CHAPTER 7

Mechanical Properties

Of

Metals - II

7-1

Recovery and Recrystallization

• Cold worked metals become brittle.

• Reheating, which increases ductility results in recovery, recrystallization and grain growth.

• This is called annealing and changes material properties.

(Adapted from Z.D. Jastrzebski, “The Nature and Properties of Engineering Materials,” 2d ed., Wiley, 1976, p.228.)

7-2

Structure of Cold Worked Metals

• Strain energy of cold work is stored as dislocations.

• Heating to recovery temperature relieves internal stresses (Recovery stage).

• Polygonization (formation of sub-grain structure) takes place.

• Dislocations are moved into lower energy configuration.

Polyganization Figure 6.4Dislocations

Slip bands Grain Boundaries

(After “Metals Handbook,” vol 7, 8th ed., American Society of Metals, 1972, p.243)

Structure of 85%Cold worked metal

TEM of 85%Cold worked metal

Structure of stressrelieved metal TEM of stress

relived metalFigure 6.2 and 6.37-3

Recrystallization

• If metal is held at recrystallization temperature long enough, cold worked structure is completely replaced with recrystallized grain structure.

• Two mechanisms of recrystallization Expansion of nucleus Migration of grains.

Nucleus of recrystallized grain

More deformed region

Expansion Migration

(After “Metals Handbook,” vol 7, 8th ed., American Society of Metals, 1972, p.243)

Figure 6.2 and 6.3Figure 6.5

Structure and TEM of

Recrystallized metal

7-4

Effects on Mechanical Properties

• Annealing decreases tensile strength, increases ductility.

• Example:

• Factors affecting recrystalization: Amount of prior deformation Temperature and time Initial grain size Composition of metal

85% Cu &15% Zn

Tensile strength75 KSIDuctility 3%

Tensile strength45 KSIDuctility 38 %

50% coldrolled

Annealed 1 h4000C

(After “Metals Handbook,” vol 2, 9th ed., American Society of Metals, 1979, p.320)

Figure 6.6

7-5

Facts About Recrystallization

• A minimum amount of deformation is needed.

• The smaller the deformation, the higher the recrystallization temperature.

• The Higher the temperature, the less time required.

• The greater the degree of deformation, the smaller the recrystallized grains.

• The Larger the original grain

size, the greater the amount of

deformation that is required

to produce equivalent

temperature.

• Recrystallization temperature

increases with purity of metals.

(After W.L. Roberts, “Flat Processing of steel,” Marcel Dekker, 1988.)

Figure 6.7bContinuous annealing

7-6

Fracture of Metals – Ductile Fracture

• Fracture results in separation of stressed solid into two or more parts.

• Ductile fracture : High plastic deformation & slow crack propagation.

• Three steps : Specimen forms neck and cavities within neck. Cavities form crack and crack propagates towards surface, perpendicular to stress. Direction of crack changes to 450 resulting in cup-cone fracture.

7-7

Brittle Fracture

• No significant plastic deformation before fracture.

• Common at high strain rates and low temperature.

• Three stages: Plastic deformation concentrates

dislocation along slip planes. Microcracks nucleate due to shear

stress where dislocations are blocked. Crack propagates to fracture.

• Example: HCP Zinc ingle crystal

under high stress along {0001}

plane undergoes brittle fracture.

Figure 6.11 & 6.13

(From ASM handbook vol 12, page 12 and 14)

SEM of ductile fracture

SEM of brittle fracture

7-8

Ductile and Brittle Fractures

Ductile fracture Brittle Fracture

Brittle Fractures (cont..)

• Brittle fractures are due to defects like Folds Undesirable grain flow Porosity Tears and Cracks Corrosion damage Embrittlement due to atomic hydrogen

• At low operating temperature, ductile to brittle transition takes place

Toughness and Impact Testing

• Toughness is a measure of energy absorbed before failure.

• Impact test measures the

ability of metal to absorb

impact.

Toughness is measured

using impact testing

machine

(After H.W. Hayden, W.G. Moffatt, and J.Wulff, “The structure and Properties of Materials,” vol. III, Wiley, 1965, p.13.)

Figure 6.14

7-9

Impact testing (Cont…)

• Also used to find the temperature range for ductile to brittle transition.

•

(After J.A.Rinebolt and W.H. Harris, Trans. ASM, 43: 1175(1951))

Figure 6.15 Figure 6.16

7-10

Fracture Toughness

• Cracks and flaws cause stress concentration.

aYK 1

K1 = Stress intensity factor.σ = Applied stress.a = edge crack lengthY = geometric constant.

KIc = critical value of stress intensity factor.(Fracture toughness)

aY f

Example:Al 2024 T851 26.2MPam1/2

4340 alloy steel 60.4MPam1/2

Figure 6.17

7-11

Measuring Fracture Toughness

• A notch is machined in a specimen of sufficient thickness B.

• B > > a plain strain condition.

• B = 2.5(KIc/Yield strength)2

• Specimen is tensile tested.

• Higher the KIc value, more

ductile the metal is.

• Used in design to find

allowable flaw size.

Courtesy of White Shell research)

Figure 6.18

7-12

Fatigue of Metals

• Metals often fail at much lower stress at cyclic loading compared to static loading.

• Crack nucleates at region of stress concentration and propagates due to cyclic loading.

• Failure occurs when

cross sectional area

of the metal too small

to withstand applied

load.

Fatigue fracturedsurface of keyedshaft

Figure 6.19

Fracture started here

Final rupture

(After “Metals Handbook,” vol 9, 8th ed., American Society of Metals, 1974, p.389) 7-13

Fatigues Testing

• Alternating compression and tension load is applied on metal piece tapered towards center.

• Stress to cause failure S

and number of cycles

required N are plotted

to form SN curve.

(After H.W. Hayden, W.G. Moffatt, and J.Wulff, “The structure and Properties of Materials,” vol. III, Wiley, 1965, p.15.)

Figure 6.20

Figure 6.23

Figure 6.21

7-14

Cyclic Stresses

• Different types of stress cycles are possible (axial, torsional and flexural).

2minmax

m 2minmax

a

minmax r

max

min

R

Mean stress =Stress amplitude =

Stress range = Stress range =

Figure 6.24

7-15

Structural Changes in Fatigue Process

• Crack initiation first occurs.

• Reversed directions of crack initiation caused surface ridges and groves called slipband extrusion and intrusion.

• This is stage I and is very slow (10-10 m/cycle).

• Crack growth changes

direction to be perpendi-

cular to maximum tensile

stress (rate microns/sec).

• Sample ruptures by ductile

failure when remaining

cross-sectional area is small to withstand the stress.

Persistent slip bandsIn copper crystal

Figure 6.26

Courtesy of Windy C. Crone, University of Wisconsin7-16

Factors Affecting Fatigue Strength

• Stress concentration: Fatigue strength is reduced by stress concentration.

• Surface roughness: Smoother surface increases the fatigue strength.

• Surface condition: Surface treatments like carburizing and nitriding increases fatigue life.

• Environment: Chemically reactive environment, which might result in corrosion, decreases fatigue life.

7-17

Fatigue Crack Propagation Rate

• Notched specimen used.

• Cyclic fatigue action is generated.

• Crack length is measured by change in potential

produced by crack opening.

Figure 6.27

(After “Metals Handbook,” Vol 8, 9th ed., American Society of Metals, 1985, p.388.)7-18

Stress & Crack Length Fatigue Crack Propagation.

σ2 σ1

ΔaΔN

ΔaΔN

1

dN

da2

dN

da

• When ‘a’ is small, da/dN is also small.• da/dN increases with inc- reasing crack length.• Increase in σ increases crack growth rate.

dN

da = fatigue crack growth rate.

ΔK = Kmax-Kmin = stress intensity factor range.

A,m = Constants depending on material, environment, frequency temperature and stress ratio.

dN

daα f(σ,a)

mKAFigure 6.28

7-19

Fatigue Crack Growth rate Versus ΔK

)()(.

)(

ALogKLogm

KALogdN

daLog m

Straight line with slope m

Limiting value of ΔK belowWhich there is no measurableCrack growth is called stressintensity factor range threshold ΔKth

(After P.C. Paris et al. Stress analysis and growth of cracks, STP 513 ASTM, Philadelphia, 1972, PP. 141-176

Figure 6.29

7-20

Fatigue Life Calculation

)( 22

22

mmmm

mmmmm

m

ayAdN

da

ayK

aYK

KAdN

da

Integrating from initial crack size a0 to final crack size af

at number of fatigue cycles Nf

ff Nmm

mm

a

a

dNayAda0

22

0

Integrating and solving for Nf

)12

(2

1)2

(0

1)2

(

mAy

aaN m

mm

mm

ff

(Assuming Y is independent of crack length)

But

Therefore

Therefore

7-21

Creep in Metals

• Creep is progressive deformation under constant stress.

• Important in high temperature applications. • Primary creep: creep rate• decreases with time due to strain hardening. • Secondary creep: Creep rate is constant due to simultaneous strain hard- ening and recovery process.• Tertiary creep: Creep rate increases with time leading to necking and fracture.

Figure 6.30

7-22

Creep Test

• Creep test determines the effect of temperature and stress on creep rate.

• Metals are tested at constant stress at different temperature & constant temperature with different stress.

High temperatureor stress

Medium temperatureor stress

Low temperatureor stress

Creep strength: Stress to produceMinimum creep rate of 10-5%/hAt a given temperature.

Figure 6.32

Figure 6.33

7-23

Creep Test (Cont..)

• Creep rupture test is same as creep test but aimed at failing the specimen.

• Plotted as log stress

versus log rupture time.

• Time for stress rupture

decreases with increased

stress and temperature.

Figure 6.34

Figure 6.35

(After H.E. McGannon [ed]. “ The making, shaping and Treating of Steel,” 9 th ed., United States Steel, 1971, p. 12567-24

Larsen Miller Parameter

• Larsen Miller parameter is used to represent creep-stress rupture data.

P(Larsen-Miller) = T[log tr + C] T = temperature(K), tr = stress-rupture time h C = Constant (order of 20)

Also, P(Larsen-Miller) = [T(0C) + 273(20+log tr)

or P(Larsen-Miller) = [T(0F) + 460(20+log tr)

• At a given stress level, the log time to stress rupture plus constant multiplied by temperature remains constant for a given material.

7-25

Larsen Miller Parameter

If two variables of time torupture, temperature andstress are known, 3rd parameter that fits L.M. parameter can bedetermined. Example: For alloy CM, at 207 MPa, LM parameter is 27.8 x 103 KThen if temperature is known,time to rupture can be found.

Figure 6.36

(After “Metals Handbook,” vol 1, 10th ed., ASM International, 1990, p.998.)7-26

L.M. Diagram of several alloys

Example: Calculate time to cause 0.2% creep strain in gammaTitanium aluminide at 40 KSI and 12000F

From fig, p = 38000

38000 = (1200 + 460) (log t0.2% + 20) t=776 h

Figure 6.37

After N.R. Osborne et. al., SAMPE Quart, (4)22;26(1992)7-27

Case Study – Analysis of Failed Fan Shaft

• Requirements Function – Fan drive support Material 1045 cold drawn steel Yield strength – 586 Mpa Expected life – 6440 km (failed at 3600 km)

• Visual examination (avoid additional damage) Failure initiated at two points near fillet Characteristic of reverse bending fracture

Failed Shaft – Further Analysis

• Tensile test proved yield strength to be 369 MPa (lower than specified 586 MPa).

• Metallographic examination revealed grain structure to be equiaxed ( cold drawn metal has elongated grains).

• Conclusion: Material is not cold drawn – it is hot rolled !.

Lower fatigue strength and stress raiser caused the failure of the shaft.

Recent Advances: Strength + Ductility

• Coarse grained – low strength, high ductility

• Nanocrystalline – High strength, low ductility (because of failure due to shear bands).

• Ductile nanocrystalline copper : Can be produced by Cold rolling at liquid nitrogen temperature Additional cooling after each pass Controlled annealing

• Cold rolling creates dislocations

and cooling stops recovery

• 25 % microcrystalline grains

in a matrix of nanograins.

Fatigue Behavior of Nanomaterials

• Nanomaterials and Ultrafine Ni are found to have higher endurance limit than microcrystalline Ni.

• Fatigue crack growth is increased in the intermediate regime with decreasing grain size.

• Lower fatigue crack growth threshold Kth observed for nanocrystalline metal.