Department of MME
BUET, Dhaka
Strengthening strategies :
Grain strengthening
Hall-Petch equation
Solid solution strengthening
Principle of alloying
Work hardening
Anisotropy in structure
Restoring ductility after work hardening
Precipitation hardening
Reference:
1. WD Callister, Jr. Materials Science and Engineering: An Introduction,
5th Ed., Ch. 7, pp.166-179.
To strengthen a metal,
make it harder for dislocations to move
There are 4 strategies for strengthening:
Grain strengthening
Solid solution strengthening
Work/strain hardening
Precipitation hardening
The price for enhancement of strength and hardness
is in the reduction of ductility !!
Obstacle: Grain boundary
Creates slip plane discontinues – causing difficulty in dislocation motion
Degree of obstacle increases
with misorientation
Small grain size
More barrier to slip
Adjacent grains have different
crystallographic orientations
The finer the grains, the larger the area of grain
boundaries that impedes dislocation motion
Grain-size reduction also improves toughness of material
Variation of yield strength with grain size
according to Hall-Petch relation:
sy = s0 + ky d -½ s0, ky are material constants
d is average grain size
Example: Brass (Cu-30Zn alloy)
sy = s0 + ky d-½
Obstacle: Impurity atoms
offers obstruction in dislocation motion
Smaller and larger substitutional tension compression
impurities produce localised
stresses at the lattice
These impurities tend to diffuse
into strained regions around the
dislocation
resulting partial cancellation of small substitutional atom large substitutional atom
impurity-dislocation lattice strains
stresses around an impurity atom
Principle of Alloying
Alloys are usually stronger than pure metals of the solvent.
Interstitial or substitutional impurities in a solution cause lattice strain. As
a result, these impurities interact with dislocation strain fields and hinder
dislocation motion.
Impurities tend to diffuse and segregate around the dislocation core
to find atomic sites more suited to their radii. This reduces the overall
strain energy but “anchor” the dislocation. The resistance to slip will
be greater because the overall lattice strain must now increase if a
dislocation is torn away from them.
Thus, a greater applied stress is necessary to: (1) torn away a
dislocation from impurity pinning and initiate plastic deformation, and
then (2) continue plastic deformation for solid solution alloys.
Example: Alloying with Ni strengthens Cu
60
Elongation in 2 inch (%)
Tensile Strength (MPa)
400 50
40
300
30
200 20
0 10 20 30 40 50 0 10 20 30 40 50
Ni Content (wt.%) Ni Content (wt.%)
What happens to the right side of these diagrams,
i.e., alloys containing more than 50 wt.% Ni?
Obstacle: Already existing dislocations
offers obstruction in motion of other dislocations
Also known as strain hardening, work hardening, or cold working
The reason for strain hardening is the increase of dislocation density
with plastic deformation due to dislocation multiplication and formation
of new ones
The average distance between dislocations decreases and dislocations
start blocking the motion of each other.
Like dislocations repeal, opposite dislocations attract
Dislocations become entangled with one another.
Dislocation motion becomes more difficult.
Ductile metals become stronger when they are deformed plastically
at temperatures well below the melting point.
Common cold working operations
Cold working – room temperature deformation
The percent cold work, %CW, is just another measure of the degree of
plastic deformation, in addition to strain or %EL. It is also known as %RA.
%CW = 100(Ao- Ad)/Ao
σy for plastically deformed sample is higher than that for annealed
sample due to hardening (materials becomes stronger).
TS
hardening
%EL or %RA
YS
Stress-strain diagram Effect of cold work on
showing strain hardening stress-strain diagram
Yield strength and hardness increased due to strain hardening
but ductility decreased (material becomes more brittle).
Yield Strength (MPa)
Ductility (%EL)
Cold Work (%CW) Cold Work (%CW)
Restoring Ductility after Work Hardening
1 hr heat treatment at different annealing temperatures
Effect of cold work reversed.
TS decreased while %EL increased !!
Restoration of ductility in 2 steps:
1. recovery
2. recrystallisation
Sometimes recrystallisation is followed by grain growth.
Restoring Ductility
after Work Hardening
Recovery Recrystallisation Grain growth
increased diffusion some residual stresses remained in some grains even after
recovery stage.
enhanced dislocation motion
these strained grains replaced by new strain-free grains with low
decreased dislocation density by annihilation.
dislocation density.
relieved internal strain energy
this occurs through nucleation and growth of new grains.
Obstacle: Hard second phase particles
offers obstruction in motion of dislocations
Example: Ceramics in metals (e.g., SiC in Iron or Aluminum)
Hard precipitates are difficult to shear!!
Formation of precipitation
