Transcript Document 7169147

Chapter 7: Dislocation and
Strengthening Mechanism
Why Study ?
 With a knowledge of the nature of
dislocation and the role they play in the
plastic deformation process, we are able to
understand the underlying mechanisms of the
techniques that are used to strengthen and
harden metals and alloys.

1
DISLOCATIONS and PLASTIC DEFORMATION
7.2 Basic Concepts

Dislocation Types
 Edge
Dislocation
 Screw

Dislocation
Review from Chapter 4 notes
2
Chapter 4 (Review)
4.4 Dislocations __ Linear Defects

A dislocation is a linear or onedimensional defect around which
some of the atoms are misaligned.

Edge dislocation: An extra portion
of a plane of atoms, or half-plane,
the edge of which terminates within
the crystal. (shown in figure )

Dislocation line: For the edge
dislocation in Figure, it is
perpendicular to the plane of the
paper.
3
Chapter 4 (Review)
4.4 Dislocations __ Linear Defects (Contd.)

Within the region around the dislocation line, there is some
localized lattice distortion.
 Atoms above the line are squeezed together
 Those below are pulled apart
 Results in slight curvature for the vertical planes of atoms
as they bend around this extra-half plane

At far position, the lattice is virtually perfect.


extra half-plane in the upper portion
extra half-plane in the bottom portion
4
Chapter 4 (Review)
4.4 Dislocations __ Linear Defects

Screw Dislocation : May be thought of
as being formed by a shear stress that
is applied to produce the distortion as
shown in figure.

The upper front region of the crystal is
shifted one atomic distance to the right
relation to the bottom portion.

Atomic distortion is also linear and along
a dislocation line, Line AB.

Derived name from the spiral or helical
path or ramp traced around the
dislocation line.
 Symbol in Figure
5
Chapter 4 (Review)
4.4 Dislocations __
Linear Defects

Most dislocations found in
crystalline materials are
probably neither pure edge nor
pure screw, but mixed.

All three dislocations are
represented in Figure 4.5

The lattice distortion that is
produced away from the two
faces is mixed, having varying
degrees of screw and edge
character.
6

Plastic deformation corresponds to the motion of large
number of dislocations.

An edge dislocation moves in response to a shear
stress applied in a direction perpendicular to its line

Figure shows the mechanics.
7

When the shear stress applied,
 Plane A is forced to the right
 This in turn pushes the top halves of planes B, C, D, and so on.

If the applied stress is of sufficient magnitude,
 The inter-atomic bonds of plane B are severed along the shear plane
 The upper half of plane B becomes the extra half-plane
 Plane A links up with the bottom half-plane of plane B
 This process is subsequently repeated
 Ultimately this extra half-plane may emerge  forming an edge that is one
atomic distance wide

Atomic arrangement of the crystal
 Only during passage of the extra half-plane the lattice structure is
disrupted
 Before and after the movement of a dislocation  ordered and perfect
8

SLIP  The process by which plastic deformation is
produced by dislocation

Slip plane  the crystallographic plane along which
the dislocation line traverses

Macroscopic plastic deformation simply
corresponds to permanent deformation that results
from the movement of dislocations, or slip, in
response to an applied shear stress

The direction of movement for
 For an edge is parallel to the applied shear stress
 For Screw dislocation is perpendicular
 Net plastic deformation for both is same
9
Dislocation Motion


Dislocation moves along slip plane in slip
direction perpendicular to dislocation line
Slip direction same direction as Burgers vector
Edge dislocation
Adapted from Fig. 7.2, Callister
7e.
Screw dislocation
10

Dislocation motion is analogous to the mode of
locomotion employed by a caterpillar

Forms hump near its posterior end by pulling last pair
of legs a unit leg distance  hump propelled forward
by repeated lifting and shifting  when hump
reached the anterior end, the entire caterpillar has
moved forward by the leg separation distance.
11

Some dislocations in all crystalline materials were introduced
during
 Solidification
 Plastic deformation
 Thermal stresses

Dislocation density expressed as
 Total dislocation length per unit volume, or equivalently
(mm/mm3)
 The number of dislocations that intersect a unit area of a
random section (mm-2)
 Carefully solidified crystals have low values: 103 mm-2
 Heavily deformed metal have high values: 109 to 1010 mm-2
 Heat treating a deformed metal diminishes to: 105 to 106 mm-2
12
7.3 Characteristics of Dislocations

When metals are deformed plastically,
 Some fraction of the deformation energy (approx.
5%) is retained internally
 Remainder is dissipated as heat

Major portion of stored energy is as strain energy
associated with dislocations.

Lattice distortions may be considered to be strain
fields
 That radiate from the dislocation line
 Extend into the surrounding atoms
 Magnitude decreases with radial distance from the
dislocation.
13

Atoms immediately above and
adjacent to the dislocation line
 squeezed together 
experiencing compressive strain

Atoms directly below  tensile
strain

Shear strain also exist in the
vicinity of edge dislocation

For screw dislocation, lattice
strains are pure shear only
14

Strain fields surrounding dislocations in close
proximity may interact

Examples
Two edge dislocations having same sign and
identical slip plane
 Compressive and tensile strain field for both lie on
the same side of the slip plane
 Strain field interaction  mutual repulsive force
that tends to move them apart.

15

Two dislocations of opposite sign and having the same
slip plane
 Attract each other
 Dislocation annihilation will occur when they meet
 Two extra half-planes align and become a complete
plane
 Are possible between edge, screw, and/or mixed
dislocations
 Result in strengthening mechanism for metals.
16
7.4 Slip Systems
Dislocations produce atomic dislocations on specific crystallographic
slip planes and in specific crystallographic slip directions.
 Slip is favored on close-packed planes since a lower shear stress for
atomic displacement is required than for less densely packed planes
 Plane having greatest planar density  Slip Plane
 If slip on the closed-packed planes is restricted due to local high
stresses, for example, then planes of lower atomic packing can
become operative
 Slip in the closed-packed directions is also favored since less energy
is required to move the atoms from one position to another if the
atoms are closer together
 Directions having highest linear density  Slip Direction
A combination of a slip plane and a slip direction is known as Slip
System.
17

Slip System
18
Deformation Mechanisms
Slip System
 Slip

plane - plane allowing easiest slippage
Wide interplanar spacings - highest planar densities
 Slip direction
densities
- direction of movement - Highest linear
Adapted from Fig. 7.6,
Callister 7e.


FCC Slip occurs on {111} planes (close-packed) in <110>
directions (close-packed)
=> total of 12 slip systems in FCC
in BCC & HCP other slip systems occur
19

For metals with FCC structure, slip takes place
{111}
 On the close-packed octahedral planes:
 In the closed-packed directions:
110

There are eight {111} octahedral planes which are crystallographically
equivalent  same planar density
 Planes at opposite faces, which are parallel, are considered the same
type of (111) slip plane
 Therefore, there are only four different types of (111) slip planes in the
FCC crystal structure

Each (111)-type plane contains three 110 directions, which are
crystallographically equivalent.
 Reverse directions are not considered different slip directions

Thus, for FCC lattice structure
4 unique slip planes x 3 independent slip directions = 12 slip systems
20
21
22
23

Possible slip systems for BCC and HCP are listed in
Table 7.1

Metals with FCC or BCC crystal structures have a
relatively large number of slip systems (at least 12)
 These metals are quite ductile because plastic
deformation is normally possible along the various
systems

HCP metals having few active slip systems are
normally quite brittle.
24

7.5 Slip in Single Crystal
Edge, Screw, and mixed dislocations
move in response to shear stresses
applied along a slip plane and in a slip
direction.

Even for applied pure normal (tensile or
compressive) stress, shear stress exists
at all but parallel or perpendicular
alignments to the applied stress
direction.  resolved shear direction

Magnitude of resolved shear stress:
 A metal single crystal has a number
of different slip systems
 Resolved shear stress normally
differs for each one
 R   cos  cos 
25
STRESS AND DISLOCATION MOTION
• Crystals slip due to a resolved shear stress, R.
• Applied tension can produce such a stress.
slip plane
normal, ns
ns
A
As
R   cos  cos 
4
26

Critical resolved
stress ( crss )
 Minimum
 R (max)  ( cos  cos  ) max
shear
stress required to
Yielding occurs, when  R (max)   crss
initiate slip
y 
 Property
of
material that
determines when
yielding occurs
 crss
(cos  cos  ) max
Minimum stress for yielding occurs when a
single crystal is oriented such that     450
 y  2 crss
27
CRITICAL RESOLVED SHEAR STRESS
• Condition for dislocation motion:
• Crystal orientation can make
it easy or hard to move disl.
R   cos  cos 
R  CRSS
typically
10-4G to 10 -2G
5
28
Single Crystal Slip
Slip occurs along
a number of
equivalent
and most
favorably
oriented
planes and
directions at
various
positions
along the
length.
On surface
these
Adapted from
Fig. 7.8, Callister 7e.
appears as
Adapted from Fig. 7.9,
Callister 7e.
29
Example 7.1
30
Ex: Deformation of single crystal
a) Will the single crystal yield?
b) If not, what stress is needed?
=60°
=35°
crss = 3000 psi
   cos  cos 
  6500 psi
Adapted from
Fig. 7.7,
Callister 7e.

 = 6500 psi
  (6500 psi) (cos 35 )(cos 60 )
 (6500 psi) (0.41)
  2662 psi
 crss  3000 psi
So the applied stress of 6500 psi will not cause
the crystal to yield.

31
Ex: Deformation of single crystal
What stress is necessary (i.e., what is the
yield stress, y)?
crss  3000 psi  y cos  cos   y (0.41)
crss
3000 psi
 y 

 7325 psi
cos  cos 
0.41
So for deformation to occur the applied stress must be
greater than or equal to the yield stress
  y  7325 psi
32
7.6 Plastic Deformation of Polycrystalline Materials


Random crystallographic orientations of the
numerous grains, the direction of slip varies
from one grain to another  deformation and
slip is complex
Photomicrograph of a polycrystalline copper
specimen
 Before deformation, the surface was
polished
 Slip lines visible
 Two sets of parallel yet intersecting sets of
lines  It appears that two slip systems
operated
 The difference in alignment of the slip lines
for the several grains  variation in grain
orientation
33

Gross plastic deformation 
distortion of individual grain by
means of slip

Mechanical integrity and
coherency are maintained  grain
boundaries usually do not come
apart or open up.

Each individual grain is
constrained by its neighboring
grains.

Figure 7.11 shows plastic
deformation
 Before deformation, grains
equiaxed (have approx. same
dimension in all direction)
 After deformation, grains
elongated along the direction of
extension or loading
34

Polycrystalline materials are stronger
 greater
stresses are required to initiate slip and
yielding
 Due
to geometrical constraints imposed on the
grains
 Even
a favorably oriented single grain can not
deform until the adjacent less favorably
oriented grains are capable of slip also
 requires a higher applied stress level.
35
Mechanism of Strengthening in Metals

The ability of a metal to plastically deform depends on the
ability of dislocations to move.

Hardness and strength are related to the ease with which
plastic deformation can be made to occur
 To enhance mechanical strength  reduce dislocation
mobility  greater mechanical forces required to
initiate plastic deformation.

Strengthening mechanism for single phase metal
 By grain size reduction
 Solid-solution alloying
 Strain-hardening
36
7.8 Strengthening by Grain Size Reduction

Adjacent grains have different crystallographic
orientation

During plastic deformation, slip or dislocation
motion must take place across the common
boundary (from grain A to grain B)

Grain boundary acts as a barrier to dislocation
motion for two reasons:

Two grains are of different orientation  a
dislocation have to change its direction of motion
 becomes more difficult as crystallographic
misorientation increases.

Atomic disorder within a grain boundary region will
result in a discontinuity of slip planes from one
grain into the other.
37

Hall-Petch Equation: For many materials, Yield strength
varies with grain size as
1 / 2 d: average grain diameter
y
0
y
0 and ky are material constants
σ σ k d

Figure 7.15 shows strength variation
for brass

Hall-Petch equation is not valid
for very large and extremely
small grain materials
38
39

High-angle grain boundaries
 Dislocations may not traverse grain boundaries during deformation
 A stress concentration ahead of a slip plane in one grain may
activate sources of new dislocation in an adjacent grain.

Small-angle grain boundaries
 Not effective in interfering because of slight misalignment

Twin boundaries
 Effectively block slip and increase the strength of the material

Boundaries between two different phases
 Impediment (obstacle/barrier) to movements of dislocations
 Important in strengthening complex alloys
40
7.9 Solid Solution Strengthening

Another technique to strengthen and
harden metals is alloying
 Adding
impurity atoms that go into either
substitutional or interstitial solid solution

High-purity metals are almost always softer
and weaker

Fig 7.16 shows the effect of alloying nickel
in copper
41
42

Alloys are stronger than pure metals
 Impurity atoms impose lattice strain on
surrounding host atoms
 Lattice strain field interaction between dislocation
and impurity atoms result
 dislocation movement is restricted

An impurity atom that is smaller than a host atom 
substitution results tensile strains on the surrounding
crystal lattice ( Fig 7.17a)

Larger substitutional atom imposes compressive
strains in its vacinity (Fig 7.18a)
43
44

Solute atoms tend to diffuse to and segregate around
dislocations  reduce strain energy  to cancel some lattice
strain surrounding a dislocation

To accomplish this,
 a smaller impurity atom is located where its tensile strain will
partially nullify some of the dislocation’s compressive strain
 A larger atom to nullify tensile strain of dislocation
 Figure 7.17b and 7.18b

Resistance to slip is greater
 Overall lattice strain must increase if dislocation is torn
away from them
 Same strain interaction exist between atoms and
dislocation that are in motion during plastic deformation
 greater applied stress is needed to initiate and continue
plastic deformation
45
7.10 Strain Hardening
 Strain hardening  a phenomenon whereby a
ductile material becomes harded and stronger as it is
plastically deformed.

Also known as work-hardening or cold working

Most metals strain harden at room temperature

Degree of plastic deformation is expressed as
percent cold work (%CW)
 A0  Ad
%CW  
 A0

 100

46

Figure demonstrates
effect of cold work
on steel, brass and
copper

Loading to plastic
deformation,
unloading and then
reloading 
requires more
applied load or
stress to yield 
metal becomes
stronger
47

Why more stronger ?

On the average, dislocation-dislocation strain
interactions are repulsive

Dislocation density increases due to
 Deformation or cold work
 Dislocation multiplication
 Formation of new dislocations

Net result  motion of dislocation is hindered by the
presence of other dislocations  higher imposed
stress is needed to deform a metal
48
Recovery, Recrystallization, and Grain Growth

Plastic deformation of polycrystalline metal at
temperatures lower than its melting temperature produces
 micro-structural and property changes
 includes
1. A change in grain shape
2. Strain hardening
3. Increase in dislocation density

Some fraction of deformation energy (about 5%) stored in
metal as strain energy
 Associated with tensile, compressive and shear zones
around newly created dislocations
Other properties (such as electrical conductivity and
corrosion resistance ) may be modified by plastic
deformation.

49

Modified Properties and structures due to plastic
deformation (cold work)
 May
revert back to the precold-worked states by
Annealing
 Annealing
is a heat treatment process

Restoration due to due different processes at
elevated temperatures
 Recovery
 Recrystallization

Above processes may be followed by grain growth.
50
7.11 Recovery

At elevated temperature
 enhanced atomic diffusion
 dislocation motion
 some stored strain energy relieved
Recovery process Involves
 Reduction in dislocation numbers
 Dislocation configuration with low strain
energy
(similar to Fig 4.8)

Physical properties are recovered to their
precold-worked state
 Electrical and thermal conductivities
51
7.12 Recrystallization

Even after recovery is complete, the grains are still in a
relatively high strain energy state.

Recrystallization is the formation of a new set of strain-free
and equiaxed grains having low dislocation densities as the
precold-worked state.

Difference in internal energy between the strained and
unstrained material  acts as the driving force to produce
new grain structure

New grains form as very small nuclei  grow until
completely replace the parent material  involves shortrange diffusion
52
7.12 Recrystallization (Contd.)
Several stages of recrystallization

(a) cold-worked
(33%) grain
structure

(b) Initial stage of
recrystallization
after heating 3 s
at 580oC
53
7.12 Recrystallization (Contd.)
Several stages of recrystallization

(c) Partial
replacement of
cold-worked grains
by recrystallized
ones (4s at 580oC)

(d) complete
recrystallization
(8s at 580oC)
54
7.12 Recrystallization (Contd.)
Several stages of recrystallization

(e) Grain growth
after 15 min at
580oC

(d) Grain growth
after 10 min at
700oC
55
7.12 Recrystallization

During recrystallization, mechanical properties restored to
their precold-worked values
Metal becomes softer, weaker, yet ductile

Some heat treatments are designed to allow recrystallization
to occur these modifications in the mechanical characteristics.

Recrystallization depends on both time and temperature

Influence of time
The degree (or fraction ) of recrystallization increases with
time (Figure 7.21a-d)
56

Influence of temperature
 Figure
7.22 shows
tensile strength and
ductility of a brass
alloy
 Constant
heat
treatment time of 1
hour
 Grain
structures at
various stages are
presented
schematically.
57

Recrystallization temperature
 The temperature at which recrystallization just reaches
completion in 1 hour.
 Recrystallization temperature of brass alloy (Fig 7.22) is
about 450oC (850oF).
 It is about 1/3 to ½ of absolute melting temperature
 Depends on several factors, such as % cold work, purity of
alloy etc.

Effect of %CW
 Increasing %CW enhances the rate of recrystallization 
recrystallization temperature is lowered
 Recrysttalization temperature approaches a constant or
limiting value at high deformation.
 Critical degree of cold work
 Below which no recrystallization
 Ususally 2 – 20 %
58
59

Effect of alloying
 Recrystallization proceeds more rapidly in pure metal than
in alloys  alloying raises recrystallization temperature
 For pure metal: normally it is 0.3(Melting temperature)
For alloys, it may run as high as 0.7(melting temperature)
Hot working : plastic deformation operations at temperatures
above the recrystallization temperature
 Material remains relatively soft and ductile during
deformation
 It does not strain harden
 Large deformations possible
60
61
7.13 Grain growth

After recrystallization is
complete, the strain-free grains
will continue to grow if the metal
specimen is left at the elevated
temperature  phenomenon is
known as grain growth.

It occurs by the migration of
grain boundaries
 Boundary motion is just the
short-range diffusion of
atoms from one side of the
boundary to the other
 Direction of boundary
movement and atomic motion
are opposite.
 Schematic reprsentationin
Fig 7.24
62

For many polycrystalline materials, grain diameter (d)
varies with time as
dn – don = Kt
do : initial grain diameter at t=0
K, n: time-dependent constants
n is equal to greater than 2

Dependence of grain size on time and temperature is
shown in Fig 7.25
 Brass alloy
 At higher temperature, rapid growth  due to
enhancement of diffusion rate
63
64

Mechanical properties at room temperature of a finegrained metal are usually superior (strength and
toughness) than coarse-grained ones.

If grain structure of a single phase alloy is coarser than
that desired
 plastically deform
 subject to recrystallization heat treatment
 refine grain size
65