chapter_08_mekanika perpatahan (pak fitrullah)

7/23/2019 Chapter_08_mekanika Perpatahan (Pak Fitrullah)

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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.

CH&2345 8674CH&+ C&9 '& 9:54



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.

<:C3 94 " ,5 3394 '& 9:54



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$

4D6 '& 9:54 E' & 2 24



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$

7E<45&349G <:C3 94 '& 9:54



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.

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J7etals Hand*oo%Jth ed 'ig$ F( p$

@F0$ Cop!right 1 8F

&"7 nternational7aterials 2ar% EH$

)7icrograph *! <$5$<ierc%s &rgonne

+ational 9a*$.

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rom J7etalsHand*oo%J th ed 'ig$

@@ p$ F($ Cop!right1 8F &"7

nternational 7aterials

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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 $.

,5 3394 '5&C3:54 ":5'&C4"



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 $

<4&9 " 54&9 7&345 &9"



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

'9&/" &54 "354"" CE+C4+35&3E5"



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



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

/H4+ <E4" & C5&CL 25E2&K&34?



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.

K4E7435G 9E&< R 7&345 &9



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 >$

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'5&C3:54 3E:KH+4""



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

<4" K+ &K& +"3 C5&CL K5E/3H



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



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@$.

9E&< +K 5&34



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

nc$ :pper "addle 5i#er +ew Aerse!$

347245&3:54



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$.

<4" K+ "35&34KG6"3&G &,E 4 3H4 <,33



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$

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'&3 K:4



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


&dapted rom 'ig$8$10)a. Callister6e.

&dapted rom 'ig$8$10)*. Callister 6e.

'&3 K:4 <4" K+ 2&5&74345"



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$.

'&3 K:4 74CH&+ "7



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


near ero or compressi#e σm

&dapted rom'ig$ 8$>> Callister6e.

725E +K '&3 K:4 9 '4



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

σ,εσ

( t



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

$

"4CE+<&5G C5442



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$.

C5442 '& 9:54



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$

":77&5G



Chapter 8-

5eading6

Core 2ro*lems6

"el -help 2ro*lems6

(

&++E:+C474+3"

chapter_08_mekanika perpatahan (pak fitrullah)

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