Chapter 7: Dislocation and Strengthening Mechanism

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Chapter 7 Dislocation and Strengthening Mechanism

• Why Study ?
• With a knowledge of the nature of dislocation and
  the role they play in the plastic deformation
  process, we are able to understand the underlying
  mechanisms of the techniques that are used to
  strengthen and harden metals and alloys.

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DISLOCATIONS and PLASTIC DEFORMATION7.2 Basic
Concepts

• Dislocation Types
• Edge Dislocation
• Screw Dislocation
• Review from Chapter 4 notes

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Chapter 4 (Review)4.4 Dislocations __ Linear
Defects

• A dislocation is a linear or one-dimensional
  defect around which some of the atoms are
  misaligned.
• Edge dislocation An extra portion of a plane of
  atoms, or half-plane, the edge of which
  terminates within the crystal. (shown in figure )
• Dislocation line For the edge dislocation in
  Figure, it is perpendicular to the plane of the
  paper.

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Chapter 4 (Review)4.4 Dislocations __ Linear
Defects (Contd.)

• Within the region around the dislocation line,
  there is some localized lattice distortion.
• Atoms above the line are squeezed together
• Those below are pulled apart
• Results in slight curvature for the vertical
  planes of atoms as they bend around this
  extra-half plane
• At far position, the lattice is virtually
  perfect.
• ? extra half-plane in the upper portion
• extra half-plane in the bottom portion

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Chapter 4 (Review)4.4 Dislocations __ Linear
Defects

• Screw Dislocation May be thought of as being
  formed by a shear stress that is applied to
  produce the distortion as shown in figure.
• The upper front region of the crystal is shifted
  one atomic distance to the right relation to the
  bottom portion.
• Atomic distortion is also linear and along a
  dislocation line, Line AB.
• Derived name from the spiral or helical path or
  ramp traced around the dislocation line.
• ? Symbol in Figure

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Chapter 4 (Review)4.4 Dislocations __
Linear Defects

• Most dislocations found in crystalline materials
  are probably neither pure edge nor pure screw,
  but mixed.
• All three dislocations are represented in Figure
  4.5
• The lattice distortion that is produced away from
  the two faces is mixed, having varying degrees of
  screw and edge character.

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• Plastic deformation corresponds to the motion of
  large number of dislocations.
• An edge dislocation moves in response to a shear
  stress applied in a direction perpendicular to
  its line
• Figure shows the mechanics.

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• When the shear stress applied,
• Plane A is forced to the right
• This in turn pushes the top halves of planes B,
  C, D, and so on.
• If the applied stress is of sufficient magnitude,
• The inter-atomic bonds of plane B are severed
  along the shear plane
• The upper half of plane B becomes the extra
  half-plane
• Plane A links up with the bottom half-plane of
  plane B
• This process is subsequently repeated
• Ultimately this extra half-plane may emerge ?
  forming an edge that is one atomic distance wide
• Atomic arrangement of the crystal
• Only during passage of the extra half-plane the
  lattice structure is disrupted
• Before and after the movement of a dislocation ?
  ordered and perfect

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• SLIP ? The process by which plastic deformation
  is produced by dislocation
• Slip plane ? the crystallographic plane along
  which the dislocation line traverses
• Macroscopic plastic deformation simply
  corresponds to permanent deformation that results
  from the movement of dislocations, or slip, in
  response to an applied shear stress
• The direction of movement for
• For an edge is parallel to the applied shear
  stress
• For Screw dislocation is perpendicular
• Net plastic deformation for both is same

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Dislocation Motion

• Dislocation moves along slip plane in slip
  direction perpendicular to dislocation line
• Slip direction same direction as Burgers vector

Edge dislocation
Adapted from Fig. 7.2, Callister 7e.
Screw dislocation
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• Dislocation motion is analogous to the mode of
  locomotion employed by a caterpillar
• Forms hump near its posterior end by pulling last
  pair of legs a unit leg distance ? hump propelled
  forward by repeated lifting and shifting ? when
  hump reached the anterior end, the entire
  caterpillar has moved forward by the leg
  separation distance.

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• Some dislocations in all crystalline materials
  were introduced during
• Solidification
• Plastic deformation
• Thermal stresses
• Dislocation density expressed as
• Total dislocation length per unit volume, or
  equivalently (mm/mm3)
• The number of dislocations that intersect a unit
  area of a random section (mm-2)
• Carefully solidified crystals have low values
  103 mm-2
• Heavily deformed metal have high values 109 to
  1010 mm-2
• Heat treating a deformed metal diminishes to 105
  to 106 mm-2

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7.3 Characteristics of Dislocations

• When metals are deformed plastically,
• Some fraction of the deformation energy (approx.
  5) is retained internally
• Remainder is dissipated as heat
• Major portion of stored energy is as strain
  energy associated with dislocations.
• Lattice distortions may be considered to be
  strain fields
• That radiate from the dislocation line
• Extend into the surrounding atoms
• Magnitude decreases with radial distance from the
  dislocation.

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• Atoms immediately above and adjacent to the
  dislocation line ? squeezed together ?
  experiencing compressive strain
• Atoms directly below ? tensile strain
• Shear strain also exist in the vicinity of edge
  dislocation
• For screw dislocation, lattice strains are pure
  shear only

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• Strain fields surrounding dislocations in close
  proximity may interact
• Examples
• Two edge dislocations having same sign and
  identical slip plane
• Compressive and tensile strain field for both lie
  on the same side of the slip plane
• Strain field interaction ? mutual repulsive force
  that tends to move them apart.

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• Two dislocations of opposite sign and having the
  same slip plane
• Attract each other
• Dislocation annihilation will occur when they
  meet
• Two extra half-planes align and become a complete
  plane
• Are possible between edge, screw, and/or mixed
  dislocations
• Result in strengthening mechanism for metals.

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7.4 Slip Systems

• Dislocations produce atomic dislocations on
  specific crystallographic slip planes and in
  specific crystallographic slip directions.
• Slip is favored on close-packed planes since a
  lower shear stress for atomic displacement is
  required than for less densely packed planes
• ? Plane having greatest planar density ? Slip
  Plane
• If slip on the closed-packed planes is restricted
  due to local high stresses, for example, then
  planes of lower atomic packing can become
  operative
• Slip in the closed-packed directions is also
  favored since less energy is required to move the
  atoms from one position to another if the atoms
  are closer together
• ? Directions having highest linear density ?
  Slip Direction
• A combination of a slip plane and a slip
  direction is known as Slip System.

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Slip System
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Deformation Mechanisms

• Slip System
• Slip plane - plane allowing easiest slippage
• Wide interplanar spacings - highest planar
  densities
• Slip direction - direction of movement - Highest
  linear densities
• FCC Slip occurs on 111 planes (close-packed) in
  lt110gt directions (close-packed)
• gt total of 12 slip systems in FCC
• in BCC HCP other slip systems occur

Adapted from Fig. 7.6, Callister 7e.
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• For metals with FCC structure, slip takes place
• On the close-packed octahedral planes
• In the closed-packed directions
• There are eight 111 octahedral planes which are
  crystallographically equivalent ? same planar
  density
• Planes at opposite faces, which are parallel, are
  considered the same type of (111) slip plane
• Therefore, there are only four different types of
  (111) slip planes in the FCC crystal structure
• Each (111)-type plane contains three
  directions, which are crystallographically
  equivalent.
• Reverse directions are not considered different
  slip directions
• Thus, for FCC lattice structure
• 4 unique slip planes x 3 independent slip
  directions 12 slip systems

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• Possible slip systems for BCC and HCP are listed
  in Table 7.1
• Metals with FCC or BCC crystal structures have a
  relatively large number of slip systems (at least
  12)
• These metals are quite ductile because plastic
  deformation is normally possible along the
  various systems
• HCP metals having few active slip systems are
  normally quite brittle.

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7.5 Slip in Single Crystal

• Edge, Screw, and mixed dislocations move in
  response to shear stresses applied along a slip
  plane and in a slip direction.
• Even for applied pure normal (tensile or
  compressive) stress, shear stress exists at all
  but parallel or perpendicular alignments to the
  applied stress direction. ? resolved shear
  direction
• Magnitude of resolved shear stress
• A metal single crystal has a number of different
  slip systems
• Resolved shear stress normally differs for each
  one

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STRESS AND DISLOCATION MOTION
Crystals slip due to a resolved shear stress,
tR.
Applied tension can produce such a stress.
slip plane normal, ns
slip direction
slip direction
slip direction
4
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• Critical resolved stress ( tcrss )
• Minimum shear stress required to initiate slip
• Property of material that determines when
  yielding occurs

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CRITICAL RESOLVED SHEAR STRESS
Condition for dislocation motion
Crystal orientation can make it easy or
hard to move disl.
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Single Crystal Slip
Slip occurs along a number of equivalent and most
favorably oriented planes and directions at
various positions along the length. On surface
these appears as lines (Figure 7.9)
Adapted from Fig. 7.9, Callister 7e.
Adapted from Fig. 7.8, Callister 7e.
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Example 7.1
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Ex Deformation of single crystal
a) Will the single crystal yield? b) If not,
what stress is needed?
?60
?crss 3000 psi
?35
Adapted from Fig. 7.7, Callister 7e.
? 6500 psi

• So the applied stress of 6500 psi will not cause
  the crystal to yield.

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Ex Deformation of single crystal
What stress is necessary (i.e., what is the
yield stress, sy)?
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7.6 Plastic Deformation of Polycrystalline
Materials

• Random crystallographic orientations of the
  numerous grains, the direction of slip varies
  from one grain to another ? deformation and slip
  is complex
• Photomicrograph of a polycrystalline copper
  specimen
• Before deformation, the surface was polished
• Slip lines visible
• Two sets of parallel yet intersecting sets of
  lines ? It appears that two slip systems operated
• The difference in alignment of the slip lines for
  the several grains ? variation in grain
  orientation

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• Gross plastic deformation ? distortion of
  individual grain by means of slip
• Mechanical integrity and coherency are maintained
  ? grain boundaries usually do not come apart or
  open up.
• Each individual grain is constrained by its
  neighboring grains.
• Figure 7.11 shows plastic deformation
• Before deformation, grains equiaxed (have approx.
  same dimension in all direction)
• After deformation, grains elongated along the
  direction of extension or loading

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• Polycrystalline materials are stronger
• greater stresses are required to initiate slip
  and yielding
• Due to geometrical constraints imposed on the
  grains
• Even a favorably oriented single grain can not
  deform until the adjacent less favorably oriented
  grains are capable of slip also
• ? requires a higher applied stress level.

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Mechanism of Strengthening in Metals

• The ability of a metal to plastically deform
  depends on the ability of dislocations to move.
• Hardness and strength are related to the ease
  with which plastic deformation can be made to
  occur
• To enhance mechanical strength ? reduce
  dislocation mobility ? greater mechanical forces
  required to initiate plastic deformation.
• Strengthening mechanism for single phase metal
• By grain size reduction
• Solid-solution alloying
• Strain-hardening

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7.8 Strengthening by Grain Size Reduction

• Adjacent grains have different crystallographic
  orientation
• During plastic deformation, slip or dislocation
  motion must take place across the common boundary
  (from grain A to grain B)
• Grain boundary acts as a barrier to dislocation
  motion for two reasons
• Two grains are of different orientation ? a
  dislocation have to change its direction of
  motion ? becomes more difficult as
  crystallographic misorientation increases.
• Atomic disorder within a grain boundary region
  will result in a discontinuity of slip planes
  from one grain into the other.

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• Hall-Petch Equation For many materials, Yield
  strength varies with grain size as
• d average grain diameter
• s0 and ky are material constants
• Figure 7.15 shows strength variation
• for brass
• Hall-Petch equation is not valid
• for very large and extremely
• small grain materials

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• High-angle grain boundaries
• Dislocations may not traverse grain boundaries
  during deformation
• A stress concentration ahead of a slip plane in
  one grain may activate sources of new dislocation
  in an adjacent grain.
• Small-angle grain boundaries
• Not effective in interfering because of slight
  misalignment
• Twin boundaries
• Effectively block slip and increase the strength
  of the material
• Boundaries between two different phases
• Impediment (obstacle/barrier) to movements of
  dislocations
• Important in strengthening complex alloys

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7.9 Solid Solution Strengthening

• Another technique to strengthen and harden metals
  is alloying
• Adding impurity atoms that go into either
  substitutional or interstitial solid solution
• High-purity metals are almost always softer and
  weaker
• Fig 7.16 shows the effect of alloying nickel in
  copper

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Strategies for Strengthening 2 Solid
Solutions
Impurity atoms distort the lattice generate
stress. Stress can produce a barrier to
dislocation motion.
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• Alloys are stronger than pure metals
• Impurity atoms impose lattice strain on
  surrounding host atoms
• Lattice strain field interaction between
  dislocation and impurity atoms result
• ? dislocation movement is restricted
• An impurity atom that is smaller than a host atom
  ? substitution results tensile strains on the
  surrounding crystal lattice ( Fig 7.17a)
• Larger substitutional atom imposes compressive
  strains in its vacinity (Fig 7.18a)

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• Solute atoms tend to diffuse to and segregate
  around dislocations ? reduce strain energy ? to
  cancel some lattice strain surrounding a
  dislocation
• To accomplish this,
• a smaller impurity atom is located where its
  tensile strain will partially nullify some of the
  dislocations compressive strain
• A larger atom to nullify tensile strain of
  dislocation
• ? Figure 7.17b and 7.18b
• Resistance to slip is greater
• Overall lattice strain must increase if
  dislocation is torn away from them
• Same strain interaction exist between atoms and
  dislocation that are in motion during plastic
  deformation
• ? greater applied stress is needed to initiate
  and continue plastic deformation

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7.10 Strain Hardening

• Strain hardening ? a phenomenon whereby a ductile
  material becomes harded and stronger as it is
  plastically deformed.
• Also known as work-hardening or cold working
• Most metals strain harden at room temperature
• Degree of plastic deformation is expressed as
  percent cold work (CW)

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Strategies for Strengthening 3 Cold Work (CW)
Room temperature deformation. Common
forming operations change the cross
sectional area
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Dislocations During Cold Work
Ti alloy after cold working
Dislocations entangle with one another
during cold work. Dislocation motion
becomes more difficult.
Adapted from Fig. 4.6, Callister 7e. (Fig. 4.6
is courtesy of M.R. Plichta, Michigan
Technological University.)
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Result of Cold Work

• Dislocation density
• Carefully grown single crystal
• ? ca. 103 mm-2
• Deforming sample increases density
• ? 109-1010 mm-2
• Heat treatment reduces density
• ? 105-106 mm-2

Yield stress increases as rd increases
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Effects of Stress at Dislocations
Adapted from Fig. 7.5, Callister 7e.
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Impact of Cold Work
As cold work is increased
Yield strength (sy) increases.
Tensile strength (TS) increases.
Ductility (EL or AR) decreases.
Adapted from Fig. 7.20, Callister 7e.
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Cold Work Analysis
What is the tensile strength ductility
after cold working?
Adapted from Fig. 7.19, Callister 7e. (Fig.
7.19 is adapted from Metals Handbook Properties
and Selection Iron and Steels, Vol. 1, 9th ed.,
B. Bardes (Ed.), American Society for Metals,
1978, p. 226 and Metals Handbook Properties
and Selection Nonferrous Alloys and Pure
Metals, Vol. 2, 9th ed., H. Baker (Managing Ed.),
American Society for Metals, 1979, p. 276 and
327.)
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• Why more stronger ?
• On the average, dislocation-dislocation strain
  interactions are repulsive
• Dislocation density increases due to
• Deformation or cold work
• Dislocation multiplication
• Formation of new dislocations
• Net result ? motion of dislocation is hindered by
  the presence of other dislocations ? higher
  imposed stress is needed to deform a metal

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Recovery, Recrystallization, and Grain Growth

• Plastic deformation of polycrystalline metal at
  temperatures lower than its melting temperature
  produces
• ? micro-structural and property changes
• ? includes
• A change in grain shape
• Strain hardening
• Increase in dislocation density
• Some fraction of deformation energy (about 5)
  stored in metal as strain energy
• Associated with tensile, compressive and shear
  zones around newly created dislocations
• Other properties (such as electrical conductivity
  and corrosion resistance ) may be modified by
  plastic deformation.

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• Modified Properties and structures due to plastic
  deformation (cold work)
• May revert back to the precold-worked states by
  Annealing
• Annealing is a heat treatment process
• Restoration due to due different processes at
  elevated temperatures
• Recovery
• Recrystallization
• Above processes may be followed by grain growth.

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7.11 Recovery

• At elevated temperature
• ? enhanced atomic diffusion
• ? dislocation motion
• ? some stored strain energy relieved
• Recovery process Involves
• Reduction in dislocation numbers
• Dislocation configuration with low strain energy
• (similar to Fig 4.8)
• Physical properties are recovered to their
  precold-worked state
• Electrical and thermal conductivities

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7.12 Recrystallization

• Even after recovery is complete, the grains are
  still in a relatively high strain energy state.
• Recrystallization is the formation of a new set
  of strain-free and equiaxed grains having low
  dislocation densities as the precold-worked
  state.
• Difference in internal energy between the
  strained and unstrained material ? acts as the
  driving force to produce new grain structure
• New grains form as very small nuclei ? grow
  until completely replace the parent material ?
  involves short-range diffusion

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7.12 Recrystallization (Contd.)Several stages of
recrystallization

• (a) cold-worked (33) grain structure
• (b) Initial stage of recrystallization after
  heating 3 s at 580oC

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7.12 Recrystallization (Contd.)Several stages of
recrystallization

• (c) Partial replacement of cold-worked grains by
  recrystallized ones (4s at 580oC)
• (d) complete recrystallization (8s at 580oC)

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7.12 Recrystallization (Contd.)Several stages of
recrystallization

• (e) Grain growth after 15 min at 580oC
• (d) Grain growth after 10 min at 700oC

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7.12 Recrystallization

• During recrystallization, mechanical properties
  restored to their precold-worked values
• ?Metal becomes softer, weaker, yet ductile
• Some heat treatments are designed to allow
  recrystallization to occur these modifications in
  the mechanical characteristics.
• Recrystallization depends on both time and
  temperature
• Influence of time
• The degree (or fraction ) of recrystallization
  increases with time (Figure 7.21a-d)

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• Influence of temperature
• Figure 7.22 shows tensile strength and ductility
  of a brass alloy
• Constant heat treatment time of 1 hour
• Grain structures at various stages are presented
  schematically.

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• Recrystallization temperature
• The temperature at which recrystallization just
  reaches completion in 1 hour.
• Recrystallization temperature of brass alloy (Fig
  7.22) is about 450oC (850oF).
• It is about 1/3 to ½ of absolute melting
  temperature
• Depends on several factors, such as cold work,
  purity of alloy etc.
• Effect of CW
• Increasing CW enhances the rate of
  recrystallization ? recrystallization
  temperature is lowered
• Recrysttalization temperature approaches a
  constant or limiting value at high deformation.
• Critical degree of cold work
• Below which no recrystallization
• Ususally 2 20

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• Effect of alloying
• Recrystallization proceeds more rapidly in pure
  metal than in alloys ? alloying raises
  recrystallization temperature
• For pure metal normally it is 0.3(Melting
  temperature)
• For alloys, it may run as high as 0.7(melting
  temperature)
• Hot working plastic deformation operations at
  temperatures above the recrystallization
  temperature
• Material remains relatively soft and ductile
  during deformation
• It does not strain harden
• Large deformations possible

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• Design Example 7.1

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7.13 Grain growth

• After recrystallization is complete, the
  strain-free grains will continue to grow if the
  metal specimen is left at the elevated
  temperature ? phenomenon is known as grain
  growth.
• It occurs by the migration of grain boundaries
• Boundary motion is just the short-range diffusion
  of atoms from one side of the boundary to the
  other
• Direction of boundary movement and atomic motion
  are opposite.
• Schematic reprsentationin Fig 7.24

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• For many polycrystalline materials, grain
  diameter (d) varies with time as
• dn don Kt
• do initial grain diameter at t0
• K, n time-dependent constants
• n is equal to greater than 2
• Dependence of grain size on time and temperature
  is shown in Fig 7.25
• Brass alloy
• At higher temperature, rapid growth ? due to
  enhancement of diffusion rate

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• Mechanical properties at room temperature of a
  fine-grained metal are usually superior (strength
  and toughness) than coarse-grained ones.
• If grain structure of a single phase alloy is
  coarser than that desired
• ? plastically deform
• ? subject to recrystallization heat treatment
• ? refine grain size