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Chapter 8-
ISSUES TO ADDRESS...
• How do faws in a material initiate ailure?• How is racture resistance quanti ed; how do di erent material classes compare?• How do we estimate the stress to racture?
1
• How do loading rate loading histor! and temperature a ect the ailure stress?
"hip-c!clic loadingrom wa#es$
Computer chip-c!clicthermal loading$
Hip implant-c!clicloading rom wal%ing$
&dapted rom 'ig$ 8$( Callister 6e. )'ig$ 8$( is *! +eil ,oen i The NewYork Times $.
&dapted rom 'ig$ 18$11/)*.Callister 6e. )'ig$ 18$11/)*. iscourtes! o +ational "emiconductorCorporation$.
&dapted rom 'ig$10$1 )*. Callister 6e.
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Chapter 8-
er!<uctile 7oderatel!<uctile ,rittle'racture*eha#ior6
9arge 7oderate=&5 or =496 "mall
>
• <uctile racture is desira*le
• Classi cation6
<uctile6 warning *e ore
racture
,rittle6 +o
warning
&dapted rom 'ig$ 8$1Callister 6e.
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Chapter 8-@
• <uctile ailure6 --one piece --large de ormation
• ,rittle ailure6 --man! pieces --small de ormation
'igures rom $A$ Colangelo and '$&$Heiser Analysis of MetallurgicalFailures )>nd ed$. 'ig$ B$1)a. and )*.p$ Aohn /ile! and "ons nc$1 80$ :sed with permission$
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Chapter 8-B
• 4#olution to ailure6nec%ing
#oidnucleation
#oid growthand lin%age
shearingat sur ace racture
σ
•5esulting
racture sur aces )steel.
F( µm
particlesser#e as #oidnucleation
sites$
F( µm
1(( µm
'rom $A$ Colangelo and '$&$ Heiser Analysis of Metallurgical Failures )>nd ed$. 'ig$ 11$>8 p$ > B Aohn/ile! and "ons nc$ 1 80$ )Erig$
source6 2$ 3hornton J. Mater. Sci $ol$ 1 01 pp$ @B0-F $.
'racture sur ace o tire cord wireloaded in tension$ Courtes! o
'$ 5oehrig CC 3echnologies<u*lin EH$ :sed with
permission$
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Chapter 8-F
• nter granular
)*etween grains.
• ntra granular
)within grains.
&l E ide)ceramic.
5eprinted wI
permission romJ'ailure &nal!sis o,rittle 7aterialsJ p$08$ Cop!right 1 (
3he &merican Ceramic"ociet! /ester#illeEH$ )7icrograph *!5$7$ Kru#er and H$
Lirchner$.
@1 "$ "teel)metal.
5eprinted wIpermission rom
J7etals Hand*oo%Jth ed 'ig$ F( p$
@F0$ Cop!right 1 8F
&"7 nternational7aterials 2ar% EH$
)7icrograph *! <$5$<ierc%s &rgonne
+ational 9a*$.
@(B "$ "teel)metal.5eprinted wIpermission
rom J7etalsHand*oo%J th ed 'ig$
@@ p$ F($ Cop!right1 8F &"7
nternational 7aterials
2ar% EH$ )7icrograph*! A$5$ Leiser and &$5$Elsen Ea% 5idge+ational 9a*$.
2ol!prop!lene)pol!mer.5eprinted wI
permission rom 5$/$Hert *erg J<e or-mation and 'racture7echanics o4ngineering7aterialsJ )Bth ed$.'ig$ 0$@F)d. p$ @(@
Aohn /ile! and "onsnc$ 1 $
@µm
B mm1 ( µm
1 mm)Erig$ source6 L$ 'riedric% Fracture 1 !!
ol$ @ C'B /aterloo C& 1 00 p$ 111 $.
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Chapter 8-
• "tress-strain *eha#ior )5oom 3.6 σ
ε
4I1(
4I1((
($1
per ect matMl-no faws
care ull! produced glass *er
t!pical ceramic t!pical strengthened metalt!pical pol!mer
3" NN 3"engineeringmaterials
per ectmaterials
• <a inci )F(( !rs ago . o*ser#ed$$$ --the longer the wire the smaller the load to ail it$• 5easons6 --faws cause premature ailure$ --9arger samples are more fawed
5eprinted wIpermission rom5$/$ Hert *ergJ<e ormation and'racture 7echanicso 4ngineering7aterialsJ )Bthed$. 'ig$ 0$B$ Aohn/ile! and "ons
nc$ 1 $
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Chapter 8-0
• 4lliptical hole in
a plate6
• "tress distri*$ in ront o a hole6
• "tress conc$
actor6
,&< L tOO@+E3"E,&<
L tP
σma
ρt
≈ >σoa +1 ρtσ
σo
>a
L t = σma Iσo
• 9arge L t promotes ailure6
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Chapter 8-8
• &#oid sharp corners
rIh
sharper llet radius
increasing wIh
( ($F 1$(1$(
1$F
>$(
>$F
"tress Conc$ 'actor L tσmaσo
P
&dapted rom 'ig$
8$>/)c. Callister 6e. )'ig$ 8$>/)c. is romK$H$ +euge*auer"ro#. $ng. )+G. ol$1B pp$ 8>-80 1 B@$.
4+K +445 +K '5&C3:54 <4" K+
r llet
radius
w
h
σo
σma
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Chapter 8-
• ρt at acrac%tip is #er!small
σ
• 5esult6 crac% tip stress is #er! large$
• Crac% propagateswhen6 the tip stress is large enough to ma%e6 distance
rom crac% tip
σtip = L >πσtip
increasing L
L Q L c
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Chapter 8-1(
• Condition or crac%propagation6
• alues o L or some standard loads Rgeometries6σ
>a>a
σ
aa
L = σ πa L =1$1σ πa
L Q L c"tress ntensit! 'actor 6--<epends on load R geometr!$
'racture 3oughness 6--<epends on the material temperature en#ironmentR
rate o loading$
unitso L 6
72a mor %si in
&dapted rom 'ig$ 8$8Callister 6e.
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Chapter 8-11
KraphiteICeramicsI"emicond
7etalsI&llo!s
CompositesI*ers2ol!mers
F
L 8 c ) 7 2 a S m ( $ F
.
1
7g allo!s&l allo!s
3i allo!s
"teels
"i cr!stalKlass-sodaConcrete
"i car*ide
2C
Klass
($F
($0
>
B
@
1(
>(
@(
N1((ON111O
<iamond
2 C22
2ol!ester
2"
243
C-C)TT *ers.1
($
0
B(F(
(0(
1((
&l o ide"i nitride
CIC) *ers. 1
&lI&l o ide)s . >
&l o idI"iC)w. @
&l o idIUrE >)p. B"i nitrI"iC)w. F
KlassI"iC)w.
G>E @IUrE >)p. B
L cmetals
L c
comp
L ccer ≈ L c
pol! i n c r e
a s
i n g
,ased on data in 3a*le ,FCallister 6e $
Composite rein orcement geometr!is6 P *ers; s P short *ers; w Pwhis%ers; p P particles$ &dditiondata as noted )#ol$ raction orein orcement.61$ )FF#ol=. ASM %an#&ook ol$ >1 &"7
nt$ 7aterials 2ar% EH )>((1. p$ ( $>$ )FF #ol=. Courtes! A$ Cornie 77C nc$/altham 7&$@$ )@( #ol=. 2$'$ ,echer et al$ Fracture
Mechanics of Ceramics ol$ 0 2lenum2ress )1 8 .$ pp$ 1-0@$B$ Courtes! Coors3e% Kolden CE$F$ )@( #ol=. "$3$ ,ulVan et al$J<e#elopment o Ceramic 7atriComposites or &pplication in 3echnolog!
or &d#anced 4ngines 2rogramJE5+9I"u*I8F->>(11I> E5+9 1 >$
$ )>(#ol=. '$<$ Kace et al$ Ceram. $ng.Sci. "roc. ol$ 0 )1 8 . pp$ 08-8>$
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Chapter 8-1>
• Crac% growthcondition6 Gσ πa• 9argest most stressed crac%s grow rst
--5esult 16 7a faw
si e dictates design stress$
--5esult >6 <esign stress
dictates ma $ faw si e$
σdesign < L c
G πa maH a ma < 1
πL c
Gσdesign
>
L Q L c
a ma
σno
racture
racture
a ma
σno
racture
racture
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Chapter 8-1@
• 3wo designs to consider$$$<esign & --largest faw is mm -- ailure stress P 11> 72a
<esign , --use same material --largest faw is B mm -- ailure stress P ?
• :se$$$ σc = L c
G πa maH
• Le! point6 G and L c are the same in *oth designs$ --5esult6
σc a maH( )& = σc a maH( ),
mm11> 72a B mm
&nswer6 σc( ), =1 872a• 5educing faw si e pa!so
• 7aterial has L c P > 72a-m ($F
<4" K+ 4D6 & 5C5&'3 / +K
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Chapter 8-1B
• ncreased loading rate$$$ --increases σ! and 3" --decreases =49• /h!? &n increased rate gi#es less time or disl$ to mo#e past o*stacles$
initial heightnal height
sample
σ
ε
σ!
σ!
3"
3"larger ε
smaller ε
)Charp!.• mpact loading6 --se#ere testing case --more *rittle
--smaller toughness&dapted rom 'ig$ 8$11)a.and )*. Callister 6e. )'ig$8$11)*. is adapted rom H$/$Ha!den /$K$ 7o att and A$/ul The Structure an#"ro'erties of Materials ol$
Mechanical (eha)ior Aohn/ile! and "ons nc$ )1 F.p$ 1@$.
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Chapter 8-1F
• ncreasing temperature$$$ --increases =49 and L c
• <uctile-to-*rittle transition temperature)<,33. $$$
,CC metals )e$g$ iron at 3 N 1BC.
8 m
p a c
t 4
n e r g !
3emperature
High strength materials ) σ! O4I1F(.
pol!mers
7ore <uctile,rittle
<uctile-to-*rittletransition temperature
&dapted rom C$ ,arrett /$ +iand &$3etelman The "rinci'lesof $ngineering Materials 'ig$ ->1 p$ >>( 2rentice-Hall 1 0@$4lectronicall! reproduced *!permission o 2earson 4ducation
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Chapter 8-1
• 2re-// 6 3he 3itanic • // 6 9i*ert!ships
• 2ro*lem6 :sed a t!pe o steel with a <,33 W 5oom
temp$
5eprinted wI permission rom 5$/$ Hert *ergJ<e ormation and 'racture 7echanics o4ngineering 7aterialsJ )Bth ed$. 'ig$ 0$1)a. p$> > Aohn /ile! and "ons nc$ 1 $ )Erig$source6 <r$ 5o*ert <$ ,allard The *isco)ery ofthe Titanic $.
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Aohn /ile! and "ons nc$ +G 1 F0$.
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Chapter 8-10
• 'atigue P ailure under c!clic
stress$
tension on *ottom
compression on top
countermotor
fe coupling
specimen
• "tress #aries with time$ --%e! parameters are " andσm
σma
σmin
σ
time
σm"
• Le! points6 'atigue$$$ --can cause part ailure e#en though σma N σc$ --causes W (= o mechanical engineering
ailures$
&dapted rom 'ig$ 8$1Callister 6e. )'ig$ 8$1is rom MaterialsScience in $ngineeringBI4 *! Carl$ &$ Le!ser2earson 4ducation
nc$ :pper "addle
5i#er +A$.
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Chapter 8-18
• 'atigue limit " at6 --no atigue i " N " at
• "ometimes the atigue limit is
ero
" at
case orsteel )t!p$.
+ P C!cles to ailure1( @ 1( F 1( 0 1(
unsa e
sa e
" P stress amplitude
case or&l )t!p$.
+ P C!cles to ailure1( @ 1( F 1( 0 1(
unsa e
sa e
" P stress amplitude
&dapted rom 'ig$8$10)a. Callister6e.
&dapted rom 'ig$8$10)*. Callister 6e.
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Chapter 8-1
• Crac% grows incrementally
dad+
= ∆L ( )mt!p$ 1 to
W ∆σ( ) a
increase in crac% length per loading c!cle
• 'ailed rotating sha t --crac% grew e#en though L ma N L c --crac% grows aster i • ∆σ increases • crac% gets longer • loading req$ increases$
crac% origin
&dapted rom'ig$ 8$1 Callister6e. )'ig$ 8$1 is
rom <$A$ /ulpi+n#erstan#ing %o wCom'onents Fail&merican "ociet!
or 7etals 7aterials
2ar% EH 1 8F$.
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Chapter 8-
1$ mpose a compressi#e sur ace stress )to suppress sur ace crac%s rom growing.
>(
--7ethod 16 shot peening
>$ 5emo#e stress concentrators$
*ad
*ad
*etter
*etter
--7ethod >6 car*uri ingC-rich gasput
sur aceinto
compression
shot
&dapted rom'ig$ 8$>@ Callister6e.
+ P C!cles to ailure
moderate tensile σmlarger tensile σm
" P stress amplitude
near ero or compressi#e σm
&dapted rom'ig$ 8$>> Callister6e.
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Chapter 8-
timeelastic
primar! secondar!
tertiar!
3 N ($B 3 m
+C54&" +K 3
(
strain ε
• Eccurs at ele#ated temperature 3 O ($B 3 melt• <e ormation changes with time$
>1
&dapted rom'igs$ 8$> and 8$>0Callister 6e.
C5442
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( t
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Chapter 8-
• 7ost o component li e spent here$
• "train rate is constant at a gi#en 3 σ --strain hardening is *alanced *! reco#er!
>>
stress e ponent )material parameter.
strain rate
acti#ation energ! or creep
)material parameter.applied stressmaterial const$
• "train rate increases
or larger 3 σ
1(>(
B(
1((>((
"tead! state creep rate )=I1(((h
1( -> 1( -1 1
εs
"tress )72a.B>0C
F@8C
B C
&dapted rom'ig$ 8$> Callister6e.)'ig$ 8$> is romMetals %an#&ook,
"ro'erties an#Selection, StainlessSteels- ToolMaterials- an#S'ecial "ur'oseMetals ol$ @ thed$ <$ ,enVamin)"enior 4d$.&merican "ociet! or
7etals 1 8( p$1@1$.
εs =L >σn e p −Xc53
$
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Chapter 8-
• 'ailure6
along grain*oundaries$
>@
time to ailure )rupture.
unction o applied stress
temperature
3)>( +logt r . =9
9)1( @L-log hr.
" t r e s s
%
s i
1((
1(
11> >( >B >81
data or"-F ( ron
>(appliedstress
g$*$ ca#ities
• 3ime to rupturet r
• 4stimate rupture time
" F ( ron 3 P 8((C σ P >(%si
3)>( +logt r . =9
1(0@L
>B 1 ( @ L-log hr
&ns6 t r P >@@hr
&dapted rom'ig$ 8$BF Callister6e.)'ig$ 8$BF is rom '$5$9arson and A$ 7illerTrans. ASM$ 74 0 F)1 F>.$.
'rom $A$ Colangelo and '$&$ Heiser Analysis ofMetallurgical Failures )>nd ed$. 'ig$ B$@> p$ 80
Aohn /ile! and "ons nc$ 1 80$ )Erig$ source62ergamon 2ress nc$.
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Chapter 8->B
• 4ngineering materials donYt reach theoretical strength• 'laws produce stress concentrations that cause premature ailure$• "harp corners produce large stress concentrations and premature ailure$• 'ailure t!pe depends on 3 and stress6
- or nonc!clic σ and 3 N ($B3 m ailure stress decreases with6 increased ma imum faw si e decreased 3 increased rate o loading$- or c!clic σ6 c!cles to ail decreases as ∆σ increases$
- or higher 3 )3 O ($B3 m .6
time to ail decreases as σ or 3 increases$
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Chapter 8-
5eading6
Core 2ro*lems6
"el -help 2ro*lems6
(
&++E:+C474+3"