‘’DISLOCATIONS AND
STRENGTHENING MECHANISMS’’
IE-114 Materials Science and General Chemistry
Lecture-7
Stress-Strain Curves
Typical Stress-Strain Curve of Non-Ferrous Alloys (Al, Cu, etc..)
 Yield point (y) : Point at which dislocations start moving (plastic deformation)
 Plastic deformation is accomplished by means of a process called SLIP. (motion of dislocation)
Dislocations
 Linear crystalline defects around which there is atomic misalignment
Edge Dislocation
Screw Dislocation
Mixed Dislocation
Characteristics of Edge Dislocations
 Introduced during solidification, plastic deformation and by thermal stresses
 There are lattice strains around the dislocation line
Compressive strains above the line (where the atoms are squeezed together)
Tensile strains below the line (where the atoms are pulled apart)
Dislocation Motion
 Shear stress () is needed for dislocation motion
 Dislocations move in a preferred plane (the most dense atomic packing)
and directions (the highest linear density)
Upon application of shear stresses extra half plane moves from left to right by successive and repeated breaking of bonds.
F
F
F
F
Slip Systems
 The process by which plastic deformation is produced by dislocation motion
is termed SLIP.
 Slip plane is that having the most dense atomic packing, that is, has the
greatest planar density
 Slip direction corresponds to the direction, in this plane, that is most closely
packed with atoms, that is, has the highest linear density.
 Slip System: the combination of slip plane and slip direction
 Slip is favored on close-packed planes since a lower shear stress for atomic
displacement is required. Moreover, slip occurs in close packed directions since
less energy is required to move atoms in these directions
Slip Systems in Some Crystals
Example: For FCC metals, slip occurs in {111} planes and <110> directions
Crystal Structure
Slip Systems
Number of Slip Systems
Ductility vs. Number of Slip Systems
 Metals having highest number of slip systems are quite ductile because
extensive plastic deformation is normally possible along the various systems.
Not all of these are
operative at room
temperature
 Ductility at room temperature:
FCC > BCC > HCP
Shear stress is required for plastic deformation
 Slip (process of dislocation motion) begins when shear stress ()
on the slip plane in the slip direction reaches a critical value (c).
Stress required to cause slip in single crystals depends on;
1)
2)
3)
4)
Crystal Structure (BCC, FCC, HCP,..)
Atomic bonding characteristics
Temperature of deformation
Orientation of the active slip planes with respect to the shear stress
Slip in Single Crystal (Schmid’s Law)
 During tension, although, applied stress may be pure tensile, shear components
exist in materials. These are termed resolved shear stress (R)
: the angle between the normal to the slip
plane and the applied stress direction
: the angle between applied stress and slip
direction
R: Resolved shear stress
R =  Cos Cos
Schmid’s Law
 Resolved Shear Stress on different slip systems
 Max. Resolved Shear Stress, max
 One slip system which is oriented most favorably, has the largest resolved shear stress
 Critical Resolved Shear Stress, crss
 Slip (dislocation movement) in a single crystal starts on the most favorably oriented slip
system when the resolved shear stress reaches some critical value
Yielding Criteria in Single Crystals
R= max = crss = y (Cos Cos)max
Slip Bands and Slip Planes in Single Crystals
Formation of Slip Bands in FCC metals
 In FCC metals, slip occurs on many slip planes
within the slipbands
SLIP LINES
Step markings on the surface; SLIP BANDS
Plastic Deformation of Polycrystalline Materials
 The direction of slip varies from one grain to another as a result of random
crystallographic orientations grains.
Slip lines
 Plastic deformation of a polycrystalline
specimen corresponds to the comparable
distortion of individual grains by means of slip.
 Polycrystalline metals are stronger than their
single-crystal equivalents, which means that
greater stresses are required to initiate slip or
for yielding.
Twinning
 Plastic deformation mechanism (commonly seen in HCP metals)
 A part of the atomic lattice is deformed so that it forms a mirror image of the
undeformed lattice next to it.
 Twinning occurs on twin planes and in a specific direction; twin direction
Differences Between Slip and Twinning
1) In slip, the atoms on one side of the slip plane all move equal distances,
whereas in twinning the atoms move distances proportional to their distance
from the twinning plane.
2) Slip leaves a series of steps (lines), whereas twinning leaves small but welldefined regions of the crystal deformed.
Slip
Twinning
Deformation twins in unalloyed titanium
 Twinning involves a small fraction of the total volume of the metal crystal, so
that amount of deformation is small
Lattice orientation changes that are caused by twinning may place new
slip systems into favorable orientation with respect to the shear stress
and thus enable additional slip to occur
 Twinning is most important for the HCP structure because of its small
number of slip systems
 Deformation Twinning occurs in;
 HCP metals (Zn, Mg, Ti) at room temperature
 BCC metals (Fe, Mo, W, Ta) at very low temperatures
 Some BCC metals at room temp. at very high strain rates
 The FCC metals show the least tendency to form deformation twins
Strengthening Mechanisms of Metals
 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 :
1) Solid solution alloying
2) Strain hardening
3) Precipitation hardening
4) Grain size reduction
1) Solid Solution Strengthening
 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.
• Smaller substitutional impurity
Impurity generates local shear at A and B that opposes
disl motion to the right.
• Larger substitutional impurity
Impurity generates local shear at C and D that opposes
disl motion to the right.
INTERSTITIAL SOLID SOLUTION
SUBSTITUTIONAL SOLID SOLUTION
2) Strain (Work) Hardening
 Strain hardening is the phenomenon whereby a ductile metal becomes harder
and stronger as it is plastically deformed at room temperature.
Deformation Processes:
- Forging
- Rolling
force
die
Ao blank
Ad
- Drawing
die
Ao
die
force
Ad
- Extrusion
tensile
force
Result of Cold Work:
 Dislocation density (rd) increases:
Undeformed sample: rd ~ 103 mm/mm3
Heavily deformed sample: rd ~ 1010 mm/mm3
 The motion of dislocation is hindered by the presence of other
dislocations, which cause increase in strength value.
 Strain hardening increases
 Yield strength (y) increases.
 Tensile strength (TS) increases.
 Ductility (%EL or %AR) decreases.
3) Precipitation Hardening
 Dislocations interact with precipitates
 Hard precipitates are difficult to shear.
Ex: Ceramics in metals (SiC in Iron or Aluminum).
CuAl2 precipitates
1.5mm
in Cu-Al alloy
1
y ~
S
4) Grain Size Reduction
 Grain boundaries are barriers to slip (dislocation motion)
 Smaller grain size:more barriers to slip.
 Fine grained metals are stronger, harder and tougher
Effect of grain diameter (d) on yield strength:
 yield  o  k y d 1/ 2 Hall-Petch Equation
o and ky are constant for a particular material
d : average grain diameter
Hall-Petch Equation does not apply to;
(1) extremely coarse and extremely fine grain sizes,
(2) metals used at elevated temperatures
Grain size can be adjusted;
 by rate of solidification from the liquid phase
 by plastic deformation followed by appropriate heat treatment.
Grain size reduction by plastic deformation
followed by heat treatment
COLD WORKING (at room temp.)
Heating to high temp.
 This reheating treatment that softens a cold-worked metal is called annealing
 During annealing metal structure will go through a series of changes called
(1) recovery, (2) recrystallization, (3) Grain Growth
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.
 Recovery of metals produces a subgrain structure with low angle grain
boundaries. This recovery process is called polygonization
2) Recrystallization
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.
33% cold
worked
brass
New crystals
nucleate after
3 sec. at 580oC.
BRASS ALLOY
Start of recrystallization
Complete recrystallization
Johnson, Mehl, Avrami, Kolmogorov approach;
X = 1 - exp(-Bt n )
X: fraction recrystallized
 The temperature at which recrystallization just reaches completion in 1 h is
called recrystallization temperature. (The recrystallization temperature for the
brass alloy is about 450oC)
* 1/3-1/2 of the absolute melting temperature (K) of the metal or alloy.
Temperature of recrystallization depends on;
 the amount of prior cold work
 initial grain size
 composition or 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.
Recrystallization Temperature of
Some Pure Metals and Alloys
3) Grain Growth
 Following up recrystallization, strain free grains continue to grow at elevated
temperature.
 At longer times, larger grains consume smaller ones. Why?
- Grain boundary area (and therefore energy) is reduced.
Grain growth
 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.
Schematic representation of grain growth
Empirical Relation for Grain Growth:
coefficient dependent on material and T.
grain diam.
at time t.
dn  dno  Kt
elapsed time
Exponent(n) typ. ~ 2
Summary
 Dislocations are observed primarily in metals and alloys.
 The process of dislocation motion is called slip. Slip occurs on planes
having highest planar density (slip plane) and in the direction which has
highest linear density (slip direction)
 Strength is increased by making dislocation motion difficult.
 Particular ways to increase strength are to:
--solid solution strengthening
--precipitate strengthening
--cold work
--decrease grain size
 Heating (annealing) can reduce dislocation density and increase grain
size.