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Chapter 9: Dislocations & Strengthening Mechanisms

ISSUES TO ADDRESS

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9.2 Basic Concepts

Plastic deformation corresponds to the motion of large numbers ofdislocations.Dislocation motion is easier in metals rather than in ceramics.

In metals, plastic deformation occurs by slip – an edge dislocation (extra halfplane of atoms) slides over adjacent plane half planes of atoms.

Callister & Rethwisch 9e.

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9.2 Basic Concepts

A dislocation moves along a slip plane in a slip direction perpendicular to thedislocation line.The slip direction is the same as the Burgers vector direction.

Dislocation density

Callister& Rethwisch 9e.

Callister & Rethwisch 9e.)

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Whenmetals are plastically deformed, some fraction of the deformationenergy (approximately 5%) is retained internally; the remainder is dissipatedas heat.The main portion of the stored energy is the strain energy associated withdislocations.

9.3 Characteristics of Dislocations

Callister & Rethwisch 9e.)

Callister & Rethwisch 9e.)

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9.4 Slip Systems

Slip System

Burgers vector, b: unit slip distance in sip directionb b b

Callister & Rethwisch 9e.

Callister & Rethwisch 9e.

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9.5 Slip in Single Crystals

Resolved shear stress, R

ns

R Fs As

AS

R

R

FS

R

R FS AS

F A

F

FS

nS

ASA

coscosRCallister & Rethwisch 9e.

90 general,In

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Critical Resolved Shear Stress (Peierls Stress)

Condition for dislocation motion:CRSSR

coscosR

R R R

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Single Crystal Slip

Callister & Rethwisch 9e. Callister & Rethwisch 9e.

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9.6 Plastic Deformation of Polycrystalline Materials

Callister & Rethwisch 9e.

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Anisotropy in yield stress can be induced by rolling a polycrystalline metal

Anisotropy in Yield Strength

Callister & Rethwisch 9e.

Rolling direction

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Mechanisms of Strengthening in Metals

Strength vs. Ductility and Toughness

Four Strategies for Strengthening:

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9.8 Strengthening by Grain Size Reduction

Grain boundary (GB) acts as a barrierto dislocation motion.

Hall Petch Equation:

dk

Callister & Rethwisch 9e.

2/10 dkYY

d

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9.9 Solid Solution Strengthening

Alloys are stronger than pure metalsbecause impurity atoms that go into solidsolution typically impose lattice strainson the surrounding host atoms.

Small impurities tend to concentrate atregions of compressive strains neardislocations.

Large impurities tend to concentrate atregions of tensile strains neardislocations.

Lattice strains around a dislocation

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Example: Solid Solution Strengthening in Copper

2/1 ~ CY

Callister &Rethwisch 9e.

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Hard precipitates are difficult to shear.

SY1~

Precipitation Strengthening

SS

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9.10 Strain Hardening

Cold Working

Forging

A Ad

Drawing

AAd

ExtrusionA

Ad

Rolling

AAd

Callister & Rethwisch 9e.100 %

0

0

AAACW d

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Callister & Rethwisch 9e.

Effect of Cold Working

Dislocation structures changeduring cold working

Dislocation density increasesduring cold working

Dislocation structure in Ti after cold working

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Impact of ColdWork

Callister & Rethwisch 9e.

y

TS

EL AR

As cold work is increased

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Mechanical Property Alterations Due to ColdWork

What are the values of yield strength, tensile strength & ductility for Cufor %CW = 35.6%?

TS EL =

EL

Callister & Rethwisch 9e. Metals Handbook: Properties and Selection: Ironsand Steels Metals Handbook: Properties and Selection:Nonferrous Alloys and Pure Metals

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Callister & Rethwisch 9e.

Effect of Heat Treating After ColdWorking

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9.11 Recovery

R

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New grains are formed that:

Callister & Rethwisch 9e.

9.12 Recrystallization

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As Recrystallization Continues…

All cold worked grains are eventually consumed/replaced.

Callister & Rethwisch 9e.

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Grain Growth

At longer times, average grain size increases.

Empirical Relation:

d

n

K

t

Callister & Rethwisch 9e.

Ktdd nn0

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TR

Callister & Rethwisch 9e.

Recrystallization Temperature

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Problem: Diameter Reduction Procedure

EL

Do Df

%8.43100 x 10

5.71100 x 44

1

100 1100 x %CW

2

2

2

o

f

o

f

o

fo

DD

xAA

AAA

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Diameter Reduction Procedure (Continued)

540

y

TS

6

EL

Fig. 9.19, Callister & Rethwisch 9e. [Adapted from Metals Handbook: Properties and Selection: Irons and 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.]

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Diameter Reduction Procedure (Continued)

380

12

15

27

EL

TSFig. 9.19, Callister & Rethwisch 9e. [Adapted from Metals Handbook: Properties and Selection: Irons and 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.]

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Diameter Reduction Procedure (Continued)

Cold work, then anneal, then cold work again!For objective we need a cold work of 12 <%CW < 27: We ll use 20%CW.Diameter after the first cold work stage (but before the second cold workstage) is calculated as follows:

100%CW1 100 1%CW 2

02

22

202

22

DD

xDD ff

mm 39.8100201mm 5.7

5.0

021 DDf

5.0

02

2

100%CW1

DDf

5.02

02

100%CW1

fDD

Diameter Reduction Procedure – Summary

20100 49.85.71%CW

2

2

24%MPa 400MPa 340

ELTS

Y

330 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Summary

Dislocations are observed primarily in metals and alloys.Strength is increased by making dislocation motion difficult.Strength of metals may be increased by:

Cold Working vs. Hot Working

A cold workedmetal that is heat treated may experience recovery,recrystallization, and grain growth – its properties will be altered.Grain size influences properties

Three annealing stages: Recovery, Recrystallization, and Grain Growth.