1. Plastic Deformation of Polycrystalline Metals

2. 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

3. 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.

4. 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

5. 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.

6. 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
d=average grain diameter
σ0 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.

7. 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:

8. 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.

9. 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:

10. 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.

11. 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.

13. 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.

14. 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

15. Following up stages of recrystallization:
Complete recrystallization
(8 s at 5800C)
Grain growth after 15 min at 5800C
and 10 min at 7000C.

16. 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

17. 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 recrystallization=1/3-1/2 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.

18. Recrystallization proceeds more rapidly in pure metals than alloys
Recrystallization proceeds more rapidly in pure metals than alloys. Alloying raises the T of recrystallization.

19. 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.

20. Dependence of diameter to T:
For many polycrystalline materials grain diameter (d) varies with time according to:
diameter at t=0, K and n are constants.
Dependence of diameter to T:
This is because diffusion
is faster at high T.