There are several mechanisms for strengthening metals and alloys: 1. Grain refinement, where reducing grain size increases strength by creating more grain boundaries that impede dislocation movement. 2. Strain hardening occurs when plastic deformation increases dislocation density, requiring more stress for further movement. 3. Solid solution strengthening uses alloying to distort the crystal lattice, impeding dislocations. Interstitial atoms are especially effective. 4. Precipitation hardening forms coherent precipitates that strongly interact with dislocations. It involves solutionizing, quenching, and aging.

1. Strengthening Mechanisms
of Metals and Alloys

2. Mechanisms of strengthening metals and alloys
1. Strengthening by Grain Refinement
2. Strain Hardening
3. Solid Solution Strengthening
4. Precipitation (or Age) Hardening
5. Dispersion Hardening
6. Particulate Strengthening
7. Phase Transformation Hardening.
The strength of a material is its resistance against deformation, especially,
against plastic deformation or yielding.

3.  Yielding occurs due to the movement of dislocations in metallic crystals.
 Movement of dislocation is stopped if some barrier or discontinuity comes in the path of
dislocations.
 To make dislocations move and cause plastic deformation, much more stress must be applied over
the material. This means the resistance of material against deformation or in other words, its
strength is increased. Grain boundaries are regions where atoms are at higher energy level and also
where atomic orientation changes.
 Dislocations cannot glide past the grain boundaries easily. Hence, if there are more grain
boundaries, there is more resistance to the movement of dislocations and hence an increase in
strength.
 If there are more grains in a given amount of material, i.e., if the size of grains or crystals is
smaller, there will be more grain boundaries compared to the case when the grains are larger.
1. Strengthening Grain Refinement

4.  Material with smaller grains or more grain boundaries will be stronger.
 Any process which tends to make the grains smaller (i.e., causes grain refinement) will increase
the strength of the material.
Yield strength a of a polycrystalline material is given by the equation-

5. Yield strength increases as the crystal dia. ‘d’ decreases.
Fine grains can be obtained by controlling the cooling rate of the
solidifying metal or by adding some alloying elements which promote
grain refinement.
For example – in case of steel, micro alloyed steels have been developed
by adding very small quantities of elements like Ti, V and Nb. The
resulting grain size of such steels is about 2 to 3 pm.
The yield strength is increased by as much as 50 %.

6. Smaller grains retard the movement of dislocations. This results in higher
strength of materials. Deformation becomes easier in case of larger
crystals and ductility, as measured in terms of percent elongation or
percent reduction in area, increases
Relationship between grain size d and yield strength σy.
Effect of grain size on percent elongation
(ductility) of metals.

7. 2. Strain Hardening
• Strain hardening occurs due to multiplication of dislocations
according to Frank-Reed source.
• During plastic deformation there is a continuous increase in
dislocation density and the stress necessary to move the
dislocations continuously increases.

8. Effect of Cold Work on Ductility
• Cold work increases hardness and
strength due to the effect of strain
hardening.
• As the degree of cold work increases
(as expressed by percent reduction in
thickness) ductility goes on
decreasing.
• Cold working is also detrimental as it
raises the ductile-brittle transition
temperature of steels.

9. 3. Solid Solution Strengthening
Another technique to strengthen and harden metals is alloying with impurity atoms that go
into either substitutional or interstitial solid solution.
Solid solution strengthening distorts the lattice and offers resistance to dislocation movement
which is greater with interstitial elements which cause asymmetric lattice distortion, e.g.,
carbon in steel.
Mechanism:
Since no two elements have the same atomic diameter, solute atoms will be either smaller or
longer in size than the solvent atoms. Due to the difference in atomic size, lattice distortion is
produced when one element is added to the other.
Smaller atoms will produce a local tensile stress field and larger solute atoms will produce a
local compressive field in the crystal.
In both cases, stress field of a moving dislocation interacts with the stress field of the solute
atom. This increases the stress required to move the dislocation through the crystal.

10. Factors affect solid solution strengthening
• (i) Atomic Size Difference:
Increase in the atomic size difference between the solute and solvent the intensity of the
stress field around solute atoms increases. This increases the resistance to the motion of
dislocations thereby increasing hardness and tensile strength.
Therefore, more the atomic size difference, higher is the hardness and tensile strength.
• (ii) Amount of Solute:
When the amount of solute or the number of solute atoms is more, greater will be the local
distortion in the lattice and hence more will be the resistance to the moving dislocations.
This will increase the hardness and strength of the material.
The increase in strength is proportional to C1/2 where C is the solute concentration. For
dilute solutions, increase in strength with concentration is approximately linear.

11. (iii) Nature of Distortion:
Hardness and tensile strength are also affected
by the nature of distortion produced by solute
atoms. Spherical distortion produced by
substitutional solute atoms is much less
effective than non-spherical distortion
produced by interstitial solute atoms.
C and N form interstitial solid solutions and produce tetragonal distortion in the
lattice whereas the other elements form substitutional solid solutions and produce
spherical distortion.

12. 4. Precipitation or Age Hardening
In case of some alloys there is increase in hardness with time at room temperature or
after heating to slightly higher temperatures. This type of hardening is called
precipitation or age hardening.
It is observed in alloys such as
Al = 4.5% Cu,
Zn = 2.5% Mg,
Cu = 2% Be, Ni = 17%,
Cu = 8% Sn, Ti = 6%, A1 = 4%, etc.

13. The conditions for precipitation or age hardening to
occur in any alloy system are
(i) The solubility of solute in the solvent must decrease with decrease in
temperature.
(ii) The precipitate that separates out from the matrix should be coherent
otherwise the material will not be hardened. There is no true interface
between the precipitate particle and the surrounding matrix. Since the
solute atoms are of different sizes from the solvent atoms, large amount of
elastic distortion is observed around the precipitate particle.

14. These coherent precipitate particles are powerful obstacles to the motion
of dislocations. This is because the large elastic distortion of the matrix
around the particles interacts strongly with the stress field of
dislocations. In some systems like Mg-Pb, Al-Mn and Al- Mg decrease
in solubility is observed with decrease in temperature, but the precipitate
is not coherent and hence the alloys from these systems cannot be
hardened by the above process.
The general steps involved in age/precipitation hardening are:
(i) Heating (solutionizing),
(ii) Quenching, and
(iii) Ageing.

15. 5. Dispersion Hardening
• The resistance to motion of dislocations, in this strengthening
mechanism, is increased by introducing finely divided hard
particles of second phase in the soft matrix. The increase in
hardness and tensile strength is due to the interaction of the
stress field around the particles with the stress field of a moving
distortion and also due to physical obstruction by the hard
particles to the moving dislocation.

16. The extent to which strengthening/hardening is
produced depends upon the following factors:
i. The amount of second phase particles;
ii. The characteristics and properties of second phase;
iii. The particle size, shape and distribution.
The maximum strengthening, hardening is observed at some
intermediate spacing of particles, not too less and not too more.
The optimum properties are usually observed at a concentration
of particles from 2 to 15 percent (by volume), their size between
0.01 and 0.1 μm, and a spacing of 0.1 to 1.0 μm between particles.

17. The increase in yield strength due to very hard and inert particles is
given by the relation:
The above equation, truly speaking, gives the stress necessary to move a
dislocation line of length I pinned at both ends with Burger’s vector of b, i.e.,
to operate a Frank- Reed source of length I through a matrix of shear
modules C.
The dispersed particles are normally oxides, carbides, borides etc. The main
advantage of dispersion hardened materials is their ability to maintain high
strength and creep resistance at elevated temperatures of the order of 80
percent of the melting point of the matrix.
Common examples of this type are:
i. Sintered aluminium powder,
ii. Thoriated polycrystalline tungsten.
The common method of manufacturing dispersion hardened material is
powder metallurgy.

18. 6. Particulate Strengthening
The particulate-strengthened systems differ from dispersion
strengthened ones in the size of the dispersed particles and their
volumetric concentration. In the former systems the particles are 1 μm
or more and of concentration of 20 to 40 volume % whereas in the
latter systems the particle size is usually less than 0.1 μm. It is very
important that the particles should be small, properly distributed and
of uniform size.
Particulate composites are made mainly by powder metallurgy
techniques that may involve solid or liquid state sintering or even
impregnation by molten metal.
Examples:
Tungsten-nickel-iron system obtained as a liquid-sintered composite
and the tungsten-nickel copper system.

19. 7. Phase Transformation Hardening
• Phase transformation is a change in the number and/or character of the
phases that constitute the microstructure of an alloy, e.g., in steel
conversion of austenite into martensite.
• Martensitic transformation occurs in steels when austenite phase is cooled
rapidly (i.e., cooled exceeding the critical cooling rate) to room
temperature or below room temperature. Due to rapid cooling, austenite
(FCC) gets transformed to a Body Centered Tetragonal (BCT) martensite
by a diffusion less process.
• Martensite is a supersaturated solid solution of carbon in BCC iron with
BCT structure and is formed from austenite by shear mechanism.
Martensite is a hard phase and its hardness depends on the carbon in the
austenite or steel.
• Because of the formation of BCT structure from FCC structure, the lattice
gets distorted and the intense stress field around the carbon atoms in
martensite effectively hinders the motion of dislocations. Martensite
transformation is very important for controlling the properties of steels.