Dire Dawa University
Dire Dawa Institute of Technology
School of Mechanical and Industrial Engineering
Post Graduate Program in Manufacturing Engineering/
Mechanical Engineering
M.sc in Manufacturing Engineering
Course Title: Advanced Materials Technology
Course code: MEng 7032
Title:
PLASTIC DEFORMATION OF SINGLE AND
POLYCRYSTALLINE MATERIALS
Prepared By:
Negesa Bekuma
ID…DDU1300723
Submitted to:
Getahun Aklilu (PhD)
Jan 4, 2022.
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CONTENTS
Introduction
1. Deformation of Materials
1.1 Elastic Deformation and Plastic Deformation
1.2 Lattice Defects
1.3 Mechanisms of Plastic Deformation in Metals
1.4 Dislocation Theory
1.5 Dislocation Behavior in BCC, FCC and HCP
Crystal Structures
1.6 Strengthening Mechanisms in Metals
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PLASTIC DEFORMATION OF SINGLE AND POLYCRYSTALLINE MATERIALS:
Fig.1. types of solid materials
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1. The deformation of materials is divided into two types’ those are
i.
Elastic deformation: Elastic deformation can be restored to its original
shape or size after the external force is removed. Elastic deformation is
reversible i.e. recoverable. Up to a certain limit of the applied stress, strain
experienced by the material will be the kind of recoverable i.e. elastic in
nature. This elastic strain is proportional to the stress applied.
The proportional relation between the stress and the elastic strain is given
by Hooke’s law, which can be written as follows:
Εασ
σ=Eε
Where, the constant E is the modulus of elasticity or Young’s modulus, Though
Hooke’s law is applicable to most of the engineering materials up to their elastic
limit, defined by the critical value of stress beyond which plastic deformation
occurs, some materials won’t obey the law.
ii.
Plastic deformation: Plastic deformation of a substance (including fluids
and solids) is caused by the action of an external force under certain
conditions. After the external force is removed, the elastic deformation part
disappears and the part of the-deformation that cannot be recovered and
remains is called plastic deformation. When the material is stressed, the
relative positions of the atoms change and when local deformation exceeds
a certain limit the bonding force between the atoms is destroyed, causing
cracks to occur. These cracks expand to break the material. The main
difference between elastic deformation and plastic deformation is that
elastic deformation is reversible and plastic deformation is irreversible.
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Fig. 2.Stress/strain curves
Left panel: a classical curve, showing elastic and plastic regions, with
hysteresis (dashed line); one deformation enters the plastic range-the material
does not regain the original shape when the stressor is removed. Right panel:
stress–strain curves for a variety of different materials (and possibly organisms)
1.1 Deformation Types in Single Crystals Materials:
 In general, the plastic deformation of a single crystal can be divided into two
types: slip and twinning.
 Slip refers to sliding of a part of the crystal on a certain crystal plane (slip
plane) along a certain direction (slip direction) relative to another part under
the action of shear stress.
 The combination of the slip surface and the slip direction is called the slip
system. Slip is more likely to occur in some crystal directions and planes than
in other directions. Slip is caused by dislocation motion.
 To move the dislocations, certain stresses must be applied to overcome the
resistance of the dislocation motion.
 Slip occurs when the shear stress applied to the slip direction on the slip
surface reaches a certain critical value.
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1. POLYCRYSTALLINE MATERIALS:
 Are made up of an aggregate of many small single crystals (also called
crystallites or grains).
 Is comprised of many small crystallites with different crystal orientations
that are separated by grain boundaries.
 Have a high degree of order over many atomic or molecular dimensions.
 Polycrystalline materials involve numerous numbers of randomly oriented
crystals (grains).
 Polycrystalline metals are stronger than their single-crystal equivalents,
which means greater stresses, are required for the slip to occur.
 This is mainly due to geometrical constraints imposed on the grains during
deformation.
1.1 .1 Plastic Deformation in Polycrystalline Materials:
 When the stress applied on a material exceeds its elastic limit, it imparts
permanent non-recoverable deformation called plastic deformation in the
material. Microscopically it can be said of plastic deformation involves
breaking of original atomic bonds, movement of atoms and the restoration of
bonds i.e. plastic deformation is based on irreversible displacement of atoms
through substantial distances from their equilibrium positions.
 Deformation and slip in polycrystalline materials is somewhat more complex.
Because of the random crystallographic orientations of the numerous grains,
the direction of slip varies from one grain to another. It is important that
deformation of grains is constrained by grain boundaries, which maintain their
integrity and coherency (i.e. typically do not come apart and open during
deformation).
 Thus even though a single grain may be favorable oriented for slip, it cannot
deform until the less favorable adjacent grains are also capable to slip.
Adjacent (and less favorably oriented) grains are capable of slip also. For large
deformation the shape of the individual crystals changes but the grain
boundaries do not come apart.
Fig.3. Polycrystalline structure
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 Lattice means a three-dimensional array of points coinciding with atom
positions (or sphere centres).
1.2. Lattice Defects:
 Lattice defects are missing atoms (vacancies) or atom clusters and
lattice misalignments such as dislocations.
 Lattice defects in the films can be reduced by increased substrate
heating during deposition or controlled concurrent ion bombardment
during deposition.
 Lattice defects in the film can affect the electrical conductivity and
electro migration in metallic films, and carrier mobility and lifetime in
semiconductor materials.
 Generally high defect concentrations result in poor electro migration
properties.
Types of lattice defects:
A. Point defect.
B. Line defects
C. Surface defects
D. Volume defects
1. Point defect:
 All the atoms in a perfect crystal are at specific atomic sites (ignoring
thermal vibrations).
 In a pure metal two types of point defect are possible, namely a vacant
atomic site or vacancy, and a self-interstitial atom.
a. Vacancy: - An atom was missing from regular lattice position. Vacancies
are present invariably in all materials.
b. Interstitial: - An atom trapped in the interstitial point (a point intermediate
between regular lattice points) is called an interstitially.
c. Impurity: - An impurity atom at the regular or interstitial position in the
lattice is another type of point defect.
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Fig.4. Types of point defects
2. Line defects:- The most important one-dimensional, or line, defect is the dislocation
 Dislocation is the region of localized lattice distortion which separates the
slipped and un-slipped portion of the crystal.
 Dislocation is the region of localized lattice distortion which separates the
slipped and not yet slipped portion of the crystal.
 The two basic types of dislocation are the edge dislocation and the screw
dislocation.
Fig.5. Edge Dislocation E.g. of line defects
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3. Surface defects:  Is known as Grain Boundaries or planes that separate a material into
regions, with each region having the same crystalline structure but a
different orientation.
 Surface defects are usually formed by surface finishing methods like
embossing or by degradation caused by weathering or environmental
stress cracking.
 Most crystalline solids are an aggregate of several crystals. Such
materials are called polycrystalline.
Fig.6. Surface defect engineering of SnS2 Nano-crystals for enhanced
photo-catalytic reduction of Cr (VI) under visible light.
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4. Volume defects:-is known as Bulk defects.
 Volume defects are Voids, i.e. the absence of a number of atoms to
form internal surfaces in the crystal.
 They have similar properties to micro-cracks because of the broken
bonds at the surface.
i. Porosity
ii. Inclusions
iii. Cracks
These defects form during manufacturing processes for various reasons and are
harmful to the material.
Fig.7. some e.g. of volume defects
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1.3 Mechanisms of plastic deformation in metals:
What is mechanism of plastic deformation?
Plastic deformation is the permanent distortion that occurs when a material is
subjected to tensile, compressive, bending, or torsion stresses that exceed its
yield strength and cause it to elongate, compress, buckle, bend, or twist.
There are two prominent mechanisms of plastic deformation, namely slip and
twinning:I.
DEFORMATION BY SLIP: The usual method of plastic deformation in metals is by the sliding of blocks
of the crystal over one another along definite crystallographic planes, called
slip planes.
As a very crude approximation, the slip, or glide of a crystal can be
considered analogous to the distortion produced in a deck of cards when it
is pushed from one end.
Slip is the prominent mechanism of plastic deformation in metals. It
involves sliding of blocks of crystal over one other along definite
crystallographic planes, called slip planes.
II.



DEFORMATION BY TWINNING: In addition to slip, plastic deformation in some metallic materials can occur
by the formation of mechanical twins, or twinning.
The second important mechanism by which metals deform is the process
known as twinning.
Twinning results when a portion of the crystal takes up an orientation that
is related to the orientation of the rest of the un-twinned lattice in a
definite, symmetrical way.
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Fig.8. Deformations by slip and twinning.
Table.1. Difference between Slip & Twinning
Slip
1. The orientation of the crystal
above and below the slip plane is
the same after deformation as
before.
2. Slip is usually considered to
occur in discrete multiples of the
atomic spacing
3. Slip occurs on relatively widely
spread planes
4. Slip appears as thin lines
5. There is very little change in
lattice orientation and the steps
are visible only on the surface of
the crystal. If the steps are
removed by polishing there will
be no evidence that slip has
taken place
Twinning
1. While twinning results in an
orientation difference across the
twin plane.
2. While in twinning the atom
movements are much less than
anatomic distance.
3. The twinned region of a crystal
every atomic plane is involved in
the deformation.
4. While twinning appears as a
board lines or bands
5. In twinning, there is a different
lattice orientation in the twinned
region; removal of the steps by
surface polishing will not destroy
the evidence of twinning. Proper
etching solutions, sensitive to the
difference in orientation will
reveal the twinned region
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III. Slip by dislocation movement: The concept of the dislocation was first introduced to explain the discrepancy
between the observed and theoretical shear strengths of metals.
For the dislocation concept to be valid it is necessary to show.
1) That the motion of a dislocation through a crystal lattice requires a stress
far smaller than the theoretical shear stress, and
2) That the movement of the dislocation produces a step, or slip band, at the
free surface. In a perfect lattice all atoms above and below the slip plane
are in minimum energy positions. When a shear stress is applied to a crystal
the same force opposing the movement acts on all atoms.
Fig.9. Dislocation movement through crystal structures

Deformation of BCC materials:  The deformation of body-centered cubic (BCC) metals such as W, Ta,
and Mo is complicated both by complex deformation mechanisms at
the atomic scale and by microstructural variations at the micro-scale.
 Pure bcc metals deform on {110} or {112} planes in the 〈111〉
direction, depending on temperature and orientation.
 The BCC lattice, although cubic, is not closely packed and forms strong
metals. E.g. A-iron and tungsten have the BCC form.
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
Deformation of FCC materials:  Because FCC crystals have high symmetry and 12 potential slip
systems; there is a wide choice of slip systems.
 The slip plane will not have to undergo much rotation before the
resolved shear stress becomes high on another {111} slip system.
 For face centered cubic (FCC) structure slip occurs on the closed
packed {111} crystal-graphic planes.
 Face-centered cubic crystal structure will deform more readily under
load before breaking than a body-centered cubic structure.
 Even though both FCC and BCC have equal number of slip systems
present in the structure, FCC is more ductile.
 Because the slip planes in the FCC structure are of the closest
packing.
 This is not true for BCC. This means that, the %empty space in a
plane is higher in BCC.

Deformation of HCP materials:  The hexagonal close packed (HCP) structure has a relatively complex
deformation mechanism in comparison with bcc and FCC structures.
 In the HCP crystal structure a number of slip systems exist which are
rather difficult to activate.
 Therefore, in some loading conditions, plastic deformation by
dislocations slip is relatively restricted and as a result the imposed
deformation is accommodated by an alternative mechanism so called
twinning.
 Because of the low symmetry and a limited number of activated slip
systems, hexagonal close-packed (HPC) metals present a deformation
behavior which is quite different from that of materials with cubic
crystalline structure.
 In HCP metals, the most popular plastic deformation mechanisms are
slip and twinning.
 In general, slip is always along the lattice close-packed direction on the
close-packed plane.
 Twinning is popularly observed in HCP metals.
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1.4 Dislocation theory
The concept of the dislocation was proposed independently by Taylor,
Orowan, and Polanyi1 in 1934, but the idea lay relatively undeveloped until
the end of World War II.
There followed a period of approximately 10 years in which the theory of
dislocation behavior was developed extensively and applied to practically
every aspect of the plastic deformation of metals.
Taylor's dislocation is a linear crystallographic defect or irregularity within
a crystal structure that contains an abrupt change in the arrangement of
atoms.
A dislocation may be defined as a disturbed region between two substantially
perfect parts of a crystal. In elasticity theory, a dislocation is defined as the
strong discontinuity of the displacement field.
The most powerful method available today for the detection of dislocations in
metals is transmission electron microscopy of thin foils. Thin sheet, less than 1
mm thick, is thinned after deformation by electro polishing to a thickness of
about 1,000 A (= 100 nm). At this thickness the specimen is transparent to
electrons in the electron microscope.
1.5 The effect on dislocation behavior of considering real FCC, BCC, or
HCP crystal structures are:
Dislocation in BCC crystals:  In body-centered cubic metals (e.g. iron, molybdenum, tantalum,
vanadium, chromium, tungsten, niobium, sodium and potassium) slip
occurs in close packed h111i directions.
 The shortest lattice vector, i.e. the Burgers vector of the perfect slip
dislocation, is of the type 1 2h111i.
 The crystallographic slip planes are {110}, {112} and {123}. Each of
these planes contains h111i slip directions and it is particularly
significant that three {110}, three {112} and six {123} planes intersect
along the same h111i direction.
 Thus, if cross slip is easy it is possible for screw dislocations to move in
a haphazard way on different {110} planes or combinations of {110}
and {112} planes, etc.
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
Dislocation in FCC crystals:  In FCC crystals dislocations can split into Shockley partials connected
by a stacking fault in a {111} glide plane.
 In order that cross-slip can take place a screw dislocation must be
constricted locally before it can dissociate in an intersecting {111}
plane.
 This process can occur by thermal activation aided by an external
stress.
 Since cross-slip events can control the overall plastic behavior of
crystals, knowledge of the activation energy and its stress dependence
is of considerable interest.

Dislocation in HCP crystals: The plastic response of HCP materials is a complex interplay between
dislocation slip and twinning.
 Dislocation interactions in HCP crystals can produce composite dislocations
with Burgers vectors larger than the unit lattice vectors.

Dislocation climb:
 An edge dislocation can glide only in the slip plane containing the
dislocation line and its Burgers vector. However, under certain conditions
an edge dislocation can move out of the slip plane onto a parallel plane
directly above or below the slip plane. This is the process of dislocation
climb.
 This type of movement is termed neoconservative, as compared with
conservative movement when a dislocation glides in its slip plane.
 Dislocation climb occurs by the diffusion of vacancies or interstitials to or
away from the site of the dislocation. Since climb is diffusion-controlled, it
is thermally activated and occurs more readily at elevated temperature.
 In positive climb atoms are removed from the extra half plane of atoms at
a positive edge dislocation so that this extra half plane moves up one
atom spacing.
 In negative climb a row of atoms is added below the extra half plane so
that the dislocation line moves down one atom spacing.
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
INTERSECTION OF DISLOCATIONS:The intersection of two dislocations produces a sharp break, a few atom
spacing’s in length, in the dislocation line. These breaks can be of two types.
A jog is a sharp break in the dislocation moving it out of the slip plane.
A kink is a sharp break in the dislocation line which remains in the slip plane.
 MULTIPLICATION OF DISLOCATIONS: One of the original stumbling blocks in the development of dislocation theory
was the formulation of a reasonable mechanism by which sources originally
present in the metal could produce new dislocations by the process of slip.
 Moreover, if there were no source generating dislocations, cold-work should
decrease, rather than increase, the density of dislocations in a single crystal.
Thus, there must be a method of generating dislocations or of multiplying the
number initially present to produce the high dislocation density found in coldworked metal.
1.6 Strengthening mechanisms in Metals: The ability of a metal to deform plastically depends on the ability of
dislocations to move.
 Hardness and strength are related to how easily a metal plastically
deforms, so, by reducing dislocation movement, the mechanical strength
can be improved.
 Ability of a metal to deform plastically depends on ease of dislocation
motion under applied external stresses. Those are:
i. Grain boundary strengthening: - Is an important strengthening mechanism in
Mg alloys. Indeed, die casting and wrought processing both induce fine grain
sizes in many magnesium alloys, so the non-trivial contribution of boundary
strengthening cannot be ignored.
Grain boundaries are barriers to slip.
ii.
Strain ageing: - It is generally accepted that strain ageing is due to the
diffusion of carbon and/or nitrogen atoms in solution to dislocations that have
been generated by plastic deformation. Initially, an atmosphere of carbon and
nitrogen atoms is formed along the length of a dislocation, immobilizing it.
Extended ageing, however, results in sufficient carbon and nitrogen atoms for
precipitates to form along the length of the dislocation.
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iii.
Solid solution strengthening: - Another technique to strengthen and
iv.
harden metals is alloying with impurity atoms that go into either substitutional
or interstitial solid solution. Accordingly, this is called solid-solution
strengthening. High-purity metals are almost always softer and weaker than
alloys composed of the same base metal.
Alloys are stronger than pure metals because impurity atoms that go into solid
solution ordinarily impose lattice strains on the surrounding host atoms.
Lattice strain field interactions between dislocations and these impurity atoms
result, and, consequently, dislocation movement is restricted.
Strengthening from fine particles: - Fine particle strengthening is a two
phase strengthening mechanism. Only a relatively small number of alloy
systems permit extensive solid solubility between two or more elements, and
only a relatively small hardening effect can be produced in most alloy systems
by solid solution additions. Therefore, most commercial alloys contain a
heterogeneous micro structure consisting of two or more metallurgical phases.
The two phases may be ductile and present in the micro structure in relatively
massive form. The strengthening produced by second-phase particles is usually
additives to the solid-solution strengthening produced in the matrix.
v. fiber strengthening: Second phase material can also be introduced into matrix in form of fibers to
strengthen it. However, mechanism of strengthening is different from either
precipitation hardening or dispersion strengthening where second phase is
introduced as fine particles.
 Prerequisites are materials to be used as fibers include high strength and/or
high strength-to-weight ratio. Fibers usually, thus, have high strength and high
modulus while the matrix must be ductile and non-reactive with the fibers.
Fibers may be long and continuous or they may be discontinuous. Examples for
fiber material: Al2O3, boron, graphite, metal, glass, etc.
vi. 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, because the temperature at which deformation takes
place is “cold” relative to the absolute melting temperature of the metal,
cold working. Most metals strain hardens at room temperature.
 It is sometimes convenient to express the degree of plastic deformation as
percent cold work rather than as strain.
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It is convenient to express the degree of plastic deformation as percent
cold work, defined as:
%CW = (
𝐴0−𝐴𝑑
𝐴0
) x100
Where, A0 is the original area of the cross section that experiences
deformation and Ad is the area after deformation.
 Strain hardening is used commercially to enhance the mechanical
properties of metals during fabrication procedures.
vii.
Martensite strengthening:This strengthening can be achieved in systems where a diffusion-controlled
invariant transformation can be suppressed by rapid cooling.
The Martensite strengthening process, thus, basically is a diffusion-less and
displacive reaction.
The martensitic phase is formed from the retained high temperature phase at
temperatures lower than the equilibrium invariant transformation
temperature. It occurs by a process of lattices shearing. Martensite under
microscope appears as lenticular plates which divide and subdivide the grains
of the parent phase. Always touching but never crossing one another.
The characteristic lenticular shape minimizes the elastic distortion in the
matrix. These platelets grow at about one-third the velocity of sound. This high
speed means activation energy for growth is very low, and thus activation
energy for nucleation determines the amount of Martensite that can form
under given conditions.
viii. Bauschinger Effect: The effect is reversible meaning the loading cycle can be tension
compression or compression tension.
 It was directionality of strain hardening.
 The yield stress in tension increases when tensile-compression cycle is
subjected on a specimen due to strain hardening, however, in compression,
it decreases.
 Bauschinger effect is a phenomenon by which plastic deformation of a metal
increases the yield strength in the direction of plastic flow and decreases the
yield strength in the opposite direction.
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 The Bauschinger effect refers to a property of materials where the
material's stress/strain characteristics change as a result of the microscopic
stress distribution of the material.
 The Bauschinger effect contributes to work softening of the work piece, for
example in straightening of drawn bars or rolled sheets, where rollers
subject the work piece to alternate bending stresses, thereby reducing the
yield strength and enabling greater cold draw-ability of the work piece.
ix. Preferred Orientation:
 Preferred orientation arises when there is a stronger tendency for the
crystallites in a powder or a texture to be oriented more one way, or one
set of ways, than all others.
 An easily visualized case of preferred orientation is that which results
when a material with a strong cleavage or growth habit is packed into a
specimen or when a metal sheet is obtained by rolling.
 Preferred orientation should not be confused with 'graininess' or
'inadequate powder average', in which there are so few crystallites being
irradiated that the number of correctly oriented crystallites varies
significantly from reflection to reflection of different types.
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