Chapter 7: Dislocations & Strengthening...

Chapter 7Dislocations & Strengthening Mechanisms

11/14/2015

11:31 AM

Mohammad Suliman Abuhaiba, Ph.D., PE1

HomeWork Assignment

7, 12, 17, 24, 29, 41, D7

Due Sunday 8/11/2015

4th Exam is on Tuesday 17/11/2015

11/14/2015 11:31 AM

Mohammad Suliman Abuhaiba, Ph.D., PE

2

WHY STUDY Dislocations and Strengthening Mechanisms?

Understand techniques used to

strengthen & harden metals and

their alloys

Design & tailor mechanical

properties of materials

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WHY STUDY Dislocations and Strengthening Mechanisms?

Strengthening mechanisms will be

applied to the development of

mechanical properties for steel alloys

Why heat treating a deformed metal

alloy makes it softer & more ductile

and produces changes in its

microstructure

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1. Describe edge & screw dislocation motion

2. Describe how plastic deformation occurs by

motion of edge & screw dislocations in response

to applied shear stresses

3. Define slip system

4. Describe how grain structure of a polycrystalline

metal is altered when it is plastically deformed.

5. Explain how grain boundaries impede dislocation

motion & why a metal having small grains is

stronger than one having large grains.

Learning Objectives

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5. Describe & explain solid-solution strengthening

for substitutional impurity atoms in terms of lattice

strain interactions with dislocations

6. Describe & explain phenomenon of strain

hardening in terms of dislocations and strain field

interactions.

7. Describe recrystallization in terms of both

alteration of microstructure & mechanical

characteristics of the material

8. Describe phenomenon of grain growth from both

macroscopic and atomic perspectives.

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Learning Objectives

7.2 BASIC CONCEPTS

Dislocation MotionCubic & hexagonal metals - plastic deformation is

by plastic shear or slip where one plane of atoms

slides over adjacent plane by dislocations motion.

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7.3 Characteristics of Dislocations

When metals are plastically

deformed:

Around 5% of deformation energy is

retained internally

remainder is dissipated as heat

Major portion of stored energy is

strain energy associated with

dislocations

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Figure 7.4: some atomic lattice distortion exists

around dislocation line because of presence of

extra half-plane of atoms.


Atoms immediately above and

adjacent to dislocation line are

squeezed together.

These atoms may be thought of as

experiencing a compressive strain relative

to atoms positioned in the perfect crystal

and far removed from the dislocation

Directly below half-plane, lattice

atoms sustain an imposed tensile strain

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Shear strains also exist in the vicinity of

edge dislocation

For a screw dislocation, lattice strains are

pure shear only

Consider lattice distortions as strain fields

that radiate from the dislocation line

Strains extend into the surrounding atoms,

and their magnitude decreases with radial

distance from the dislocation.

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7.3 Characteristics of DislocationsStrain fields surrounding

Figure 7.5 (a): Two edge dislocations of same sign

& lying on same slip plane exert a repulsive force

on each other

Compressive & tensile strain fields for both lie on

same side of the slip plane; there exists between

these two isolated dislocations a mutual repulsive

force that tends to move them apart

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Figure 7.5 (b) Edge dislocations of opposite

sign & lying on same slip plane exert an

attractive force on each other. Upon

meeting, they annihilate each other and

leave a region of perfect crystal

7.3 Characteristics of Dislocationsstrain fields surrounding

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7.4 Slip Systems Slip plane - plane allowing easiest slippage

Wide inter-planar spacing - highest planar densities

Slip direction - direction of movement - Highest

linear densities

FCC Slip occurs on {111} planes in <110> directions

=> total of 12 slip systems in FCC

in BCC & HCP other slip systems occur

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Table 7.1: Slip Systems for FCC,

BCC, and HCP Metals

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7.5 Slip in Single Crystals

coscosR

Crystals slip due to a

resolved shear stress, R.

Applied tension can

produce such a stress.

= angle between

stress direction & Slip

direction

= angle between

stress direction &

normal to slip plane

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Condition for dislocation motion: CRSS R

Crystal orientation can make it

easy or hard to move dislocation

10-4 GPa to 10-2 GPa

typically

coscosR

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Critical Resolved Shear Stress

R = 0

=90°

R = /2=45°=45°

R = 0

=90°

7.5 Slip in Single Crystals

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Resolved (shear stress) ismaximum at = = 45º

And

CRSS = y/2 for dislocations tomove (in single crystals)

Determining & angles for Slip in

Crystals

For cubic crytals, angles betweendirections are given by:

1 1 2 1 2 1 2

2 2 2 2 2 2

1 1 1 2 2 2

u u v v w wCos

u v w u v w

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EXAMPLE PROBLEM 7.1Consider a single crystal of BCC iron oriented

such that a tensile stress is applied along a

[010] direction.

a. Compute the resolved shear stress along a

(110) plane and in a direction when a

tensile stress of 52 MPa is applied.

b. If slip occurs on a (110) plane and in a [-

111] direction, and the critical resolved

shear stress is 30MPa, calculate magnitude

of the applied tensile stress necessary to

initiate yielding.

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Stronger since grain boundaries

pin deformations

Slip planes & directions (, )

change from one crystal to

another

R will vary from one crystal to

another.

Crystal with largest R yields first

Other (less favorably oriented)

crystals yield (slip) later.

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7.6 Plastic Deformation ofPolycrystalline Materials

300 mm

7.6 Plastic Deformation of Polycrystalline Materials

Ordinarily ductility is sacrificed when analloy is strengthened.

The ability of a metal to plasticallydeform depends on the ability ofdislocations to move.

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7.6 Plastic Deformation of Polycrystalline Materials

Strengthening principle: Restricting orHindering dislocation motion renders amaterial harder & stronger

We will consider strengthening singlephase metals by:

1. Grain size reduction

2. Solid-solution alloying

3. Strain hardening

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7.8 Strengthening by Grain Size Reduction

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Grain boundaries are barriers to slip

Barrier "strength" increases with Increasing

angle of mis-orientation.

Smaller grain size: more barriers to slip

Hall-Petch equation:

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21 /

yoyield dk

7.8 Strengthening by Grain

Size Reduction

Figure 7.15: Influence

of grain size on yield

strength of a 70 Cu–

30 Zn brass alloy

D-1/2, (mm-1/2)

Yie

ld S

tren

gth

(M

Pa

)

Yie

ld S

trength

(K

si)

Increase Rate of solidification from liquid phase

Perform Plastic deformation followed by an

appropriate heat treatment

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7.8 Strengthening by Grain Size

ReductionGrain Size Reduction Techniques:

Grain size reduction improves toughness of many

alloys.

Small-angle grain boundaries are not effective in

interfering with the slip process because of small

crystallographic misalignment across the boundary.

Boundaries between two different phases are also

impediments to movements of dislocations.

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7.8 Strengthening by Grain Size Reduction

Impurity atoms distort the lattice & generate stress.

Stress can produce a barrier to dislocation motion.

7.9 Solid-solution Strengthening

• Smaller substitutional

impurity

Impurity generates local stress at A

and B that opposes dislocation

motion to the right.

A

B

• Larger substitutional

impurity

Impurity generates local stress at C

and D that opposes dislocation

motion to the right.

C

D

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small impurities tend to concentrate at

dislocations on the “Compressive stress side”

reduce mobility of dislocation increase

strength

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Large impurities concentrate at dislocations on

“Tensile Stress” side – pinning dislocation


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• Tensile strength & yield strength increase with wt% Ni.

• Empirical relation:

• Alloying increases y and TS

21 /

y C~

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-Forging

Ao Ad

force

die

blank

force

7.10 Strain Hardening Low temperature (varies with material) deformation

Common forming operations change cross

sectional area:

-Drawing

tensile force

Ao

Addie

die

-Extrusion

ram billet

container

container

forcedie holder

die

Ao

Adextrusion

100 x %o

do

A

AACW

-Rolling

roll

Ao

Adroll

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Ti alloy after cold working:

Dislocations entangle &

multiply

Thus, Dislocation motion

becomes more difficult

0.9 mm

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7.10 Strain Hardening

Dislocation density =

Carefully grown single crystal

up to 103 mm / mm3

Deforming sample increases density

109-1010 mm / mm3

Heat treatment reduces density

105-106 mm / mm3

Yield stress increases as rd increases

total dislocation length

unit volume

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Figure 7.20:

influence of cold

work on stress

strain behavior of a

low-carbon steel

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What is the tensile strength & ductility after cold

working?

%6.35100 x %2

22

o

do

r

rrCW

Cold Work Analysis

Do =15.2mm Dd =12.2mm

Copper Cold Work

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Results for polycrystalline iron:

y & TS decrease with increasing temperature

%EL increases with increasing temperature

- e Behavior vs. Temperature

-200C

-100C

25C

800

600

400

200

0

Strain

Str

ess (

MP

a)

0 0.1 0.2 0.3 0.4 0.5

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Recovery, Recrystallization,

and Grain Growth

Properties & structures may revert back to

the precold-worked states by appropriate

heat treatment (annealing treatment).

Restoration results from different processes

that occur at elevated temperatures:

1. Recovery

2. Recrystallization

3. Grain growth

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1 hour treatment at

Tanneal... decreases TS and

increases %EL.

Effects of cold work

are reversed!

3 Annealing stages

to discuss...

Recovery, Recrystallization, & Grain

Growth

ten

sile

str

en

gth

(M

Pa

)

du

ctilit

y (

%E

L)tensile strength

ductility

600

300

400

500

60

50

40

30

20

Annealing Temperature (ºC)200100 300 400 500 600 700

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7.11 RECOVERYDuring recovery, some of the stored internal strain

energy is relieved by virtue of dislocation motion,

due to enhanced atomic diffusion at elevated

temperature.

There is some reduction in number of dislocations,

and dislocation configurations are produced

having low strain energies.

Physical properties such as electrical and thermal

conductivities are recovered to their precold-

worked states.

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Even after recovery is complete, grains are still

in a relatively high strain energy state.

Recrystallization = formation of a new set of

strain-free and equiaxed grains that have

low dislocation densities and are

characteristic of the pre-cold-worked condition.

7.12 Recrystallization

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The driving force to produce this new grain

structure is the difference in internal energy

between the strained and unstrained

material.

The new grains form as very small nuclei and

grow until they completely consume the

parent material, processes that involve short-

range diffusion.


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33% cold

worked

brass

New crystals

nucleate after

3 sec. at 580C.

0.6 mm 0.6 mm


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Figure 7.21

All cold-worked grains are consumed.

After 4

seconds

After 8

seconds

0.6 mm0.6 mm

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Recrystallization temperature =

temperature at which recrystallization just

reaches completion in 1 h.

Recrystallization temperature for brassalloy of Figure 7.22 is about 450°C.

Typically, TR = 1/ 3 to 1 / 2 Tm

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TR

º

º

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Figure 7.22: Annealing

temperature influence

(for an annealing time

of 1 h) on tensile

strength & ductility of a

brass alloy.


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Figure 7.23

Critical degree

of CW below

which

recrystallization

cannot be

made to occur

(between 2%

and 20% CW)

Recrystallization proceeds more

rapidly in pure metals than in

alloys.

During recrystallization, grain

boundary motion occurs as the

new grain nuclei form and then

grow.

For pure metals, TRC = 0.4Tm

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At longer times, larger

grains consume

smaller ones.

Grain boundary area

(and therefore energy)

is reduced.

Empirical Relation:

After 8 s,

580ºC

After 15 min,

580ºC

0.6 mm 0.6 mm

7.13 Grain Growth

Ktdd n

o

n

coefficient dependent on

material & Temp.

grain dia. At time t.

elapsed timeexponent typ. ~ 2

This is: Ostwald Ripening

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Design Example 7.1

A cylindrical rod of non-cold-worked brass

having an initial diameter of 6.4 mm is to be

cold worked by drawing such that the cross-

sectional area is reduced. It is required to

have a cold-worked yield strength of at least

345 MPa and a ductility in excess of 20 %EL; in

addition, a final diameter of 5.1 mm is

necessary. Describe the manner in which this

procedure may be carried out.

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Chapter 7: Dislocations & Strengthening...

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