LECTURE #11: DISLOCATIONS AND

STRENGTHENING MECHANISMS

ENGR 151: Materials of Engineering

DISLOCATIONS & PLASTIC DEFORMATION

Edge Dislocation:

Lattice distortion along the end of an extra half-

plane of atoms

Screw Dislocation:

Resulting from shear distortion, dislocation line

passes through the center of a spiral

PLASTIC DEFORMATION

Corresponds to the motion of large numbers of

dislocations.

Edge: dislocation moves in response to a shear stress

applied perpendicularly to dislocation line

Before and after the movement of dislocation through

material, the atomic arrangement is ordered and perfect

SLIP

Process by which plastic deformation is

produced by dislocation motion

Plane along which the dislocation line traverses is

the slip plane

Plastic deformation corresponds to permanent

deformation that results from the movement of

dislocations (slip as result of shear stress)

DISLOCATION MOTION

Similar to movement of a caterpillar

Caterpillar hump corresponds to extra half-plane

DISLOCATION MOTION

Screw Dislocation:

Direction of movement is perpendicular to stress

direction

DISLOCATION MOTION

Edge Dislocation:

Direction of movement is parallel to shear stress

DISLOCATION DENSITY

The number of dislocations in a material:

The total dislocation length per unit volume or area

Carefully solidified metal crystals (103 mm-2)

Heavily deformed metals (106 mm-2)

Ceramic materials (104 mm-2)

Silicon single crystal (1 mm-2)

CHARACTERISTICS OF DISLOCATIONS

Strain fields: exist around dislocations; used to

determine the mobility of the dislocations and

ability to multiply

Plastic deformation: fraction (5%) of

deformation energy is retained internally; the

rest is dissipated as heat

LATTICE STRAIN

The fraction of energy that remains is strain energy associated with dislocations

Edge: atoms immediately above and adjacent to the dislocation line are squeezed together (compressive strain)

Atoms below the half-plane, tensile strain is imposed

Screw: lattice strains are pure shear only

PLASTIC DEFORMATION

Number of dislocations increases dramatically

May be as high as 1010/sq. mm in deformed metal

structure

Existing dislocations multiply

Nicks, cracks and other such irregularities may act

as stress concentrations

Dislocation formation sites

SLIP SYSTEMS

Dislocations do not occur in arbitrary directions

Different degrees of “ease of slip” associated with

different crystallographic directions

Slip Plane: Direction along which dislocation

occurs

Slip Direction: Direction of movement

Slip may or may not occur in the same direction as

applied stress.

SLIP SYSTEMS

Slip System: Combination of slip plane and the

slip direction

Dependent on crystal structure

Minimum atomic distortion associated dislocation

motion

For a particular crystal structure, the slip plane

is the plane that has the most dense atomic

packing (greatest planar density)

Slip direction has the highest linear density

SLIP SYSTEMS

Slip can occur within any of the {111} plane

family, along the -type directions for the

FCC crystal structure

SLIP SYSTEMS

Some metals have different crystal structures at

different temperatures

Slip systems change for these metals with changing

temperature

SLIP IN SINGLE CRYSTALS

Dislocations move in response

to shear stresses applied along

a slip plane and in a slip

direction

Shear components exist at all

but parallel or perpendicular

alignments to the stress

direction

Resolved Shear Stresses:

magnitude depends on applied

stress and orientation of slip

plane and direction

RESOLVED SHEAR STRESS

σ = applied stress

φ = angle between normal to slip plane and applied stress direction

λ = angle between slip and stress directions

In general, φ + λ ≠ 90°

SLIP IN SINGLE CRYSTALS

Multiple slip systems, multiple resolved

stresses

One slip system is generally oriented most

favorably (largest resolved shear stress)

CRITICAL RESOLVED SHEAR STRESS

Slip in a system starts on the most favorably

oriented slip system when shear stress is at a

critical value (critical resolved shear stress) -

τcrss

Minimum shear stress required to initiate stress

Single crystal plastically deforms when:

SLIP IN SINGLE CRYSTALS

The minimum stress necessary to introduce

yielding occurs when a single crystal is oriented

(φ = λ = 45°):

Occurs when denominator reaches its

maximum value

SLIP IN SINGLE CRYSTALS

EXAMPLE 7.1

EXAMPLE 7.1 – SOLUTION

EXAMPLE 7.1 – SOLUTION

PLASTIC DEFORMATION OF POLYCRYSTALLINE

MATERIALS

Random

crystallographic

orientations or

numerous grains

causes the variation

of slip from one

grain to another

Dislocation motion

occurs along the slip

system that has the

most favorable

orientation

Single Crystal Polycrystalline

PLASTIC DEFORMATION OF POLYCRYSTALLINE

MATERIALS

During deformation, mechanical

integrity and coherency are

maintained along the grain

boundaries (grain boundaries do

not come apart)

Individuals grains are constrained

by neighboring grains

Before deformation, grains have

approximately the same

dimension (average) in all

directions

Grains become elongated in

direction of tensile force

MECHANISMS OF STRENGTHENING IN METALS

Materials engineers have to design alloys with

high strengths, ductility and toughness.

Several hardening techniques are at the

disposal of an engineer

The ability of a metal to plastically deform

depends on the ability of dislocations to move

MECHANISMS OF STRENGTHENING IN METALS

Reducing the mobility of dislocations (limiting

plastic deformation) enhances mechanical

strength

Restricting or hindering dislocation motion

renders a material harder and stronger

STRENGTHENING BY GRAIN SIZE REDUCTION

Grain boundary can act as a barrier to

dislocation motion

Strengthening effect

STRENGTHENING BY GRAIN SIZE REDUCTION

Since two grains are of different orientations, a

dislocation passing into grain B will have to

change its direction of motion (more difficult as

the number of crystals increases)

The atomic disorder within a grain boundary

region will result in a discontinuity of slip

planes from one grain into another

STRENGTHENING BY GRAIN SIZE REDUCTION

Finer-grained material is harder and stronger

than coarse-grained material

Greater total grain boundary area to impede

dislocation motion

HALL-PETCH EQUATION

Yield strength vs. grain size:

σo , ky = constants for particular material

d: grain size

What does equation tell us?

What is d for a single crystal?

SOLID-SOLUTION STRENGTHENING

Technique to harden and strengthen metals

Alloy with impurity atoms (substitutional or

interstitial)

High purity metals are typically softer or weaker

than alloys composed of the same base metal.

WHY ARE ALLOYS STRONGER?

Impurity atoms that go into solid solution

ordinarily impose lattice strains on the

surrounding host atoms.

Lattice strain field interaction between

dislocations and impurity atoms restrict

movement (cancels some of the strain

surrounding a dislocation)

STRAIN HARDENING

Occurs when a ductile metal becomes harder

and stronger as it is plastically deformed (work

hardening, cold working)

Percent Cold Work (degree of plastic

deformation) :

STRAIN HARDENING

Figure 6.17, pg 173

The metal with yield

strength σyo is plastically

deformed to point D

The stress is released,

then reapplied with a

new yield strength σyi.

The metal has become

stronger since σyi > σyo

UNDERSTANDING STRAIN HARDENING

Dislocation density in a metal increases with

deformation or cold work (dislocation

multiplication, formation of new dislocations)

Average distance of separation between

dislocations decreases

Strains between dislocations are repulsive

Motion of dislocation is hindered by the presence of

other dislocations

As strength and hardness increase ductility

decreases.

STRAIN HARDENING

MECHANISMS OF STRENGTHENING IN METALS –

SUMMARY

Strengthening by grain size reduction

Solid-solution strengthening (alloys)

Strain hardening

QUIZ ON MARCH 29

Topic: Resolved Shear Stress