Chief.pptx

DEFORMATION AND STRENGTHENING MECHANISMS
• Metallic materials may experience two kinds of deformation viz, elastic and plastic.
• Plastic deformation is permanent; strength and hardness are measures of material’s resistance to
this deformation.
• On a microscopic scale, plastic deformation corresponds to a net movement of large numbers of
atoms in response to an applied stress.
• Plastic deformation most often involves the motion of dislocations (linear crystalline defects).
• Dislocation theory explains the physical and mechanical phenomenon in crystalline materials
particularly metals and ceramics. The theory explains;
1) The discrepancy between the theoretical and observed yield strength.
2) Strengthening mechanisms imparted on materials.
3) The mechanical behaviour of materials when stressed under various conditions.

• Any process or procedure that delays the onset of plastic deformation of a material under
stress is termed a strengthening mechanism.
• Plastic deformation corresponds to the motion (slip) of dislocations along planes in which they
lie, (Slip-planes).
• Under an applied stress the net plastic deformation is among other factors, dependant on the
number of dislocations (dislocation density) in the material.
Dislocation Density = Total dislocation length per unit volume.
• Plastic deformation leads to
 increase of dislocation density
 increase in internal energy
 Dissipation of heat
Read Sections 8.1-8.8 Callister

• Ability of a metal to plastically deform depends on the ability of dislocations to move.
• Thus, by reducing the mobility of dislocation, hardness and mechanical strength (yield
strength and ultimate tensile strength) are enhanced.
• Virtually all strengthening mechanisms rely on the principle that restricting or hindering
dislocation mobility renders a material harder and stronger.
Mechanisms to Consider
a) Grain refinement
b) Solid solution strengthening
c) Strain hardening
d) Strain Ageing
e) Cold work, recovery and recrystallization
f) Precipitation hardening.

Grain refinement:
• The size of the grains, or average grain diameter, in a
polycrystalline metal influences the mechanical properties.
• Adjacent grains (say A and B in the figure ) normally have
different crystallographic orientations and, of course a common
grain boundary.
• During plastic deformation, slip or dislocation motion must take
place across this common boundary as indicated in the figure
The grain boundary acts as a barrier to dislocation motion for two
reasons:
1. Since the two grains are of different orientations, a dislocation
passing into grain B will have to change its direction of motion;
this becomes more difficult as the crystallographic
misorientation increases.
2. The atomic disorder within a grain boundary region will result in
a discontinuity of slip planes from one grain into the other.

Grain refinement:
• A fine grained material is stronger than one that is coarse grained, since the former has
greater total grain boundary area to impede dislocation motion.
• For many materials, the yield stress δy is related to the grain size by the Hall- Petch equation.
• Fine grained structure has high grain boundary energy because of high grain boundary area.
•

Grain refinement:
• Under applied stress, dislocations are generated in a grain and they traverse on their slip plane
towards the grain boundary where they cause dislocation pile ups.
 The number of dislocations in the pile ups increases with increasing grain size and applied
stress. (It is easier to generate more dislocations in larger grains than in smaller ones. In fine
grain sized material there is high boundary area, which acts as an obstacle to the formation of
dislocations).
 The pile ups at the grain boundary cause a stress concentration in the next grain. This stress
concentration is also enhanced by the applied stress experienced in the grain till yielding
occurs in the grain.
 Thus the yield stress (δy ) can be constructed as being of two components.
δy = δa + δb , Where δa is the applied stress and δb is the stress due to dislocation pile-ups
 Therefore for coarse grained material δb is high and a low applied stress δa is required to
cause slip. Or for fine grained materials, high applied stress is required. Therefore fine grained
materials are stronger

Grain refinement:
Limitations of the Hall-Petch equation
• If the h-p equation is extrapolated to the smallest grain (i.e. 40 Å) it could predict strength
close to the theoretical cohesive shear strength. This is erroneous.
• Thus the equation is not valid for both very large (i.e., coarse) grains and extremely fine grain
polycrystalline materials
Other relations:
The H-p equation also predicts that hardness is dependant on grain size
• Grain size may be regulated by the rate of solidification from the liquid phase, and also by
plastic deformation followed by an appropriate heat treatment.

Grain refinement:
Note:
o Theoretically, a material could be made infinitely strong if the grains are made infinitely small.
This is, unfortunately, impossible because the lower limit of grain size is a single unit cell of the
material.
o Even then, if the grains of a material are the size of a single unit cell, then the material is in
fact amorphous, not crystalline, since there is no long range order, and dislocations can not be
defined in an amorphous material.
o It has been observed experimentally that the microstructure with the highest yield strength is
a grain size of about 10 nanometers, because grains smaller than this undergo another
yielding mechanism, grain boundary sliding.
o Producing engineering materials with this ideal grain size is difficult because only thin foils can
be produced with grains of this size.

2. Solid Solution Strengthening
I. Alloying pure metal with impurity atoms that go into substitutional or interstitial solid
solutions increases the strength of the metal and hardness of the metal.
II. Impurity atoms impose lattice strains on the surrounding host atoms
Example of effect of substitutional impurity
I. Lattice strain field interactions between dislocations and the impurity atoms occur and
consequently, dislocation mobility is restricted. Hence increase in strength and hardness of
the metal.
II. Strength and hardness of the alloy increases with increasing concentration of the Impurity or
alloying atoms.

Example CU –Zn (Brasses).
Variation with nickel content of
(a)tensile strength,
(b)yield strength
(c)ductility (%EL) for copper–
nickel alloys, showing
strengthening

Solid solution strengthening depends on:
 Concentration of solute atoms
 Shear modulus of solute atoms
 Size of solute atoms
 Valency of solute atoms (for ionic materials)
• Nevertheless, one should not add so much solute as to precipitate a new phase. This occurs if
the concentration of the solute reaches a high critical point given by the binary system phase
diagram.
• This critical concentration therefore puts a limit to the amount of solid solution strengthening
a material can have, as the material cannot be infinitely strengthened.

3. Strain Hardening:
• Strain hardening is the phenomenon whereby a ductile metal becomes harder and stronger as
it is plastically deformed.
• Sometimes it is also called work hardening or, cold working because the temperature at which
deformation takes place is “cold” relative to the absolute melting temperature of the metal.
Most metals strain harden at room temperature.
• Strain hardening is demonstrated in a stress–strain
diagram presented in Figure.
• Initially, the metal with yield strength σyo is plastically
deformed to point D.
• The stress is released, then reapplied with a resultant
new yield strength, σyi .
• The metal has thus become stronger during the process
because σyi is greater than σyo.

• For the low carbon steel, from 0-A the dislocation have been stressed elastically.
• At A dislocations are pinned down,so a high stress is needed to move them until point B. after
point B, the dislocations are now able to move at a lower stress.

It is sometimes convenient to express the degree of plastic deformation as percent
cold work rather than as strain. Percent cold work (%CW) is deﬁned as
Generally with strain hardening:
- Strength increases
- Hardness increases
- Ductility decreases
- Toughness decreases.

Explanation of strain hardening
(1) Plastic deformation or cold work of a metal increases the dislocation density and as result
dislocation interaction with another dislocation and other obstacles –leading to generation of
dislocation.
(2) Separation between dislocation decreases and dislocation – dislocation strain interaction
tend to be repulsive, motion of dislocation is hindered by presence of other dislocations.
(3) Hence as the dislocation density increases, the resistance to dislocation motion increases.
Therefore the stress necessary to deforms the metal increases with increasing cold work.

4. Strain Ageing:
A
Upon immediate reloading the material deform elastically up to point W of unloading (due to strain
hardening). There after, it deforms plastically without showing yield elongation. Because dislocations
are not pinned and are free to move
B
Re-testing after say Six months the new. Stress – stain curve shows the reappearance Of the yield
elongation and upper and lower yield point. This phenomenon is Called Stain Ageing. The time of six
month is to facilitate diffusion of interstitial atoms to hinder dislocations

4. Strain Ageing:
Strain ageing is a unique form of strain hardening of particular metals, particularly annealed low
carbon mild steels. The stress-strain curve shows an upper and lower yield points and a yield
elongation. Explanation
1. When low carbon annealed steel is strained, it should yield at a
stress equal to the lower yield point. However, due to presence of
the interstitial carbon and nitrogen atoms, the dislocations are
pinned down by the interstitial atoms called dislocation on Cottrell
atmospheres. As such a higher stress is required to unpin the
dislocation. Therefore the stress is increased to the upper yield
point. Once the dislocations are unpinned they can be moved at a
lower stress, which is lower yield stress. Hence, stress decreased
2. Due to continuous attraction of the atmosphere to the
dislocations, and continuous unpinning a yield elongation Y-Z occurs
until a metal starts to deform plastically with strain hardening till
fracture

4. Strain Ageing:
Explanation
3. When the metal is strained into plastic region to a stress below
the UTS, it strain hardens. Upon unloading and immediate reloading
it is observed that;
a) The metal deforms elastically up to the point of unloading and
then yields
b) The yielding stress is higher than the original elastic limit eg
lower yield point (why)
4. When strained and then unstrained, and the metal specimen is
kept say at room
temperature for six months and then retested, it is observed that:
a) The yield elongation reappears(why)
b) The upper and lower yield points are higher so is the UTS (why)
c) Ductility is lower (why)

Cold work, recovery, recrystallisation and grain growth
Cold work
• This is the plastic deformation or working of a ductile metal at a temperature below that at
which new and stress free grains can be nucleated by thermal assistance.
• The lowest temperature at which new equiaxed and stress free grains appear in the structure
of a previously plastically deformed metal is called the recrystallization temperature, hence
the maximum cold working temperature.
• The recrystallisation temperature depends on many factors, the principle of which are
 Severity of plastic deformation
 Grain size prior to the plastic deformation (the smaller the grains, the lower the
recrystallisation temperature)
 Temperature at which plastic deformation occurs
 Presence of dissolved or undissolved elements
 Melting temperature of the metal

Cold work
• The lower the deformation temperature the lower the recrystallisation temperature for same amount of material.
• Recrystallisation is a nucleation and growth process, therefore, the higher the undissolved elements, the higher the
nucleation energy, thus smaller temperature of recrystallisation.
Effect of cold work
1. Lattice distortion leading to increase of internal energy and hence internally strained or stressed structure. It thus
leads to an increase in dislocation density.
2. Internal energy increases with increasing degree of deformation. Therefore the properties will also change
accordingly:
Strength increases
Ductility decreases
Toughness decreases
Hardness increases
3. Change in grain shape
4. Some fraction of the energy expended in deformation is stored in metal as strain energy which is associated with
tensile, compressive and shear zones around the newly created dislocations.

Recovery
• During recovery, some of the stored internal strain energy is relieved by virtue of dislocation
motion (in the absence of an externally applied stress), as a result of enhanced atomic
diffusion at the elevated temperature.
• There is some reduction in the number of dislocations, and dislocation conﬁgurations (similar
to that shown in are produced having low strain energies.
• In addition, physical properties such as electrical and thermal conductivities and the like are
recovered to their precold-worked states.

Recrystallisation
• 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 (i.e., having
approximately equal dimensions in all directions) that have low dislocation densities and are
characteristic of the precold-worked condition.
• The driving force to produce this new grain structure is the difference in internal energy
between the strained and unstrained material.
• Also, during recrystallization, the mechanical properties that were changed as a result of cold
working are restored to their precold-worked values; that is, the metal becomes softer,
weaker, yet more ductile.

Recrystallisation
• Recrystallization is a process the extent of which depends on both
time and temperature. The degree (or fraction) of recrystallization
increases with time.
• The inﬂuence of temperature is demonstrated in Figure 8.22, which
plots tensile strength and ductility (at room temperature) of a brass
alloy as a function of the temperature and for a constant heat
treatment time of 1 h. The grain structures found at the various
stages of the process are also presented schematically
• The recrystallization behavior of a particular metal alloy is sometimes
speciﬁed in terms of a recrystallization temperature, the temperature
at which recrystallization just reaches completion in 1 h.
• Thus, the recrystallization temperature for the brass alloy of Figure is
about 450◦C (850◦F).
• Typically, it is between one-third and onehalf of the absolute melting
temperature of a metal or alloy and depends on several factors such
as; amount of prior cold work and the purity of the alloy

Recrystallisation
• Increasing the percentage of cold work enhances the rate of
recrystallization, with the result that the recrystallization
temperature is lowered, and it approaches a constant or limiting
value at high deformations; this effect is shown in Figure
• Furthermore, it is this limiting or minimum recrystallization
temperature that is normally speciﬁed in the literature.
• There exists some critical degree of cold work below which
recrystallization cannot be made to occur, as shown in the ﬁgure;
normally, this is between 2% and 20% cold work.
• Recrystallization proceeds more rapidly in pure metals than in
alloys (refer to Callister for explanation)
In short, recrystallisation results in:
 More grains being formed
 Decrease of strength and hardness with increasing temperature
 Increase of ductility

Grain growth
• After recrystallization is complete, the strain-free grains will continue to grow if the metal
specimen is left at the elevated temperature; this phenomenon is called grain growth.
• Energy is associated with grain boundaries. As grains increase in size, the total boundary area
• decreases, yielding an attendant reduction in the total energy; this is the driving force for
grain growth.
 It is temperature dependent
 Results in uniform grains if the metal was uniformly cold worked
 Non-uniform deformation results in growth of abnormally large and non uniform grains.
 The mechanical properties of a fine-grained material are usually superior (i.e. higher strength
and toughness) to those of coarse grained ones.

Grain growth
• For many polycrystalline materials that have been cold worked and then annealed (to cause
recovery and recrystallisation), the grain diameter varies with time at a particular temperature
according to the relationship;
Reading Questions, check sections 8.15 and 8.16 in Callister
1. Explain why crystalline ceramics are hard and brittle when compared to metals
2. Explain why the deformation mechanism in non crystalline ceramics differs from that of
metals.

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