mse 3300-lecture note 12-chapter 07 dislocation and strengthening mechanisms

8/18/2019 MSE 3300-Lecture Note 12-Chapter 07 Dislocation and Strengthening Mechanisms

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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 -

Lecture 12. Dislocations andStrengthening Mechanisms (2)Learning Objectives

After this lecture, you should be able to do the following:

1. Explain how grain boundaries impede dislocation motion and why a

metal having small grains is stronger (grain size reduction).

2. Describe solid-solution strengthening for substitutional impurity atoms

(solid-solution alloying).

3. Explain the phenomenon of strain hardening (or cold working) in terms

of dislocations and strain field interactions.

Reading

• Chapter 7: Dislocations and Strengthening Mechanisms (7.8–7.13)

Multimedia

• Virtual Materials Science & Engineering (VMSE):

http://www.wiley.com/college/callister/CL_EWSTU01031_S/vmse/

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Mechanisms of Strengthening in

Metals

2

• Early materials studies: the theoretical strengths of perfect crystals are many

times greater than those actually measured.

• The discrepancy could be explained by a type of linear crystalline defect:

dislocation (1930s).

• Design materials to have high strength yet some ductility and toughness


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1. Elastic Deformation• Elastic deformation is nonpermanent: when the applied load is released, the

piece returns to its original shape (not breaking atomic bonds).

• Hooke’s Law

E [Pa]: Modulus of elasticity, or Young’s modulus

3

Linear elastic deformation Nonlinear elastic deformation


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Yield Strength,σ

y

4

• Yield strength: The stress level at which plastic deformation begins, or

yielding occurs.

P: Proportional limit

(onset of plastic

deformation at the

microscopic level

Strain offset of 0.002

Yield Strength, σ y

Yield point phenomenon

* Yield stress for nonlinear elastic deformation

(Figurer 6.6): stress required to produce some

amount of strain (e.g., =0.005)


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MSE 3300 / 5300 UTA Fall 2014 Lecture 12 - 5

Tensile Strength, TS

• Metals: occurs when noticeable necking starts.

• Polymers: occurs when polymer backbone chains are aligned and about to break.

• Tensile strength: Maximum

stress on engineering

stress-strain curve;

maximum stress that can besustained by the structure in

tension

• If this stress is applied,

fracture will result.Necking

TS

F = Fracture or ul timate

strength

Neck acts as stress

concentrator; fracture

occurs at the neck.

M = Tensile strength (TS)


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Ductility

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S t r e s s

Strain

• Ductility: Measure of the degree

of plastic deformation that has

been sustained at fracture

• Brittle: little or not plastic

deformation (approximately, afracture strain < 5%)

• Ductility usually increases with

temperature.

• Percent elongation

• Percent reduction in area

1. It indicates the degree to which a structure will deform plastically before fracture

2. It specifies the degree of allowable deformation during fabrication operations


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• Tensile toughness: Measure of the ability of the material to absorb energy

without fracture

• The area under the entire stress-strain curve up to fracture (Unit: J/m3)

• Fracture toughness: Material’s resistance to fracture when a crack (or otherdefect) is present

Measures of Energy Capacity 2:

Toughness

Brittle fracture: elastic energy

Ductile fracture: elastic + plastic energy

very small toughness(unreinforced polymers)

Engineering tensile strain, e

Engineering

tensile

stress, σ

small toughness (ceramics)

large toughness (metals):strength + ductili ty

f

d U f

0


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Measures of Energy Capacity 1:

Resilience

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S t r e

s s

Strain

• Resilience: Capacity of a material to absorb

energy when it is deformed elastically and

then, upon, unloading, to have the energy

recovered.

• Modulus of resilience [J/m3] Measure of

the ability of material to store elastic energy;

Strain energy per unit volume required to

stress a material from an unloaded state upto the point of yielding

y

d U r

0


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Mechanisms of Strengthening in

Metals

9

• Early materials studies: the theoretical strengths of perfect crystals are many

times greater than those actually measured.

• The discrepancy could be explained by a type of linear crystalline defect:

dislocation (1930s).

• Design materials to have high strength yet some ductility and toughness

• Strengthening mechanisms: Relation between dislocation motion and

mechanical behavior of metals

• Macroscopic plastic deformation: motion of large numbers of dislocations; theability of a metal to deform plastically depends on the ability of dislocations to

move.

- Reduce the mobility of dislocations enhance mechanical strength

• Principles: Restricting or hindering dislocation motion renders a material

harder and stronger (1) Grain size reduction

(2) Solid-solution alloying

(3) Strain hardening


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1. Mechanism of Strengthening:

Grain Size Reduction

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• The size of the grains, or average grain diameter, in a polycrystalline metal

influence the mechanical properties. Why?

• Grain boundary: Barrier to dislocation motion(1) When crossing a grain boundary, a dislocation’s direction of motion must change.

(2) There is a discontinuity of slip planes within the vicinity of a grain boundary.

Slip planes are discontinuous andchange directions across the

boundary

For high angle grain boundaries,

dislocations tend to “pile up” at

the boundaries, which introduce

stress concentration and

generate new dislocations in

adjacent grains.


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Hall-Petch equation

The yield strength varies withgrain size:

where d is the average grain

diameter.

* A metal that has small grains is

stronger than one with largegrains because the former has

more grain boundary area (more

barriers to dislocation motion).

Mechanism of Strengthening:

Grain Size Reduction

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Strategies for Strengthening:

1: Reduce Grain Size

• Grain boundaries are

barriers to slip.• Barrier "strength"

increases with

Increasing angle of

misorientation.

• Smaller grain size:

more barriers to slip.

• Hall-Petch Equation:

Fig. 7.14, Callister & Rethwisch 9e.(From L. H. Van Vlack, A Textbook of Materials

Technology , Addison-Wesley Publishing Co., 1973.

Reproduced with the permission of the Estate of

Lawrence H. Van Vlack.)


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Grain Size Influences Properties

• Metals having small grains – relatively strong

and tough at low temperatures

• Metals having large grains – good creep

resistance at relatively high temperatures

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Solid-Solution Strengthening

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• Solid-solution strengthening: Alloying with impurity atoms that go into either

substitutional or interstitial solid solution.

• Solid-solution strengthening results from lattice strain interactions between

impurity atoms and dislocations; these interactions decrease dislocationmobility.

(a) Tensile lattice strains imposed on

host atoms. (b) Partial cancellation of

impurity-dislocation lattice strains.

(a) Compressive strains imposed on

host atoms. (b) Partial cancellation of

impurity-dislocation lattice strains.


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Dislocation Motion: Edge Dislocation

Dislocation motion and plastic deformation

• Metals - plastic deformation occurs by slip: an edge dislocation (extra

half-plane of atoms) slides over adjacent plane half-planes of atoms.

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


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Solid-Solution Strengthening

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• Solid-solution strengthening: Alloying with impurity atoms that go into either

substitutional or interstitial solid solution


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Lattice Strains Around Dislocations

Fig. 7.4, Callister & Rethwisch 9e.(Adapted from W.G. Moffatt, G.W. Pearsall, and J. Wulff,

The Structure and Properties of Materials, Vol. I, Structure,

p. 140, John Wiley and Sons, New York, 1964.)


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Strengthening by Solid

Solution Alloying• Small impurities tend to concentrate at dislocations

(regions of compressive strains) - partial cancellation ofdislocation compressive strains and impurity atom tensile strains

• Reduce mobility of dislocations and increase strength

Fig. 7.17, Callister &

Rethwisch 9e.


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Strengthening by Solid

Solution Alloying• Large impurities tend to concentrate at

dislocations (regions of tensile strains)


Rethwisch 9e.


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VMSE Solid-Solution Strengthening Tutorial

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Ex: Solid Solution

Strengthening in Copper • Tensile strength & yield strength increase with wt% Ni.

• Empirical relation:

• Alloying increases σ y and TS.

Adapted from Fig.

7.16 (a) and (b),

Callister &

Rethwisch 9e.

T e n s i l e

s t r e n g t h ( M P

a )

wt.% Ni, (Concentration C )

200

300

400

0 10 20 30 40 50 Y i e l d

s t r e n g t h ( M P a

)

wt.%Ni, (Concentration C )

60

120

180

0 10 20 30 40 50


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Strain Hardening

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• Strain hardening: The enhancement of strength (and decrease of ductility) of

a metal as it is deformed plastically deformed (cold working or work

hardening)

>

• Percent cold work (%CW):

Degree of plastic deformation


Rethwisch 9e.

S t r e s

s

Strain

3. Reapplyload

2. Unload

D

Elastic strain

recovery

1. Load

σ y o

σ y i


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Strain Hardening

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• Strain hardening: A ductile metal becomes harder and stronger as it is

plastically deformed (cold working or work hardening)


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Strategies for Strengthening:

Cold Work (Strain Hardening)

• Deformation at room temperature (for most metals).

• Common forming operations reduce the cross-sectional

area:

Adapted from Fig.11.9, Callister &

Rethwisch 9e.

-Forging

Ao Ad

force

die

blank

force-Drawing

tensileforce Ao

Ad die

die

-Extrusion

ram billet

container

container

force

die holder

die

Ao

Ad extrusion

-Rolling

roll

Ao

Ad roll


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• Dislocation structure in Ti after cold working.

• Dislocations entangle with one another

during cold work.

• Dislocation motion becomes more

difficult.

• During plastic deformation, dislocation

density increases, the average

distance between dislocationsdecreases, and, because dislocation-

dislocation strain field interactions are

on average repulsive, dislocation

mobility becomes more restricted; thus

the metal becomes harder andstronger.

Dislocation Structures Change

During Cold Working


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Dislocation Density Increases

During Cold Working

Dislocation density =

– Carefully grown single crystals

ca. 103 mm-2

– Deforming sample increases density 109-1010 mm-2

– Heat treatment reduces density

105

-106

mm-2

• Yield stress increases as ρd increases:

total dislocation length

unit volume


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Impact of Cold Work

Adapted from Fig. 7.20,

Callister & Rethwisch 9e.

• Yield strength (σ y) increases.

• Tensile strength (TS) increases.

• Ductility (%EL or % AR ) decreases.

As cold work is increased

low carbon steel


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• What are the values of yield strength, tensile strength &

ductility after cold working Cu?

Mechanical Property Alterations

Due to Cold Working

Do = 15.2 mm

Cold

Work

Dd = 12.2 mm

Copper

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Mechanical Property Alterations

Due to Cold Working

% Cold Work

100

300

500

700

Cu

200 40 60

σ y = 300 MPa

300 MPa

% Cold Work

200

Cu

0

400

600

800

20 40 60

% Cold Work

20

40

60

20 40 6000

Cu340 MPa

TS = 340 MPa

7%

%EL = 7%

• What are the values of yield strength, tensile strength &

ductility for Cu for %CW = 35.6%?

y i e l d s t r e

n g t h ( M P a )

t e n s i l e s t r e

n g t h ( M P a )

d u c t i l i t

y ( % E L )

Fig. 7.19, Callister & Rethwisch 9e. [Adapted from Metals Handbook: Properties and Selection: Ironsand Steels, Vol. 1, 9th edition, B. Bardes (Editor), 1978; and Metals Handbook: Properties and Selection: Nonferrous

Alloys and Pure Metals, Vol. 2, 9th edition, H. Baker (Managing Editor), 1979. Reproduced by permission of ASM

International, Materials Park, OH.]29


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Summary

1. Plastic deformation and dislocation mobility:

Restricting dislocation motion leads to increased

hardness and strength

2. Mechanisms of Strengthening in Metals:

(1) Grain size reduction

(2) Solid-solution alloying

(3) Strain hardening

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mse 3300-lecture note 12-chapter 07 dislocation and strengthening mechanisms

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