chapter 9 failure of materials. failure of materials why study materials failure? - design of...

Chapter 9Failure of Materials

Failure of Materials

Why study materials failure? - design of component @ structure needs the engineer to minimize (prevent) failure. - important to understand the concept of 3 failure modes; 1. Fracture. 2. Fatigue. 3. Creep.

Ship-cyclic loading from waves.Computer chip-cyclic thermal loading. Hip implant-

cyclic loading from walking.Adapted from Fig. 22.30(b), Callister 7e. (Fig. 22.30(b) is courtesy of National Semiconductor Corporation.) Adapted from Fig. 22.26(b), Callister 7e.

Adapted from chapter-opening photograph, Chapter 9, Callister & Rethwisch 3e. (by Neil Boenzi, The New York Times.)

Other examples of failure

• Brittle fracture: -- many pieces -- small deformations

• Ductile fracture: -- one piece -- large deformation

Failure of materials… - failure of engineering materials is undesirable.- several cause of failure: -- improper materials selection, processing & design. -- defects (i.e: internal/external flaws/cracks). -- economic losses. -- interference with availability of products & services.- need an appropriate preventive

measurement to against failure.

Fundamental concept

- flaws @ crack (defects).

- characteristic & mechanisms.

Testing techniques

- modes of failure.

- produce & prevent failure.

mode

Fracture

Fatigue

Creep

Ductile fracture

Brittle fracture

mechanism testing technique

Impact test

Initial crack

Crack grow

Topics covered in this chapter…

Fatigue test

Creep test


- fracture mechanics.


brittle fracture

mode of failure: Fracture

ductile fracture brittle fracture

Very ductile Moderately ductile BrittleFracture behavior

Large Moderate%AR or %EL SmallDuctile fracture is usually more desirable than brittle fracture!

Ductile: Warning before

fracture

Brittle: No warning

- accompanied by significant plastic

deformation & slow crack propagation. - common at low strain rate & high temp.- three steps : 1. Specimen forms neck & cavities within neck. 2. Cavities form crack & crack propagates towards surface, perpendicular to stress. 3. Direction of crack changes to 45o resulting in cup-cone fracture.

- little @ no significant plastic deformation

before fracture & high crack propagation. - Catastrophic (rapid crack propagation).- common at high strain rates & low temp.- three stages: 1. Plastic deformation concentrates dislocation along slip planes. 2. Microcracks nucleate due to shear stress where dislocations are blocked. 3. Crack propagates to fracture.

cha

ract

eris

tic o

f fr

act

ure

SEM micrograph

SEM micrograph

ductile fracture

At low operating temp., ductile to brittle transition (DBT) takes place

Schematic diagram

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


brittle fracture


Moderately ductile fracture

brittle fracture surfaces

SEM micrograph

SEM micrograph

ductile fracture

Intergranular (between grains)304 S. Steel (metal)Reprinted w/permission from "Metals Handbook", 9th ed, Fig. 633, p. 650. Copyright 1985, ASM International, Materials Park, OH. (Micrograph by J.R. Keiser and A.R. Olsen, Oak Ridge National Lab.)

Polypropylene(polymer)Reprinted w/ permission from R.W. Hertzberg, "Defor-mation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.35(d), p. 303, John Wiley and Sons, Inc., 1996.

4 mm

Intragranular (within grains)

Al Oxide(ceramic)

Reprinted w/ permission from "Failure Analysis of Brittle Materials", p. 78.

Copyright 1990, The American Ceramic

Society, Westerville, OH. (Micrograph by R.M. Gruver and H.

Kirchner.)

316 S. Steel (metal)

Reprinted w/ permission from "Metals Handbook", 9th ed, Fig. 650, p. 357.

Copyright 1985, ASM International, Materials

Park, OH. (Micrograph by D.R. Diercks, Argonne

National Lab.)

3 mm

160 mm

1 mm

neckings

void nucleation

shearing at surface fracture

void growth & linkage

100 mm

Fracture surface of tire cord wire loaded in tension. Courtesy of F. Roehrig, CC Technologies, Dublin, OH. Used with permission.

evolution to failure

V-shaped “chevron”

origin of crack


brittle fracture


brittle fracture (in ceramics)

ductile fracture (in thermoplastic polymer)SEM micrograph

SEM micrograph

ductile fracture - characteristic of fracture behavior: -- origin point. -- initial region (mirror) is flat & smooth. -- after reaches critical velocity crack branches (mist & hackle).

- characteristic of fracture behavior: -- craze formation prior to cracking. -- during crazing, plastic deformation of spherulites. -- and formation of micro voids and fibrillar bridges.

fibrillar bridges microvoids crack

aligned chains


- engineering materials don't reach theoretical strength.- flaws produce stress concentrations that cause premature failure.

t

Results from crack propagation.Griffith Crack

m 2o

at

1/ 2

Kto

where t = radius of curvatureso = applied stresssm = stress at crack tip

Stress concentration at crack tipFlaws are stress concentrators Engineering Fracture Design- avoid sharp corners.

, r fillet

radius

w

h

o

smax

r/h

sharper fillet radius

increasing w/h

0 0.5 1.01.0

1.5

2.0

2.5

Stress Conc. Factor, K t =smax

s0

Crack Propagation- cracks propagate due to sharpness of crack tip.

ductile

brittle deformed region


concept of fracture mechanics


Crack Propagation

- crack propagates if above critical stress.21

2/

sc a

E

i.e., sm > sc or Kt > Kc

whereE = modulus of elasticitys = specific surface energya = one half length of internal crackKc = c/so

Design Against Crack Growth


- crack growth condition:

K ≥ Kc = aY



- largest, most stressed cracks grow first!

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

max

cdesign

aY

K

s

amax

no fracture

fracture

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

2

1

design

cmax Y

Ka

amax

sno fracture

fracture

TS << TSengineeringmaterials

perfectmaterials

s

e

E/10

E/100

0.1

perfect mat’l-no flaws

carefully produced glass fiber

typical ceramic typical strengthened metaltypical polymer

Stress-strain curves (Room T) perfect & engineering materials

Design Example: Aircraft Wing

• 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

• Use...max

cc

aY

K

B max Amax aa cc 9 mm112 MPa 4 mm

-- Result:





Fracture Toughness, KIC for selected materials

Graphite/ Ceramics/ Semicond

Metals/ Alloys

Composites/ fibersPolymers

5K

Ic(M

Pa·

m0.

5)

1

Mg alloys

Al alloys

Ti alloys

Steels

Si crystal

Glass -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



testing technique: Impact test

final height initial height

(Charpy)

- classify into 3: 1. Charpy impact test. 2. Izod impact test. 3. Drop weight impact test.

Important information from impact test…1. Fracture (brittle @ ductile).2. Brittleness (impact energy @ % shear).3. Ductility (impact energy @ % shear). 4. Toughness (energy absorbed).5. Ductile-to-Brittle Transition (DBT) temperature.

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, The Discovery of the Titanic.)

Pre-WWII: The Titanic

WWII: Liberty ships

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, "Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 1957.)

Design Strategy: Stay above the DBT!

BCC metals (e.g., iron at T < 914°C)

Imp

act

En

erg

y

Temperature

High strength materials(sy > E/150)

& polymers

DBT temperature

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

more brittle more ductile

Adapted from Fig. 9.18(b), Callister & Rethwisch 3e. (Fig. 9.18(b) is adapted from H.W. Hayden, W.G. Moffatt, and J. Wulff, The Structure and Properties of Materials, Vol. III, Mechanical Behavior, John Wiley and Sons, Inc. (1965) p. 13.)

- aim: to investigate the energy absorbed &

fracture of materials during impact loading at various temperature.

- fracture behavior can be shown in impact energy vs temperature curves.

• Sinking of Titanic: Titanic was made up of steel which has DBT temperature 32oC. On the day of sinking, sea temperature was –2oC which made the the structure highly brittle and susceptible to more damage.


mode of failure: Fatigue

- metals often fail at much lower stress at cyclic

loading compared to static loading. - crack nucleates at region of stress concentration & propagates due to cyclic loading.- failure occurs when cross sectional area of the metal too small to withstand applied load.

Fatigue fractured surface of keyed shaft

Fracture started here

Final rupture

Key points: Fatigue...- failure under cyclic loading. - can cause part failure, even

though smax < sc.- causes ~ 90% of mechanical engineering failures.

- stress varies with time. -- key parameters are: 1. stress amplitude, S (@ a). 2. mean stress, sm. 3. frequency, f (will convert to no. of cycle, N).

smax

smin

s

time

smS

2minmax

m

Mean stress

2minmax

a

Stress amplitude

minmax rStress range

max

min

RStress range

Stress amplitude, S = stress to cause failureNumber of cycle, N = 1/f

- fatigue behavior can be shown in SN curves.

testing technique: Fatigue test

Important point from fatigue test… 1. Fatigue limit. 2. Fatigue strength. 3. Fatigue life.

tension on bottom

compression on top

countermotor

flex coupling

specimen

bearing bearing

Failure of Materialsmode of failure: Fatigue

Fatigue Design Parameters

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

Adapted from Fig. 9.25(a), Callister & Rethwisch 3e.

Sfat

N = Cycles to failure10 3 105 10 7 10 9

unsafe

safe

S = stress amplitude

example: SN curves for typical steel

- Sometimes, the fatigue limit is zero!

-- fatigue occurs at any time.

Adapted from Fig. 9.25(b), Callister & Rethwisch 3e.

N = Cycles to failure103 105 107 109

unsafe

safe

S = stress amplitude

• Fatigue limit: - PMMA, PP, PE

• No fatigue limit: - PET, Nylon (dry)

example: SN curves for typical polymers

Improving Fatigue Life1. Impose a compressive surface stress (to suppress surface cracks from growing)

--Method 1: shot peeningshot

--Method 2: carburizingC-rich gas

put surface into compression

2. Remove stress concentrators.

bad

bad

better

betterAdapted from Fig. 9.32, Callister & Rethwisch 3e.


mode of failure: Creep

- Creep is progressive deformation under constant stress.- Occurs at elevated temperature, T > 0.4 Tm

-- important in high temperature applications.

Primary creep: - creep rate (slope) decreases with time due to strain hardening. Secondary creep: - creep rate is constant due to

simultaneous strain hardening and recovery process. -- steady-state.Tertiary creep: - creep rate (slope) increases with time leading to necking & fracture.

testing technique: Creep test

- Creep test determines the effect of temperature & stress on creep rate.- Metals are tested at constant stress at different temperature & constant temperature with different stress.

,s e

0 t

s

Important information from -t curve…

Adapted from Fig. 9.35, Callister & Rethwisch 3e.

Ada

pted

fro

m F

igs.

9.3

6,

Cal

liste

r &

Ret

hwis

ch 3

e.

elastic

primary secondary

tertiary

Data from creep test… 1. creep strain, 2. temperature, T 3. time, t

- creep behavior can be shown in -t curves.

tr = time to failure (rupture)L = function of applied stress

T = temperature

L)t(T r log20Time to rupture, tr

Creep failure along grain boundaries.

appliedstress

g.b. cavitiescreep calculation…

Estimate rupture time for S-590 Iron, T = 800°C & s = 20 ksi

example:

24x103

1073K

Ans: tr = 233 hr

L(103K-log hr)

Str

ess,

ksi

100

10

112 20 24 2816

data for S-590 Iron

20

T(20 + log tr) = L

• Engineering materials don't reach theoretical strength.

• Flaws produce stress concentrations that cause premature failure.

• Sharp corners produce large stress concentrations and premature failure.

• Failure type depends on T and stress:

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

- increased maximum flaw size, - decreased T, - increased rate of loading.- for cyclic s: - cycles to fail decreases as Ds increases.

- for higher T (T > 0.4Tm): - time to fail decreases as s or T increases.

SUMMARY

chapter 9 failure of materials. failure of materials why study materials failure? - design of...

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