MATERIALS SCIENCE

Week 5Fracture, Toughness, Fatigue, and Creep

2

ISSUES TO ADDRESS...

• How do flaws in a material initiate failure?• How is fracture resistance quantified; how do different material classes compare?• How do we estimate the stress to fracture?• How do loading rate, loading history, and temperature affect the failure stress?

Ship-cyclic loadingfrom waves.

Computer chip-cyclicthermal loading.

Hip implant-cyclicloading from walking.

Mechanical Failure

What is a Fracture?

Fracture is the separation of a body into two or more pieces in response to an imposed stress that is static and at temperatures that are low relative to the melting temperature of the material.

The applied stress may be tensile, compressive, shear, or torsional

Any fracture process involves two steps—crack formation and propagation—in response to an imposed stress.

4

Fracture mechanisms

Ductile fracture Occurs with plastic deformation

• Brittle fracture

– Little or no plastic deformation

– Catastrophic

5

Ductile vs Brittle Failure

Very Ductile

ModeratelyDuctile BrittleFracture

behavior:

Large Moderate%AR or %EL Small

• Ductile fracture is usually desirable!

• Classification:

Ductile: warning before

fracture

Brittle: No

warning

6

• Ductile failure:

--one/two piece(s) --large deformation

Example: Failure of a Pipe

• Brittle failure:

--many pieces --small deformation

7

• Evolution to failure:

• Resulting fracture surfaces

(steel)

50 mm

particlesserve as voidnucleationsites.

50 mm

100 mm

Moderately Ductile Failure

necking

void nucleation

void growth and linkage

shearing at surface fracture

8

Ductile vs. Brittle Failure

cup-and-cone fracture brittle fracture

Transgranular vs Intergranular Fracture

Transgranular Fracture

Intergranular Fracture

10

• Intergranular

(between grains)• Transgranular

(within grains)

Al Oxide(ceramic)

316 S. Steel (metal)

304 S. Steel (metal)

Polypropylene(polymer)

3 mm

4 mm160 mm

1 mm

Brittle Fracture Surfaces

11

• Stress-strain behavior (Room T):

Ideal vs Real Materials

TS << TSengineeringmaterials

perfectmaterials

E/10

E/100

0.1

perfect mat’l-no flaws

carefully produced glass fiber

typical ceramic typical strengthened metaltypical polymer

• DaVinci (500 yrs ago!) observed...

-- the longer the wire, the smaller the load for failure.• Reasons: -- flaws cause premature failure. -- Larger samples contain more flaws!

12

Flaws are Stress Concentrators!

Results from crack propagationGriffith Crack

where t = radius of curvature

o = applied stress

m = stress at crack tip

Kt = Stress concentration factor

ot

/

tom K

a

21

2

t

13

Concentration of Stress at Crack Tip

14

Engineering Fracture Design

r/h

sharper fillet radius

increasing w/h

0 0.5 1.01.0

1.5

2.0

2.5

Stress Conc. Factor, K tmax

o=

• Avoid sharp corners!

r ,

fillet

radius

w

h

o

max

15

Crack Propagation

Cracks propagate due to sharpness of crack tip A plastic material deforms at the tip, “blunting” the

crack. deformed region

brittle

Energy balance on the crackElastic strain energy-

energy stored in material as it is elastically deformed this energy is released when the crack propagates creation of new surfaces requires energy

plastic

16

When Does a Crack Propagate?

Crack propagates if above critical stress

where E = modulus of elasticity s = specific surface energy (J/m2) a = one half length of internal crack

For ductile => replace s by s + p

where p is plastic deformation energy

212

/

sc a

E

i.e., m > c

ot

/

tom K

a

21

2

17

• Crack growth condition:

• Largest, most stressed cracks grow first!

Fracture Toughness: Design Against Crack Growth

K ≥ Kc = aY

--Result 1: Max. flaw size dictates design stress.

max

cdesign

aY

K

amax

no fracture

fracture

--Result 2: Design stress dictates max. flaw size.

2

1

design

cmax Y

Ka

amax

no fracture

fracture

Fracture Toughness

For relatively thin specimens, the value of Kc will depend on specimen thickness. However, when specimen thickness is much greater than the crack dimensions, Kc becomes independent of thickness.

The Kc value for this thick-specimen situation is known as the plane strain fracture toughness KIC

19

Fracture ToughnessGraphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibers

Polymers

5

KIc

(MP

a ·

m0

.5)

1

Mg alloys

Al alloys

Ti alloys

Steels

Si crystalGlass -soda

Concrete

Si carbide

PC

Glass 6

0.5

0.7

2

4

3

10

20

30

<100>

<111>

Diamond

PVC

PP

Polyester

PS

PET

C-C(|| fibers) 1

0.6

67

40506070

100

Al oxideSi nitride

C/C( fibers) 1

Al/Al oxide(sf) 2

Al oxid/SiC(w) 3

Al oxid/ZrO 2(p)4Si nitr/SiC(w) 5

Glass/SiC(w) 6

Y2O3/ZrO 2(p)4

Kc = aY

20

• Two designs to consider...Design A --largest flaw is 9 mm --failure stress = 112 MPa

Design B --use same material --largest flaw is 4 mm --failure stress = ?

• Key point: Y and Kc are the same in both designs.

Answer: MPa 168)( B c• Reducing flaw size pays off!

• Material has Kc = 26 MPa-m0.5

Design Example: Aircraft Wing

• Use...max

cc

aY

K

c amax A

c amax B

9 mm112 MPa 4 mm --Result:

21

Loading Rate

• Increased loading rate...

-- increases y and TS -- decreases %EL

• Why? An increased rate gives less time for dislocations to move past obstacles and form into a crack.

y

y

TS

TS

larger

smaller

22

Impact Testing

final height initial height

• Impact loading:

-- severe testing case -- makes material more brittle -- decreases toughness

(Charpy)

Impact Tests

A material may have a high tensile strength and yet be unsuitable for shock loading conditions

Impact testing is testing an object's ability to resist high-rate loading.

An impact test is a test for determining the energy absorbed in fracturing a test piece at high velocity

Types of Impact Tests -> Izod test and Charpy Impact test

In these tests a load swings from a given height to strike the specimen, and the energy dissipated in the fracture is measured

A. Izod Test

The Izod test is most commonly used to evaluate the relative toughness or impact toughness of materials

Izod test sample usually have a V-notch cut into them

Metallic samples tend to be square in cross section, while polymeric test specimens are often rectangular

Izod Test - Method

It involves striking a suitable test piece with a striker, mounted at the end of a pendulum

The test piece is clamped vertically with the notch facing the striker.

The striker swings downwards impacting the test piece at the bottom of its swing.

Determination of Izod Impact Energy

At the point of impact, the striker has a known amount of kinetic energy.

The impact energy is calculated based on the height to which the striker would have risen, if no test specimen was in place, and this compared to the height to which the striker actually rises.

Tough materials absorb a lot of energy, whilst brittle materials tend to absorb very little energy prior to fracture

B. Charpy Test

Charpy test specimens normally measure 55 x 10 x 10mm and have a notch machined across one of the larger faces

The Charpy test involves striking a suitable test piece with a striker, mounted at the end of a pendulum.

The test piece is fixed in place at both ends and the striker impacts the test piece immediately behind a machined notch.

Factors Affecting Impact Energy

1. For a given material the impact energy will be seen to decrease if the yield strength is increased

2. The notch serves as a stress concentration zone and some materials are more sensitive towards notches than others

3. Most of the impact energy is absorbed by means of plastic deformation during the yielding. Therefore, factors that affect the yield behavior (and hence ductility) of the material such as temperature and strain rate will affect the impact energy

29

• Increasing temperature...

--increases %EL and Kc

• Ductile-to-Brittle Transition Temperature (DBTT)...

Effect of Temperature on Toughness

BCC metals (e.g., iron at T < 914°C)

Imp

act

Ene

rgy

Temperature

High strength materials (y > E/150)

polymers

More Ductile Brittle

Ductile-to-brittle transition temperature

FCC metals (e.g., Cu, Ni)

Fatigue Test

Fatigue is concerned with the premature fracture of metals under repeatedly applied low stresses

A specified mean load (which may be zero) and an alternating load are applied to a specimen and the number of cycles required to produce failure (fatigue life) is recorded.

Generally, the test is repeated with identical specimens and various fluctuating loads.

Data from fatigue testing often are presented in an S-N diagram which is a plot of the number of cycles required to cause failure in a specimen against the amplitude of the cyclical stress developed

Fatigue Testing Equipment

Fatigue Loading

Fatigue Test - S-N Curve

This S–N diagram indicates that some metals can withstand indefinitely the application of a large number of stress reversals, provided the applied stress is below a limiting stress known as the endurance limit

34

• Crack grows incrementally

typ. 1 to 6

a~

increase in crack length per loading cycle

• Failed rotating shaft

--crack grew even though

Kmax < Kc

--crack grows faster as • increases • crack gets longer • loading freq. increases.

crack origin

Fatigue Mechanism

mKdN

da

35

Improving Fatigue Life

1. Impose a compressive surface stress (to suppress surface cracks from growing)

N = Cycles to failure

moderate tensile mLarger tensile m

S = stress amplitude

near zero or compressive mIncreasing

m

--Method 1: shot peening

put surface

into compression

shot--Method 2: carburizing

C-rich gas

2. Remove stress concentrators.

bad

bad

better

better

4. Creep Test

Creep is defined as plastic (or irrevresible) flow under constant stress

Creep is high temperature progressive deformation at constant stress

A creep test involves a tensile specimen under a constant load maintained at a constant temperature.

At relatively high temperatures creep appears to occur at all stress levels, but the creep rate increases with increasing stress at a given temperature.

Creep Test

Creep occurs in three stages: Primary, or Stage I; Secondary, or Stage II, and Tertiary, or Stage III

Creep Test

Stage I occurs at the beginning of the tests, and creep is mostly transient, not at a steady rate.

In Stage II, the rate of creep becomes roughly steadyIn Stage III, the creep rate begins to accelerate as

the cross sectional area of the specimen decreases due to necking decreases the effective area of the specimen

39

• Occurs at elevated temperature, T > 0.4 Tm

Creep

elastic

primarysecondary

tertiary

40

• Strain rate is constant at a given T,

stress exponent (material parameter)

strain rateactivation energy for creep(material parameter)

applied stressmaterial const.

• Strain rate increases for higher T,

10

20

40

100

200

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

s

Stress (MPa)

427°C

538°C

649°C

RT

QK cn

s exp2

Secondary Creep

41

Creep Failure• Estimate rupture time

S-590 Iron, T = 800°C, = 20 ksi• Failure:

along grain boundaries.

time to failure (rupture)

function ofapplied stress

temperature

L)t(T r log20

appliedstress

g.b. cavities

• Time to rupture, trL)t(T r log20

1073K

Ans: tr = 233 hr

24x103 K-log hrL(103K-log hr)

Str

ess,

ksi

100

10

112 20 24 2816

data for S-590 Iron

20

Numerical Problems

Problems 8.1 – 8.10; 8.14 – 8.23; and 8.27