K.Srinivasulureddy-SNIST-Metallurgy & Material Science-MMS-UNIT-1

Metallurgy and Material Science
5BC07
Syllabus

Mechanical Behavior of Metals: Slip systems in BCC, FCC and HCP. Deformation behavior of
BCC, FCC and HCP crystal structures. Theoretical shear strength of the material comparison to
actual strength of various metal systems Dislocation theory and slip phenomenon; Frank Read
Source of dislocation; Dislocation pile-up; Theory of strain hardening: Temperature effect on
deformation of and strain hardening ; Concept of single and polycrystals; Effect on grain size on
ductility of metal, Theory of cold-working and hot-working. Intermediate annealing, Recovery,
Recrystallization and grain growth; Recrystallization temperature, Definition of Creep,
mechanism of creep and creep-curve.
UNIT-I

...Perfection's a gift of
The gods, few can boast they possess it - and most
Of you, my dears, don’t.
- Ovid, The Art of Love
A perfect crystal is an idealization; there is
no such thing in nature.
Atom arrangements in real materials do not
follow perfect crystalline patterns

Imperfections or defects
➢ Any deviation from the perfect atomic arrangement in a crystal is said to
contain imperfections or defects. In fact, using the term “defect” is sort of a
misnomer since these features are commonly intentionally used to
manipulate the mechanical properties of a material.
➢ Adding alloying elements to a metal is one way of introducing a crystal
defect.
➢ Crystal imperfections have strong influence upon many properties of
crystals, such as strength, electrical conductivity and hysteresis loss of
ferromagnets.
➢ Thus some important properties of crystals are controlled by as much as
by imperfections and by the nature of the host crystals.

✓ The conductivity of some semiconductors is due entirely to trace amount of
chemical impurities.
✓ Color, luminescence of many crystals arise from impurities and imperfections
✓ Atomic diffusion may be accelerated enormously by impurities or imperfections
✓ Mechanical and plastic properties are usually controlled by imperfections

Imperfections in crystalline solids are normally classified according to their
dimension as follows:
1. Point imperfections (Zero dimensional defects)
2. Line imperfections (one dimensional defects)
3. Plane or surface imperfections (Two dimensional defects)
4. Volume imperfections (three dimensional defects)

1.Point defects
•self interstitial - extra atom
•vacancy - missing atom
•substitutional impurity - impurity atom in lattice
•interstitial impurity - impurity atom not in regular lattice site
Crystalline Defects:
The ideal crystal has an infinite 3D repetition of identical units, which may be
atoms or molecules. Real crystals are limited in size, and they have some
disorder in stacking which are called defects.

Point Defects: A Point Defect involves a single atom change to the normal
crystal array.
➢ There are three major types of point defect:
Vacancies, Interstitials and Impurities.
➢ They may be built-in with the original crystal growth, or activated by heat. They
may be the result of radiation, or electric current etc, etc.

Vacancies: A Vacancy is the absence of an atom from a site normally occupied in
the lattice. Due to thermal excitation, extensive plastic deformation, high energy
particle bombardment.
Interstitials: An Interstitial is an atom on a non-lattice site. There needs to be
enough room for it, so this type of defect occurs in open covalent structures, or
metallic structures with large atoms.
An atom that is trapped inside the crystal at a point intermediate between normal
lattice positions. This is due to radiation damage.
Impurity atom: Impurity atom which is present in the lattice, resulting in local
disturbance of the lattice

Substitutional solid
solution.
Example: Cu in Ni.
Increases the strength of
the Nickel.
Interstitial solid solution.
Example: when C occupies
interstitial sites of the Fe
crystal lattice, the Fe becomes
steel which is an important
engineering alloy.
Zero-dimensional - Point Defects ..cont.,
Substitutional defect. Interstitial defect.

Imperfections in ceramics - Defect structure
1. Because atoms exists as charged ions, conditions of
electroneutrality must be maintained.
2. Electroneutrality means equal # of positive and equal number
of negative ions.
3. As a consequence, defects in ceramics do not occur alone;
Defects occur in pair.

Imperfections in Ceramics – Ionic Solids
Anion is larger compared to cations.
Anion interstitial is not likely.

Imperfections in ceramics - Defect structure (cont.,)
Two types of paired defect structures are:
(i) Frankel defect. (Cation vacancy & Cation interstitial)
(ii) Schottky defect. (Cation vacancy & Anion vacancy)

Frankel defect: Cation-vacancy & cation interstitial.

Imperfections in AX type ceramics
Schottky defect: A cation-vacancy & anion –vacancy pair is
known as Schottky defect.

Line Defects: One dimentional defects
Dislocation: A Dislocation is a line discontinuity in the regular crystal
structure.
There are two basic types: Edge dislocations, and Screw dislocations.

K.Srinivasulureddy-SNIST-Metallurgy & Material Science-MMS-UNIT-1

Representation of analogy between caterpillar and dislocation motion
Atomic arrangements that accompany the motion of an edge dislocation as it moves in
response to an applied shear stress. (a) The extra half –plane of atoms is labeled ‘A’.
(b) The dislocation moves one atomic distance to the right as ‘A’ links up to the lower
portion of plane ‘B’.

An Edge dislocation in a Metal may be regarded as the insertion
(or removal) of an extra half plane of atoms in the crystal structure.

The screw dislocation is slightly more difficult to
visualize. The motion of a screw dislocation is also a
result of shear stress, but the defect line movement is
perpendicular to direction of the stress and the
atom displacement, rather than parallel.
The atoms represented by the blue circles have not yet
moved from their original position. The atoms
represented by the red circles have moved to their new
position in the lattice and have reestablished metallic
bonds. The atoms represented by the green circles are
in the process of moving. It can be seen that only a
portion of the bonds are broke at any given time.
As was the case with the edge dislocation, movement in
this manner requires a much smaller force than
breaking all the bonds across the middle plane
simultaneously.
The screw dislocation will move upward in the image,
which is perpendicular to direction of the stress.
Recall that the edge dislocation moves parallel to the
direction of stress.
SCREW DISLOCATION

Two types of dislocations in crystals that can induce slip are:
1.Edge dislocations and
2.Screw dislocations.
➢Edge dislocations have the direction of the burgers vector perpendicular
to the dislocation line, while screw dislocations have the direction of the
burgers vector parallel to the dislocation line.
➢The type of dislocations generated largely depends on the direction of
the applied stress, temperature and other factors.

Mixed Edge/Screw
Dislocation.
(a) Schematic representation of a
dislocation that has edge, screw,
and mixed character ,
(b) Top view, where open circles
denote atom positions above the
slip plane. Solid circles, atom
positions below. At point A, the
dislocation is pure screw, while at
point B, it is pure edge.
For regions in between where there
is curvature in the dislocation line,
the character is mixed edge &
screw.

1. The magnitude and direction of the lattice distortion
associated with a dislocation is expressed by Burgers vector,
denoted by b.
2. Burgers vector will point in a close packed crystallographic
direction & magnitude equal to the interatomic spacing.
➢Perfect lattice.
➢Back at the same atom.
➢With an edge dislocation.
➢Need to go back an atomic spacing to
end at the same atom.

3. The motion of dislocation allows plastic deformation.
4. Using TEM, dislocations can be seen.
5. Burgers vector is parallel to the direction of shear stress.
Perfect lattice.
Back at the same atom.
With an edge dislocation.
Need to go back an atomic
spacing to end at the same atom.
(..cont.,)

A Transmission electron
micrograph(TEM) of a
titanium alloy in which the
dark lines are dislocations.
51,450X
One-dimensional Defects – dislocation in cubic crystal

Crystalline
Polycrystalline
Amorphous
Atoms
GrainGrain boundary

Planar Defects(Surface Defects): Grain Boundaries
➢A Grain Boundary is a general planar defect that separates regions of different
crystalline orientation (i.e. grains) within a polycrystalline solid.
➢The atoms in the grain boundary will not be in perfect crystalline arrangement.
Grain boundaries are usually the result of uneven growth when the solid is
crystallising. Grain sizes vary from 1 µm to 1 mm.
➢Several cells form a crystal, if many
crystals are growing in a melt, at the
same time, where they meet, grain
boundary is formed.
➢ A grain boundary is the interface
between two grains, or crystallites, in a
polycrystalline material.
➢ Grain boundaries are 2D defects in the
crystal structure, and tend to decrease
the electrical and thermal conductivity
of the material.

Grain Boundaries in Polycrystals:
➢ Up to this point, the discussion has focused on defects of single crystals.
However, solids generally consist of a number of crystallites or grains. Grains
can range in size from nanometers to millimeters across and their orientations
are usually rotated with respect to neighboring grains.
➢ Where one grain stops and another begins is know as a grain boundary. Grain
boundaries limit the lengths and motions of dislocations.
➢ Therefore, having smaller grains (more grain boundary surface area)
strengthens a material. The size of the grains can be controlled by the cooling
rate when the material cast or heat treated.
➢ Generally, rapid cooling produces smaller grains whereas slow cooling result
in larger grains.

Twist boundary: Rotation axis is perpendicular to
the boundary plane.
Low angle grain boundaries that appear as an
array of screw dislocations.
Tilt boundary: Between two slightly mis-aligned
grains appear as an array of edge dislocations.
Rotation axis is parallel to the boundary plane

Stacking Faults
➢ A stacking fault is a one or two layer interruption in the stacking sequence of
atom planes. Stacking faults occur in a number of crystal structures, but it is
easiest to see how they occur in close packed structures.
➢ For hcp and fcc structures, the first two layers arrange themselves identically,
and are said to have an AB arrangement. If the third layer is placed so that its
atoms are directly above those of the first (A) layer, the stacking will be ABA.
This is the hcp structure, and it continues ABABABAB.
➢ However it is possible for the third layer atoms to arrange themselves so that
they are in line with the first layer to produce an ABC arrangement which is
that of the fcc structure. So, if the hcp structure is going along as ABABAB and
suddenly switches to ABABABCABAB, there is a stacking fault present.

➢ For, fcc arrangement the pattern is ABCABCABC. A stacking fault in an fcc
structure would appear as one of the C planes missing. In other words the pattern
would become ABCABCAB_ABCABC.
➢ If a stacking fault does not corrects itself immediately but continues over some
number of atomic spacings, it will produce a second stacking fault that is the twin of
the first one.
➢ For example if the stacking pattern is ABABABAB but switches to ABCABCABC for
a period of time before switching back to ABABABAB, a pair of twin stacking faults
is produced.

Defects in crystals. (a) Vacancies–missing atoms. (b) Foreign (solute) atom on interstitial
and substitutional sites.
(c) Line Defect = A dislocation–an extra half-plane of atoms. (d) Grain boundaries.
Alloying and
heat treating
Little
impact on
strength
Course GB = weak,
Fine GB = strong and
ductile
Greatest
impact
on
strength
and
ductility!!

Volume or Bulk Defects
➢ Bulk defects occur on a much bigger scale than the rest of the crystal
defects discussed.
➢ Voids are regions where there are a large number of atoms missing from
the lattice.
➢ The image is a void in a piece of metal. The image was acquired using a
Scanning Electron Microscope (SEM).

▪ Voids can occur for a number of reasons. When voids occur due to air
bubbles becoming trapped when a material solidifies it is commonly called
porosity.
▪ When a void occurs due to the shrinkage of a material as it solidifies, it is
called cavitation.
▪ Another type of bulk defect occurs when impurity atoms cluster together to
form small regions of a different phase. The term ‘phase’ refers to that
region of space occupied by a physically homogeneous material. These
regions are often called precipitates or inclusions.

What is the most significant defect?
Answer: The line defect (edge dislocation or screw dislocation)

➢Slip is an important mode of deformation mechanism in crystals
➢The slip planes and slip directions in a crystal have specific
crystallographic forms.
➢The slip planes are normally the planes with the highest density of
atoms, and the direction of the slip is the direction in the slip plane in
which atoms are most closely spaced.
➢A slip plane and a slip direction constitute a slip system. A critical
resolved shear stress is required to initiate a slip.

➢a slip system describes the set of symmetrically identical slip
planes and associated family of slip directions for
which dislocation motion can easily occur and lead to plastic deformation.
➢Depending on the type of lattice, different slip systems are present in the
material. More specifically, slip occurs on close-packed planes (those
containing the greatest number of atoms per area), and in close-
packed directions (most atoms per length).
The magnitude and direction of slip are represented by the Burgers vector.

HCP (1x3=3) FCC(4x3=12) BCC(48)
Slip systems(no. of planes x no. of slip direction) in HCP,FCC and BCC
structures
6x2=12
12x1=12
24x1=24

Structure Slip Plane Slip direction No. of Slip
systems(=No. of
slip planes x No. of
slip directions)
HCP {0001} <1120> 1x3=3
FCC {111} <110> 4x3=12
BCC {110} <111> 6x2=12
{211} <111> 12x1=12
{321} <111> 24x1=24
Probable slip planes, slip-directions and slip systems in HCP,FCC and
BCC structures
FCC & BCC are more ductile than HCP

➢ Slip is the movement of dislocation in the atomic level. This
phenomena favors the plane which has the highest planar density
and the direction which has highest linear density of the atom.
➢ When it comes to ductility ,we need to deform the material and as
a result of which the dislocation present inside them will also
travel, but as mentioned earlier slip is the movement of dislocation
and in FCC the atoms are closed pack and has a predominant slip
system and hence the slip can travel easily inside it and the
material can be deformed easily as a result it will be more ductile
while in case of BCC the dislocation cannot travel with such an
ease. And hence we can conclude that the FCC structure has more
ductility than BCC.
Slip & Ductility

Slip systems
• FCC and BCC materials have large numbers of slip systems (at
least 12) and are considered ductile.
• HCP systems have few slip systems and are quite brittle.
Ductility: FCC>BCC>HCP

An initially perfect crystal is shown in (a). The passage of the dislocation across the
slip plan, shown in the sequence (b), (c) and (d), shears the upper part of the crystal
over the lower part by the slip vector b. When it leaves, the crystal has suffered a
shear strain g.
Slip due to line defects

= Resolved shear stress in the slip direction
= Unidirectional stress applied to the cylinder
A is larger than A0
Shear stress on the slip plane along the slip direction is given by

➢Critical resolved shear stress is the component of shear stress, resolved in the
direction of slip, necessary to initiate slip in a grain. It is a constant for a
given crystal.
➢Tests have been conducted on single crystals of metals to measure the shear
stress required to initiate plastic deformation, or cause atomic planes to slip. Since
this is a threshold value, it is referred to as critical; and since it is a component of
the applied force or stress, it is said to be resolved; that is, the critical resolved
shear stress. The critical resolved shear stress is the value of resolved shear
stress at which yielding begins; it is a property of the material.
➢Resolved shear stress is given by Ƭ = σ cos Φ cos λ where σ is the magnitude
of the applied tensile stress, Φ is the angle between the normal of the slip plane
and the direction of the applied force and λ is the angle between the slip direction
and the direction of the applied force. whereas, critical resolved shear stress value
is given by Ƭ= σ (cosΦ cosλ)max
Critical Resolved Shear Stress(CRSS)
τ = P · cos λ/(A/cos φ) = (P/A) · cos λ · cos φ

The quantity cos φ cos λ is called the Schmid factor

The critical resolved shear stress is the value of resolved shear stress at which
yielding begins; it is a property of the material.

Single & Polycrystal materials
Polycrystalline: Macroscopically homogeneous,
microscopically heterogeneous
Multiple grain boundaries and second phase
particles present in polycrystalline materials.
It is easier to study plastic deformation in a
single crystal to eliminate the effects of grain
boundaries and second phase particles

➢Application of single crystal solids is in materials science in the production of
high strength materials with low thermal creep, such as turbine blades.
➢Absence of grain boundaries actually gives a decrease in yield strength, but
more importantly decreases the amount of creep which is critical for high
temperature, close tolerance part applications.
➢A single crystal or monocrystalline solid is a material in which the crystal
lattice of the entire sample is continuous and unbroken to the edges of the
sample, with no grain boundaries.
➢Single crystal silicon is used in the fabrication of semiconductors.
➢In polycrystals, many grain boundaries will present, which offer resistance to
dislocations of atoms.
➢In single crystals, there is no such resistance as there is no grain boundary. At high
temperatures, these large grains are useful to avoid yielding.
➢Single crystal copper has better conductivity than polycrystalline copper
Single crystalline materials

➢Presence of grain boundaries in polycrystalline, makes the structure susceptible to
creep and cracking along those boundaries under centrifugal forces at elevated
temperatures.
➢Hence single crystal materials are preferred in High temp. applications like gas
turbine blades.
Single crystalline Materials: Materials in which the atomic order extends uninterrupted
over the entire of the material
Ex: Single crystal silicon(used in semiconductor)
Single crystal nickel(used in turbine blades)
Single crystalline materials Contd..

• Most engineering materials are polycrystals.
• Each "grain" is a single crystal.
• If grains are randomly oriented, overall component properties are not
directional.(Isotropic)
• Grain sizes typ. range from 1 nm to 2 cm
1 mm
Polycrystals
Anisotropic: physical property which has a different value when measured in different
directions.(Ex. Single crystal) An example is wood, which is stronger along the grain
than across it.

Polycrystalline Materials
1. Crystallographic orientation varies from grain to grain
2. Atomic mismatch exists with in the region where two
grains meet, this area is called grain boundary.

• Some engineering applications require single crystals
• Properties of crystalline materials often related to crystal structure.
Ex: Quartz fractures more easily along some crystal
planes than others.
➢diamond single crystals for abrasives
(MCD-Mono Crystalline Diamond)
➢ turbine blades (Nickel based super alloys)

➢Single crystal – only one grain or crystal and hence, no
grain boundaries.
➢Useful for applications where grain boundaries are harmful.
For example, high temperature deformation or creep

➢Polycrystalline metals are stronger than their single-crystal equivalents,
which means that greater stress are required to initiate slip and the
attendant yielding
Deformation of polycrystalline materials
➢Commercial metal products are usually polycrystalline aggregates. These are
made up of a tremendous number of small single crystals or grains.
➢The individual small single crystals in polycrystalline aggregates can not
deform like single crystals because in polycrystalline materials, the crystals are
not free to deform since they are surrounded by other crystals and also there will
be the influence of grain boundaries.
➢Hence a larger stress is required for deformation of polycrystalline materials
because each grain restricts the deformation of neighboring grains.
➢The boundaries between the grains plays a vital role during the plastic
deformation of a polycrystalline aggregates.
Polycrystalline metals

➢Size of the grain has a tremendous influence in the early stages of deformation of
polycrystalline materials.
➢During the early stages of deformation, grain boundary obstacles for dislocations are
most effective and for deformation to proceed further these obstacles have to be broken.
Thus yield strength of polycrystalline material is more dependent on grain size than
tensile strength.
➢The yield strength increases with decrease in grain size because smaller the grains
more in the number of grain boundaries and hence more obstacles for the movement
of dislocations.
➢Grain boundaries act as an obstacle to the motion of dislocations and pile up of
dislocations occur along the slip planes at the grain boundary.
➢Under the influence of applied stresses, more and more number of dislocations pile up
and causes high shear stresses to develop at the leading dislocation in the pile up.
➢These high stresses eventually become high enough to produce movement of
dislocations in the neighboring grain across the boundary.
Polycrystalline materials Contd..

67
Polycrystalline Materials Contd..
Grain Boundaries
▪ regions between crystals
▪ transition from lattice of one region to
another
(a) The atoms near the boundaries of the 3
grains do not have an equilibrium
spacing or arrangement; slightly
disordered.
(b) Grains and grain boundaries in a
stainless steel sample. low density in
grain boundaries

The Effect of Grain Boundries
• Dislocations pile up at GB and can’t go further
– this effectively strengthens the crystal!
Dislocations pile up-Polycrystalline metals

69
• Single Crystals
-Properties vary with direction:
anisotropic.
-Example: the modulus
of elasticity (E) in BCC iron:
• Polycrystals
-Properties may/may not
vary with direction.
-If grains are randomly
oriented: isotropic.
(Epoly iron = 210 GPa)
-If grains are textured,
anisotropic.
200 mm
Single vs Polycrystals
E (diagonal) = 273 GPa
E (edge) = 125 GPa
Before rolling
After rolling
Polycrystalline metals are stronger than their single-crystal equivalents, which means that greater
stresses are required to initiate slip or for yielding.

When a single crystal is deformed under a tensile
stress, it is observed that plastic deformation
occurs by slip on well-defined parallel crystal
planes.
Sections of the crystal slide relative to one
another, changing the geometry of the sample as
shown in the diagram.
http://www.doitpoms.ac.uk/tlplib/slip/printall.php
The increase in length of the specimen
depends on the orientation of the active
planes and the direction with the
specimen axis.

71
• Stronger - grain boundaries
• Slip planes & directions
(l, f) change from one
crystal to another.
• tR will vary from one
crystal to another.
• The crystal with the
largest tR yields first.
• Other (less favorably
oriented) crystals
yield later.
Slip Motion in Polycrystals
s
300
mm
Slip lines
The direction of slip varies from one grain to another
as a result of random crystallographic orientations
grains.

➢It is observed that slip occurs intensely on a small number of crystal planes
and, during the process, some hundreds of dislocations move.
➢Obviously, there must be some effective creators or some mechanisms
by which these numerous dislocations are produced on a given slip
plane.
➢These are called as Frank-Read sources. A single Frank-Read
dislocation source can form hundreds of new dislocations.
Frank-Read source

Frank-Read source
➢Frank-Read source is a mechanism explaining
the generation of multiple dislocations in
specific well-spaced slip planes in crystals when
they are deformed.
➢The Frank-Read source is a mechanism based on dislocation multiplication in a slip
plane under shear stress.
➢Cold working of metal increases the number of dislocations by the Frank-Read mechanism.
Higher dislocation density increases yield strength and causes work hardening of metals.

The Frank –Read Source-Dislocation Generator:
The generation of dislocations can be explained
by the Frank-Read mechanism which involves
Frank-Read source and its operation.
Under applied shear stress the dislocation segment(line) bows out and move to the left, causing
the line to form an arc with its ends fixed at end points x and y. This arc is shown by the symbol
’a’. Further increase in applied stress causes the curved dislocation to expand to the successive
positions ‘b’ and ‘c’.
At ‘c’ the loop intersects itself at point ‘m’ and breaks the dislocation into two segments marked
‘d’, one of which is circular and expands to the surface of the crystal, producing a shear of one
atomic distance. The other component remains as a regenerated positive edge dislocation line
lying between points x and y, where it is in a position to repeat the cycle.
Many dislocation loops can be generated in this way on the same slip plane. This type of
dislocation generator is called as Frank-Read source.
A Frank-Read source consists of a dislocation
line fixed at nodes. Consider a positive edge
dislocation segment xy.

➢It is observed in practical tests that under relatively high stresses, the incidence of plastic
deformation is high in most metals through the combined movement of many hundred thousand
of dislocations in individual crystals. Plastic deformation in real crystals is effected by
successive movements of dislocations. Frank-Read mechanism helps to explain the
existence of so called dislocation mills or multiplication of dislocations.
➢Let us consider a dislocation line, shown by AB in a crystal. We see that the dislocation line or
Frank-Read source consists of two nodes A and B. In the first situation, when the Burger vector is
perpendicular to the line AB, a shear stress parallel to the plane of the figure will exert a force
on the dislocation line AB. Due to the action of the shear stress the dislocation line bent
outward and produces slip. A slip plane usually contains tens of dislocations.
➢For a given stress, the dislocation line AB assume a certain radius of curvature. On
further increasing the stress, the dislocation line becomes unstable and expands indefinitely.
Figure illustrates the successive stages.

If the dislocation movement is passed through a soft particle(second phase particle), it will cut through
that particle.(just like cutting butter with knife)
When the deformation is stopped by obstacle (hard phase)-frank read source type dislocations will
form and which improves the strength.

➢Under the action of the applied stress, the fixed dislocation line AB is bent outward
until it becomes hemispherical (Fig. (a) and (b)) of radius AB/2. We must note that if
the stress is removed at any stage upto this point AB will regain its original shape.
➢If the stress is further increased to the stage (Fig. (c)) at which the bulge becomes
greater than a semicircle, a new system of balance exists and a lower strain energy
will be attained by the loop becoming larger (i.e., radius of loop increasing again).
From that moment on, the bent dislocation propagates spontaneously in the form
of two spirals.
➢As the spirals meet, they give rise to an expanding dislocation loop and a
dislocation section. The dislocation section occupies an initial position and the
dislocation source is ready to repeat the cycle.
➢A single Frank-Read dislocation source can form hundreds of new dislocations.
➢The strengthening effect produced in metals by deformation (strain hardening) is
based primarily on an increase of dislocation density.

How to Strengthen Metals
• Key: prevent dislocations from moving through crystal structure!!!
1. Finer grain boundaries – can be done by recrystallizing (and cold
working)
2. Increase dislocation density via COLD WORKING (strain hardening)
3. Add alloying elements to give –SOLID SOLUTION HARDENING.
4. Add alloying elements to give precipitates or dispersed particles –
PRECIPITATION HARDENING (Age Hardening or particle
hardening)
5. DISPERSION HARDENING– fine particles (carbon) impede
dislocation movement.

Several cells form a crystal, if many crystals are growing in a melt at the same
time, where they meet = grain boundry as shown below:
d
ky
oy ss
Material
constants
Average
grain
diameter
Called Hall-Petch
equation
Microstructure of pure iron (X100). Dark areas are grain boundaries

A general relationship between mechanical properties and
grain size is given by the Hall-Petch equation
σo = Material constant, Friction stress opposing the motion of a dislocation
K= constant and depends on the extent to which dislocations are piled up at barriers
σy = σo + K d-1/2
σy = yield strength d= grain size

No. of grains(N) per square inch(645mm2)
at a magnification of 100X
= 2n-1
Where n= ASTM no.

Deformation process of polycrystalline material
When a polycrystalline material is subjected to an applied stress, the material
behaves perfectly elastic in the first stage since all the crystals are deformed only
elastically. In the second stage only a few crystals undergo plastic deformation by
crossing the elastic limit.
At this stage if the load is removed, the plastically deformed crystals slowly come
back to their original shape due to the stresses that arise between the elastically
and plastically deformed crystals.
This gradual return is called the elastic after effect which is observed only in
polycrystalline materials and not in single crystals.
In the third stage, majority of the crystals cross the elastic limit and deform
plastically which causes permanent deformation in the material.
And in the last stage, all the crystals deform plastically and results in yielding of the
material.

Small Grains Large Grains
Definitely valid:
1.High Strength
2. Low Ductility
Definitely valid:
1.Low strength
2.High Ductility
May or May not valid
1.High Density
2.Anti corrosive
May or May not valid
1.Low density
2.Corrosive

Principle of work hardening
➢When a metal is subjected to stress, the strain increases with stress and the curve reaches a
point A on the plastic range. If at point A, the specimen is unloaded, the strain does not recover
along the original path AO but moves along the path AB. Then if the specimen is reloaded
immediately without lapse of time, the curve again rises from B to A, but follows another path
and reaches the point C, and if the loading is continued it will follow the curve ACD.
➢At point A, if the specimen is not unloaded, the stress-strain curve would have followed the
dotted path AD’. Comparing the paths ACD and AD’ it can be concluded that the cold working
(Plastic deformation) has increased the yield strength and ultimate strength of the metal since
S2 is greater than S1.

Theory of work Hardening
➢Several theories are put forward to explain the phenomenon of work hardening. All these
theories says that work hardening is due to the increased resistance to the motion of
dislocations inside the crystal when the metal has been subjected to cold
working(plastic deformation).
➢Taylor’s classical theory of work hardening is based on dislocations which have been
arrested inside a crystal. He assumes that some dislocations get stuck inside the
crystal and act as source of internal stress which oppose the movement of other
dislocations i.e, work hardening arises due to the interactions between
dislocations.
➢Hence the stress required to move a dislocation in the stress field of other dislocations
surrounding it, will have to be increased for further plastic deformation to occur.
Taylor has given the following relationship between the stress and strain ε
2
1
. 






L
b
KG t
K = a constant
G =Shear modulus
b =burgers vector
L=The distance to which a positive and negative dislocation separate before being stopped

➢When a metal is cold worked, a finite fraction of the energy expended in cold work is
stored in the metal as strain energy.
➢Cold working increases greatly the number of dislocations in a metal. Heavily cold
worked metals will have approximately 1012 dislocation lines per cm2
➢As the dislocation density increases, the strain energy of the metal increases since
each dislocation is associated with some amount of lattice strain. This stored strain
energy produces internal stresses in a cold worked metal. In order to bring the cold
worked metal back to its strain free condition by releasing the internal or residual
stresses, a particular process of heat treatment called annealing is employed.
➢After certain amount of cold working of wire drawing and stopped, if it is required to
continue the drawing operation further, to achieve the desired shape and size, the metal
should be brought back to its original strain free condition prior to deformation.
This can again be achieved by a process called annealing. Annealing involves heating
the metal below its melting point so that the metal softens and returns back to a
strain-free condition and this can be achieved by the following three stages such as
a)Recovery b) Recrystallization and c) Grain Growth
Recovery, Recrystallization and Grain Growth

Recovery Recrystallization and Grain Growth
AnnealingCold working

Recovery, Recrystallization, and Grain Growth Effects
Schematic illustration of the effects of recovery, recrystallization, and grain growth on mechanical
properties and on the shape and size of grains.
Note the formation of small new grains during recrystallization.

Recovery
➢Recovery involves heating the metal to about 0.1 Tm, where Tm is the melting point of the
metal in the absolute temperature scale. The main effect of recovery is to relieve internal
stresses that are induced during cold working such as in rolled, drawn, and extruded objects.
Recovery also prevents season cracking in brasses.
➢Recovery causes very little changes in mechanical properties and has no effect on
microstructure. During recovery a rapid increase occurs in electrical conductivity and
only slight increase occurs in tensile and yield strengths.
Recrystallization
➢Recrystallization occurs by a nucleation and growth process and it follows recovery.
Recrystallization occurs at a higher temperature than recovery. During recrystallization
period entirely new, strain free crystals are formed from the deformed metal and the
distorted elongated grains disappear.
➢The small strain free nuclei usually appear at the most severely deformed portions of
the grains usually the grain boundaries and slip planes.
➢Recrystallization can be detected by metallographic methods.

Recrystallization Temperature
➢Recrystallization temperature is the temperature at which a particular metal with a
particular amount of cold deformation, will completely recrystallize in a definite period of
time, usually one hour.
➢For pure metals the recrystallization is about 0.3 Tm and for alloys it is 0.5 Tm where
Tm is the melting point.

Recrystallization temperature depends upon the following variables
1.Amount of prior deformation: If the degree of cold work is more, then, the recrystallization
temp. will be lowered and grain size will also become smaller.
If the degree of deformation is less, then the temp. required to cause recrystallization will be
high.
2.Particular metal: Recrystallization temp. varies with each metal. It has one value for
copper and another value for nickel.
3.Purity of Metal: Recrystallization temp. decreases with increasing purity of the metal.
Solid solution alloying additions always increases the recrystallization temp.
For example very pure aluminium crystallizes below room temp. while commercial
aluminium recrystallizes 150-200 0C
4.Annealing Time: Increased annealing time decreases the recrystallization temp.
5.Initial Grain size: The finer the initial grain size of cold worked metal, the lower is the
recrystallization temperature.

Effect of recrystallization on properties and micro structure
a)Recryallization causes much change in mechanical properties. Strength and hardness
decrease where ductility increases.
b)Recrystallization causes the disappearance of distorted and elongated cold worked grains
c)Recrystallization does not change the crystal structure; a B.C.C metal remains as B.C.C
d)Recrystallization causes further relief of internal or residual stresses.

Grain growth
➢Grain growth is the third stage of annealing that follows recrystallization.
Recrystallization produces strain-free small equiaxed grains.
➢When the temp. is increased above that of recrystallization or held for longer time after
recrystallization, these strain-free crystals grow in size by the coalenscence of some
of the new grains formed.
➢Strength and hardness decrease with grain growth but ductility increases

c)Rate of heating: Slow heating causes the formation of few nuclei and favours grain growth
d)Degree of prior deformation: Severe deformation produces large number of nuclei
during recrystallization and results in a small grain size whereas light deformation
produces few nuclei during recrystallization and results in large grain size.
e)Insoluble impurities: The greater the amount and the finer the distribution of insoluble
impurities, the finer the final grain size.
f) Alloying elements: Vanadium carbide particles restrict the grain growth of austenite
during the heat treatment of high speed steel. Addition of alloying element like nickel
restricts the grain growth during annealing in steel and other nonferrous alloys.
Coarse grains are generally undesirable since they impair mechanical properties and
result in serious consequences if a metal consisting coarse grains is put in service
b)Annealing time: Grain growth is rapid during initial time period and then growth
occurs more slowly with the passage of annealing time.
a)Annealing temp: Grain growth increases with increase in annealing temp.
Factors influencing grain growth

Cold working: Grain elongate when force is applied in cold working. More and more
dislocations created, which is called as dislocation pile up. Dislocations keep on
increasing to certain value.
All these dislocations stop at grain boundaries because of which there is no further
plastic deformation. To move the piled up dislocations more stress is required. Very high
stress is required for further plastic deformation.
So Hardness and Strength of cold worked material increases. But ductility decreases.
Hot working: Dislocations generate and merge with one another during high
temperature diffusion processes.

Properties of C10 steel Hot rolled Cold rolled
Ultimate tensile strength, MPa 427 558
Yield Strength, MPa 220 345
Brinnel’s Hardness Number 94 174
Cold, Warm & Hot working
T=Room Temp.
Tm=MP Temp.
Homologous temperature expresses the temperature of a material as a fraction of its melting
point temperature using the Kelvin scale. For example, the homologous temperature of lead at room
temperature is approximately 0.50 (TH = T/Tmp = 298K/601K = 0.50).

➢The effects of cold working can be reversed by annealing the
metal:
Heating it in a temperature range for a period of time and there
by allowing successive processes of recovery, recrystallization,
and grain growth to take place.
➢Deformation at room temperature (cold working) results in
higher strength but reduced ductility of the metal. It generally
causes anisotropy, a state in which the properties are different in
different directions.
➢Metals can be plastically deformed(worked) at room, warm or
high temperatures. Their behavior and workability depend largely
on whether deformation takes place below or above the
recrystallization temperature.
Cold, Warm & Hot working

Effects of Hot Rolling
Changes in the grain structure of cast or of large-grain wrought metals during hot rolling.
Hot rolling is an effective way to reduce grain size, ultimately keeps the yield
strength and hardness low and ductility high.This contrasts with cold working.
Cast structures of ingots or continuous castings are converted to a wrought structure by
hot working.

COLD AND HOT WORKING OF METALS
Cold Working
➢Plastic deformation of metals below the recrystallization temperature is
known as cold working.
➢It is generally performed at room temperature. In some cases, slightly
elevated temperatures may be used.
➢Cold working offers a number of distinct advantages, and for this reason
various cold-working processes have become extremely important.
➢Strengthening occurs because of dislocation movements within the
crystal structure of the material.

➢Cold worked material is harder and stronger than material
deformed at other temperatures. These harder materials are
advantageous for applications such as machine parts and
mechanical supports.
➢While cold-working, a metal will tend to increase its strength,
other properties such as ductility or corrosion resistance may be
negatively affected.
➢To remove internal stresses of cold work, it is sometimes
desirable to heat treat the metal after cold working (Annealing).
Cold Working
% Cold Work = {(Ao-Ad)/Ao } x 100
Ao- original cross-sectional area
Ad- area after deformation
%CW is another measure of degree of plastic deformation, like strain

In comparison with hot working, the advantages of cold working are
1. No heating is required
2. Better surface finish is obtained
3.Better dimensional control is achieved; therefore no secondary
machining is generally needed.
4. Products possess better reproducibility and interchangeability.
5. Better strength, fatigue, and wear properties of material.
6. Directional properties can be imparted.
7. Contamination problems are almost negligible.

Some disadvantages associated with cold-working processes are:
1. Higher forces are required for deformation.
2. Heavier and more powerful equipment is required.
3. Less ductility is available.
4. Metal surfaces must be clean and scale-free.
5. Strain hardening occurs (may require intermediate annealing).
6. Undesirable residual stresses may be produced.
7.Better suited to large-scale production of parts because of the
cost of the required equipment and tooling.
8.Brittle materials can’t be cold worked

Advantages
➢ Increases strength and hardness due to strain hardening.
➢ No oxide formation, good surface finish. No decarburisation of
surface
➢ Better dimensional accuracy.
➢ It is easy to handle cold parts.
Disadvantages
➢ Material has high yield strength at low temperature.
Hence, amount of deformation given to it is limited.
➢ Metals get strain hardened. the maximum amount of deformation
can be given is limited.
➢ Excessive cold work will lead to fracture before final size has been
reached.
➢ Metals which are brittle cannot be cold worked. complexity of
shapes is limited.
Summary of Cold working

Worm working is metal forming at temperatures above the room
temperature but below recrystallization one.
Advantages:
Lower forces and power
More complex part shapes
No annealing is required
Disadvantages:
Some investment in furnaces is needed.
Warm working or Warm forming

Hot Working
➢First step of converting a cast ingot into a wrought product
➢Plastic deformation of metal carried out at temperature above the
recrystallization temperature, is called hot working (with or without actual
heating).
➢For Lead, Tin, R.T is below room temp.
For Steels, R.T is of order 10000C
(At 9000C is also cold working)
➢In hot working, the temperature at which the working is completed is critical
since any extra heat left in the material after working will promote grain
growth, leading to poor mechanical properties of material.

➢The lower limit of the hot working temp. is determined by its
recrystallization temp.
➢The upper limit for hot working is determined by excessive oxidation,
grain growth, undesirable phase transformation
Hot working

In comparison with cold working, advantages of hot working are:
1.No strain hardening(work hardening). So no additional annealing is
required.
2.Lesser forces are required for deformation
3.Greater ductility of material is available, and therefore more
deformation is possible.
4.Favorable grain size is obtained leading to better mechanical
properties of material
5.Equipment of lesser power is needed
6.No residual stresses in the material.

Disadvantages associated in the hot-working of metals are:
1.Heat energy is needed
2.Poor surface finish of material due to scaling of surface
3.Poor accuracy and dimensional control of parts
4.Poor reproducibility and interchangeability of parts
5.Handling and maintaining of hot metal is difficult and troublesome
6.Lower life of tooling and equipment.
7.Due to high temperature, surface oxidation and decarburization can not
be prevented

S.No Hot working Cold working
1
Above recrystallisation
temp., any amount of
working can be imparted as
there is no strain hardening
(work hardening)
Below recrystallisation temp.
Cold working increases
strength and hardness of the
material due to strain
hardening, which would be
beneficial in some situations.
2
At a high temp, material
would have higher amount
of ductility and no limit on
the amount of hot working
that can be done a material.
Even brittle materials can be
hot worked.
Some materials which are
brittle can’t be cold worked
(Ex. Cast Iron)

S.No Hot working Cold Working
3 Since shear stresses gets reduced
at higher temp, hot working
requires less force to achieve the
necessary deformation
Since the material has higher yield
strength at lower temps, the
amount of deformation that can
be given is limited by the capability
of the processes or hammers used.
4 If temp. and rate of working are
properly controlled, a very
favorable grain size could be
achieved giving better mechanical
properties.
Ex: Rolling, forging, extrusion
Since the material gets strain
hardened, the max. amount of
deformation that can be given is
limited. Any further amount of
deformation can be given after
annealing.
Ex: Rolling, forging, extrusion,
wire/tube drawing, swaging,
coining

S.No Hot working Cold working
5 At higher temp. surface finish
obtained is poor
Since the working is done in cold
state, no oxide would form on
the surface and consequently,
good surface finish is obtained
6 Because of the thermal
expansion of metals, the
dimensional accuracy in hot
working is difficult to achieve
since it is difficult to control the
temp. of work pieces
Better dimensional accuracy is
achieved.
7 Handling and maintaining of hot
metal is difficult and
troublesome
It is far easier to handle cold
parts and it is also economical
for smaller sizes

CREEP
Creep is a progressive time dependent plastic deformation when material is
subjected to constant values of load or stress
Creep is progressive i.e. permanent and time dependant deformation of a material
at a constant stress below the yield strength of the material. Creep is seen in all
types of materials and is observed to be severe in materials that are utilized in
applications involving high operating temperatures for long periods of time.
Deformation is not an elastic one nor is it a brittle one. It is time dependent
inelastic strain under sustained load and elevated temperature.

Creep can be defined as the slow and progressive deformation of a material with time
under a constant stress at temperatures approximately above 0.4Tm (where Tm is
the melting point of the metal or alloy in degrees Kelvin)
Most of the metals exhibit creep at high temperatures. However , some metals like
Pb,Sn etc. having low melting points show creep at room temperature.
Creep is a thermally activated process and hence is a function of temperature and time.
The creep behaviour of metals is important in determining their suitability for a
continuous high temperature service under stressed conditions, for example, metals
for jet engine components, gas and steam turbines, nuclear reactors, and tungsten
filaments for electric bulbs.
➢Creep strength of a material is the highest stress that the material can withstand
for a specified length of time without exceeding the specified deformation at a
given temperature. It is also called a creep limit.
CREEP

High Temp. Behavior of Materials:
• Gas Turbine and jet Turbine
• Nuclear reactors
• Power plants
• Spacecraft
• Chemical processing
CREEP
➢If the creep is continued until fracture occurs, the test is called as creep-rupture
test. It determines the time necessary for fracture of the test piece.

• Creep occurs as a result of long term exposure to levels of stress
that are below the yield strength of the material.
• Creep is more severe in materials that are subjected to heat for
long periods, and near the melting point. Creep always increases
with temperature.
• The rate of this deformation is a function of the material properties,
exposure time, exposure temperature and the applied structural
load.
• Depending on the magnitude of the applied stress and its duration,
the deformation may become so large that a component can no
longer perform its function - for example creep of a turbine blade
will cause the blade to contact the casing, resulting in the failure of
the blade.

➢The creep mechanism is sufficiently complex so that no direct correlation have been
established between the creep behaviour and the mechanical properties such as yield
strength, tensile strength, hardness etc. of various materials.
➢Hence, the creep properties are determined experimentally, either in actual service
or through long time tests under constant stress conditions at constant temperatures.
Testing Method
➢The usual method of creep testing consists of subjecting the specimen at constant
tensile stress at constant temperature and measuring the extent of deformation or
strain with the time (IS 3407 and IS 3408)
➢Creep is also determined in compression, shear, and bending. The data is
presented by plotting the creep curve as, deformation(or strain) versus time at
constant stress and temperature.
The strain generally lies between 0.1 to 1% and the period of testing does not exceed 10,000 hr.

Creep test data is presented as a plot between time and strain known as creep
curve. The slope of the creep curve is designated as creep rate.

The constant load creep machine consists of a loading platform, foundation,
fixture devices and furnace. The fixture devices are the grips and pull rods.
•Load platform or sometimes called load hanger is where the object will
endure pressure at a constant rate.
•Grips are used to hold the material you are testing in a certain position.
Position is important because if the alignment is off, the machine will deliver
inaccurate readings of the creep of the material.
•Dial Gauge is used to measure the strain. It is the object that captures the
movement of the object in the machine. The load beam transfers the
movement from the grip to the dial gauge.
•Heating Chamber is what surrounds the object and maintain the
temperature that the object is subjected to.

Creep testing machine sectional front elevation.

Creep Curve
Primary Creep: slope (creep rate)
decreases with time. Strain rate is
relatively high. But slows with
increasing strain. This is due to work
hardening.
The strain rate eventually reaches
minimum and reaches constant. This
is due to balance between work
hardening and annealing(Recovery).
This is called as thermal softening.
This stage is called secondary creep.
Secondary Creep: steady-state
i.e., constant slope.
Tertiary Creep: slope (creep rate) increases with time exponentially
i.e. acceleration of rate because of necking phenomenon.
• Occurs at elevated temperature, T > 0.4 Tm

Creep curve
Creep curve is considered to be consists of three portions.
After initial rapid elongation, ε0, the creep rate decreases continuously with
time, and is known as primary or transient creep.
Primary creep is followed by secondary or steady-state or viscous creep, which
is characterized by constant creep rate.
This stage of creep is often the longest duration of the three modes.
Finally, a third stage of creep known as, tertiary creep occurs that is
characterized by increase in creep rate.

When a load is applied at the beginning of a creep test, the instantaneous elastic
deformation AB occurs. The elastic deformation is followed by primary or transient
creep BC. Then by the secondary or steady state creep CD, and finally by tertiary or
accelerated creep DE.
The above three regions of the creep curves are essentially due to the following two factors
1. Due to application of stress, strain hardening occurs in the specimen which
tries decrease the deformations.
2. Due to high temperature, annealing or softening of specimen occurs which
tries to increase the deformations.
➢At the beginning, strain hardening effect supersedes the softening effect and
hence during primary or transient creep, deformation is observed at a decreasing
rate.
➢During the secondary or steady-state creep, constant and minimum creep rate is
observed due to the equilibrium between the strain hardening effect and the
annealing effect.

➢The tertiary or the accelerated creep occurs at a fast rate and actually represents a
process of progressive damage to the intercrystalline regions by the formation of voids
or heavy oxidation of metal leading to fracture of the material.
➢Microstructural changes such as recrystallization or coarsening of precipitate
particles also contribute to the tertiary creep.

Creep in different stages
➢ First stage creep is associated with strain hardening of the sample.
➢ Constant creep rate during secondary creep is believed to be due to balance
between the competing processes of strain hardening and recovery. Creep rate
during the secondary creep is called the minimum creep rate.
➢Third stage creep occurs in constant load tests at high stresses at high
temperatures. This stage is greatly delayed in constant stress tests. Tertiary creep
is believed to occur because of either reduction in cross-sectional area due to
necking or internal void formation.
➢Third stage is often associated with metallurgical changes such as coarsening of
precipitate particles, recrystallization, or diffusional changes in the phases that are
present.

➢The determination of creep strength of a material for different service conditions
requires suitable data on stress-strain-time relationship at various temperatures.
➢The creep tests may be carried out at different temperatures and different stress
levels.
➢For each test, minimum creep rate is determined by measuring slope of the creep
curve in the secondary creep region as shown in creep curve.(Min. creep rate)
Creep rate – Stress & Temperature effects

Creep rate – Stress & Temperature effects Contd..
Two most important parameter that influence creep rate are:
stress and temperature.
With increase in either stress or temperature
(a) instantaneous elastic strain increases
(b) steady state creep rate increases and
(c) rupture lifetime decreases.

Creep Fracture
➢At low temperatures, grain boundaries are stronger than the grains and at
high temperatures grains are stronger than the grain boundaries.
➢The temperature at which the strength of the grain boundary is equal to the
strength of grains is called Equicohesive Temperature.
➢Crack always moves through weak regions and hence below equicohesive
temperature, fracture is transgranular or transcrystalline i.e it moves through
the grains (Fig a).
➢Above equicohesive temperature, fracture is intergranular or intercrystalline
i.e it moves along the grain boundaries as shown in Fig b.
➢Creep is a high temperature process and hence creep fractures are always
intergranular.

REQUIREMENTS for CREEP RESISTANT MATERIALS
They should be capable of withstanding elevated temps. without undergoing
creep beyond the specified limit, which may cause dimensional changes
beyond permissible limit used in the design.
1.It should have high melting point, as creep becomes significant above 0.4 Tm
Ex: Iron, Nickel, Cobalt
2. It should have coarse grained structure. The grain boundary region
becomes quasi-viscous at creep temperature. Since in coarse grained
materials grain boundary area is less, less amount of quasi-viscous region
is formed with a less tendency to flow, reducing the creep deformation.
Single crystals have no grain boundary and hence have highest creep
resistance. Also dendritic structures show better creep resistance than
equiaxed structures because of more resistance to grain boundary sliding.

3.It should be precipitation hardenable(Age hardening). It should have fine
insoluble precipitates at the operating temperature.
Ex: Nickel base and iron –nickel-base super alloys
4.Dispersion hardening improves creep resistance. In dispersion hardening,
hard insoluble particles of second phase are uniformly distributed in a finely
divided form in the metal matrix. These particles do not allow to move the
grain boundaries and hence reduce the creep deformation.
Such components are usually manufactured by powder metallurgy. By
mixing the metal and hard material in powder form, compacting and then
sintering e.g thoria(ThO2) dispersed polycrystalline tungsten is used for
filaments of electric bulbs.
5. It should have high oxidation resistance i.e the oxide film should follow
either a logarithmic or cubic law of growth

Face centered cubic crystals
Slip in face centered cubic (fcc) crystals occurs along the
close packed plane. Specifically, the slip plane is of type
{111}, and the direction is of type <110>. In the diagram, the
specific plane and direction are (111) and [110], respectively.
Given the permutations of the slip plane types and direction
types, fcc crystals have 12 slip systems. In the fcc lattice,
the norm of the Burgers vector, b, can be calculated using the
following equation

Body centered cubic crystals(BCC)
➢Slip in body-centered cubic (bcc) crystals occurs along the plane of
shortest Burgers vector. However, unlike fcc, there are no truly close-packed
planes in the bcc crystal structure. Thus, a slip system in bcc requires heat
to activate. Some bcc materials (e.g. α-Fe) can contain up to 48 slip systems.
➢There are 6 slip planes of type {110}, each with two <111> directions (12
systems). There are 24 {123} and 12 {112} planes each with one <111> direction
(36 systems, for a total of 48).
➢While the {123} and {112} planes are not exactly identical in activation energy to
{110}, they are so close in energy that for all intents and purposes they can be
treated as identical. In the diagram on the right the specific slip plane and direction
are (110) and [111], respectively

The Hexagonal Close-Packed Crystal Structure (HCP)
(a) a reduced-sphere unit cell (a and c represent the short and long edge lengths,
respectively), and (b) an aggregate of many atoms.
In a close-packed structure the close packed directions are the directions in which
atoms are touching.
➢For a hcp structure the close packed directions are [100], [010] and [110] and their
negatives. Directions that are related by symmetry are represented using the notation
<UVW>. The close packed directions for hcp are then <100>.

Hexagonal close packed crystals
➢Slip in hexagonal close packed (hcp) metals is much more limited than in bcc
and fcc crystal structures.
➢Usually, hcp crystal structures allow slip on the densely packed basal {0001}
planes along the <1120> directions.
➢The activation of other slip planes depends on various parameters, e.g. the c/a
ratio. Since there are only 3 independent slip systems on the basal planes, for
arbitrary plastic deformation, additional slip or twin systems needs to be activated.
This typically requires are much higher resolved shear stress and results in the
brittle behavior of hcp polycrystals.
➢Cadmium, zinc, magnesium, titanium, and beryllium have a slip plane at {0001}
and a slip direction of <1120>. This creates a total of three slip systems,
depending on orientation. (Remember that a slip system is a combination of a slip
plane and a slip direction). Other combinations are also possible.

https://en.wikipedia.org/wiki/Template:Life_timeline
http://www.makin-metals.com/about/history-of-metals-
infographic/
http://www.visualcapitalist.com/history-of-metals/

➢The dislocations move along the densest planes of atoms in a material,
because the stress needed to move the dislocation increases with the
spacing between the planes.
➢FCC and BCC metals have many dense planes, so dislocations move
relatively easy and these materials have high ductility.
➢Metals are strengthened by making it more difficult for dislocations to
move. This may involve the introduction of obstacles, such as interstitial
atoms or grain boundaries, to “pin” the dislocations.
➢Also, as material plastically deforms, more dislocations are produced and
they will get into each others way and impede movement. This is why strain
or work hardening occurs.
https://www.nde-ed.org/EducationResources/CommunityCollege/Materials/Structure/linear_defects.htm
Dislocations & Ductility

➢Slip occurs when the shearing stress on the slip plane in the slip
direction reaches a critical resolved shear stress.
➢Schmid calculated the critical resolved shear stress from a single crystal
tested in tension.

K.Srinivasulureddy-SNIST-Metallurgy & Material Science-MMS-UNIT-1

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