Chapter 5: Dislocation & Strengthening Mechanism

You will learn about:

• Why are dislocations observed primarily in metals and alloys?

• How are strength and dislocation motion related?

• How do we increase strength?

• How can heating change strength and other properties?

Chapter Outlines:Chapter Outlines:

5.1 Introduction

5.2 Dislocation & Plastic Deformation

Motion of dislocations in response to stress Slip systems Plastic deformation in single crystal & polycrystalline materials

5.3 Mechanisms of Strengthening in Metals

Grain size reduction Solid solution strengthening Strain hardening

5.4 Recovery, Recrystallization & Grain Growth

5.1 Introduction5.1 Introduction In next chapter, we will learn about 2 kinds of deformations:

elastic deformation & plastic deformation

Plastic deformation: Corresponds to the net movement of large numbers of atoms in

response to an applied stress Interatomic bonds must be ruptured and then reformed Involves the motion of dislocations (linear crystalline defects) for

crystalline solids

In this chapter, we will learn about …

“the characteristics of dislocations and their involvement in plastic deformation…”

Regarding to…Taylor, Orowan and Polyani (1934):

“Plastic deformation is due to the motion of a large number of

dislocations.”

“Discrepancy in mechanical strengths could be explained by a type of linear

crystalline defects (dislocation)”

In addition, we will learn several techniques for strengthening single phase metals (the mechanisms of which are described in terms of dislocations)

Finally, we will learn about recovery, recrystallization & grain growth (processes that occur in plastically deformed metals, normally at elevated temperatures)

5.2.1 Basic Concepts

5.2 Dislocations & Plastic Deformation5.2 Dislocations & Plastic Deformation

Plastic deformation corresponds to the motion of large numbers of dislocations

An edge dislocation moves in response to a shear stress applied in a direction perpendicular to its line

The mechanisms of dislocation motion are as below:

1) Let the initial extra half- plane of atoms be plane 1

2) When the shear stress is applied , plane 1 is forced to the right

3) This in turn pushes the top halves of planes 2, 3, 4 and so on, in the same direction

4) If the applied shear stress is of sufficient magnitude, the interatomic bonds of plane 2 are severed along the shear plane, and the upper half of plane 2 becomes the extra half- plane as plane 2 links up with the bottom half of plane 2

This process is repeated for the other planes, such that the extra half plane, by discrete steps, moves from left to right by successive and repeated breaking of bonds and shifting by interatomic distances of upper half- planes.

The process by which plastic deformation is produced by dislocation motion is termed ‘SLIP’‘SLIP’

While the crystallographic plane along the dislocation line traverses is ‘SLIP PLANE’‘SLIP PLANE’

In addition, slip always takes place along a consistent set of directions within these planes – these are called ‘SLIP ‘SLIP DIRECTIONS’DIRECTIONS’

The combination of slip plane and slip direction together makes up a ‘SLIP SYSTEM’‘SLIP SYSTEM’

Plastically stretched zinc

single crystal.

• When a single crystal is deformed under a tensile stress, it is observed that plastic deformation occurs by slip on well-defined parallel crystal planes. Sections of the crystal slide relative to one another, changing the geometry of the sample as shown in the diagram.

Direction of the dislocation motion:

Analogous of dislocation motion:

Representation of the analogy between caterpillar and dislocation motion

5.2.2 Characteristics of Dislocations

Strain field around dislocationsStrain field around dislocations

Dislocations have strain fields arising from distortions at their cores - strain drops radially with distance from dislocation core

Edge dislocations introduce compressive, tensile, and shear lattice strains, screw dislocations introduce shear strain only.

Interactions Between DislocationsInteractions Between Dislocations

The strain fields around dislocations cause them to interact (exert force on each other). When they are in the same plane, they repel if they have the same sign (direction of the Burgers vector) and attract/annihilate if they have opposite signs.

C = compressionT = tension

The number of dislocations in a material is expressed as the

dislocation density - the total dislocation length per unit volume or the number of dislocations intersecting a unit area.

Most crystalline materials, especially metals, have dislocations in their as-formed state, mainly as a result of stresses (mechanical, thermal...) associated with the forming process.

Where do Dislocations Come From?Where do Dislocations Come From?

The number of dislocations increases dramatically during plastic deformation. Dislocations spawn from existing dislocations, grain boundaries and surfaces.

This picture is a snapshot from simulation of plastic deformation in a fcc single crystal (Cu) of linear dimension 15 micrometers.

5.2.3 Slip Systems

As you can see the B.C.C unit cell contains nine atoms while the F.C.C unit cell contains fourteen atoms one at each corner of the cube and one at the centre of each of the six faces.

This of course leads us the assumption that the atoms are more densely packed in the F.C.C unit cell. The density of packing is very important in the analysis of slip planes.

Slip means part of  a metal slip over itself and this happens in metals when they are subjected to shear - type forces. We will now take a look at slip occurring within a B.C.C and a F.C.C crystalline structure.

• As you can see in figure above it takes a large force to cause the atoms in a B.C.C structure to slip

• If you now take a look at the more densely packed F.C.C structure you should have very little trouble realizing the reasons why an F.C.C structure does not require as large a force to cause slip as in the case of the B.C.C structure. Why? Because the atoms are more densely  packed in the F.C.C structure.

• The fact that F.C.C structures require less force before slip occurs of course explains why metals with an F.C.C unit cell are more ductile as the atoms are so densely packed they find it easier to slip over one another than in the case of a metal with a B.C.C unit cell which will be brittle.

5.2.4 Slip in Single Crystals

Dislocations move in particular directions on particular planes (the slip system) in response to shear stresses applied along these planes and directions we need to⇒ determine how the applied stress is resolved onto the slip systems.

Let us define the resolved

shear stress, τR, (which produces

plastic deformation) that result from

application of a simple tensile stress, σ.

• Φ = represent the angle between the normal to the slip plane and applied stress direction

• λ = the angle between the slip plane and stress directions

5.2.5 Plastic Deformation of Polycrystalline Materials

Grain orientations with respect to applied stress are random.

The dislocation motion occurs along the slip systems with favourable orientation (i.e. that with highest resolved shear stress).

Slip lines on the surface of a polycrystalline specimen of copper that was polishedand subsequently deformed

2

1

Larger plastic deformation corresponds to elongation of grains along direction of applied stress.

Alteration of the grain structure of polycrystalline metal as a result of plastic deformation

(a) Before deformation (grains are equaixed)

(b) After deformation (grains are elongated)

Dislocations cannot easily cross grain boundaries because of changes in direction of slip plane and

disorder at grain boundary

As a result, polycrystalline metals are stronger than single crystals

5.3 Mechanisms of Strengthening in Metals5.3 Mechanisms of Strengthening in Metals

The ability of a metal to deform depends on the ability of dislocations to move.

Restricting dislocation motion makes the material stronger

Mechanisms of strengthening in single- phase metals:

1. Grain Boundaries & Grain Size

2. Strain Hardening (Work Hardening)

3. Solid-solution Strengthening

Ordinarily, strengthening reduces ductility

1.1. Effect of Grain Boundaries & SizeEffect of Grain Boundaries & Size

Grain boundaries strengthen metals and alloys by acting as barriers to dislocation movement. Thus, polycrystalline is harder than single crystal.

During plastic deformation, slip or dislocation motion must take place across the grain boundary- let say from grain A to grain B

The motion of a dislocationas it encounters a grain boundaries,illustrating how the boundary actsas a barrier to continued slip. Slipplanes are discontinuous and change directions across theboundary

The grains boundary acts as a barrier to dislocation motion for two reasons:

1. Since the two grains are of different orientations, a dislocation passing into grain B will have to change its direction of motion; this becomes more difficult as the crystallographic misorientation increases

2. The atomic disorder within a grain boundary region will result in a discontinuity of slip planes from one grain into the other.

A fine grained material (one that has small grains) is harder & stronger than one that is coarse grained, since the former has a greater total grain boundary area to impede dislocation motion (more barrier to overcome i.E. Crack to propagate)

Small- angle grain boundaries - are not effective in interfering with the slip process because of the slight crystallographic misalignment across the boundary.

High- angle grain boundaries - block slip and increase strength of the material.

Grain size d can be controlled by the rate of solidification, by plastic deformation and by appropriate heat treatment

The influence of grain size on the yield strength of a 70 Cu-

30 Zn brass alloy (note that the grain diameter increases from right to left, not linear)

Grains Directions

A phenomenon whereby ductile metal becomes harder and stronger with increasing deformation

Strengthening by increase of dislocation density

(Strain Hardening = Work Hardening = Cold Working)

Called work hardening, because the temperature at which deformation takes place is “cold” relative to the absolute melting temperature of the metal or “cold working”

2.2. Strain HardeningStrain Hardening

Ductile metals become stronger when they are deformed plastically at temperatures well below the melting point.

The reason for strain hardening is the increase of dislocation density with increased cold deformation.

New dislocations are created by the cold deformation and must interact with those already existing.

As the dislocation density increases with deformation, it becomes more and more difficult for the dislocations to move through the existing “forest of dislocations”.

And thus, the metal work or strain hardens with increased cold deformation.

The average distance between dislocations decreases

and dislocations start blocking the motion of each other.

The percent cold work (%CW) is often used to express the degree of plastic deformation:

Yield strength vs % cold work Tensile strength vs % cold work

Ductility vs % cold work

For 1040 steel, brass and copper, (a) theincreases in yield strength, (b) the increases in tensile strength and (c) the deceases in ductility (%EL) with percent cold work.

Problem:

A 70% Cu.30% Zn brass wire is cold-drawn 20 percent to a diameter of 2.80 mm. The wire is then further cold-drawn to a diameter of 2.45 mm.

(a) Calculate the total percent cold work thatthe wire undergoes (b) Estimate the wire’s tensile and yield strengths and elongation from Fig. 5.46.

FIGURE 5.46

3.3. Solid Solution StrengtheningSolid Solution Strengthening

Strengthen and harden metals by alloying with impurity atoms – substitutional or interstitial solid solution.

High purity metals are almost always softer and weaker than alloys composed of the same base metal

Increasing the concentration of the impurity results in an attendant increase in tensile and yield strengths

Alloys are stronger than pure metals because impurity atoms impose lattice strains on the surrounding host atoms.

High purity metals are almost always softer and weaker than alloys composed of the same base metal

Interstitial or substitutional impurities in a solution cause lattice strain. As a result, these impurities interact with dislocation strain fields and hinder dislocation motion.

(a) Representation of tensile lattice

strains imposed on host atoms by a

Smaller substitutional impurity atom.

(b) Possible locations of smaller

impurity atoms relative to an edge

dislocation such that there is partial

cancellation of impurity–dislocation

lattice strains.

(a) Representation of compressive

strains imposed on host atoms by a

larger substitutional impurity atom.

(b) Possible locations of larger impurity

atoms relative to an edge dislocation

such that there is partial cancellation of

impurity–dislocation lattice strains.

Variation with nickel content of (a) tensile strength, (b) yield strength and (c) ductility(% EL) for copper- nickel alloys, showing strengthening

Are the processes that occur in plastically deformed metals, normally at elevated temperatures

These processes produces microstructural and property changes that include:

1. A change in grain shape2. Strain hardening3. An increase in dislocation density

Plastic deformation increases dislocation density and changes grain size distributions

This correspond to stored strain energy in the system (dislocation strain fields and grain distortions)

5.4 Recovery, Recrystallization & Grain 5.4 Recovery, Recrystallization & Grain GrowthGrowth

When applied external stress is removed- most of the dislocations, grain distortions and associated strain energy are retained

Restoration to the state before cold- work can be done by heat treatment and involves 2 processes: recovery & recrystallization and followed by grain growth.

1.1. RecoveryRecovery

Heating increased diffusion enhanced dislocation motion relieves internal strain energy and reduces the number of dislocation. The electrical and thermal conductivity are restored to the values existing before cold working.

During recovery, some of the stored internal strain energy is relieved by virtue of dislocation motion (in the absence of an externally applied stress), as a result of enhanced atomic diffusion at the elevated temperature.

There is some reduction in the number of dislocations and dislocation configurations are produced having low strain energies

.

2.2. RecrystallizationRecrystallization

Even after recovery the grains can be strained. These strained grains of cold-worked metal can be replaced, upon heating, by strain-free grains with low density of dislocations.

This occurs through recrystallization – nucleation and growth of new grains.

The driving force for recrystallization is the difference in internal energy between strained and unstrained material.

Grain growth involves short-range diffusion - the extend of recrystallization depends on both temperature and time.

Recrystallization is slower in alloys as compared to pure metals

Several stages of the recrystallization and grain growth of brass

1. Cold worked (33%CW) grain structure

2. Initial stage of recrystallization After heating 3 s at 580 C ( the very small grains are those that have recrystallized)

3. Partial replacement of cold workedGrains by recrystallized ones (4 s at 580 C)

4.Complete recrystallization(8 s at 580 C)

5. Grain growth after 15 min at 580 C 6. Grain growth after 10 min at 700 C

3.3. Grain GrowthGrain Growth

Phenomenon that occur after recrystalliztion is complete, the strain- free grains will continue to grow if the metal specimen is left at the elevated temperature

As grains increase in size, the total boundary area decrease, yielding an attendant reduction in the total energy; this is the driving force for grain growth

Grain growth 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

Schematic representation of grain growth via atomic diffusion

The influence of annealing temperature on the tensile strength and ductility of a brassalloy. Grain size as a function of annealing

temperature is indicated.

Summary…