nus me2151-chp6
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Lecture notesTRANSCRIPT
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6-1
C H A P T E R 6
D I S L O C A T I O N S , D E F O R M A T I O N A N D S T R E N G T H E N I N G I N M E T A L S
6.1 PLASTIC DEFORMATION BY SLIP
6.2 DISLOCATIONS AND SLIP
6.3 STRENGTHENING MECHANISMS 6.3.1 Dis locat ion Stress F ie lds and
Stra in Energies 6.3.2 Stra in Hardening 6.3.3 Gra in S ize Strengthening 6.3.4 Sol id Solut ion Strengthening 6.3.5 Dispers ion Hardening 6.3.6 Combined Strengthening
Mechanisms
6.4 ANNEALING 6.4.1 Recovery 6.4.2 Recrysta l l i zat ion 6.4.3 Gra in Growth
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6-2
6.1 PLASTIC DEFORMATION BY SLIP
Plastic deformation in a crystal mostly involves the sliding
of one plane of atoms over another under the action of a
shear stress (Fig. 6.1-1); this process is known as slip.
Fig. 6.1-1 Plastic deformation by slip in an ideal crystal occurs when one plane of atoms slides over another, producing a step of one atomic spacing.
The plane and direction in which slip occurs are the slip
plane and slip direction. The slip direction always lies
within the slip plane. The combination of a slip plane and a
slip direction forms a slip system.
Slip does not take place in any arbitrary plane or direction.
The preferred slip planes and directions are those in which
the atoms are most densely packed. This is because slip
occurs in steps of one atomic spacing, so moving atoms
from one stable site to the next would involve the least
energy when the atoms are closest together (Figs. 6.1-2 & 3).
6-3
!
"max #ba
Fig. 6.1-2 The maximum shear stress, !max, required to move one plane of atoms
over another by one atomic spacing is a function of the interatomic distances, such that smaller stresses are necessary for closely-spaced atoms.
Fig. 6.1-3 Slip requires less energy on (a) a close-packed plane in a close-
packed direction than on (b) a less closely-packed plane and direction.
Since most engineering alloys are polycrystalline, the
change in orientation from grain to grain means that each
grain is strained differently by an applied stress (Fig. 6.1-4).
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6-4
Fig. 6.1-4 Resolving a uniaxial tensile stress " into shear stress
!
" = F sin#A/cos# = $ sin# cos#
Slip will begin on a slip system when the resolved shear
stress acting on the slip plane in the slip direction reaches a
critical value. If two or more slip systems have the required
shear stress acting on them, they all slip together (Fig. 6.1-5).
Fig. 6.1-5 Slip lines on the surface of polycrystalline copper that has been deformed. Slip lines are actually a series of fine steps on the surface.
Note that the slip lines change direction at grain boundaries. Note also intersecting sets of lines within the same grain, indicating the operation of more than one slip system.
6-5
In a polycrystalline solid, the deformation in each grain
must be compatible with its neighbours to maintain
mechanical integrity and coherency along the grain
boundaries. This requires the grains of various orientations
to slip on 5 independent systems simultaneously.
Metals with FCC and BCC structures are ductile because
they possess a relatively large number of slip systems (12 in
FCC; up to 48 in BCC) (Table 6.1-1).
The slip systems in FCC and BCC are also well-distributed
in space, such that at least one slip system would be
favourably oriented for slip at low applied stresses.
Table 6.1-1 Primary slip systems in the common metal structures. BCC and HCP contain secondary slip systems, which are not shown.
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Furthermore, slip systems in FCC and BCC intersect, so if
one system be constrained, slip can continue on a different
intersecting slip system; this is known as cross-slip.
However, unlike the FCC structure, the BCC structure does
not contain close-packed planes, so slipping atoms must
move greater distances from one equilibrium lattice
position to another. Higher shear stresses are thus
necessary for slip in BCC than in FCC metals (Fig. 6.1-2 & Table
6.1-2), which translates into higher strengths for BCC metals.
[Note: critical shear stress is the shear stress required to move a dislocation in its slip system.
Although the HCP structure contains both close-packed
planes and directions, its geometry gives rise to fewer slip
systems. Furthermore, the slip systems, being parallel, do
not intersect, so cross-slip is not possible (Fig. 6.1-6). Most
polycrystalline HCP metals are relatively brittle. 6-7
Fig. 6.1-6 Comparison of the slip systems in
(a) an FCC structure, and (b) an HCP structure.
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6-9
6.2 DISLOCATIONS AND SLIP
In a perfect crystal, slip would involve a whole plane of
atoms sliding over another in a single movement, which
would require the simultaneous stretching, breaking, and
remaking of all atomic bonds in the slip plane. The
theoretical shear strengths of metals have been roughly
estimated to be in the order of 1010 N/m2 (10 GPa).
However, the actual measured yield strengths of bulk
metals are at least 1,00010,000 times lower than this
value (Table 6.2-1). This is because slip in real metal crystals
occurs via the movement of dislocations, during which only
a small fraction of atomic bonds are broken at any one
time, with minimal disruption to the crystal lattice.
Table 6.2-1 Comparison of theoretical and experimental yield strengths of some metals.
Dislocations are linear or one-dimensional crystal defects
where local faults in the atomic arrangement lie along a
straight line, curve or loop through the crystal.
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Dislocations can be introduced into a crystal in a number
of ways: during solidification, during plastic deformation,
or as a result of thermal stresses arising from rapid cooling.
All bulk crystalline materials (metals and ceramics) contain
dislocations.
There are two fundamental types of dislocations: edge and
screw. An edge dislocation may be thought of as an extra
half-plane of atoms inserted into the crystal (Fig. 6.2-1). The
bottom edge of half-plane that ends within crystal is the
edge dislocation line. [Note: the extra half-plane of atoms itself is not the dislocation.]
Fig. 6.2-1 An edge dislocation, showing the extra half planes of atoms.
Note the regions of compression and tension around the dislocation line.
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A screw dislocation may be thought of as making a cut
half-way through the crystal, and then skewing the two
halves by one atomic spacing (Fig.6.2-2).
Fig. 6.2-2 A screw dislocation, showing the spiral screw-like arrangement of atoms above and below the plane of the cut.
Most dislocations, however, are mixed dislocations, which
contain both edge and screw dislocation components with
a transition region in between (Fig. 6.2-3).
Fig. 6.2-3 A mixed dislocation. Fig. 6.2-4 Transmission electron micrograph of a titanium alloy in which dark lines are dislocations.
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When a shear stress is applied to the edge dislocation
shown in Fig. 6.2-5, the extra half-plane of atoms, plane A,
will be forced to the right; this in turn pushes the top
halves of planes B, C, D, etc., to the right.
If the shear stress is high enough, plane A eventually
becomes closer to the bottom half of plane B than the top
half of plane B itself. It is then more favourable
energetically for the atomic bonds across the two halves of
plane B to be severed and for plane A to bond with the
bottom half of plane B.
The extra half-plane moves by discrete steps through the
crystal and ultimately emerges from the surface, forming a
slip step that is one atomic distance wide (~10-10m).
Macroscopic plastic deformation is the cumulative effect of
the motion of large numbers of dislocations.
Fig. 6.2-5 The step-by-step movement of an edge dislocation
under a low shear stress produces a unit step of slip.
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Before and after the movement of a dislocation through a region of the crystal, the atomic arrangement is perfect and ordered; it is only during the passage of the dislocation that the lattice structure is disrupted. Only a relatively small shear stress is required to operate in the immediate vicinity of the dislocation in order to produce a step-by-step shear.
Fig. 6.2-6 Heimlich
the caterpillar illustrating (a) the difficulty of
moving without (b) a dislocation mechanism.
Although the edge, screw and mixed dislocation move in different directions, the result is the same shear (Fig. 6.2-7).
Partially sheared Totally sheared
Fig. 6.2-7 Shear produced by motion of (a) edge, (b) screw and (c) mixed dislocations. The dark arrows indicate the direction in which the dislocations move.
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While bulk ceramics and other crystalline compounds contain dislocations, the shear stress required for dislocation motion is at least 2-4 times that in metals. Not only are covalent and ionic bonds stronger, but ions in the more complex ceramic structures must also move greater distances between equilibrium lattice positions.
In addition, ceramics in which the bonding is predominantly ionic contain very few slip systems. If slip were to occur in some directions, ions of the same charge would be brought close together (see also Sec. 3.8.4), generating strong electrostatic repulsion that would resist slip (Fig. 6.2-8).
Fig. 6.2-8 (a) Before slip; (b) like charges repel in this slip direction; (c) slip possible.
For ceramics with highly covalent bonding, the directional nature of the bonds makes the displacement of atoms from their lattice sites extremely difficult.
The shear stress that must be applied to activate slip in bulk ceramics is higher than that required to cause fracture (Chp. 7). Ceramics are therefore hard and brittle, and do not generally undergo plastic deformation by slip, except at high temperatures (~ 0.5-0.7 TM [Note: TM is the melting temperature]).
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6.3 STRENGTHENING MECHANISMS IN METALS
Because plastic deformation in metals corresponds to the
movement of large numbers of dislocations, the capacity
of a metal for plastic deformation depends on the ability of
dislocations to move.
Since the hardness and strength of a metallic alloy are
related to the stress at which plastic deformation can be
made to occur (and thus, the stress at which dislocations
are able to move), there are two possible methods of
hardening or strengthening a metal:
! Eliminating all crystal defects, including dislocations
this has only been achieved in whiskers (very thin
single crystals only a few m in diameter), in which
strengths approaching theoretical values are possible.
! Creating so many crystal defects that they restrict or
hinder the passage of dislocations this is the method
used to strengthen bulk metals, but yield strengths are
still much lower than theoretical levels.
In the second approach, strengthening is achieved through
interactions of the stress fields of moving dislocations with
those created by other crystal defects.
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6.3.1 Dislocation Stress Fields and Strain Energies
Atoms surrounding a dislocation are displaced from their
equilibrium lattice positions. Such elastic strain produces
an elastic stress field around the dislocation.
In an edge dislocation, the presence of the extra half plane
of atoms above the dislocation line means that atoms in its
vicinity are squeezed together, resulting in compressive
stresses. Conversely, the atoms below the dislocation line
experience tensile stresses due to an increase in
interatomic separation in this region (Fig. 6.3-1).
Fig. 6.3-1 (a) Regions of compression and tension located around an edge dislocation. (b) Detailed stress state of an edge dislocation showing
compressive, tensile and shear stresses.
In a screw dislocation, the lattice spirals around the centre
of the dislocation. The stress field is one of pure shear and
is symmetrical about the dislocation line (Fig. 6.3-2).
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Fig. 6.3-2 Shear stress and strain associated with a screw dislocation.
The distortion of atomic bonds around any dislocation
increases potential energy because of non-equilibrium
interatomic separations (see also Sec. 3.7). This energy is known
as strain energy, since it is associated with the strain or
distortion of the crystal lattice.
When a dislocation is in close proximity to another, the
stress fields surrounding each dislocation will interact. For
example, if the compressive and tensile stress fields of two
edge dislocations lie on the same sides of the slip plane (Fig.
6.3-3a), the overall strain energy will be raised if the two
fields overlap; this gives rise to mutual repulsion as the
dislocations approach each other.
Conversely, if the compressive and tensile stress fields were
on opposite sides (Fig. 6.3-3b), the dislocations would
annihilate each other when they meet, with a lowering of
the overall strain energy; the dislocations would thus be
attracted to each other.
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Fig. 6.3-3 (a) The interaction of two edge dislocations of the same sign causes repulsion, (b) while that of different signs causes attraction and annihilation.
C and T denote compressive and tensile regions, respectively.
Two dislocations can attract and annihilate each other only
if they meet exactly on the same slip plane, and the
components of their stress fields match exactly and are of
opposite signs (Fig. 6.3-3b); i.e. tension cancels compression,
but tension/compression does not interact with shear.
Since most dislocations are randomly curved mixed
dislocations, there is a only a very low probability that all
the conditions for dislocation annihilation will be fulfilled
simultaneously. Thus, dislocation interactions with one
another tend to be mutually repulsive.
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These repulsive interactions obstruct the motion of those
interacting segments of different dislocations, while non-
interacting segments continue to move, creating many
dislocation tangles (Figs. 6.3-4&5) during plastic deformation.
Dislocations are therefore obstacles to the movement of
other dislocations.
Fig. 6.3-4 An edge dislocation (wavy black line) moving through a forest of other dislocations (red verticle lines). Intersecting segments that are mutually obstructive
tangle with one another, distorting and lengthening the original dislocation.
Fig. 6.3-5 Tangling dislocations marked with a b.
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6.3.2 Strain Hardening
Strain hardening, or work hardening is the phenomenon whereby a ductile metal becomes harder and stronger as it is plastically deformed. It is also known as cold working because the temperature at which deformation takes place is cold relative to the melting temperature of the metal.
During plastic deformation, dislocations move under the action of a shear stress and encounter other dislocations. Since their interactions are generally repulsive (Sec. 6.3.1), a higher applied stress is necessary to overcome this mutual repulsion such that dislocation movement can continue; i.e. the metal has become stronger/harder.
Furthermore, many new dislocations are continuously
created during plastic deformation (Fig. 6.3-6), significantly increasing the dislocation density. The average distance between dislocations decreases, and the mutual resistance to motion becomes more pronounced, requiring an increasingly higher applied stress for continued plastic deformation; thus, the metal strengthens until fracture.
Crystals that have intersecting slip systems, e.g. FCC and
BCC, often strain-harden rapidly because slip tends to occur in more than one slip system, causing dislocations on different systems to intersect, impeding mutual motion.
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Fig. 6.3-6 The sequence of events for the multiplication of a dislocation from a Frank-Read source. A segment of dislocation pinned at two points bows out into a loop.
Continued stress will cause the loop to expand and the residual segment to bow out again into another loop. This process repeats over and over, sending out a set of concentric loops away from the source, creating many new dislocations. This is
analogous to the ripples generated when a pebble is dropped into a quiet pond.
The yield strength and tensile strength of a metal increases
with increasing cold work, but ductility decreases (Figs. 6.3-7 &
6.3-8). Physical properties such as thermal and electrical
conductivity are also reduced due to the scattering of
electrons and phonons by dislocations.
Strain hardening in metals explains why the true stress-
strain curve obtained during a tensile test shows a rising
stress from the start of yielding to fracture (Sec. 2.2.5).
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Fig. 6.3-7 Stress-strain diagram showing the effects of strain hardening.
(a) Initially, yielding beings at A; (b) upon unloading and re-loading, yielding now occurs at the higher stress B.
Fig. 6.3-8 The effects of cold work on the mechanical properties of copper.
Metals may be shaped and strengthened at the same time
by cold working (Fig. 6.3-9).
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Fig. 6.3-9 Common metalworking processes: (a) rolling, (b) forging
(open and closed die), (c) extrusion (direct and indirect), (d) wire drawing, (e) stamping.
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6.3.3 Grain Size Strengthening
In a polycrystal, each grain is has a different orientation to
its neighbours. Since slip occurs only on specific planes,
dislocations cannot move from one grain into another in a
straight line (Fig. 6.3-10). Furthermore, the atomic disorder at
grain boundaries interrupts the continuity of the slip
planes, and acts as a barrier to dislocation motion.
Fig. 6.3-10 Slip planes are discontinuous and change directions across the grain
boundary. Dislocations cannot move through the
grain boundary.
A dislocation can move only within the grain in which it
was created. Dislocations pile up at the grain boundary,
causing strain energy to increase locally, creating a back
stress that repels other dislocations approaching the pile-
up (Fig. 6.3-11). A higher applied stress is needed to overcome
this repulsion for continued dislocation movement.
Fig. 6.3-11 Dislocation pile-up
at a grain boundary.
6-25
The more grain boundaries there are (i.e. the smaller the
grain size), the more obstacles there are to dislocation
motion, and the higher the stress needed to cause plastic
deformation; i.e. the metal becomes stronger/harder.
The relationship between yield strength and grain size is
expressed by the Hall-Petch equation: "y = "0 +
kyd
where "y = yield strength
d = average grain diameter
"0, ky = material constants
Generally, polycrystals are stronger than single crystals (Fig.
6.3-12); fine-grained metals are stronger than coarse-grained
(Fig. 6.3-13). Effective strengthening can be realized only when
the grain size is of the order of 5 m or less.
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Fig. 6.3-12 Stress-strain curves for single crystal and polycrystalline copper.
Fig. 6.3-13 Hall-Petch plot for brass, showing the effects of grain size on yield strength.
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Grain size strengthening is one of the major reasons for the
interest in nanocrystalline materials, in which grain sizes are
less than 100 nm. However, as grain size is reduced below
~ 20 nm and becomes comparable to the width of grain
boundaries, a reverse Hall-Petch effect is observed, where
decreasing grain size causes softening (Fig. 6.3-14).
Fig. 6.3-14 Hardness of a metal as a function of grain size.
Grain size may be refined by cooling quickly from the
molten state, inoculation of the melt (i.e. adding numerous
impurity particles to the liquid to encourage solidification
on the particles), or by extensive plastic deformation
followed by rapid annealing (Sec. 6.4). Other special
techniques are required to obtain grain sizes in the
nanometre range.
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6.3.4 Solid Solution Strengthening
All materials contain small amounts of foreign atoms
(element or compound). These impurities may arise
unintentionally from raw materials and processing, or may
be added intentionally to obtain specific properties.
Impurities added intentionally are also known as alloying
elements in metals, additives in polymers and ceramics,
and dopants in semiconductors.
Within a crystal, impurities (solute) may occupy interstitial
sites or substitute for atoms of the host material (solvent),
depending on the relative sizes of solute and solvent
atoms. The incorporation of solute atoms without altering
the crystal structure of the host results in a solid solution.
Solute atoms distort the surrounding lattice and increase
the strain energy of the crystal (Fig. 6.3-15).
Fig. 6.3-15 Compressive strain imposed on host atoms by
(a) an interstitial solute atom, and (b) a large substitutional atom. (c) Tensile strain imposed by a small substitutional atom.
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The solute stress field could interact with that of an
approa-ching dislocation such that repulsion arises (Fig. 6.3-
16), similar to repulsion between dislocations of like signs
(Sec 6.3-1). A higher applied stress is needed to overcome this
repulsion.
Fig. 6.3-16 Repulsion between compressive stress fields of solute and dislocation.
On the other hand, if an interstitial or large substitutional
solute atom with a compressive stress field were to be
located in the tensile region around a dislocation, lattice
strain is reduced (Fig. 6.3-17). A similar reduction in strain is
seen for a small substitutional atom with tensile strain field
located in the compressive region of a dislocation (Fig. 6.3-18).
Once such a configuration of low strain are established
between a solute atom and dislocation, further movement
of the dislocation (i.e. away from the solute) would again
raise strain energy (Fig. 6.3-19). This increase in energy is met
by applying a higher stress; i.e. the metal strengthens. 6-29
Fig. 6.3-17 (a) Compressive strains imposed by a large substitutional solute atom.
(b) Possible locations of large solute atoms relative to an edge dislocation, leading to a reduction in overall lattice strain.
Fig. 6.3-18 (a) Tensile strains imposed by a small substitutional solute atom.
(b) Possible locations of small solute atoms relative to an edge dislocation, leading to a reduction in overall lattice strain.
Fig. 6.3-19 Interaction with a suitable solute lowers dislocation strain energy. Continued plastic deformation requires the movement of dislocation away from the
solute, which returns the dislocation and solute to their states before interaction. A higher stress is needed to restore the original strain energies of dislocation and solute.
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Higher stresses are thus required for dislocation movement in the presence of solute atoms, which act as obstacles. The more solute added (without exceeding the solubility limit), the greater the strengthening (Fig. 6.3-20). Metals are seldom used pure, but are usually alloyed for strength.
The degree of solid solution strengthening depends on the
relative sizes of the solute and solvent atoms. The larger the size difference, the greater the distortion of the surrounding lattice, and the stronger the strengthening effect (Fig. 6.3-20). Too large a size difference, however, would lower solute solubility in the host lattice (Sec. 9.3.1).
Fig. 6.3-19 The effects of several alloying elements on the yield strength of copper.
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The strengthening effect further depends whether the
solute is substitutional or interstitial. The stress field of a
substitutional solute atom is spherically symmetric, without
any shear component, and as such, does not interact with
the shear stress fields of screw dislocations. Conversely,
interstitial solute atoms in BCC crystals cause a tetragonal
distortion, generating a stress field that can interact with
both edge and screw (and thus, mixed) dislocations.
Interstitial carbon solute atoms, having sufficient diffusivity
in iron even at room temperatures, tend to move to
favourable locations around dislocations in iron that would
lead to mutual lowering of strain energy, thus pinning
down these dislocations. During the initial stages of plastic
deformation, a higher stress is needed to tear away the
dislocations from their interstitial carbon solute atoms,
after which only a lower stress is necessary to keep the
dislocations moving. This gives rise to the yield point
phenomenon in the stress-strain behaviour of steel (Fig. 6.3-21).
Fig. 6.3-21 Dislocations in iron pinned down by interstitial carbon artoms require a higher stress to begin moving, resulting in the yield point phenomenon in the stress-strain curve of steel during tensile testing.
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6.3.5 Dispersion Hardening
Small, hard particles of a second phase dispersed in a
softer, ductile matrix are effective obstacles to dislocation
motion, and lead to significant strengthening. Such
particles may be introduced intentionally, or arise naturally
from precipitation reactions in an alloy, the latter
producing a precipitation or age hardening effect.
The interaction between dislocation and dispersed particle
depends on the nature of the particle-matrix boundary. For
particles that are intentionally incorporated, and for many
precipitates, the particle-matrix interface is non-coherent
and disordered (Fig. 6.3-22a); i.e. there is no atomic matching
between the crystal lattice of the particle and matrix. Such
particles do not distort the surrounding lattice.
Fig. 6.3-22 (a) A particle that has no relationship with the crystal structure of the
surrounding matrix forms a non-coherent interface with the matrix. (b) When there is a definite relationship between the crystal structures of the precipatate
and matrix, a coherent or semi-coherent interface exists.
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At a non-coherent interface between particle and matrix
(Fig. 6.3-22a), there is a discontinuity of slip planes, much like
that at grain boundaries (Sec. 6.3.3). A dislocation would be
unable to move through such a particle.
The dislocation may be forced to keep on moving by
extruding or bowing between the particles (Fig. 6.3-23). Since
a curve between two points is longer than a straight line,
the bowed dislocation introduces greater lattice distortion
and higher strain energy than the original, straight
dislocation. A larger shear stress must now be applied to
cause such bowing and continued plastic deformation.
Fig. 6.3-23 A view looking down on a slip plane showing the bowing of a dislocation past particles having a non-coherent interface with the matrix.
[Note that the circles represent particles, not single atoms.]
After a dislocation has bowed past, dislocation loops are
left around the particles (Fig. 6.3-23). The stress fields of these
loops would interact with subsequent dislocations, and
add resistance to their motion, leading to further
strengthening.
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Fine particles that are precipitated from an alloy often have
planes of atoms in their crystal structures that are related
to, or even continuous with, planes in the matrix lattice;
such precipitate-matrix interfaces are said to be coherent
(Fig. 6.3-22b).
Since a coherent precipitate does not usually share the
same lattice parameters as the matrix, this results in lattice
strain. The stress field thus generated would interact with
passing dislocations in a manner analogous to that of solid
solution strengthening (Sec. 6.3.4).
Because the stress field generated by a coherent precipitate
is relatively wide, interactions with dislocations would
occur wherever the stress fields impinge upon one
another. The precipitate does not need to be on the slip
plane of a dislocation to have a strengthening effect.
When a coherent precipitate lies directly in the path of a
dislocation, the coherency at the interface would allow the
slip plane of the dislocation to pass from the matrix into
the precipitate and shear the precipitate (Fig. 6.3-24).
However, the creation of new matrix-precipitate surface
area after shearing raises interfacial energy. For such
shearing to occur, a higher stress must be applied to fund
the increase in energy, thus strengthening the alloy.
6-35
Fig. 6.3-24 The formation of new precipitate-matrix interfaces when a
dislocation cuts through a coherent precipitate.
The degree of strengthening depends on the number and
distribution of dispersed particles and precipitates: these
should be as numerous as possible and uniformly
distributed, so that they are closely spaced.
Dispersion hardening is the principle behind metal matrix
composites (MMCs), in which an alloy is strengthening by a
dispersion of fine, hard particles, usually of a ceramic
material. Ceramics retain their shape, distribution and
superior hardness when heated, and are more effective at
strengthening an alloy at high temperatures than
precipitates, which tend to agglomerate (and hence,
reduce in number) and re-dissolve into the matrix.
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6.3.6 Combined Strengthening Mechanisms
Two or more strengthening mechanisms may operate
simultaneously to improve strength and hardness in metals
(Tables 6.3-1&2 & Fig. 6.3-25).
Table 6.3-1 The effectiveness of the various strengthening mechanisms on copper.
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Fig. 6.3-25 Strengthening mechanisms in copper alloys and the variation in properties.
Table 6.3-2 Metal alloys with typical applications, and the strengthening mechanisms used.
Alloy Typical uses Solution hardening Precipitation hardening
Work hardening
Pure Al Kitchen foil !!! Pure Cu Wire !!! Cast Al, Mg Automotive parts !!! !
Bronze (Cu-Sn), Brass (Cu-Zn) Marine components !!! ! !!
Non-heat-treatable wrought Al Ships, cans, structures !!! !!!
Heat-treatable wrought Al Aircraft, structures ! !!! !
Low-carbon steels Car bodies, structures, ships, cans !!! !!!
Low alloy steels Automotive parts, tools ! !!! !
Stainless steels Pressure vessels !!! ! !!! Cast Ni alloys Jet engine turbines !!! !!! Symbols: !!! = Routinely used. ! = Sometimes used.
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6.4 ANNEALING
There is a limit to which metals may be plastically
deformed, beyond which fracture occurs.
During forming operations, it is sometimes necessary to
restore the ductility of work-hardened metals to their state
prior to deformation, in order to carry out further plastic
deformation.
Work hardening also lowers the thermal and electrical
conductivity of metals, which might require restoring; e.g.
copper electrical wires.
The effects of work hardening can be removed by heating
the metal to a sufficiently high temperature in a process
called annealing. Annealing replaces the highly distorted
work-hardened grains with new, equiaxed grains
containing few dislocations.
The driving force for annealing is the reduction of strain
energy associated with the high density of dislocations in a
severely work-hardened metal.
In annealing, there are three temperature ranges (from low
to high) in which different phenomena occur: recovery,
recrystallization and grain growth.
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6.4.1 Recovery
When heated sufficiently, dislocations in a strain hardened
metal rearrange themselves into configurations with lower
strain energy, forming the cell boundaries of a subgrain
structure within the old grains (Fig. 6.4-1c), in a process called
polygonization.
Dislocation density is lowered slightly through mutual
annihilation, but because the reduction is not significant,
hardness, strength and ductility are almost unchanged (Fig.
6.4-2). However, thermal and electrical conductivity are
restored close to their pre-cold-worked states.
6.4.2 Recrystall ization
After recovery is complete, the strain energy of the crystal
is still relatively high due to the large number of
dislocations remaining. If the temperature were raised
further, recrystallization will follow.
New, small, dislocation-free grains nucleate at the high-
energy cell boundaries of the polygonized subgrain
structure (Fig. 6.4-1d), eliminating most of the dislocations as
they grow and replace the strain hardened grains (Fig. 6.4-1e).
6-41
Fig. 6.4-1 Microstructural changes in cold working and annealing: (a) original state with few dislocations; (b) high density of dislocations after
cold working; (c) recovery; (d) recrystallization; (e) fully recrystallized structure of new relatively strain-free grains with few dislocations.
Since recrystallized grains are relatively free of dislocations,
the hardness, strength and ductility of the metal are
restored to their pre-cold-worked values; i.e. hardness and
strength decrease while ductility increases (Fig. 6.4-2).
The low strength and high ductility of a recrystallized
metal are exploited in hot working, in which plastic
deformation of a metallic alloy is carried out at
temperatures above its recrystallization temparature
(usually above 0.6 TM). The continually recrystallizing metal
allows extensive deformation without strain hardening.
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The main disadvantage of hot working is the poor surface
finish as a result of oxidation of the metal surface at high
temperatures. Dimensional accuracy is also an issue due to
the elastic recovery (springback) and thermal contraction
that occur when the component is cooled subsequently.
Fig. 6.4-2 The effects of annealing temperature on mechanical properties and grain size.
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6.4.3 Grain Growth
If heating were to continue after complete recrystallization
has occurred, the new grains will grow in size. [Note that grain growth occurs in all polycrystalline materials at sufficiently high temperatures; it is not related
to cold-working. Only in cold-worked metals do recovery and recrystallization take place
before grain growth.]
The driving force for grain growth is the reduction of the
interfacial energy associated with the atomic disorder at
grain boundaries (Sec. 4.7). Grain growth results in fewer
grains, thereby decreasing the total area of grain
boundaries and lowering the interfacial energy.
Grain growth involves the diffusion of atoms across the
grain boundary from one grain to another, such that some
grains grow at the expense of others (Fig. 6.4-3).
Fig. 6.4-3 Grain growth occurs as atoms diffuse across the brain boundary
from one grain to another.
Grain growth reduces the strength and hardness of
metallic alloys (Sec. 6.3.2), because the number of grain
boundaries, which are barriers to dislocation motion, are
now fewer.