of atoms within the lattice structure can take place to give rise to this
permanent deformation.
4.11 Plastic deformation proceeds in metals by a process known as
'slip',
that is, by one layer or plane of atoms gliding over another. Imagine
a pile of pennies as representing a single metallic crystal. If we apply any
force which has a horizontal component, ie any force not acting vertically,
the pile of pennies will be sheared as one slides over another, provided
that the horizontal component is sufficient to overcome friction between
the pennies.
The results of slip in a polycrystalline mass of metal may be observed
by microscopical examination. The direction of the slip planes is indicated
in such a piece of metal after deformation by the presence of slip bands
which form on the surface of the metal. If a piece of soft iron is polished
and etched and then squeezed in a vice so that the polished surface is not
scratched, these slip bands can be seen on the surface. Their method of
formation is indicated in Fig. 4.2. Such slip bands are generally parallel in
any individual crystal but differ in orientation from one crystal to another.
It has been shown by electron microscopy that a single visible slip band
consists of a group of roughly 10 steps on the surface, each about 40 atoms
thick and approximately 400 atoms high. If the deformation has been
excessive, the presence of slip bands is apparent even when a specimen is
ELASTIC
AND
PLASTIC DEFORMATION
Fig.
4.1
Diagrams illustrating
the
difference,
in
action
and
effect,
of
deformation
by
elastic
and plastic means.
Fig.
4.2 The
formation
of
slip bands.
(A) Indicates
the
surface
of
the specimen before straining,
and (B) the
surface after straining.
The relative slipping along
the
crystallographic planes
is
apparent
as
ridges (visible under
the microscope)
on the
surface
of the
metal.
polished
and
etched after deformation. Heavily stressed parts
of the
crystal
—which contain considerable strain energy—dissolve more quickly during
etching, revealing these so-called 'strain bands'.
4.12
All
metals
of
similar crystal structure slip
on the
same crystallo-
graphic planes
and in the
same crystallographic directions. Slip occurs
when
the
shear stress resolved along these planes reaches
a
certain value
—the critical resolved shear stress. This
is a
property
of the
material
and
does
not
depend upon
the
structure.
The
process
of
slip
is
facilitated
by
the presence
of the
metallic bond, since there
is no
need
to
break direct
bonds between individual atoms
as
there
is in
co-valent
or
electro-valent
structures,
nor is
there
the
problem
of
repulsion
of
ions
of
like charge
as
BEFORE
STRESSING
STRESS
ACTING
STRESS
REMOVED
ELASTIC DEFORMATION ONLY
BEFORE
STRESSING
STRESS
ACTING
STRESS
REMOVED
Plate 4.1 'Slip' in metallic crystals.
(i) Shows 'slip steps' (see Fig. 4.3) in a single crystal of cadmium approx 2mm in diameter.
This was grown as a single crystal in the form of wire which was then stretched by hand, x
15.
(ii) Illustrates 'slip bands' on the surface of annealed copper. The specimen was polished,
etched and then squeezed gently in the jaws of a vice, x 200.
there is for an electro-valently bonded crystal. When slip occurs in co-
valent or electro-valent structures it does so with much greater difficulty
than in metals. Some types of crystal are more amenable to deformation
by slip than others. For example, in the face-centred cubic type of structure
there are a number of different planes along which slip could conceivably
take place, whereas with the hexagonal close-packed structure slip is only
possible on the basal plane of the hexagon. Thus, metals with a face-
centred cubic structure, such as copper, aluminium and gold, are far more
malleable and ductile than metals with a hexagonal close-packed lattice
like zinc.
4.13 It is possible, under controlled conditions, to grow single crystals
of some metals, and under application of adequate stress such crystals
behave in a manner very similar to that of the pile of pennies. An offset
on one side of the crystal is balanced by similar offset on the other side
(Fig. 4.3), and both offsets lie on a single continuous plane called a slip
plane. Whilst in the case of the pile of pennies the force necessary to cause
slip was that required to overcome friction between them, in a single
metallic crystal the force necessary to cause slip is related to that required
to overcome the resistance afforded by the metallic bond.
For a single crystal the shear component, T (Fig. 4.4) of a tensile stress,
a, resolved along the direction of slip, OS
7
on a slip plane, F, can be
calculated. ON is normal to P.
Component of a along OS = a.cos (3
Area of projection on C of unit area of P = cos a
T = o cos a. cos (3
Experiments show that different single crystals of the same metal slip at
different angles and different tensile stresses, but if the stresses are resolved
along the slip plane, all crystals of the same metal slip at the same critical
value of resolved shear stress.
4*14 From a knowledge of the forces acting within the metallic bond
it is possible to derive a
theoretical
value for the stress required to produce
slip by the simultaneous movement of atoms along a plane in a metallic
crystal. However, the stress, T, actually obtained practically in experiments
on single crystals as outlined above, is only about one thousandth of the
theoretical value assuming simultaneous slip by all atoms on the plane.
Obviously then slip cannot be a simple simultaneous block movement of
one layer of atoms over another. Nor does such a simple interpretation
of the idea of slip explain the work-hardening which takes place during
mechanical deformation. A perfect material in plastic deformation would
presumably deform without limit at a constant yield stress as indicated in
Fig. 4.5A, but in practice a stress-strain relationship of the type indicated
in Fig. 4.5B exists.
4.15 Earlier theories which sought to explain slip by the simultaneous
gliding of a complete block of atoms over another have now been discarded
and the modern conception is that slip occurs step by step by the movement
of so-called 'dislocations' within the crystal.
If the reader has ever tried his hand at paper-hanging he will know that
wrinkles have a habit of appearing in the paper when it is laid on the wall.
Attempts to smooth out these wrinkles by pulling on the edge of the paper
would undoubtedly prove fruitless, since the tensile force necessary to
cause the whole sheet of paper to slide would be so great as to tear it.
Fig.
4.4.
Fig.
4.3.
SLIP
PLANE
Fig.
4.5.
Instead, gentle coaxing
of the
wrinkles individually with
the aid of a
brush
or cloth leads
to
their successful elimination, causing them
to
glide
and
'pass
out of the
system', with
the
application
of a
force which
is
small
compared with that necessary
to
slide
the
whole sheet
of
paper simul-
taneously.
The
movement
of
dislocations
on a
slip plane
in a
metallic
crystal probably follows
a
similar pattern.
Dislocations
are
faults
or
distorted regions (Fig.
4.6) in
otherwise perfect
Fig.
4.6 (i) A
'ball-and-wire' model
of an
edge dislocation,
(ii)
Crystallographic planes
containing
an
edge dislocation,
as
they appear
in
aluminium
at a
magnification
of
several
millions.
(A
sketch
of the
structure
as
revealed
by a
high-resolution electron microscope).
STRESS
STRESS
YIELD STRESS
APPROACHING
PERFECTLY PLASTIC — DEFORMS
CONTINUOUSLY AT A CONSTANT
YIELD STRESS.
STRAIN
FRACTURE
YIELD
STRESS
STRAIN
NORMAL METAL
5LIP
PLANE
Ci)
(ii)
crystals and the step-by-step movement of such faults explains why the
force necessary to produce slip is of the order of 1000 times less than the
theoretical, assuming simultaneous slip over a whole plane.
The fundamental nature of a dislocation is illustrated in Fig. 4.7 (in
which for the sake of clarity only the centres of atoms are indicated).
Assume that a shearing stress, a, has been applied to the crystal causing
the top
half,
APSE, of the face, ADHE, to move inwards on a slip plane,
PQRS, by an amount PPi (one atomic step). There has been no corre-
sponding slip, however, at face BCGF. Consequently the top half of the
crystal contains an extra half-plane as compared with the bottom part of
length PiQ. In Fig. 4.7 this is the half-plane WXYZ and the line XY is
known as an edge dislocation. It separates the slipped part PXYS of the
slip plane from the unslipped part
XQRY.
During slip this 'front' XY
moves to the right through the crystal.
The movement of such an edge dislocation under the action of a shearing
force is illustrated in Fig. 4.8. Here an edge dislocation exists already (i),
and the application of the shearing stress (ii) causes the dislocation to glide
along the slip plane in the manner suggested. In this case it has been
assumed that the dislocation glides out of the crystal completely, producing
a slip step of one atom width at the edge of the crystal (iii). The dislocation
can be moved through the crystal with relative ease, since only one plane
is moving at a time and then only through a small distance.
Slip can also take place by the movement of 'screw' dislocations. These
differ from edge dislocations in that the direction of movement of the
dislocation is normal to the direction of formation of the slip step. The
STRESS CT
STRESS
(i)
(11)
STRESS
STRESS
Fig.
4.7 The formation of an edge dislocation by the application of stress.
Fig.
4.8.
mechanism of the process is indicated in Fig. 4.9. Here a shear stress, o,
had displaced P to P\ and Q to Qi on one face of the crystal so that
PiQiYX has slipped relative to
PQYX.
In this case the screw dislocation
XY separates the slipped part PQYX from the unslipped part XYRS of
the slip plane PQRS. It will be noted that XY is moving in a direction
which is normal to the direction in which slip is being produced.
It is also possible for slip to take place by the combination of a screw
dislocation with an edge dislocation. A curved dislocation is thus evolved
which moves across the slip plane (Fig. 4.10).
4.16 Until comparatively recently much of the foregoing commentary
concerning dislocations was of a speculative nature. Whilst many of the
properties of a metal could be best explained by postulating the existence
of dislocations, no one had actually seen a dislocation in a metallic structure
since dimensions approaching atomic size are involved. True, dislocations
had been observed in structures of crystalline complex compounds and it
was reasonable to suppose that similar dislocations occurred in the crystal-
line structures of metals. During the last few years the rapid development
of electron microscope techniques has made it possible to observe crystallo-
graphic planes within metallic structures. With the aid of high-resolution
electron microscopy, photographs of edge dislocations in metals such as
aluminium have been produced (Fig. 4.6(ii)).
Since the stress required to produce dislocations is great, it is assumed
that they are not generally initiated by stress application but that the major-
ity of them are formed during the original solidification process. During
any subsequent cold-working process, dislocations have a method of repro-
ducing themselves from what are called Frank-Read sources (Fig. 4.11),
so that in the cold-worked metal the number of dislocations has greatly
increased.
The relationship between the force necessary to initiate dislocations and
to move those which already exist is notably demonstrated by the tensile
properties of metallic 'whiskers'. These are hair-like single crystals grown
under controlled conditions and generally having a single dislocation run-
ning along the central axis. If a tensile stress is applied along this axis the
dislocation is unable to slip. As no other dislocations are available, the
crystal cannot yield until a dislocation is initiated at E (Fig. 4.12). The
stress then falls to that necessary to move the dislocation (Y), and dislo-
cations then reproduce rapidly so that plastic flow proceeds.
STRESS
STRESS