MT-201B Fractrure Fatigue and Creep

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Mechanical Failure

• How do flaws in a material initiate failure?

• How is fracture resistance quantified; how do different

• How do we estimate the stress to fracture?

• How do loading rate, loading history, and temperature

affect the failure stress?

Cyclic loading

from waves: Ship

Cyclic thermal loading:

Computer chip

Cyclic loading due to

walking: Hip implant.

Callister’s Materials Science andEngineering, Adapted Version.



Fracture mechanisms

• Ductile fracture

– Occurs with plastic deformation

•

– Little or no plastic deformation

– a as rop c

2



Ductile vs Brittle Failure

Very ModeratelyFracture• Classification:

uc e uc ebehavior:

Adapted from Fig. 8.1,

.

Large Moderate% AR or %EL Small• Ductile

fracture is usually

Ductile:

warning before

fracture

Brittle:

No

warnin

3



Exam le: Failure of a Pi e

• Ductile failure:--one piece

--large deformation

• Brittle failure:--man ieces

--small deformation

4V.J. Colangelo and F.A. Heiser, Analysis

of Metallurgical Failures (2nd ed.),



Moderatel Ductile Failure• Evolution to failure:

neckingvoid void growth shearing

fracture

σ

• Resulting 50 mm50 mm

surfaces

steel

particles

serve as voidFrom V.J. Colangelo and F.A. Heiser,

Analysis of Metallurgical Failures (2nd

100 mm

Fracture surface of tire cord wire

loaded in tension. Courtesy of F.

5

nucleation

sites.

. , . . , . ,

Sons, Inc., 1987. (Orig. source: P.

Thornton, J. Mater. Sci., Vol. 6, 1971, pp.

347-56.)

, , ,

OH. Used with permission.



Ductile vs. Brittle Failure

cup-and-cone fracture brittle fracture

6



Brittle Failure

failure

7

From Fig. 11.5(a)Callister’s Materials Science and Engineering, Adapted Version.



Brittle Fracture Surfaces• Inter granular (between grains)

• Intragranular (within grains)

. ee

(metal)

304 S. Steel

(metal))

Al OxidePolypropylene

4mm

ceram cpo ymer .

81mm(Orig. source: K. Friedrick, Fracture 1977, Vol.

3, ICF4, Waterloo, CA, 1977, p. 1119.)



Stress-Strain Curves

Brittle solids:

Ceramics andDuctile materials:

Metals and Polymers (above



Ductile and brittle fracture

--fracture in Alfracture in Al

••CeramicsCeramics alonalon withwith somesome ol mersol mers andand metalsmetals(steels(steels atat lowlow temperature)temperature) showshow littlelittle ductilityductility– – failurefailureinin anan unun predictablepredictable brittlebrittle manner manner under under tensiletensile

loadingloading



Fracture and Flow

propagation of crack: dislocation motion:

lastic flow



Why metals are tough?

When stress ahead of a crack tip exceeds the metal’s yield

-

blunts the crack tip, and leads to toughness.

σ

y e strengt

x

app e

crack





Why ceramics are brittle??

Ionic bonding (dislocation movement restricted only to specificplanes due to charge neutrality conditions)

Covalent bonding (high energy required to distort highly

directional bonds)

Dislocation core width is narrower than that in metals

-

Less than five independent and active slip systems

(failure of Von Mises criterion!)

Difficult for a ceramic grain to change its shape by

rotation : strain incompatibilities at grain boundaries

lead to high localised stresses and brittle fracture!!



Ideal vs Real Materials

• Stress-strain behavior (Room T):

TS << TSengineering

materials

perfect

materials

σE/10 perfect mat’l-no flaws

carefull roduced lass fiber

E/100

typical ceramic typical strengthened metal

ε0.1

• Reprinted w/...-- the longer the wire, the

smaller the load for failure.

permission from R.W.

Hertzberg,

"Deformation and

Fracture Mechanics

of En ineerin

• Reasons:

-- flaws cause premature failure.

--

Materials", (4th ed.)

Fig. 7.4. John Wiley

and Sons, Inc., 1996.

15



Flaws are Stress Concentrators!

Results from crack propagation

• Griffith Crack

/ 21

ot

t

om Ka

σ=⎟⎟⎜⎜ ρσ=σ 2

where

ρt = radius of curvature

σo = applied stressσm = stress at crack tip

16

From Fig. 11.8(a)

Callister’s Materials Science and Engineering, Adapted Version.



Concentration of Stress at Crack Ti

17



En ineerin Fracture Desi n

• Avoid sharp corners!

Stress Conc. Factor, K tmax

σo

=

w.

r , h

max

increasing w/h2.0filletradius

1.5 Adapted from Fig.

8.2W(c), Callister 6e.

(Fig. 8.2W(c) is from G.H.

r /h0 0.5 1.0

1.0, . .

(NY), Vol. 14, pp. 82-87

1943.)

18



Crack Pro a ation

Cracks propagate due to sharpness of crack tip

• A plastic material deforms at the tip, “blunting” the

crack.deformed

region

• Elastic strain energy-

• ener stored in material as it is elasticall deformed

• this energy is released when the crack propagates

• creation of new surfaces requires energy

19



Griffith Theory of Brittle Fractureσ Energy criterion

•Increase in surface ener associated

with crack : Us = 4cγs

2c

energy: Uel = σ 2π c2 /2E

σ

Overall system energy U= Us- Uel

For the spontaneous crack extension above a critical crack length22

⎞⎛ cd dU π σ

2=

⎠⎝ −=

E dcdc s

2/1

⎠⎝ = c

s

f π σ



When Does a Crack Pro a ate?

Crack propagates if above critical stress

2/1

2 ⎞⎛ E sγ i.e., σm > σc

⎠⎝ cc

π or Kt > Kc

– E = modulus of elasticity

– =s

– c = one half length of internal crack

– Kc = σc/σ0

For ductile => replace γs by γs + γp

21

whereγp

is plastic deformation energy



Crack opening in different mode of loading geometries

Cracks in engineering components loaded in one of three ways (or a

combination of all three):

Mode I is the most dan erous since the K-factor is much

mode I mode II mode III

larger in mode-I than in other modes of crack opening as

the tensile stress tries to open up the crack more severely.



Measurement of K

Long crack fracture toughness measurement :

SENB

Short crack fracture toughness measurement :

Indentation tests



Single Edge Notched Beam test (SENB)



Indentation Microfracture method

KIc

= 0.016 (E/H)1/2P/c3/2 (Anstis’s formula)

. . ,(K

Ic) can be computed from the expression given by Niihara et al.:

( K ϕ /H a1/2)*(H/Eϕ)2/5 = 0.035(l/a)-1/2ϕ ϕ

Where ϕ = 3 and l= Plamqvist crack length =c-a



Indentation Microfracture method

For median cracks (c/a ≥2.5), the corresponding expression is

ϕ ϕ -Icϕ ϕ = .

Shett at el.163 modified the e uation of Niihara et al.

KIc = 0.025(E/H)0.4

(HW)1/2

where W= P/4a (P the indentation load, 2a the Vickers diagonal).

I d i h i B di



Indentation strength in Bending

K = η(E/H)1/8(σP1/3)3/4

Chantikul’s formula

where η= 0.59

and σ the failure

.





Fracture Tou hnessGraphite/Ceramics/Semicond

Metals/ Alloys

Composites/fibers

Polymers

100

Ti alloys

Steels- ers

40

506070

Based on data in Table B5,Callister’s Materials Science and

Engineering, Adapted Version. 0 . 5 ) Mg alloys

20

30

Al/Al oxide(sf) 2

Composite reinforcement geometry is: f

= fibers; sf = short fibers; w = whiskers;p = particles. Addition data as noted

(vol. fraction of reinforcement):1. (55vol%) ASM Handbook, Vol. 21, ASM Int.,

a ·10

Diamond7

C/C( fibers) 1 Al oxid/SiC(w) 3

Al oxid/ZrO 2(p)4

Si nitr/SiC(w) 5

Y2O3/ZrO 2(p)4

Materials Park, OH (2001) p. 606.

2. (55 vol%) Courtesy J. Cornie, MMC, Inc.,

Waltham, MA.

3. (30 vol%) P.F. Becher et al., Fracture

Mechanics of Ceramics, Vol. 7, Plenum Press

5

I c ( M

car e

4

3PVC

PP

PET Al oxideSi nitride

Glass/SiC(w)

. . - .

4. Courtesy CoorsTek, Golden, CO.

5. (30 vol%) S.T. Buljan et al., "Development of

Ceramic Matrix Composites for Application in

Technology for Advanced Engines Program",

ORNL/Sub/85-22011/2, ORNL, 1992.

PC2

29

6. (20vol%) F.D. Gace et al., Ceram. Eng. Sci.

Proc., Vol. 7 (1986) pp. 978-82.Si crystal

Glass -sodaConcrete

Glass

0.50.7

<111>

Polyester

PS

0.6



Desi n A ainst Crack Growth

• Crack growth condition:

• Largest, most stressed cracks grow first!

c = aπσ

--Result 1: Max. flaw size

dictates design stress.

--Result 2: Design stress

dictates max. flaw size.

cdesign

aYKπ

<σ

2

1⎟⎟ ⎞⎜⎜⎛

σπ<

desi n

cmax

YKa

σ amax

no

fracture

no

fracture

30

max



Desi n Exam le: Aircraft Win

• Material has Kc = 26 MPa-m0.5

...

Design A

--largest flaw is 9 mm

Design B

--use same material--failure stress = 112 MPa --largest flaw is 4 mm

--failure stress = ?

• Use...cK

=σ

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

aY π

σ a = σ a

9 mm112 MPa 4 mm-- esu :

Answer: MPa168)( B =σc

A B

31

• Reducing flaw size pays off!



Loadin Rate

• Increased loadin rate... • Wh ? An increased rate

-- increases σy and TS

-- decreases %EL

gives less time for

dislocations to move pasto s ac es.

σ

σy larger

TSsmaller

ε

ε

σy

32



Im act Testin

• Impact loading: (Charpy)

-- makes material more brittle

-- decreases toughness

Adapted from Fig. 11.12(b),

Callister’s Materials Science and

Engineering, Adapted Version.

(Fig. 11.12(b) is adapted fromH.W. Hayden, W.G. Moffatt, and

J. Wulff, The Structure and

Pro erties of Materials, Vol. III,

Mechanical Behavior , John Wiley

and Sons, Inc. (1965) p. 13.)

final height initial height

33



Tem erature

• Increasing temperature...--increases %EL and K

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

° y

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

. .,

t E n e

r

polymers

More DuctileBrittle

I m p a

High strength materials (σy > E/150)

Temperature

Ductile-to-brittle

. .Callister’s Materials Science

and Engineering,

Adapted Version.

34

rans on empera ure

D i St t



Design Strategy:

• re- : e an c • : er y s ps

Reprinted w/ permission from R.W. Hertzberg,

"Deformation and Fracture Mechanics of Engineering

Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and

Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard,

Reprinted w/ permission from R.W. Hertzberg,

"Deformation and Fracture Mechanics of Engineering

Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and

Sons, Inc., 1996. (Orig. source: Earl R. Parker,The Discovery of the Titanic.) "Behavior of Engineering Structures", Nat. Acad. Sci.,

Nat. Res. Council, John Wiley and Sons, Inc., NY,

1957.)

35

.

F ti



Fatigue

• Fatigue = failure under cyclic stress.Ex: Rotating shafts, connecting rods, aircraft wings and leaf

spr ngs e c. . . ,

Callister’s Materials

Science and Engineering,

Adapted Version.

compression on top

motor

specimen

g. . s rom

Materials Science in

Engineering, 4/E by Carl.

A. Keyser, Pearson

Education, Inc., U ertension on bottom

flex coupling

ear ng ear ng

• tress var es w t t me.-- key parameters are S, σm, and σmax

σmS

Saddle River, NJ.)

σmin time

• Key points: Fatigue...--can cause part failure, even though σmax < σc.

-- ~

36

.



Fati ue

• Fatigue = failure under cyclic stress.

. . ,


Science and Engineering,

Adapted Version.

compression on top

counter motor

specimen

bearing bearingg. . s rom

Materials Science in

Engineering, 4/E by Carl.

A. Keyser, Pearson

Education, Inc., U er

tension on bottom

flex coupling

• tress var es w t t me.-- key parameters are S, σm, and σmax

σmS

Saddle River, NJ.)

σmin time

• Key points: Fatigue...--can cause part failure, even though σmax < σc.

-- ~

37

.



Fati ue Desi n Parameters

• Fatigue limit, Sfat: case forS = stress amplitude

-- fat

Sfat

s ee yp.unsa e

From Fig. 11.19(a),

Callister’s MSE

Adapted Version.10

310

510

710

9

• Sometimes, theS = stress am litude

Al (typ.)unsafe

From Fig. 11.19(b),

Callister’s MSE

Adapted Version.

safe

38N = Cycles to failure

10 10 10 10



Fati ue Mechanism

• Crack grows incrementally

.

a~ σΔ

( )mK

dN

daΔ=

increase in crack length per loading cycle

crack ori in• a e ro a ng s a

--crack grew even though

--crack grows faster as• σ increases From Fig. 11.21,

’• crac ge s onger

• loading freq. increases.

Science and

Engineering, Adapted

Version.

(Fig. 11.21 is from D.J.

39

u p , n ers an ng

How Components Fail,

American Society forMetals, Materials Park,

OH, 1985.)



Im rovin Fati ue Life

1. Impose a compressive S = stress amplitudeFrom Fig. 11.24,


Science and

(to suppress surface

cracks from growing) moderate tensile σm

near zero or compressive σmIncreasing

σm

ng neer ng, ap e

Version.

N = Cycles to failure

-- e o : s o peen ng

putsurface

shot

-- e o : car ur z ng

C-rich gas

intocompression

2. Remove stress

concentrators. From Fig. 11.25,

bad better

40

a s er s a er a s

Science and

Engineering, AdaptedVersion.

bad better



Cree

Sample deformation at a constant stress (σ) vs. time

σ

,

0 t

s g emp. e orma on . m; (Tm is MP in K)



Cree

• Occurs at elevated temperature, T > 0.4 Tm

tertiary

elastic

secondary

rom gs. . ,


Science and Engineering, Adapted Version.

C



Creep

Primary Creep: slope (creep rate) decreases with time.Secondary Creep: steady-state i.e., constant slope.

, . . .



Secondar Cree

• Strain rate is constant at a given T, σ-- strain hardening is balanced by recovery

stress exponent (material parameter)

strain rateactivation energy for creep(material parameter)⎟ ⎠⎜⎝ −σ=ε RT

QK

cn

s exp2&

applied stressmaterial const.



• ,

100

427°C

538°C

20

40

649°C

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

From Fig. 11.31, Callister’s Materials Science and Engineering, Adapted Version.



C F il



Cree Failure• Failure:

along grain boundaries.

g.b. cavities

stress

From V.J. Colangelo and F.A. Heiser, Analysis ofMetallurgical Failures (2nd ed.), Fig. 4.32, p. 87, John

Wiley and Sons, Inc., 1987. (Orig. source: Pergamon

LtT =+ lo20

• Time to rupture, tr

Press, Inc.)

function of

a lied stresstemperature

time to failure (rupture)

C F il



Cree Failure

• Estimate rupture timeS-590 Iron, T = 800°C, σ = 20 ksi

From Fig. 11.32,


Science and

En ineerin Ada ted i

100

Version.

(Fig. 11.32 is from F.R.

Larson and J. Miller, t r e s s ,

k s

10

20

. , ,

(1952).)

112 20 24 2816

data for

S-590 Iron

LtT =+ lo20

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

1073K

ns: tr = r



Dr. Anandh, IITK



Dr. Anandh, IITK



Dr. Anandh, IITK





Dr. Anandh, IITK



• Engineering materials don't reach theoretical strength.

• Flaws produce stress concentrations that cause

premature failure.

• arp corners pro uce arge s ress concen ra ons

and premature failure.

•

- for noncyclic σ and T < 0.4Tm, failure stress decreases with:

- increased maximum flaw size

- decreased T,

- increased rate of loading.

-- cycles to fail decreases as Δσ increases.

- for higher T (T > 0.4Tm):

- time to fail decreases as σ or T increases.

Documents

MT-201B Fractrure Fatigue and Creep