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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.
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DISLOCATIONS and PLASTIC DEFORMATION7.2 Basic Concepts
Dislocation Types
Edge Dislocation
Screw Dislocation
Review from Chapter 4 notes
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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.
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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 apartResults 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
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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
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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.
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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.
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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
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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 stressFor Screw dislocation is perpendicularNet plastic deformation for both is same
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Dislocation Motion Dislocation moves along slip plane in slip
direction perpendicular to dislocation line Slip direction same direction as Burgers vector
Edge dislocation
Screw dislocation
Adapted from Fig. 7.2, Callister 7e.
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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.
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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
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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.
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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
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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.
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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.
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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.
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Slip System
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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
Deformation Mechanisms
Adapted from Fig. 7.6, Callister 7e.
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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 structure4 unique slip planes x 3 independent slip directions = 12 slip systems
011
}111{
011
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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.
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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
coscosR
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• Crystals slip due to a resolved shear stress, R. • Applied tension can produce such a stress.
Rcoscos
Relation between and R
R=Fs/As
Fcos A/cosns
AAs
STRESS AND DISLOCATION MOTION
Applied tensile stress: = F/A
FA
Fsli
p
direct
ion
Resolved shear stress: R=Fs/As
As
R
R
Fs
slip
direct
ion
slip plane
normal, ns
F
Fssli
p
direct
ion
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Critical resolved stress ( crss )
Minimum shear stress required to initiate slip
Property of material that determines when yielding occurs crssy
crssy
crssR
R
2
45 such that oriented is crystal single
a when occurs yieldingfor stress Minimum
)cos(cos
(max) when occurs, Yielding
)coscos((max)
0
max
max
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• Condition for dislocation motion: R CRSS
• Crystal orientation can make it easy or hard to move disl.
10-4G to 10-2G
typically
Rcoscos
CRITICAL RESOLVED SHEAR STRESS
R = 0
=90°
R = /2=45°=45°
R = 0
=90°
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Single Crystal Slip
Adapted from Fig. 7.8, Callister 7e.
Adapted from Fig. 7.9, Callister 7e.
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)
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Example 7.1
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Ex: Deformation of single crystal
So the applied stress of 6500 psi will not cause the crystal to yield.
cos cos 6500 psi
=35°
=60°
(6500 psi) (cos35)(cos60)
(6500 psi) (0.41)
2662 psi crss 3000 psi
crss = 3000 psi
a) Will the single crystal yield? b) If not, what stress is needed?
= 6500 psi
Adapted from Fig. 7.7, Callister 7e.
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Ex: Deformation of single crystal
psi 732541.0
psi 3000
coscoscrss
y
What stress is necessary (i.e., what is the yield stress, y)?
)41.0(cos cos psi 3000crss yy
psi 7325 y
So for deformation to occur the applied stress must be greater than or equal to the yield stress
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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
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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
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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.
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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
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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.
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Hall-Petch Equation: For many materials, Yield strength varies with grain size as
d: average grain diameter
0 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
210
/yy dkσσ
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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
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7.9 Solid Solution Strengthening Another technique to strengthen and
harden metals is alloyingAdding 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
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Alloys are stronger than pure metals Impurity atoms impose lattice strain on
surrounding host atomsLattice 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)
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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
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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)
100%0
0
A
AACW d
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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
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Why more stronger ?
On the average, dislocation-dislocation strain interactions are repulsive
Dislocation density increases due toDeformation or cold workDislocation multiplicationFormation 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
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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.
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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 temperaturesRecoveryRecrystallization
Above processes may be followed by grain growth.
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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
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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
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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
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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)
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7.12 Recrystallization (Contd.)Several stages of recrystallization
(e) Grain growth after 15 min at 580oC
(d) Grain growth after 10 min at 700oC
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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 timeThe degree (or fraction ) of recrystallization increases with time (Figure 7.21a-d)
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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.
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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 %
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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
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Design Example 7.1
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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
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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
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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