Chapter 8 - 1

Chapter 8 - 3

•Deformation mechanisms proposed to explain the deformation behaviors of metals

•Techniques that may be used to strengthen metals in terms of these deformation mechanisms

ISSUES TO ADDRESS...

Chapter 8 - 5

Plastic deformation:•A net movement of large numbers of atoms in response

to an applied stress

•Interatomic bonds must be ruptured and then reformed

• Early studies: theoretical strengths of perfect crystals are many times greater than their measured strengths!!!

Plastic deformation

Chapter 8 -

Dislocation Motion

• Dislocations: edge, screw and mixed types

• Most often Plastic deformation corresponds to the motion of large numbers of dislocations.

Figure 8.1. Atomic rearrangements that accompany the motion of an edge dislocation as it moves in response to an applied shear stress.

Chapter 8 -

Dislocation Motion

• An edge dislocation (extra half-plane of atoms) slides over adjacent plane half-planes of atoms.

• Slip: The process by which plastic deformation is produced by dislocation motion

• Slip plane: The crystallographic plane along which the dislocation line moves

Chapter 8 -

Dislocation Motion

• In response to an applied shear stress:

An edge dislocation, moves parallel to the stress direction.

A screw dislocation moves perpendicular to the stress direction.

• If dislocations can't move, plastic deformation doesn't occur!

• However, the net plastic deformation for the motion of both dislocation types is the same.

Chapter 8 -

CHARACTERISTICS OF DISLOCATIONS

• Dislocations are introduced during solidification, during plastic deformation, and as a consequence of thermal stresses that result from rapid cooling.

• Dislocation density: the total dislocation length per unit volume, or the number of dislocations that intersect a unit area of a

random section. Carefully solidified metal crystals: 103 mm−2

Heavily deformed metals: 109 to 1010 mm−2

A heat treated deformed metal: 105 to 106 mm−2

Ceramic materials: 102 and 104 mm−2

Silicon single crystals used in ICs: 0.1-1 mm−2

11

Chapter 8 - 12

A lithium fluoride (LiF) single crystal. The small pyramidal pits

represent positions at which dislocations intersect the surface.

CHARACTERISTICS OF DISLOCATIONS

Chapter 8 -

• Strain fields exist around dislocations

• Some atomic lattice distortion

around the dislocation line

There are regions in which

compressive, tensile, and shear

lattice strains are imposed on

the neighboring atoms.

• The strains magnitude decreases with radial distance from the dislocation.

• These influence:the mobility of the dislocations, and their ability to multiply

13

CHARACTERISTICS OF DISLOCATIONS

Figure 8.4. Regions of compression (green) and tension (yellow) around an edge dislocation.

Chapter 8 - 14

CHARACTERISTICS OF DISLOCATIONS

•The strain fields surrounding dislocations may interact

• Two dislocations of the same sign • Identical slip plane

a mutual repulsive force

•Two dislocations of opposite sign• Identical slip plane

a mutual attraction dislocation annihilation.

Chapter 8 - 15

Slip System– Slip plane - plane on which easiest slippage occurs

• Highest planar densities (and large interplanar spacings).

– Slip directions - directions of movement • Highest linear densities

Deformation Mechanisms

– FCC Slip occurs on {111} planes (close-packed) in <110> directions (close-packed)

=> total of 12 slip systems in FCC– For BCC & HCP there are other slip systems.

Chapter 8 - 16

• FCC or BCC crystals: a large number of slip systems (at least 12) Extensive plastic deformation is possible along the various systems Quite ductile

• HCP metals: few active slip systems normally quite brittle

Chapter 8 - 17

Stress and Dislocation Motion

• Resolved shear stress, R: results from applied tensile stresses

slip plane

normal, ns

Resolved shear stress: R =Fs/As

slip

directi

on

AS

R

R

FS

coscosR

• SLIP IN SINGLE CRYSTALS

φ: the angle between the normal to the slip plane and the applied stress direction

λ: the angle between the slip and stress directions

Chapter 8 - 18

• Condition for dislocation motion: CRSS R

• Ease of dislocation motion depends on crystallographic orientation

10-4 GPa to 10-2 GPa

typically

coscosR

• Critical Resolved Shear Stress

maximum at = = 45º

R = 0

=90°

R = /2=45°=45°

R = 0

=90°

Chapter 8 - 19

• Single Crystal Slip

• Slip along a number of equivalent and most favorably oriented planes and directions at various positions along the specimen length

• Each step results from the movement of a large number of dislocations along the same slip plane.

A zinc single crystal

Chapter 8 - 22

• Slip planes & directions (, ) change from one crystal to another. R will vary from one crystal to another.

• The crystal with the largest R yields first.

• Other (less favorably oriented) crystals yield later.

• Two sets of parallel intersecting lines Two slip systems operated for most of the grains

• Note that during deformation, the grain boundaries usually do not come apart or open up.• Stronger - grain boundaries pin deformations.

• Slip Motion in Polycrystals

300 m

Polycrystalline copper

Chapter 8 - 23

• Polycrystals are stronger than single-crystals!

• Each individual grain is constrained by its neighboring grains.

• A single grain may be favorably oriented, but it cannot deform until the adjacent and less favorably oriented grains are capable of slip also.

Before deformation, equiaxed grains

After deformation, elongated grains

• Slip Motion in Polycrystals

Chapter 8 - 27

Mechanisms of Strengthening in Metals

• Hardness and strength (both yield and tensile) are related to the ease with which plastic deformation can be made

•Plastic deformation depends on the ability of dislocations to move

•By reducing the mobility of dislocations, the mechanical strength may be enhanced

•Restrict dislocation motion harder and stronger material

Chapter 8 - 28

• During plastic deformation, slip or dislocation motion must take place across the grain boundaries

• Grain boundaries are barriers to slip:

Barrier "strength“ increases with increasing angle of misorientation.The atomic disorder within a grain boundary region will result in a discontinuity of slip planes.

• Smaller grain size: more barriers to slip.

1. Grain Size Reduction

Mechanisms of Strengthening in Metals

Chapter 8 - 29

•Grain size may be regulated by the solidification rate and by plastic deformation followed by an appropriate heat treatment.

d: the average grain diameter, σ0 and ky are constants for a particular material.

21 /yoyield dk • Hall-Petch Equation:

Chapter 8 - 30

2. Solid Solutions Strengthening

Mechanisms of Strengthening in Metals

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

24 caret gold Vs 18 caret Gold!

Chapter 8 - 32

Substitutional impurity atoms: If smaller than the host atom exert tensile strains on the surrounding crystal lattice

If larger than the host atom exert compressive strains on the surrounding crystal lattice,

A

B

C

D

2. Solid Solutions Strengthening

Chapter 8 - 33

• Solute atoms tend to segregate around dislocations to reduce some of the strain in the lattice surrounding a dislocation.

• Smaller impurity atoms segregate above the slip plane.

• Larger impurity atoms segregate below the slip plane.

• Greater resistance to slip when impurity atoms are present because the overall lattice strain must increase if a dislocation is torn away from them.

2. Solid Solutions Strengthening

Chapter 8 - 34

Solute atoms, reduce mobility of dislocation!

• Greater applied stress is necessary to first initiate and then continue plastic deformation for solid-solution alloys

Increased strength and hardness

• The same lattice strain interactions will exist between impurity atoms and dislocations

that are in motion during plastic deformation.

• Impurity atoms distort the lattice and generate stress.

• Stress can produce a barrier to dislocation motion.

2. Solid Solutions Strengthening

Chapter 8 - 35

• Hard precipitates/phases are difficult to shear. Ex: Carbide/ oxide particles in metals (TiC in Iron or Al2O3 Aluminum, ….)

S~y

1

3. Precipitation Strengthening

Large shear stress needed to move dislocation toward precipitate and shear it.

Dislocation “advances” but precipitates act as “pinning” sites with spacing S

Side View

precipitate

Top View

Slipped part of slip plane

Unslipped part of slip plane

S

Mechanisms of Strengthening in Metals

Chapter 8 - 36

Interaction of a dislocation with solid phase precipitates. The dislocation moves from left to right in each frame.

3. Precipitation Strengthening

•If dislocation can shear the precipitate

Chapter 8 - 38

3. Precipitation Strengthening

•If dislocation can’t shear the precipitate

Chapter 8 - 39

• Internal wing structure on Boeing 767

• Aluminum is strengthened with precipitates (e.g. Al2Cu) formed by alloying and heat treatment.

1.5m

3. Precipitation Strengthening

Chapter 8 - 40

4. Strain hardening/ Work hardening/ Cold working

• Strengthening and hardening of a ductile metal by plastic deformation at close to room temperature

• Cross sectional area changes by forming operations.

Degree of plastic deformation (%CW) :

-Rolling

roll

AoAd

roll

Mechanisms of Strengthening in Metals

-Extrusion

ram billet

container

containerforce

die holder

die

Ao

Adextrusion

Chapter 8 - 41

4. Strain/ Work hardening

Chapter 8 - 42

4. Strain/ Work hardening

Chapter 8 - 43

Ti alloy after cold working

• Dislocation density in a metal increases with deformation or cold working

• Dislocations entangle with one another during cold working.

• Dislocation motion becomes more difficult.

• Thus, the imposed stress necessary to deform a metal increases with increasing cold working.0.9 m

4. Strain/ Work hardening

Chapter 8 - 45

– Carefully grown single crystal

ca. 103 mm-2

– Deforming sample increases density

109-1010 mm-2

– Heat treatment reduces density

105-106 mm-2

• When making hardness measurements, what will be the effect of making an indentation very close to a preexisting indentation? Why?

4. Strain/ Work hardening

Chapter 8 - 47

Tensile strength= 340 Mpa

Ductility=7%

Chapter 8 - 48

• Results for polycrystalline iron:

• YS and TS decrease and %El increases with increasing test temperature.

• Why?

Vacancies help Dislocations move past obstacles.

- Behavior vs. Temp.

2. vacancies replace atoms on the disl. half plane

3. disl. glides past obstacle

-200C

-100C

25C

800

600

400

200

0

Strain

Str

ess

(M

Pa)

0 0.1 0.2 0.3 0.4 0.5

1. disl. trapped by obstacle

obstacle

4. Strain/ Work hardening

Chapter 8 - 49

• 1 hour treatment at Tanneal … decreases TS and increases %El.• Effects of cold work are reversed!

3 Annealing stages!

Holding time has a similar effect.

Effect of Heating After %CW

TR = Recrystallization Temp.= point of highest rate of

property change

Chapter 8 - 50

• Annihilation reduces dislocation density:

• Recovery

Scenario 1

4. opposite dislocations

meet and annihilate

2. grey atoms leave by vacancy diffusion allowing dislocation to“climb”

R

1. dislocation blocked; can’t move to the right

Obstacle (dislocation or particle)

3. “Climbed” disl. can now move on new slip plane

Scenario 2Results from diffusion

Dislocations annihilate and form a perfect atomic plane.

extra half-plane of atoms

extra half-plane of atoms

atoms diffuse to regions of tension

Chapter 8 - 51

• New grains are formed that: -- have a small dislocation density -- are small -- consume cold-worked grains.

33% cold worked brassNew crystals nucleate after 3 sec. at 580C

0.6 mm 0.6 mm

• Recrystallization

Chapter 8 - 52

• All cold-worked grains are consumed.

After 4 seconds at 580C After 8 seconds at 580C

0.6 mm0.6 mm

• Recrystallization

Chapter 8 - 53

• TR 0.3 - 0.6 Tm (K)

• Recrystallization

Chapter 8 - 54

• Recrystallization

Chapter 8 - 55

• At longer times, larger grains consume smaller ones. • Why? Grain boundary area (and therefore energy) is reduced.

After 10 min, 700ºCAfter 15 min, 580ºC

0.6 mm 0.6 mm

• Grain Growth

Chapter 8 - 56

• Empirical Relation (Ostwald Ripening):

Ktdd no

n elapsed time

Coefficient dependenton material and Temp.

grain diam.at time t

exponent = ~ 2

• Grain Growth

Chapter 8 - 57

Chapter 8 - 58

Chapter 8 - 59

Chapter 8 - 74

• Dislocations are observed primarily in metals and alloys.• Strength is increased by making dislocation motion difficult.

• Particular ways to increase strength are to: -- decrease grain size -- solid solution strengthening -- precipitate strengthening -- cold work

• Heating (annealing) can reduce dislocation density and increase grain size. This decreases the strength.

Summary