MSNE 301 midterm #2 review October 2019

Chapter 16 -

MSNE 301 midterm #2 review October 2019

1

Chapter 6 - 2

DiffusionDiffusion - Mass transport by atomic motion

• Interdiffusion - diffusion of atoms of one material into another material

• Self-diffusion – atomic migration in a pure metal

• Diffusion Mechanisms- Gases & Liquids – random (Brownian) motion- Solids – vacancy diffusion and interstitial

diffusion

Chapter 6 - 3

• Atoms tend to migrate from regions of high concentration to regions of low concentration.

Before diffusion

Figs. 6.1 & 6.2, Callister & Rethwisch 5e.

Diffusion

After diffusion

Concentration Profiles

Chapter 6 - 4

Diffusion Mechanism I

• atoms and vacancies exchange positions • applies to host and substitutional impurity atoms • diffusion rate depends on: -- number of vacancies -- activation energy to exchange.

increasing elapsed time

Vacancy Diffusion

Chapter 6 - 5

Diffusion Mechanism II

• Small, interstitial atoms move from one interstitial position to an adjacent one

More rapid than vacancy diffusionFig. 6.3 (b), Callister & Rethwisch 5e.

Interstitial Diffusion

Chapter 6 - 6

Rate of Diffusion• Diffusion is a time-dependent process.• Rate of Diffusion - expressed as diffusion flux, J

M =mass

diffusedtime

• Measured experimentally– Use thin sheet (or membrane) – cross-sectional area A– Impose concentration gradient across sheet– Measure mass of diffusing species (M) that passes through

the sheet over time period (t)

Chapter 6 - 7

Steady-State Diffusion

Fick’s first law of diffusionC1

C2

x

C1

C2

x1 x2

D = diffusion coefficient

Rate of diffusion (or flux) independent of timeFlux (J) proportional to concentration gradient:

C = concentrationx = diffusion direction

C

Chapter 6 - 8

Influence of Temperature on Diffusion

• Diffusion coefficient increases with increasing T

D = Do exp − Qd

RT

= pre-exponential [m2/s]= diffusion coefficient [m2/s]

= activation energy [J/mol] = gas constant [8.314 J/mol-K]= absolute temperature [K]

DDo

Qd

RT

Chapter 6 - 9

transform data

D

Temp = T

ln D

1/T

Influence of Temperature on Diffusion (cont.)

take natural log of both sides

Chapter 6 - 10


Adapted from Fig. 6.7, Callister & Rethwisch 5e. (Data for Fig. 6.7 taken from E.A. Brandes and G.B. Brook (Ed.) Smithells Metals Reference Book, 7th ed., Butterworth-Heinemann, Oxford, 1992.)

D has exponential dependence on T

Dinterstitial >> DsubstitutionalC in α-FeC in γ-Fe

Al in AlFe in α-FeFe in γ-Fe

1000 K/T

D (m2/s) C in α-Fe

C in γ-Fe

Al in

Al

Fe in α-Fe

Fe in γ-Fe

0.5 1.0 1.510-20

10-14

10-8T(°C)15

00

1000

600

300

Chapter 6 - 11


Subtracting equation at T1 from equation at T2

Derive an equation relating the diffusion coefficients at two temperature T1 and T2 using the equation derived on slide 15.

Take the exponential of each side to get the final equation

Chapter 6 - 12

Non-steady State Diffusion

• The concentration of diffusing species is a function of both time and position C = C(x,t)

• For non-steady state diffusion, we seek solutions to Fick’s Second Law

Fick’s Second Law

This form of the equation assumes D is independent of concentration

Chapter 6 - 13

Non-steady State Diffusion

Fig. 6.5, Callister & Rethwisch 5e.

at t = 0, C = Co for 0 ≤ x ≤ ∞

at t > 0, C = CS for x = 0 (constant surface conc.)

C = Co for x = ∞

• Consider the diffusion of copper into a bar of aluminum

pre-existing conc., Co of copper atoms

Surface conc., C of Cu atoms bars

Cs

Boundary/Initial Conditions

Chapter 6 - 14

• Fick’s First Law of Diffusion

• Solid-state diffusion is mass transport within solid materials by stepwise atomic motion

Summary

• Two diffusion mechanisms - Vacancy diffusion - Interstitial diffusion

• Fick’s Second Law of Diffusion - non-steady state diffusion

• Diffusion coefficient - Effect of temperature

Chapter 6 - 15https://en.wikipedia.org/wiki/Dama

scus_steel

https://en.wikipedia.org/wiki/Damascus_steel

https://en.wikipedia.org/wiki/Damascus_steel

Chapter 7 - 16

ISSUES TO ADDRESS...• When a metal is exposed to mechanical forces, what parameters are used to express force magnitude and degree of deformation?• What is the distinction between elastic and plastic deformations? • How are the following mechanical characteristics of metals measured?

(a) Stiffness(b) Strength(c) Ductility(d) Hardness

• What parameters are used to quantify these properties?

Chapter 7: Mechanical Properties

Chapter 7 - 17

• Simple tension:

Δl = Fl oEAo

Δd = - ν FdoEAo

• Deflection is dependent on material, geometric, and loading parameters.• Materials with large elastic moduli deform less

Useful Linear Elastic Relationships

Ao

Adapted from Fig. 7.9, Callister & Rethwisch 5e.

Chapter 7 - 18

Elastic deformation is nonpermanent and reversible!

Elastic Deformation

2. Small load

Force, F

Δl

bonds stretch

1. Initial 3. Unload

return to initial

F

Δl

Linear- elastic

Non-Linear-elastic

Atomic configurations—before, during, after load (force) application

= metal atom

Chapter 7 - 19

Linear Elastic Properties

• Hooke's Law:σ = E ε

σ

Linear- elastic

• Modulus of Elasticity, E: (also known as Young's modulus)

E

ε

• Elastic deformation is nonpermanent and reversible! – generally valid at small deformations – linear stress strain curve

compression

tension

Units:E: [GPa] or [psi]1 GPa = 109 Pa

Chapter 7 - 20

Plastic Deformation

• Stress-strain plot for simple tension test:

stress, σ

strain, ε

Stressed into Plastic Region,Elastic + Plastic

εp

plastic strain

ElasticDeformation

Adapted from Fig. 7.10(a),Callister & Rethwisch 5e.

Stress Removed, Plastic Deformation Remains

• Plastic Deformation is permanent and nonrecoverable

Chapter 7 - 21

• Yield strength = stress at which noticeable plastic deformation has occurred

when εp = 0.002

Yield Strength

σy = yield strength

Note: for 5 cm sample

ε = 0.002 = Δz/z

Δz = 0.01 cm

Adapted from Fig. 6.10 (a),Callister & Rethwisch 9e.

σ (stress)

ε (strain)

σy

εp = 0.002

• Transition from elastic to plastic deformation is gradual

Chapter 7 - 22

Tensile Strength

• Metals: Maximum on stress-strain curve appears at the onset of noticeable necking


σy

strain

Typical response of a metal

Fracture strength

Neck – acts as stress concentrator

eng

inee

ring

TS s

tress

engineering strain

• Tensile strength (TS) = maximum stress on engineering stress-strain curve.

Chapter 7 - 23

• Ductility = amount of plastic deformation at failure:• Specification of ductility -- Percent elongation:

-- Percent reduction in area:

Ductility

lfAo Af

lo


tensile strain, ε

tensile stress, σ

low ductility

high ductility

Chapter 7 - 24

• Toughness of a material is expressed in several contexts • For this chapter, toughness = amount of energy absorbed before fracture • Approximate by area under the stress-strain curve—units of energy per unit volume

Toughness

Brittle fracture: small toughnessDuctile fracture: large toughness

very small toughness (unreinforced polymers)

tensile strain, ε

tensile stress, σ

small toughness (ceramics)

large toughness (metals)

Chapter 7 - 25

Mechanical PropertiesCeramic materials are more brittle than metals.

Why is this so?• Consider mechanism of deformation

– In crystalline, by dislocation motion– In highly ionic solids, dislocation motion is difficult

• few slip systems• resistance to motion of ions of like charge (e.g., anions) past

one another

Chapter 7 - 26

• Applied mechanical force—normalized to stress

• Elastic deformation:−−non-permanent; occurs at low levels of stress−−stress-strain behavior is linear

Summary

• Plastic deformation−−permanent; occurs at higher levels of stress−−stress-strain behavior is nonlinear

• Degree of deformation—normalized to strain

• Stiffness—a material's resistance to elastic deformation−−elastic (or Young's) modulus

Chapter 7 - 27

• Strength—a material's resistance to plastic deformation−−yield and tensile strengths

• Ductility—amount of plastic deformation at failure−−percents elongation, reduction in area

Summary (cont.)

• Hardness—resistance to localized surface deformation & compressive stresses

−−Rockwell, Brinell hardnesses

Chapter 8 - 28

ISSUES TO ADDRESS...• How are dislocations involved in the plastic deformation of materials?• Does the crystal structure of a material affect its mechanical characteristics? If so, how and why? • How are mechanical properties affected by dislocation mobilities?

Chapter 8: Deformation & Strengthening Mechanisms

• What techniques are used to increase the strength/hardness of metals/alloys?• How are mechanical characteristics of deformed metal specimens altered by heat treatments?

Chapter 8 - 29

Motion of Edge and Screw Dislocations

• Direction of edge disl. line ( ) motion—in direction of applied shear stress τ.

Edge dislocation

Screw dislocation


• Direction of screw disl. line ( ) motion—perpendicular to direction of applied shear stress.

Chapter 8 - 30

Slip System—Combination of slip plane and slip direction – Slip Plane

• Crystallographic plane on which slip occurs most easily

• Plane with high planar density

– Slip Direction • Crystallographic direction along which slip occurs

most easily• Direction with high linear density

Slip Systems

Chapter 8 -

• For FCC crystal structure – slip system is– Dislocation motion on planes– Dislocation motion in directions– A total of 12 independent slip systems for FCC

31

Slip Systems (cont.)


direction

plane

• For BCC and HCP— other slip systems

Chapter 8 -

Slip in Single CrystalsResolved Shear Stress

• Applied tensile stress—shear stress component when slip plane oriented neither perpendicular nor parallel to stress direction

-- From figure, resolved shear stress, τR

32

ϕ

λ

• τR depends on orientation of normal to slip plane and slip direction with direction of tensile force F:


Chapter 8 - 33

• Dislocation motion—on specific slip system—when τR reaches critical value: -- “Critical resolved shear stress”, τCRSS -- Slip occurs when τR > τCRSS -- Typically 0.1 MPa < τCRSS < 10 MPa

• One slip system for which τR is highest: τR(max) > σ (cosλ cosϕ )max -- Most favorably oriented slip system

Slip in Single Crystals:Critical Resolved Shear Stress

• In a single crystal there are -- multiple slip systems -- a variety of orientations

• Yield strength of single crystal, σy, when

Chapter 8 - 34

Strengthening Mechanisms for Metals • For a metal to plastically deform—dislocations must move

• Mechanisms for strengthening/hardening metals—decrease disl. mobility

• 3 mechanisms discussed -- Grain size reduction -- Solid solution strengthening -- Strain hardening (cold working)

• Strength and hardness—related to mobility of dislocations -- Reduce disl. mobility—metal strengthens/hardens -- Greater forces necessary to cause disl. motion -- Increase disl. mobility—metal becomes weaker/softer

Chapter 8 - 35

Strengthening Mechanisms for Metals Mechanism I – Reduce Grain Size

Fig. 8.14, Callister & Rethwisch 5e. (From L. H. Van Vlack, A Textbook of MaterialsTechnology, Addison-Wesley Publishing Co., 1973.Reproduced with the permission of the Estate ofLawrence H. Van Vlack.)

• Grain boundaries act as barriers to dislocation motion• At boundary — Slip planes change directions (note in illustration) — Discontinuity of slip planes• Reduce grain size — increase grain boundary area — more barriers to dislocation motion — increase yield strength, tensile strength & hardness• Dependence of σy on average grain diameter, d:

—σ0, ky = material constants

Chapter 8 - 36

Strengthening Mechanisms for MetalsMechanism II – Solid-Solution Strengthening

Fig. 8.4, Callister & Rethwisch 5e. (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.)

• Lattice strains around dislocations– Illustration notes locations of tensile, compressive

strains around an edge dislocation

Chapter 8 - 37

Solid Solution Strengthening (cont.)


• Lattice strain interactions with strains introduced by impurity atoms• Small substitutional impurities introduce tensile strains• When located above slip line for edge dislocation as shown:

– partial cancellation of impurity (tensile) and disl. (compressive) strains– higher shear stress required to cause disl. motion

Chapter 8 - 38

Solid Solution Strengthening (cont.)


• Large substitutional impurities introduce compressive strains• When located below slip line for edge dislocation as shown:

– partial cancellation of impurity (compressive) and disl. (tensile) strains– higher shear stress required to cause disl. motion

Chapter 8 - 39

Strengthening Mechanisms for MetalsMechanism III – Strain Hardening

• Plastically deforming most metals at room temp. makes them harder and stronger • Phenomenon called "Strain hardening (or cold working)”

-Rolling

roll

AoAd

roll

• Deformation amt. = percent coldwork (%CW)

• Deformation—often reduction in cross-sectional area.

Chapter 8 - 40

Strain Hardening (cont.)


• Yield strength (σy) increases.• Tensile strength (TS) increases.• Ductility (%EL or %AR) decreases.

As %CW increases

low carbon steel

Chapter 8 - 41

Strain Hardening (cont.)


Lattice strain interactions between dislocations

Chapter 8 - 42

Recovery

• Scenario 1

• Scenario 2

4. dislocations of oppositesign meet and annihilate

Dislocation annihilation- half-planescome together

extra half-plane of atoms

extra half-plane of atoms

atoms diffuse to regions of tension

2. grey atoms leave by vacancy diffusion allowing disl. to “climb”1. dislocation blocked; can’t move to the right

Obstacle dislocation

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

During recovery – reduction in disl. density – annihilation of disl.

Chapter 8 - 43

Fig. 8.21 (a),(c), Callister & Rethwisch 5e. (Photomicrographs courtesy of J.E. Burke, General Electric Company.)

33%CW brass before heat treatment

Recrystallized grains

Recrystallization• New grains form that: -- have low dislocation densities -- are small in size -- consume and replace parent cold-worked grains.

After 4 sec. at 580°C

Chapter 8 - 44

Fig. 8.21 (d),(e), Callister & Rethwisch 5e. (Photomicrographs courtesy of J.E. Burke, General Electric Company.)

Grain Growth• Grain growth occurs as heat treatment continues.

-- Average grain size increases-- Small grains shrink (and ultimately disappear)-- Large grains continue to grow

After 8 sec. at 580°C After 15 min. at 580°C

Chapter 8 - 45

Fig. 8.22, Callister & Rethwisch 8e. (Adapted from G. Sachs and K. R. Van Horn,Practical Metallurgy, Applied Metallurgyand the Industrial Processing of Ferrous andNonferrous Metals and Alloys, 1940.Reproduced by permission of ASMInternational, Materials Park, OH.)

TR = recrystallization temperature

TR

º

Recovery, Recrystallization, & Grain GrowthSummary

annealing time = 1 h

Chapter 8 -

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

46

Chapter 8 - 47

• Plastic deformation occurs by motion of dislocations

• Deformation of polycrystals—change of grain shapes

Summary

• Strengthening techniques for metals: -- grain size reduction -- solid solution strengthening -- strain hardening (cold working)

• Crystallographic considerations: -- Minimum atomic distortion from dislocation motion - in slip planes - along slip directions

• Strength is increased by decreasing dislocation mobility.

Chapter 8 - 48

Summary (cont.)

• Heat treatment of deformed metal specimens: -- Processes - Recovery - Recrystallization - Grain growth -- Consequences—property alterations - Softer and weaker - More ductile

Chapter 9 -

• Simple fracture – the separation of a body into two or more pieces in response to a static stress

• Propagation of cracks accompanies fracture

49

Fracture

• Two general types of fracture– Ductile

• Slow crack propagation• Accompanied by significant plastic deformation• Fails with warning

– Brittle• Rapid crack propagation• Little or no plastic deformation• Fails without warning

• Ductile fracture generally more desirable than brittle fracture

Chapter 9 -

• Fracture occurs as result of crack propagation • Measured fracture strengths of most materials

much lower than predicted by theory – microscopic flaws (cracks) always exist in materials– magnitude of applied tensile stress amplified at the

tips of these cracks

50

Principles of Fracture Mechanics

Chapter 9 - 51

Fracture Mechanics (cont.)

where ρt = radius of curvature

σo = applied stressσm = stress at crack tip

ρt

Fig. 9.8(a), Callister & Rethwisch 5e.

Flaws are Stress Concentrators!

Crack

Chapter 9 - 52

Crack Propagation

• Stress concentration higher for sharp cracks—propagate at lower stresses than cracks with blunt tips

• For ductile materials—plastic deformation at crack tip when stress reaches yield strength—tip blunted—lowers stress conc.

ductilebrittle

deformed region

Chapter 9 - 53

Criterion for Crack PropagationCritical stress for crack propagation (σc) of brittle materials

where– σc = crack-tip stress– E = modulus of elasticity– γs = specific surface energy– a = one half length of internal crack

For ductile materials replace γs with γs + γp where γp is plastic deformation energy

- materials have numerous cracks with different lengths and orientations

- crack propagation (and fracture) occurs when σm > σc for crack with lowest σc

- Largest, most highly stressed cracks grow first!

Chapter 9 -

Fracture Toughness• Measure of material’s resistance to brittle

fracture when a crack is present• Defined as

KC = YσC√π a

54

= dimensionless parameterY= critical stress for crack propagation [MPa] σc= crack length [m]a

= fracture toughness [MPa √m ]Kc

• For planar specimens with cracks much shorter than specimen width, Y ≈ 1

Chapter 9 - 55

• Crack growth condition:

Design Against Fracture

--Scenario 1: KIc and flaw size a specified - dictates max. design (critical) stress.

σc

a

no fracture

fracture

--Scenario 2: KIc and stress level specified - dictates max. allowable flaw size.

ac

σ

no fracture

fracture

KIc < YσC√π a

Chapter 9 - 56

Influence of T on Impact Energy


• Some BCC metals exhibit Ductile-to-Brittle Transition Temperature (DBTT)

• When impact tests conducted as function of temperature— three kinds of behavior observed for metals

BCC metals (e.g., low strength steels)

Impa

ct E

nerg

y

Temperature

High strength materials

polymers

FCC and HCP metals (e.g., Cu, Ni)ductile fracture

brittle fracture

Metals having DBTT should only be used at temperatures where ductile.

Chapter 9 - 57

Types of Fatigue Behavior

Adapted from Fig. 9.26(a), Callister & Rethwisch 5e.

- Fatigue limit, Sfat: no fatigue if S < Sfat

Sfat

case for steel (typ.)

N = Cycles to failure103 105 107 109

unsafe

safe

S =

stre

ss a

mpl

itude

- For some materials, there is no fatigue limit!

Adapted from Fig. 9.26(b), Callister & Rethwisch 5e.

case for Al (typ.)

N = Cycles to failure103 105 107 109

unsafe

safe

S =

stre

ss a

mpl

itude

• Fatigue data plotted as stress amplitude S vs. log of number N of cycles to failure.• Two types of fatigue behavior observed

• Fatigue Life Nf = total number of stress cycles to cause fatigue failure at specified stress amplitude

Chapter 9 - 58

Improving Fatigue Life• Three general techniques to improve fatigue life

1. Reducing magnitude of mean stress2. Surface treatments3. Design changes

Adapted fromFig. 9.33, Callister & Rethwisch 5e.

N = Cycles to failure

moderate tensile σmLarger tensile σmS

= s

tress

am

plitu

de

near zero or compressive σm Incre

asing σ m

Decreasing mean stress increases fatigue life

Chapter 9 - 59



Imposing compressive surface stresses increases surface hardness – suppresses surface cracks from growing

--Method 1: shot peening

put surface

into compression

shot

surface compressive stress due to plastic deformation of outer surface layer

--Method 2: carburizing

C-rich gas

surface compressive stress due to carbon atoms diffusing into outer surface layer

Chapter 9 - 60



Remove stressconcentrators Fig. 9.34, Callister &

Rethwisch 5e.

bad better

sharp corner – point of stress concentration

rounding corner reduces stress concentration

Chapter 9 - 61

CreepMeasure deformation (strain) vs. time at constant stress


σσ

0 t

σ

Occurs at elevated temperature for most metals, T > 0.4 Tm (in K)

Stages of Creep- Primary Creep: slope (creep rate) decreases with time.

- Secondary Creep: steady-state i.e., constant slope (Δε /Δt).

- Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate.

ε

Δε

Chapter 9 - 62

Steady-State Creep Rate• constant for constant T, σ -- strain hardening is balanced by recovery -- dependence of steady-state creep rate on T, σ

• Steady-state creep rate increases with increasing T, σ

102040

100200

10-2 10-1 1Steady state creep rate (%/1000hr)εs

Stre

ss (M

Pa) 427°C

538°C

649°C

Adapted fromFig. 9.40, Callister & Rethwisch 5e. [Reprinted with permission from Metals Handbook: Properties and Selection: Stainless Steels, Tool Materials, and Special Purpose Metals, Vol. 3, 9th ed., D. Benjamin (Senior Ed.), ASM International, 1980, p. 131.]

stress exponent (material parameter)

activation energy for creep(material parameter)

applied stressmaterial const.

Chapter 9 - 63

SUMMARY• Simple fracture – one type of failure

• Small cracks or flaws exist in all materials

• Fracture toughness – measurement of material’s resistance to brittle fracture

- Occurs by crack propagation- Ductile fracture: some plastic deformation – slow crack propagation- Brittle fracture: no plastic deformation – crack propagation- Fracture surfaces – different for ductile and brittle

- Applied tensile stress amplified at tips of flaws- Fracture – when stress at tip of crack reaches theoretical strength

- A function of applied stress and crack length

• Impact tests – Impact energy measured vs. temperature- Some ductile materials experience brittle fracture – low temps.

Chapter 9 - 64

SUMMARY (cont.)

• Fatigue failure – stress fluctuations with time

• Creep failure – at elevated temperatures and constant strain

- Occurs at applied stress < TS- Important parameters: fatigue limit, fatigue strength/lifetime

- Important parameters: steady-state creep rate, rupture lifetime- Data extrapolation – Larson-Miller parameter

Chapter 9 - 65

Phase Equilibria: Solubility Limit

Question: What is the solubility limit for sugar in water at 20°C?

Answer: 65 wt% sugar. At 20°C, if C < 65 wt% sugar: syrup At 20°C, if C > 65 wt% sugar:

syrup + sugar

65

• Solubility Limit: Maximum concentration for which only a single phase solution exists.

Sugar/Water Phase Diagram

Suga

r

Tem

pera

ture

(°C

)

0 20 40 60 80 100 C = Composition (wt% sugar)

L

(liquid solution i.e., syrup)

Solubility Limit L

(liquid) + S

(solid sugar)20

40

60

80

100

Wat

er


• Solution – solid, liquid, or gas solutions, single phase• Mixture – more than one phase

Chapter 9 - 66

70 80 1006040200

Tem

pera

ture

(°C

)

C = Composition (wt% sugar)

L

(liquid solution i.e., syrup)

20

100

40

60

80

0

L (liquid)

+ S

(solid sugar)

Effect of Temperature & Composition• Altering T can change # of phases: path A to B.

• Altering C can change # of phases: path B to D.

water-sugarsystem


D (100°C,C = 90)2 phases

B (100°C,C = 70)1 phase

A (20°C,C = 70)2 phases

Chapter 9 - 67

Criteria for Solid Solubility

CrystalStructure

electroneg r (nm)

Ni FCC 1.9 0.1246Cu FCC 1.8 0.1278

• Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume – Rothery rules) suggesting high mutual solubility.

Simple system (e.g., Ni-Cu solution)

• Ni and Cu are totally soluble in one another for all proportions.

Chapter 9 -

wt% Ni20 40 60 80 10001000

1100

1200

1300

1400

1500

1600T(°C)

L (liquid)

α

(FCC solidsolution)

L + α

liquidus

solidusCu-Niphase

diagram

68

Phase Diagrams:Determination of phase(s) present

• Rule 1: If we know T and Co, then we know: -- which phase(s) is (are) present.

• Examples:A(1100°C, 60 wt% Ni): 1 phase: α

B(1250°C, 35 wt% Ni): 2 phases: L + α

B (1

250º

C,3

5) A(1100ºC,60)

Fig. 10.3(a), Callister & Rethwisch 5e. (Adapted from Phase Diagrams of BinaryNickel Alloys, P. Nash, Editor, 1991. Reprintedby permission of ASM International, MaterialsPark, OH.)

Chapter 9 - 69

• Rule 3: If we know T and C0, then can determine: -- the weight fraction of each phase.• Examples:

At TA: Only Liquid (L) present

WL = 1.00, Wα = 0

At TD:

Only Solid (α ) present

WL = 0, W

α = 1.00

Phase Diagrams:Determination of phase weight fractions

wt% Ni20

1200

1300

T(°C)

L (liquid)

α(solid)L + α

liquidus

solidus

30 40 50

L + α

Cu-Ni system

TAA

35C0

32CL

BTB

DTD

tie line

4Cα

3

R S

At TB:

Both α

and L present

= 0.27

WL= S

R +S

Wα= R

R +S

Consider C0 = 35 wt% Ni

Fig. 10.3(b), Callister & Rethwisch 5e. (Adapted from Phase Diagrams of BinaryNickel Alloys, P. Nash, Editor, 1991. Reprintedby permission of ASM International, MaterialsPark, OH.)

Chapter 9 - 70

• Tie line – connects the phases in equilibrium with each other – also sometimes called an isotherm

The Lever Rule

What fraction of each phase? Think of the tie line as a lever (teeter-totter)

ML Mα

R S

wt% Ni20

1200

1300

T(°C)

L (liquid)

α(solid)L + α

liquidus

solidus

30 40 50

L + αB

TB

tie line

C0CL Cα

SR

Adapted from Fig. 10.3(b), Callister & Rethwisch 5e.

Chapter 9 - 71

wt% Ni20

1200

1300

30 40 50110 0

L (liquid)

α

(solid)

L + α

L + α

T(°C)

A

35C0

L: 35 wt%NiCu-Ni

system

• Phase diagram: Cu-Ni system.


• Consider microstuctural changes that accompany the cooling of a C0 = 35 wt% Ni alloy

Ex: Cooling of a Cu-Ni Alloy

46354332

α: 43 wt% Ni L: 32 wt% Ni

Bα: 46 wt% NiL: 35 wt% Ni

C

EL: 24 wt% Ni

α: 36 wt% Ni

24 36D

α: 35 wt% Ni

Chapter 9 - 72

L+αL+β

α + β

200

T(°C)

18.3

C, wt% Sn20 60 80 1000

300

100

L (liquid)

α 183°C

61.9 97.8β

• For a 40 wt% Sn-60 wt% Pb alloy at 150°C, determine: -- the phases present Pb-Sn

system

EX 1: Pb-Sn Eutectic System

Answer: α + β-- the phase compositions

-- the relative amount of each phase

150

40C0

11Cα

99Cβ

SR

Answer: Cα = 11 wt% SnCβ = 99 wt% Sn

Wα =Cβ - C0Cβ - Cα

= 99 - 4099 - 11 = 59

88 = 0.67

SR+S =

Wβ

=C0 - CαCβ - Cα

=RR+S

= 2988

= 0.33= 40 - 1199 - 11

Answer:

Fig. 10.8, Callister & Rethwisch 5e. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 3, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

Chapter 9 - 73

• For alloys for which 2 wt% Sn < C0 < 18.3 wt% Sn• Result: at temperatures in α + β range -- polycrystalline with α grains and small β-phase particles


Microstructural Developments in Eutectic Systems II

Pb-Snsystem

L + α

200

T(°C)

C, wt% Sn10

18.3

200C0

300

100

L

α

30

α + β

400

(sol. limit at TE)

TE

2(sol. limit at Troom)

Lα

L: C0 wt% Sn

αβ

α: C0 wt% Sn

Chapter 9 - 74

• For alloy of composition C0 = CE • Result: Eutectic microstructure (lamellar structure) -- alternating layers (lamellae) of α and β phases.


Microstructural Developments in Eutectic Systems III

Fig. 10.14, Callister & Rethwisch 5e. (From Metals Handbook, 9th edition, Vol. 9,Metallography and Microstructures, 1985.Reproduced by permission of ASM International, Materials Park, OH.)

160 μm

Micrograph of Pb-Sn eutectic microstructure

Pb-Snsystem

L + β

α + β

200

T(°C)

C, wt% Sn20 60 80 1000

300

100

L

α

βL+ α

183°C

40

TE

18.3

α: 18.3 wt%Sn

97.8

β: 97.8 wt% Sn

CE61.9

L: C0 wt% Sn

Chapter 9 - 75

L+αL+β

α + β

200

C, wt% Sn20 60 80 1000

300

100

L

α

βTE

40

(Pb-Sn System)

Hypoeutectic & Hypereutectic


160 μmeutectic micro-constituent


hypereutectic: (illustration only)

β

βββ

β

β

Adapted from Fig. 10.17, Callister & Rethwisch 5e. (Illustration only)

(Figs. 9.14 and 9.17 from Metals Handbook, 9th ed., Vol. 9, Metallography and Microstructures, 1985.Reproduced by permission of ASM International,Materials Park, OH.)

175 μm

α

α

α

ααα

hypoeutectic: C0 = 50 wt% Sn


T(°C)

61.9eutectic

eutectic: C0 = 61.9 wt% Sn

Chapter 9 - 76

Intermetallic Compounds

Mg2Pb

Note: intermetallic compound exists as a line on the diagram - not an area - because of stoichiometry (i.e. composition of a compound is a fixed value).

Fig. 10.20, Callister & Rethwisch 5e. [Adapted from Phase Diagrams of Binary Magnesium Alloys, A. A. Nayeb-Hashemi and J. B. Clark (Editors), 1988. Reprinted by permission of ASM International, Materials Park, OH.]

Chapter 9 - 77

• Eutectoid – one solid phase transforms to two other solid phasesS2 S1+S3 γ α + Fe3C (For Fe-C, 727°C, 0.76 wt% C)

intermetallic compound - cementite

coolheat

Eutectic, Eutectoid, & Peritectic• Eutectic - liquid transforms to two solid phases

L α + β (For Pb-Sn, 183°C, 61.9 wt% Sn) coolheat

coolheat

• Peritectic - liquid and one solid phase transform to a second solid phase S1 + L S2

δ + L γ (For Fe-C, 1493°C, 0.16 wt% C)

Chapter 9 - 78

Eutectoid & PeritecticCu-Zn Phase diagram


Eutectoid transformation δ γ + ε

Peritectic transformation γ + L δ

Chapter 9 - 79

Iron-Carbon (Fe-C) Phase Diagram• 2 important points

- Eutectoid (B):

γ ⇒ α +Fe3C

- Eutectic (A):

L ⇒ γ +Fe3C


Fe3C

(cem

entit

e)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

γ (austenite)

γ+L

γ+Fe3C

α+Fe3C

α+ γ

δ

(Fe) C, wt% C

1148°C

T(°C)

α 727°C = Teutectoid

4.30Result: Pearlite = alternatinglayers of α and Fe3C phases

120 μm

Fig. 10.31, Callister & Rethwisch 5e. (From Metals Handbook, Vol. 9, 9th ed.,Metallography and Microstructures, 1985.Reproduced by permission of ASM International, Materials Park, OH.)

0.76

Bγ γ

γγ

A L+Fe3C

Fe3C (cementite-hard)α (ferrite-soft)

Chapter 9 - 80Fe

3C (c

emen

tite)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

γ (austenite)

γ+L

γ + Fe3C

α + Fe3C

L+Fe3C

δ

(Fe) C, wt% C

1148°C

T(°C)

α727°C

(Fe-C System)

C0

0.76

Hypoeutectoid Steel

Adapted from Figs. 10.28 and 10.33, Callister & Rethwisch 5e. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

Adapted from Fig. 10.34, Callister & Rethwisch 5e. (Photomicrograph courtesy of Republic Steel Corporation.)

proeutectoid ferritepearlite

100 μm Hypoeutectoidsteel

α

pearlite

γγ γ

γααα

γγγ γ

γ γγγ

Chapter 9 -Fe

3C (c

emen

tite)

1600

1400

1200

1000

800

600

4000 1 2 3 4 5 6 6.7

L

γ (austenite)

γ+L

γ + Fe3C

α + Fe3C

L+Fe3C

δ

(Fe) C, wt% C

1148°C

T(°C)

α727°C

(Fe-C System)

C0

81

Hypereutectoid Steel

0.76

C0

Fe3C

γγγ γ

γγγ γ

γγγ γ

Adapted from Fig. 10.37, Callister & Rethwisch 5e. (Copyright 1971 by United States Steel Corporation.)

proeutectoid Fe3C

60 μmHypereutectoid steel

pearlite

pearlite

Adapted from Figs. 10.28 and 10.36, Callister & Rethwisch 5e. [Adapted from Binary Alloy Phase Diagrams, 2nd edition, Vol. 1, T. B. Massalski (Editor-in-Chief), 1990. Reprinted by permission of ASM International, Materials Park, OH.]

Chapter 9 - 82

Chapter 9 - 83

• Heat treatments of Fe-C alloys produce microstructures including: -- pearlite, bainite, spheroidite, martensite, tempered martensite• Precipitation hardening --hardening, strengthening due to formation of precipitate particles. --Al, Mg alloys precipitation hardenable.• Polymer melting and glass transition temperatures

Summary

Chapter 9 - 84

• Phase diagrams are useful tools to determine:-- the number and types of phases present,-- the composition of each phase,-- and the weight fraction of each phase given the temperature and composition of the system.

• The microstructure of an alloy depends on -- its composition, and -- whether or not cooling rate allows for maintenance of equilibrium.

• Important phase diagram phase transformations include eutectic, eutectoid, and peritectic.

Summary

MSNE 301 midterm #2 review October 2019

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