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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

21

22

23

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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