chapter 8 - 1. 2 issues to address... why are the number of dislocations present greatest in metals...
TRANSCRIPT
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