This chapter discusses dislocation theory and behavior in metals. Key topics covered include:
- Observation techniques for dislocations like etching and transmission electron microscopy
- Burgers vectors and dislocation loops that describe the geometry and movement of dislocations
- Dislocation behavior depends on the crystal structure, including dissociation in FCC into Shockley partials and easy cross-slip
- Dislocations interact through stress fields and forces, which influence deformation and strengthening mechanisms in metals
OUTCOMES:
-Describes slips plane and slips direction
-Explain the types of dislocation.
-Understand the metallic crystal structure, FCC, BCC and HCP
-Understand the crystallographic direction and planes, and able to find the linear and planar density
-Explain about slip systems, the way to determine it and its effect on the metal characteritcs.
OUTCOMES:
-Describes slips plane and slips direction
-Explain the types of dislocation.
-Understand the metallic crystal structure, FCC, BCC and HCP
-Understand the crystallographic direction and planes, and able to find the linear and planar density
-Explain about slip systems, the way to determine it and its effect on the metal characteritcs.
Dispersion Hardening:
Hard particles:
Mixed with matrix powder
Consolidated
Processed by powder metallurgy techniques
Second phase – Very little solubility (Even at elevated temp.)
No coherency
So thermally Stable at very high temp.
Resists :
Grain growth
Over aging
Recrystallization
Mobility of dislocation
Different from particle Metallic Composites (Volume Fraction is 3 to 4% max.) (Does not affect stiffness)
Examples : Al2O3 in Al or Cu, ThO2 in Ni
"Fracture Toughness I" is the first half of a 2-hour presentation on Fracture Mechanics by metallurgical expert Carl Ziegler of Stork Testing and Metallurgical Consulting , Houston, Texas. In this webinar, Mr. Ziegler will cover many aspects of Fracture Toughness, including theory, applications, specifications, testing methods, and the effects of various stresses, strains and environmental conditions on your materials.
Mumbai University
Mechanical engineering
SEM III
Material Technology
Module 1.4
Strain Hardening:
Definition importance of strain hardening, Dislocation theory of strain hardening, Effect of strain hardening on engineering behaviour of materials, Recrystallization Annealing: stages of recrystallization annealing and factors affecting it
Dispersion Hardening:
Hard particles:
Mixed with matrix powder
Consolidated
Processed by powder metallurgy techniques
Second phase – Very little solubility (Even at elevated temp.)
No coherency
So thermally Stable at very high temp.
Resists :
Grain growth
Over aging
Recrystallization
Mobility of dislocation
Different from particle Metallic Composites (Volume Fraction is 3 to 4% max.) (Does not affect stiffness)
Examples : Al2O3 in Al or Cu, ThO2 in Ni
"Fracture Toughness I" is the first half of a 2-hour presentation on Fracture Mechanics by metallurgical expert Carl Ziegler of Stork Testing and Metallurgical Consulting , Houston, Texas. In this webinar, Mr. Ziegler will cover many aspects of Fracture Toughness, including theory, applications, specifications, testing methods, and the effects of various stresses, strains and environmental conditions on your materials.
Mumbai University
Mechanical engineering
SEM III
Material Technology
Module 1.4
Strain Hardening:
Definition importance of strain hardening, Dislocation theory of strain hardening, Effect of strain hardening on engineering behaviour of materials, Recrystallization Annealing: stages of recrystallization annealing and factors affecting it
Material remains intact
Original crystal structure is not destroyed
Crystal distortion is extremely localized
Possible mechanisms:
Translational glide (slipping)
Twin glide (twinning)
Rosa alejandra lukaszew tests of the gurenvich odel toward larger field gra...thinfilmsworkshop
SRF properties are inherently a surface phenomenon involving a material thickness of a few microns thus opening up the possibility of using thin film coatings to achieve a desired performance. I will describe our experimental attempts to test the superconducting/insulating/superconducting (SIS) multilayer model proposed by A. Gurevich [1] to shield the bulk of the cavity from vortex penetration and hence enable larger accelerating fields than presently possible.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
1. Chapter 5
Dislocation theory
Subjects of interest
• Introduction/Objectives
• Observation of dislocation
• Burgers vector and the dislocation loop
• Dislocation in the FCC, HCP and BCC lattice
• Stress fields and energies of dislocations
• Forces on dislocations and between dislocations
Suranaree University of Technology Tapany Udomphol May-Aug 2007
2. Chapter 5
Dislocation theory
Subjects of interest (continued)
• Dislocation climb
• Intersection of dislocations
• Jogs
• Dislocation sources
• Multiplication of dislocations
• Dislocation-point defect interactions
• Dislocation pile-ups
Suranaree University of Technology Tapany Udomphol May-Aug 2007
3. Objectives
• This chapter emphasises the understanding of the
effects of dislocation behaviour on FCC, BCC and HCP
crystal structures.
• This includes the interaction of dislocations such as
climb, jogs, intersection and multiplication of dislocations
and the roles of dislocations on plastic deformation of
metals.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
4. Introduction
Dislocations introduce imperfection into the structure and therefore
these could explain how real materials exhibit lower yield stress value
than those observed in theory.
• Lower the yield stress from
theoretical values.
Produce • Produce plastic deformation
imperfection in (strain hardening).
crystal structures
51450 x • Effects mechanical properties
Dislocations of materials.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
5. Observation of dislocations
A variety of techniques have been used to observe dislocations in
the past 20 years to aid the better understanding of dislocation
behaviour.
Chemical (etch–pit) technique
• Using etchant which forms a pit at the
point where a dislocation intersect the
surface.
• Preferential sites for chemical attack are
due to strain field around dislocation sites
(anodic).
• Can be used in bulk samples but limited in
low dislocation density crystal (104 mm-2).
5000 x
Note: Pits are 500 Ao apart and with Etch pits on slip bands in alpha
the dislocation density of 108 mm-2. brass crystals
Suranaree University of Technology Tapany Udomphol May-Aug 2007
6. Decoration of dislocation technique
A small amount of impurity is added to form precipitates after
suitable heat treatment to give internal structure of the
dislocation lines.
• Hedges and Mitchell first used
photolytic to decorate dislocation in
AgBr.
• Rarely used in metals but in ironic
crystals such as AgCl, NaCl, KCl
and CaF2.
Hexagonal network of dislocations
in NaCl detected by a decoration
technique.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
7. Transmission electron microscope (TEM)
TEM is the most powerful technique used to study dislocations.
• A thin foil of 100 nm is prepared using
electropolishing from a ~1 mm thick sheet.
• This thin foil is transparent to electrons in
the electron microscope and this makes it
possible to observed dislocation
networks, stacking faults, dislocation
pile-ups at grain boundaries.
• By using the kinematic and dynamic 32500 x
theories of electron diffraction it is possible
to determine the dislocation number, Dislocation network in cold-worked
Burgers vectors and slip planes. aluminium.
Note: The sampling area is small therefore the properties
observed cannot represent the whole materials.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
8. X-ray microscopy
• Using an X-ray technique to detect dislocation structure.
• The most common techniques are the Berg-Barret reflection
method and the Lang topography method.
• The resolution is limited to 103 dislocations/mm2.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
9. Burgers vector and the
dislocation loop
Burgers vector is the most
characteristic feature of a
dislocation, which defines the
magnitude and the direction of slip.
• Edge Burgers vector is to the
dislocation line.
• Screw Burgers vector is // to the
dislocation line.
• Both shear stress and final
Macroscopic deformation produced by glide of
deformation are identical for both (a) edge dislocation and (b) screw dislocation.
situations.
Note: Most dislocations found in crystalline materials are
probably neither pure edge or pure screw but mixed.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
10. Dislocation loops
Dislocations in single crystals are straight lines. But in general,
dislocations appear in curves or loops, which in three
dimensions form and interlocking dislocation network.
• Any small segments of the dislocation
can be resolved into edge and screw
components.
• Ex: pure screw at point A and pure edge
at point B where along most of its length
contains mixed edge and screw. But with
the same Burgers vector.
Dislocation loop lying in
a slip plane.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
11. Burgers circuit
Burgers circuit is used to define the Burgers vector of dislocation.
(a) (b)
Burgers circuits
around edge
dislocation
Burgers circuits
around screw
dislocation
• If we trace a clockwise path from start to finish, the closure
failure from finish to start is the Burgers vector b of the
dislocation, see fig (a).
• A right-handed screw dislocation, fig (b), is obtained
when transversing the circuit around the dislocation line and
we then have the helix one atomic plane into the crystal.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
12. Cross slip
In FCC cubic metals, the screw dislocations move in {111} type
planes, but can switch from one {111} type plane to another if it
contains the direction of b. This process is called cross-slip.
Dislocation • A screw dislocation at S is free to
glide in either (111) or (111)
closed-packed planes.
S
• Double cross slip is shown in (d).
Cross slip in a face-centred cubic crystal.
Cross slip on the polished surface
of a single crystal of 3.25% Si iron.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
13. Dislocation dissociation
Dislocation dissociation occurs when the strength of
dislocation is more than unity. The system becomes unstable
dislocation therefore dissociate into two dislocation.
Note: Dislocation of unit strength is a dislocation with a Burgers
vector equal to one lattice spacing.
The dissociation reaction b1 b2 + b3 will occur
when b12 > b22 + b32.
• A dislocation of unit strength has a minimum energy
when its Burgers vector is parallel to a direction of closest
atomic packing.
• In close-packed lattices, dislocations with strength less
than unity are possible. therefore crystals always slip in
the close-packed direction.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
14. Dislocations in FCC lattice
• Slip occurs in the FCC lattice on the {111} plane in the <110> direction
and with a Burgers vector (a/2)[110].
• The {111} planes are stacked on a close packed sequence ABCABC
and vector b = (ao/2)[101] defines one of the observed slip direction,
which can favourably energetically decompose into two partial
dislocations. Extended dislocation
b1 → b2 + b3 Faulted
region
ao a a
[101] → o [211] + o [112]
2 6 6
Shockley partials
Fully slipped No slip
This Shockley partials creates a
stacking fault ABCAC/ABC.
Dissociation of a dislocation to
Suranaree University of Technology Tapany Udomphol
two partial dislocations. May-Aug 2007
15. Dissociation of a dislocation into two
partial dislocations Extended dislocation
• The combination of the two partials AC and Faulted
region
AD is known as an extended dislocation.
• The region between them is a stacking
fault which has undergone slip.
• The equilibrium of these partial dislocations
Fully slipped No slip
depends on the stacking fault energy.
www.msm.cam.ac.uk
Stacking fault
Group of stacking fault in 302 stainless
steel stopped at boundary
Suranaree University of Technology Tapany Udomphol May-Aug 2007
16. Stacking faults
The wider region between partial dislocation,
Stacking fault Slip plane
the lower stacking fault energy Partial
dislocations
• Characteristics of metals with
low SPF;
1) Easy to strain harden
Model of a stacking fault.
2) Easy for twin annealing to occur
3) Temperature dependent flow
stress
Typical values of stacking fault energy
Metal Stacking fault energy (mJ m-2)
• Aluminium – high stacking fault energy
Brass <10
more likely to cross slip. 303 stainless steel 8
304 stainless steel 20
• Copper – lower stacking fault energy 310 stainless steel 45
cross slip is not prevalent. Silver
Gold
~25
~50
Copper ~80
Nickel ~150
Aluminium ~200
Suranaree University of Technology Tapany Udomphol May-Aug 2007
17. Frank partial dislocations
Frank partial dislocations are
another type of partial dislocation in
FCC lattice, which provide
obstacles to the movement of other
dislocations.
Frank partial dislocation or sessile
dislocation.
• A set of (111) plane (viewed from the edge) has a missing middle A
plane with a Burgers vector (ao/3) [111] perpendicular to the central
stacking fault.
• Unlike perfect dislocation, Frank partial dislocation cannot move
by glide (sessile dislocation) but by diffusion of atom.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
18. Lomer-Cortrell barrier
Intersection of {111} plane during
duplex slip by glide of dislocations is
called Lomer-Cortrell barrier.
Ex: consider two perfect dislocations
lying in different {111} planes and
both parallel to the line of intersection
of the {111} plane.
Lomer-Cortrell barrier
ao a a
[101] + o [110] → o [011]
2 2 2
The new dislocation obtained has reduced energy.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
19. Dislocations in HCP lattice
• Slip occurs in the HCP lattice on the basal (0001) plane in the
<1120> direction.
• The basal (0001) plane the close packed of a sequence ABABAB
and a Burgers vector b = (ao/3)[1120].
• Dislocations in the basal plane can reduce their energy by
dissociating into Shockley partials according to the reaction.
ao a a
[1120] → o [1010] + o [0110]
3 3 3
The stacking fault produced by this reaction lies in the basal
plane, and the extended dislocation which forms it is confined to
glide in this plane.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
20. Dislocations in BCC cubic lattice
• Slip occurs in the BCC lattice on {110}, {112}, {123} planes in the
<111> direction and a Burgers vector b = (ao/2)[111].
Cottrell has suggested a dislocation reaction which appears to cause
immobile dislocations. (ao/2[001] in iron) leading to a crack
nucleus formation mechanism for brittle fracture.
σ Applied stress
ao a
[111] + o [111] → a o [001] a
(101) Slip plane
2 2 [111]
2
(001) Cleavage plane
b = a[001]
the dislocation is immobile since
the (001) is not a close-packed slip a
[111] Cleavage knife crack of length c
2 for displacement nb
plane, the (001) plane is therefore (101) Slip plane
the cleavage plane when brittle
fracture occurs. σ
a
[111] + a [111] → a[001]
2 2
Slip on intersecting (110) plane.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
21. Stress fields of dislocations
A dislocation is surrounded by an elastic stress field that
produces forces on other dislocations and results in interaction
between dislocations and solute atoms.
• The cross section of an elastic cylindrical y
piece (dashed line) has been distorted after
b
an edge dislocation running through point O
r
parallel to the z axis (blue line). P
O Q x
θ
• The strain is zero in the z axis and A’ A
ro
therefore can be treated in plane strain (x-y).
• The stresses vary inversely with distance
from the dislocation line and become
infinite at r = 0.
Deformation of a circle containing
− τ b sin θ
…Eq. 1 σ r = σθ = o an edge dislocation.
r
• The shear stress τxy is a maximum τ xy =τo 2
(
bx x 2 − y 2 ) …Eq. 2
in the slip plane, when y = 0. (x + y 2 )2
Suranaree University of Technology Tapany Udomphol May-Aug 2007
22. Strain energies of dislocations
The strain energy involved in the y
formation of an edge dislocation can
be estimated from the work involved in b
displacement the cut OA a distance b r
P
along the slip plane. O θ
Q x
ro A’ A
Gb 2 r1
U= ln …Eq. 3
4π (1 − ν ) ro
The strain energy of a screw
Deformation of a circle containing
dislocation is given by
an edge dislocation.
Gb 2 r1
U= ln …Eq. 4 The dislocation energy per unit
4π ro length simplifies to
Note: the total strain energy is the Gb 2
sum of elastic strain energy and U= …Eq. 5
the core energy of dislocation. 2
Suranaree University of Technology Tapany Udomphol May-Aug 2007
23. Forces on dislocation
• A dislocation line moving in the
direction of its Burgers vector under the
influence of a uniform shear stress τ.
dl
• The force per unit length of dislocation F ;
b
ds dW
F= = τb …Eq. 6
dlds
• This force is normal to the dislocation
line at every point along its length and is
Force acting on a dislocation line.
directed toward the unslipped part of
the glide plane.
• The Burgers vector is constant along
the curved dislocation line.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
24. Forces between dislocations
• Dislocations of opposite sign on the same slip plane will
attract each other, run together, and annihilate each other.
• Dislocations of alike sign on the same slip plane will repel
each other
The radial force Fr between The radial and tangential
two parallel screw dislocations forces between two parallel
edge dislocations
Gb 2
Fr = τ θz b =
2πr …Eq. 7 Gb 2 1 Gb 2 sin 2θ
Fr = , Fθ =
2π (1 − ν ) r 2π (1 − ν ) r
Parallel screw (same sign) +
Aniparallel screw (opposite sign) - …Eq. 8
Suranaree University of Technology Tapany Udomphol May-Aug 2007
25. Dislocation climb
Dislocation climb is a non conservative movement of dislocation
where and edge dislocation can move out of the slip plane onto a
parallel directly above or below the slip plane.
• Climb is diffusion-controlled (thermal activated) and occurs more
readily at elevated temperature. important mechanism in creep.
• Positive direction of climb is when
the edge dislocation moves upwards.
Removing extra atom (or adding vacancy
around ). Compressive force
produces + climb.
(a) Diffusion of (b) Dislocation
• Negative direction of climb is when vacancy to edge climbs up one
the edge dislocation moves downwards. dislocation. lattice spacing.
Atom is added to the extra plane. Tensile
forces to produce – climb.
Note: Glide or slip of a dislocation is the direction parallel to its
direction whereas climb of dislocation is in the vertical direction.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
26. Intersection of dislocations
The intersection of two dislocations produces a sharp
break (a few atom spacing in length) in dislocation line.
This break can be of two types;
• Jog is a sharp break in the dislocation
moving it out of the slip plane.
• Kink is a sharp break in the dislocation line
which remains in the slip plane.
Note: Dislocation intersection mechanisms play an important
role in the strain hardening process.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
27. Jogs and Kinks
Jogs are steps on the dislocation which move it from one atomic
slip plane to another.
Kinks are steps which displace it on the same slip plane.
(a), (b) Kinks in edge and
screw dislocations
(c), (d) Jogs in edge and
screw dislocations.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
28. Intersection of two dislocations
1) Intersection of two dislocations with
Burgers vectors at right angle to each other.
• An edge dislocation XY with Burgers vector b1
is moving on plane Pxy and cuts through
dislocation AB with Burgers vector b2.
• The intersection causes jog PP’ in dislocation b1
AB parallel to b1 and has Burgers vector b2.
and with the length of the jog = b1.
• It can readily glide with the rest of dislocation.
b2
Note: b1 is normal to AB and jogs AB, while
b2 is parallel to XY and no jog is formed.
Intersection of two
edge dislocations
Suranaree University of Technology Tapany Udomphol May-Aug 2007
29. Intersection of two dislocations
2) Intersection of two dislocations with
Burgers vectors parallel to each other
• Both dislocations are jogged.
• The length of jog PP’ is b1 and Before
intersection
the length of jog QQ’ is b2.
• The jogs both have a screw
orientation and lie in the original
slip plane. This is called Kink.
not stable.
After
intersection
Intersection of edge dislocations
with parallel Burgers vectors.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
30. Intersection of two dislocations
3) Intersection of edge and 4) Intersection of two screw
screw dislocations. dislocations.
The intersection produces jogs
of edge orientation in both screw
Intersection produces a jog with an dislocations. very important in
edge orientation on the edge plastic deformation.
dislocation and a kink with an edge Note: at temperature where climb
orientation on the screw dislocation. cannot occur the movement of screw
dislocation is impeded by jogs.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
31. Jogs
• A stable jog length of the dislocation line energy of the crystal
(a) Many intersections occur when a
screw dislocation encounter a forest of
screw dislocations. producing
vacancy jogs and/or interstitial jogs.
(b) Jogs act as pinning points and (a) Straight dislocation under zero stress.
cause dislocations to bow out with
the radius R when the shear stress
τ is applied.
(b) Dislocation bowed out in slip plane
(c) At some critical radius Rc the τ between the jogs due to applied shear stress.
required to further decrease R > the
stress needed for non-conservative
climb. Then the dislocation will move
forward leaving a trail of vacancies
(interstitials) behind each jog. (c) Movement of dislocation leaving trails of
vacancies behind the jogs.
Movement of jogged screw dislocation
Suranaree University of Technology Tapany Udomphol May-Aug 2007
32. Superjogs
Superjog is a jog that has more than one atomic slip plane spacing high.
As the stress increases, the dislocation bows out between the
superjogs, generating dislocation dipoles and later break into
isolated loops.
(a) Dislocation dipole. (b) Elongated loop and (c) Row of small loops.
jogged dislocation.
Formation of dislocation loops from a dislocation dipole
Suranaree University of Technology Tapany Udomphol May-Aug 2007
33. Dislocation Sources
• All metals initially contain an appreciable number of
dislocations produced from the growth of the crystal from
the melt or vapour phase.
• Gradient of temperature and composition may affect
dislocation arrangement.
• Irregular grain boundaries are believed to be responsible
for emitting dislocations.
• Dislocation can be formed by aggregation and collapse of
vacancies to form disk or prismatic loop.
• Heterogeneous nucleation of dislocations is possible from
high local stresses at second-phase particles or as a result
of phase transformation.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
34. Multiplication of dislocations
Frank & Read proposed that dislocations
could be generated from existing dislocations.
• The dislocation line AB bulges out
(A and B are anchored by impurities)
and produces slip as the shear
stress τ is applied.
• The maximum τ for Gb Gb
semicircle dislocation τ≈ ≈
bulge, fig (b)
2R l
• Beyond this point, the dislocation loop
continues to expand till parts m and n The operation of Frank-Read source
meet and annihilate each other to form a
large loop and a new dislocation.
Note: Repeating of this process producing a
dislocation loop, which produces slip of one
Burgers vector along the slip plane.
Suranaree University of Technology Frank Read source in a silicon crystal May-Aug 2007
35. Dislocation-point defect interactions
Point defect and dislocation will interact elastically and
exert forces on each other.
Negative interaction energy attraction
Positive interaction energy repulsion
If the solute atom is The atom will be repelled from the
larger than the compressive side of a positive edge
solvent atom (ε > 1) dislocation and will be attracted to the
tension side.
If the solute atom is
The atom will be attracted to the
smaller than the
compression side.
solvent atom (ε < 1)
• Vacancies will be attracted to regions of compression.
• Interstitials will be collected at regions of tension.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
36. Dislocation pile-ups
Dislocations often pile up
on slip planes at barriers
i.e., grain boundaries or
second phase particles.
High stress concentration on the
leading dislocations in the pile-up. Dislocation pile-ups at an obstacle.
If the pile-up stress > theoretical shear stress yielding
A pile-up of n dislocations along The breakdown of a barrier occur by
a distance L can be considered 1) Slip on a new plane.
as a giant dislocation with a 2) Climb of dislocation around the
Burgers vector nb. barrier.
3) Generation of high enough tensile
stress to produce a crack.
Suranaree University of Technology Tapany Udomphol May-Aug 2007
37. References
• Dieter, G.E., Mechanical metallurgy, 1988, SI metric edition,
McGraw-Hill, ISBN 0-07-100406-8.
• Sanford, R.J., Principles of fracture mechanics, 2003, Prentice
Hall, ISBN 0-13-192992-1.
• W.D. Callister, Fundamental of materials science and
engineering/ an interactive e. text., 2001, John Willey & Sons, Inc.,
New York, ISBN 0-471-39551-x.
• Hull, D., Bacon, D.J., Introduction to dislocations, 2001, Forth
edition, Butterworth-Heinemann, ISBN 0-7506-4681-0.
Suranaree University of Technology Tapany Udomphol May-Aug 2007