Plastic Deformation of Polycrystalline Metals

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Plastic Deformation of Polycrystalline Metals

• Chp. 8-cont.

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• The direction of slip varies from one grain to
  another as a result of random crystallographic
  orientations.

Variation in grain orientation is also clear from
the difference in the alignment of the slip
lines. During deformation, mechanical integrity
and coherency are maintained along the
grain boundaries. The grain boundaries do not
come apart or open up.
Slip lines
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• The manner in which the grains distort as a
  result of gross plastic deformation

Polycrystalline metals are stronger than their
single-crystal equivalents, which means greater
stresses are required for the slip to occur. This
is mainly due to geometrical constraints imposed
on the grains during deformation.
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• Mechanisms of Strengthening in Metals
• Macroscopic plastic deformation corresponds to
  the motion of large numbers of dislocations.
• Therefore strengthening of metals relies on this
  simple principle
• Restricting or hindering dislocation motion
  renders a material harder and stronger.
• The strengthening mechanisms for a single phase
  metals are discussed here, which are by
• Grain size distribution
• Solid solution alloying
• Strain hardening

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• Strengthening by grain size reduction
• Adjacent grains normally have different
  crystallographic orientations and a common grain
  boundary as shown below

• During plastic deformation, slip or dislocation
  motion must take place across this
• common boundary, which acts as a barrier to
  dislocation due to two major reasons
• Crystallographic misorientation of the grains
• Atomic disorder within a grain boundary resulting
  in discontinuity of slip planes.

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• If the grain boundary is a high angle boundary,
  it may also possible to observe stress
  concentration ahead of slip plane in one grain
  activating new dislocations.
• Fine grained material is harder and stronger
  simple due to greater total grain boundary area
  compared to coarse grained material.
• For many materials

Hall-Petch equation
daverage grain diameter s0 and ky are constants
for a particular material. This equation is not
valid for both very large and extremely small
grain size materials.
The toughness of the alloy also increases
as grain size decreases.
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• Small angle grain boundaries are not very
  effective in interfering with the slip process
  because of the slight misalignment across the
  boundary. Twin boundary can block the slip
  effectively and increase the strength of the
  material. Boundaries between two phase systems
  are also effective in preventing the movement of
  dislocations and this is important for
  strengthening more complex alloys.
• Solid-Solution Strengthening This is simply
  alloying the metals with impurity atoms, which is
  solid solution (interstitial or substitutional).
• High purity metals are always softer and weaker
  than alloys composed of the same base metal. This
  is because the impurity atoms that go into solid
  solution impose lattice strains on the
  surrounding host atoms. Lattice strain between
  dislocations and impurity atoms result and
  dislocation movement is restricted.
• This is illustrated as follows

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The impurity atoms tend to diffuse to and
segregate around dislocations in a way so as to
reduce the overall strain energy.
small impurity atoms creating tensile strain.
large impurity atoms creating compressive strain.
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• The resistance to slip is greater when impurity
  atoms are present because the overall lattice
  strain must increase if a dislocation takes place
  away from them. This requires a greater stress to
  be applied to initiate plastic deformation. This
  is evidenced by the enhancement of strength and
  hardness as shown below

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• Strain hardening It is a phenomenon whereby a
  ductile metal becomes harder and stronger as it
  is plastically deformed. It is also work
  hardening or cold working. Most metals strain
  harden at room temperature.
• Degree of plastic deformation is expressed as
  percent cold work

A0 is the original area of the cross section that
experiences deformation Ad is the area after
deformation.
Initial yield strength is lower than the new
yielding strength after plastic
deformation. Therefore the meaterial is stronger
as it is plastically deformed.
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• The influence of cold work on stress-strain
  behavior of a low C steel

The strain hardening is a result of increasing
dislocation numbers due to plastic deformation.
The dislocation density in a metal increases with
cold work and the average distance between
dislocations decreases. It is observed
dislocation-dislocation interactions are
repulsive and therefore the motion of a
dislocation is hindered by the presence of other
dislocations. Therefore, the imposed stress
necessary to deform the material increases with
cold work.
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• Recovery, Recrystallization and Grain Growth
• Plastic deformation of a polycrystalline metal at
  T lower than its absolute melting temperature may
  result in
• change in grain shape
• strain hardening
• increase in dislocation density
• The properties and structures may revert back to
  the precold worked states by appropriate heat
  treatment (annealing treatment).
• This process takes place at elevated temperature
  and recovery, recrystallization and grain growth
  are the major processes.
• 1. Recovery Some fraction of the energy expended
  in deformation is stored in the metals as strain
  energy. During recovery, some of this energy is
  relieved by dislocation motion which is the
  result of enhanced atomic diffusion at elevated
  temperature. There will be reduction in the
  number of dislocations and new dislocation
  configurations with low strain energies are
  produced.

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• 2) Recrystallization is the formation of new
  strain-free and equiaxed grains with low
  dislocation densities and they have
  characteristic of the precold-worked condition.
  The driving force for the formation of new grains
  is the difference in the internal energy of
  strained and unstrained one. Recrystallization of
  cold-worked material is used to refine the grain
  structure.

Brass
Initial stage of recrystallization after heating
3 s at 5800C.
Cold worked grain structure
small grains at the beginning of recrystallization
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• Following up stages of recrystallization

Complete recrystallization (8 s at 5800C)
Grain growth after 15 min at 5800C and 10 min at
7000C.
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• During recyrstallization, the mechanical
  properties changed as a result of cold working
  are also restored to their precold worked values.

constant heat treatment time is 1 hour
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• The temperature at which recrystallization just
  reaches completion in 1 h is called
  recrystallization temperature. Thus, the
  recrystallization temperature for the brass alloy
  is about 4500C.
• T of recrystallization1/3-1/2 of the absolute
  melting temperature of the metal or alloy.
• Of course T of recrystallization also depends on
  the amount of prior cold work and purity of the
  alloy.
• Increasing the percentage of CW enhances the rate
  of recrystallization and decreases the T of
  recrystallization. The rate of crystallization
  approaches a constant or limiting value at high
  deformations. This value is reported in the
  literature as the T of recrystallization.

Below the critical deformation there is no
recrystallization.
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• Recrystallization proceeds more rapidly in pure
  metals than alloys. Alloying raises the T of
  recrystallization.

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• Grain growth Following up recrystallization,
  strain free grains continue to grow at elevated
  temperature. As the grain size increases, total
  energy reduces and this is major drive for grain
  formation.
• Grain growth occurs by the migration of grain
  boundaries. Some of them grow, while the others
  shrink. Boundary motion is just a short range
  diffusion of atoms from one side to other.

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• For many polycrystalline materials grain diameter
  (d) varies with time according to

diameter at t0, K and n are constants.
Dependence of diameter to T
This is because diffusion is faster at high T.