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

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).

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.

6-6

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.

6-8

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.

6-10

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.

6-11

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.

6-12

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.

6-13

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.

6-14

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]).

6-15

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.

6-16

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).

6-17

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.

6-18

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.

6-19

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.

6-20

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.

6-21

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).

6-22

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).

6-23

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.

6-24

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.

.

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.

6-26

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.

6-27

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.

6-28

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.

6-30

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.

6-31

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.

6-32

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.

6-33

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.

6-34

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.

6-36

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.

6-37

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.

6-38

6-39

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.

6-40

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.