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Lecture 1

MECH 4003 Lecture Notes - Lecture 1: Zirconium


Department
Mechanical Engineering
Course Code
MECH 4003
Professor
wing
Lecture
1

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1
MAAE4102‐Materials:Strength&Fracture

Assignment1(coverssection1‐6)


1‐1Describethephenomenaof(a)brittlefractureand(b)cleavagefracture.Ensurethatyouranswer
clearlydifferentiatesthetwophenomena.
1‐2CleavageoccursinBCCcrystallinematerials(Carbonsteel,alloyedsteelandferriticstainlessstee)
on(100)planes,considerwhatmighthappentothefractureenergyofarandomlyoriented
polycrystallineBCCsampleifthegrainsizewerereducedseveralfold.
1‐3Carefullypreparedrodsofsiliconcanwithstandextremelyhighstressbeforefracturing.When
fracturedoesoccur,thesampleexplodesintopowder.Why?
1‐4Explainwhybiaxialtensileloadingincreasestheprobabilityofcleavage.
1‐5Itwasobservedthatwhentwosteelsrodsofthesamediameterwerebrazedendtoendwith
silver(fcc)andpulledintension,neckingstartedinthesilverlayerandthenfracturetookplaceby
cleavageofthesilver.Thesteelhadnotbeenstressedtoit'syieldpointwhenfailureoccurred.
Explainwhycleavagefailurewouldoccurinthesilver.
1‐6A3.5kgsteelriflefiresabulletweighing14gramswithaninitialvelocityof800m/second.What
istheaveragestresslevelrequiredintherifletoprovidesufficientstoredelasticenergyequaltothe
kineticenergyofthebullet?(forsteel;Young'sModulus=200GPa,density=7.8x103kg/m3).[about2
GPa].

2‐1InourcasestudyofSCConstainlesspipes,SEMwasusedtoanalyzethecompositionofthe
surfacedeposits.ItisknownthatbothCandOcontentsshownwereoverestimatedduetothe
inabilityofSEMtodetectlightelementsandpossiblecontamination.Recalculatethewt%ofthe
elementsgiveninFigure4afterexcludingbothCandO.
2‐2ListtheavailablefunctionsofSEMinthefieldoffailureanalysis.Specifycaseswherethe
capabilitiesofSEMarelimitedandotheranalyticaltechniquesarerequired.
2‐3Discusstheadvantagesandlimitationsofusingputtytomakeareplicaofthefracturesurface.
2‐4Whenanalyzingfailedcomponents,itisimportanttosectionthroughthefracturesurfaceand
examinethemicrostructureofthesurfacesnormaltothefracturesurface.Givethreeexamples
wherethemicrostructureofthecrosssectionprovidescriticalinformationtodeterminethefailure
cause.

3‐1BCCmetalsoftenfractureinabrittlemanneratlowtemperature,particularlywhenimpactloads
areapplied.Incontrast,FCCmetalsareductileeventothelowesttemperatures.Explainwhythis
differencebetweenFCCandBCCmetalsexists.
3‐2Engineerswhointhepastdesignedrivetedshipspaidlittleattentiontotransitiontemperatures,
unlikethosewhocurrentlydesignweldedships.Why?
3‐3Definethedesignimplicationsof(1)DBTT(forBCCmetals)and(2)Tg(foramorphousorsemi‐
crystallinepolymers).
3‐4Listfivefactorscontributingtobrittlefailureofengineeringmetals.


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4‐1Asteelbarfracturesinabrittlemanneratastressof300MPa.TheASTMgrainsizenumberis3.
Assumethatthecriticalcracklengthequalsthegraindiameter.Calculatefracturesurfaceenergy.[90
J/m2]

4‐2TheeKIcforasteelis186MPamÂœ.Asemi‐infiniteplateofthismaterialistobeloadedtoastress
levelof900MPa.Ifa9mmpre‐existingcrackexistsattheedgeoftheplate,determineifunderthe
appliedstressthecrackwilladvance.[σc≈987MPa,socrackwillnotgrow]

4‐3AmaterialpossessingaKIcof50MPa√mandYSof1000MPaistobemadeintoalargepanel.
(a)Ifthepanelisstressedto250MPa,whatisthemaximumsizeflawthatcanbetoleratedbefore
catastrophicfailure?(Assumetheflawisremotefromanyedges.)
(b)Atfracture,whatisthesizeoftheplasticzoneatthemiddleofthepanelalongthecrackfront?
(c)Ifthepanelwere2.5cmthick,wouldthisconstituteaplanestraincondition?
(d)Ifthethicknesswereincreasedto10cm,wouldtherebeachangeinthecriticalflawsize
calculatedinpart(a)?[(a)2a=0.025m,(b)1.3x10‐4m,(c)yes,planestrain,(d)no]

4‐4Alargeplateofgoodqualitysteelistobeputinserviceandwillexperienceplanestraintensile
loads.Theminimumflawsizefordetectionofacentralcrackis2mmlengthandthedesignstressis
takenasœtheU.T.S.
(a)ThesteelinitiallyselectedforthisapplicationhasaU.T.S.of1500MPaandfracturetoughnessof
70MPam1/2.Isthissteelsatisfactory?
(b)Inordertoreducethemassofthestructureitisproposedtoaltertheheattreatmentofthesteel
toraisetheU.T.S.to2000MPawithaconsequentreductioninKIcto35MPam1/2.Giventhese
propertiesisitpossibletoreducethemass?
[(a)yes,itissatisfactory,(b)2000MPasteelwillcausebrittlefailure]

4‐5Awingstructuralelementforanaircraftistocarryamaximumstressof300MPaandwillhavea
thicknessof15mm.Thecomponentistobemanufacturedofeither2024‐T3or7075‐T6aluminum.
Theyieldstressandplanestrainfracturetoughnessforthesetwomaterialsaregivenbelow.The
planestressfracturetoughnessisapproximately2.5timestheplanestrainfracturetoughness.
Calculatetheratiobetweenthecriticalcracksizethatwillcauseunstablecrackgrowthforthetwo
materials.Whichdoyourecommendfortheapplication?(Assumethatthestressintensityfactor
calculatedforaninfiniteplateisvalidforthegeometryofthewingstructuralelement.)
Material YieldStress(MPa) KIcMPa√m
2024‐T3  345   44.0
2024‐T8  455   25.5
7075‐T6  495   25.5
(a) Aredesignoftheaerodynamicprofileofthewingincreasestheexpectedstressto425MPa.Thus,
the2024‐T3hasinsufficientstrengthanditisproposedthat2024‐T8couldbeusedinstead.Given
therevisedstresslevel,whichmaterialispreferred,2024‐T8or7075‐T6?
[(a)use2024‐T3,(b)use7075‐T6]

4‐6Thefracturetoughnessasafunctionofplatethicknessisgivenintheplotshown.Auniaxially
loadedpartofthismaterialis2.5mmthickness.Itisdesiredtoincreasethefractureloadcarrying

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capacitybyafactorofthree.Ifthethicknessweretripled,whatwouldbetheratioofthenew
fractureloadtotheoriginalfractureloadif(a)nocracksorflawsarepresent,and(b)ifthroughcracks
ofthesamelengtharepresentatboththicknesses?[(a)fractureloadistripled,(b)newload/oldload
=1.6]


4‐7(a)Youaredesigningalandinggearstrutforasmallutilityaircraft.Thestrutis12incheslongand
willbecircularincross‐sectionandmustcarryaloadduringlandingof40,000pounds.Sinceifthe
strutfailsthepilotwillloosecontroloftheplaneduringlandingthemaximumdesignstressisnotto
exceedŒofthematerialyieldstrength.Thestrutwillbeperiodicallyinspectedandedgecracksthat
are0.3incheslongaredetectable.Giventhepropertiesofthetwomaterialsbelow,whichoneis
mostsuitable,ifthestrutistohaveaminimumweight.(ForedgecracksassumeKIc=1.2σ√πa)

MaterialY.S.FractureToughness Density
ksi ksiin
1/2
  lb/in
3

TiAlloy 100 90  0.16
AlAlloy70 22  0.10

(b)Youhavefoundthatsomecarelessoperatorsmaynotinspectthelandingstrutatthe
recommendedintervalsandconsequentlycracks>0.3inchesmayremaininservice.Shouldyoualter
yourselectionofmaterialtoensurethestrutwillnotfail,evenforthecarelessoperator?[(a)useAl,
(b)yeschangetoTi]

4‐8Thethickwalledcylindricaldiearrangementillustratedisusedtoconsolidatepowderedmetal
intofullydensecomponents.Theinsideradiusriis6.4mmandtheouterradiusr0is38mm.
Unfortunatelythefirsttimethediewasloadeditfailedatapressureof340MPa,asaresultofthe
thumbnailcrackshownforwhicha=1.2mm.
(a)Estimatethefracturetoughnessofthediematerial.
(b)Iftheyieldstrengthofthediesteelwas2000MPaandthevesselwasdesignedagainstplastic
yieldingwithasafetyfactorof3.Estimatethefracturetoughnessrequiredtopreventfracturewith
theexisting1.2mmthumbnailcrack.
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