1. 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.

2. DISLOCATIONS and PLASTIC DEFORMATION 7.2 Basic Concepts
Dislocation Types
Edge Dislocation
Screw Dislocation
Review from Chapter 4 notes

3. Chapter 4 (Review) 4.4 Dislocations __ Linear Defects
A dislocation is a linear or one-dimensional 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.

4. 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

5. 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

6. 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.

7. 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.

8. 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

9. 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

10. IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
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
By: Dr. A.F.M. Arif

11. 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.

12. 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

13. 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.

14. 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

15. 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.

16. 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.

17. 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.

18. Slip System

19. Deformation Mechanisms
IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
Deformation Mechanisms
Slip System
Slip plane - plane allowing easiest slippage
Wide interplanar spacings - highest planar densities
Slip direction - direction of movement - Highest linear densities
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
Adapted from Fig. 7.6, Callister 7e.
By: Dr. A.F.M. Arif

20. For metals with FCC structure, slip takes place
On the close-packed octahedral planes:
In the closed-packed directions:
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 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

24. 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.

25. 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

26. STRESS AND DISLOCATION MOTION
• Crystals slip due to a resolved shear stress, tR.
• Applied tension can produce such a stress.
slip plane
normal, ns
direction
slip
direction
slip
direction
slip 4

27. Critical resolved stress ( tcrss )
Minimum shear stress required to initiate slip
Property of material that determines when yielding occurs

28. CRITICAL RESOLVED SHEAR STRESS
• Condition for dislocation motion:
• Crystal orientation can make
it easy or hard to move disl. 5

29. IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
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 appears as lines (Figure 7.9)
Adapted from Fig. 7.9, Callister 7e.
Adapted from Fig. 7.8, Callister 7e.
By: Dr. A.F.M. Arif

30. Example 7.1

31. Ex: Deformation of single crystal
IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
Ex: Deformation of single crystal
a) Will the single crystal yield?
b) If not, what stress is needed?
=60°
crss = 3000 psi
=35°
Adapted from Fig. 7.7, Callister 7e.
 = 6500 psi
So the applied stress of 6500 psi will not cause the crystal to yield.
By: Dr. A.F.M. Arif

32. Ex: Deformation of single crystal
IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
Ex: Deformation of single crystal
What stress is necessary (i.e., what is the yield stress, sy)?
So for deformation to occur the applied stress must be greater than or equal to the yield stress
By: Dr. A.F.M. Arif

33. 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

34. 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

35. 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.

36. 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

37. 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.

38. Hall-Petch Equation: For many materials, Yield strength varies with grain size as
d: average grain diameter
s0 and ky are material constants
Figure 7.15 shows strength variation
for brass
Hall-Petch equation is not valid
for very large and extremely
small grain materials

40. 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

41. 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

43. Strategies for Strengthening: 2: Solid Solutions
IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
Strategies for Strengthening: 2: Solid Solutions
• Impurity atoms distort the lattice & generate stress.
• Stress can produce a barrier to dislocation motion.
• Smaller substitutional
impurity
Impurity generates local stress at A and B that opposes dislocation motion to the right. A B
• Larger substitutional
impurity
Impurity generates local stress at C and D that opposes dislocation motion to the right. C D
By: Dr. A.F.M. Arif

44. 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)

46. 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

47. 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)

48. Strategies for Strengthening: 3: Cold Work (%CW)
IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
Strategies for Strengthening: 3: Cold Work (%CW)
• Room temperature deformation.
• Common forming operations change the cross
sectional area:
Adapted from Fig. 11.8, Callister 7e.
-Forging A o d
force
die
blank
-Rolling
roll A o d
-Drawing
tensile
force A o d
die
-Extrusion
ram
billet
container
force
die holder
die A o d
extrusion
By: Dr. A.F.M. Arif

49. Dislocations During Cold Work
IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
Dislocations During Cold Work
• Ti alloy after cold working:
0.9 mm
• Dislocations entangle
with one another
during cold work.
• Dislocation motion
becomes more difficult.
Adapted from Fig. 4.6, Callister 7e.
(Fig. 4.6 is courtesy of M.R. Plichta, Michigan Technological University.)
By: Dr. A.F.M. Arif

50. IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
Result of Cold Work
total dislocation length
unit volume
Dislocation density =
Carefully grown single crystal
 ca. 103 mm-2
Deforming sample increases density
 mm-2
Heat treatment reduces density
 mm-2
Again it propagates through til reaches the edge
large hardening
small hardening s e y0 y1
• Yield stress increases
as rd increases:
By: Dr. A.F.M. Arif

51. Effects of Stress at Dislocations
IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
Effects of Stress at Dislocations
Adapted from Fig. 7.5, Callister 7e.
By: Dr. A.F.M. Arif

52. IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
Impact of Cold Work
As cold work is increased
• Yield strength (sy) increases.
• Tensile strength (TS) increases.
• Ductility (%EL or %AR) decreases.
Adapted from Fig. 7.20, Callister 7e.
By: Dr. A.F.M. Arif

53. IBCAST: Introduction to Nonlinear FEA
14th June, 2002.
Cold Work Analysis
Cold
Work D d
=12.2mm
Copper
• What is the tensile strength &
ductility after cold working? D o
=15.2mm
% Cold Work
100
300
500
700 Cu 20 40 60
yield strength (MPa)
% Cold Work
tensile strength (MPa)
200 Cu
400
600
800 20 40 60
ductility (%EL)
% Cold Work 20 40 60 Cu s y
= 300MPa
300MPa
340MPa
TS = 340MPa 7%
%EL
= 7%
Adapted from Fig. 7.19, Callister 7e. (Fig is adapted from Metals Handbook: Properties and Selection: Iron and Steels, Vol. 1, 9th ed., B. Bardes (Ed.), American Society for Metals, 1978, p. 226; and Metals Handbook: Properties and Selection: Nonferrous Alloys and Pure Metals, Vol. 2, 9th ed., H. Baker (Managing Ed.), American Society for Metals, 1979, p. 276 and 327.)
By: Dr. A.F.M. Arif

54. 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

55. Recovery, Recrystallization, and Grain Growth
Plastic deformation of polycrystalline metal at temperatures lower than its melting temperature produces
 micro-structural and property changes
 includes
A change in grain shape
Strain hardening
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.

56. 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.

57. 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

58. 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 short-range diffusion

59. 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

60. 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)

61. 7.12 Recrystallization (Contd.) Several stages of recrystallization
(e) Grain growth after 15 min at 580oC
(d) Grain growth after 10 min at 700oC

62. 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)

63. 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.

64. 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 %

66. 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

67. Design Example 7.1

68. 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

69. 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

71. Mechanical properties at room temperature of a fine-grained 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