L 7Properties of Mechanical 01.docx

L 7Properties of Mechanical 01.docx

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L7PropertiesofMechanical01

PropertiesofMaterials

II.MechanicalProperties

Themechanicalpropertiesareaboutthebehaviourofmaterialswhensubjecttoforces.Whenamaterialissubjecttoexternalforces,theninternalforcesaresetupinthematerialwhichopposetheexternalforces.

Whenamaterialissubjecttoexternalforceswhichstretchitthenitissaidtobeintension.

Tensile

Whenamaterialissubjecttoforceswhichsqueezeitthenitissaidtobeincompression.

Compression

Ifamaterialissubjecttoforceswhichcauseittotwistoronefacetosliderelativetoanoppositefacethenitissaidtobeshear.

Shearforces

Stress:

Theforceperunitarea.

=

=

Unitforstress:

1Pa=1N/m2,1MPa=1N/mm2

Q1.Abarofmaterialwithacross-sectionalareaof50mm2issubjecttotensileforcesof100N.Whatisthetensilestress?

（Answer:

2MPa）

Q2.Calculatethestressproducedina12.5mmdiameteraluminiumalloytestpiecewhenamassof3000Kgisappliedaxiallyalongthebar.（Answer:

239MPa）

Q3.A10mmdiameterbarisclampedatoneendandsuspendvertically.Calculatethestressinthebarifamassof2000Kgishungfromthefreeendofthebar.

（Answer:

249.6MPa）

Strain:

Whenamaterialissubjecttotensileorcompressiveforce,itchangesinlength.

Strain=

=

=

=

Sincestrainisaratiooftwolengthsithasnounits.

=0.01indicatethatthechangeinlengthis0.01×theoriginallength.

%ofstrain=

×100

Q4.Astripofmaterialhasalengthof50mm.Whenitissubjecttotensileforcesitincreasesinlengthby0.020mm.Whatisthestrain?

（Answer:

0.0004）

Q5.IfYoung’sModulusofelasticityforthissteelis210,000MPa,andthesteelbehaveselasticallyatthestresscalculatedinQ3,howmuchstrainwouldbeinducedbythe2000Kg.（Answer:

0.0012）

Q6.Comparetheforcerequiredtoproduceastressof170MPaina25mmdiameterbarandina50mmdiameterbar.（Answer:

i）83.4kN,ii）333kN）

Young’sModulusofElasticity（E）

E=

=

Thisappliesonlywhilstthematerialbehaveselasticallyi.eiftheforceisremoved,thematerialwillreturntoitsoriginaldimensions.Young’sModulusdescribestheelasticflexibilityorstiffnessofthematerial.

TypicalvaluesforEare:

Steel

210,000MPa

Rubber

7MPa

Aluminium

70,000MPa

Plastic

1,400MPa

Copper

100,000MPa

Wood

13,500MPa

Strength

Strengthreferstotheabilityofamaterialtowithstandstresswithoutfailure.

Thestrengthofamaterialistheabilityofittoresisttheapplicationofforceswithoutbreaking.Theforcescanbetensile,compressiveorshear.

Thetensilestressthematerialcanwithstandwithoutbreaking,i.e

Tensilestrength=

Thecompressivestrengthandshearstrengtharedefinedinasimilarway.

TheunitofstrengthisthePa.

TensileStrength

Stress

LimitofproportionalityUpperYieldStress

LowerYieldStress

Strain

Stress–straingraph

Q7.Tworods25mmindiameterofaluminiumalloymustsupportaloadof222kN.

（i）Whatisthestress?

（ii）Whatisthestrain?

（iii）Ifthealuminiumrodsarereplacedbycoppersandthestraincannotexceedthatinthealuminium,whatdiameterisrequired.

Hardness

Anothermechanicalpropertythatmaybeimportanttoconsiderishardness,whichisameasureofamaterial’sresistancetolocalisedplasticdeformation（e.g.asmalldentorascratch）.[Callister,Jr.W.D.,]

Hardnessisapropertythatisoftenrelatedtoabroadrangeofmechanicalandevenphysicalproperties.Theengineeringdefinitionofhardnessis“amaterial’sresistancetopermanentindentationunderstaticordynamicforces”–thetestsusedtodeterminethehardnessofamaterialarecalledindentationhardnesstests.

Theindentationhardnessisbyfarthemostoftenusedmethodformeasuringhardness.Therearethreestandardisedindentationhardnesstests:

SEEBELOW

▪TheBrinellhardnesstest

▪TheVickershardnesstest

▪TheRockwellhardnesstest

Thehardnessofmetalscanbedefinedasresistancetoplasticdeformationandtestmethodsarebasedonforcinganindenterintothesurfaceunderaknownload.

（i）TheBrinellhardnesstest

Thistestutilisesasteelballasanindenter.Theballispressedintothesurfaceofatestspecimenusingforcesrangingfrom9.8Nto29,400N（mass1kgto3000kg）.Ahardsteelballindenterisused.Indenterdiametersmaybe1,2,5or10mm.

Brinellhardnessisdeterminedfromtheformula:

HardnessNumber,HB=

WhereF=appliedforceinNewtons,D=diameterofindenter（mm）andd=diameterofindentation（impression,mm）.

TomakeaBrinelltest,thesurfaceofthespecimenshouldbeflatandreasonablywellpolished.Careisrequiredthatthehardnessisnotaffectedbytheproceduresusedinpreparingthespecimen.

Brinellhardnesstestresultsarealwaysreportedas:

xHBy/z,e.g.250HB10/3000

where,x=hardnessnumber,y=indenterdiameterinmm,z=massusedinkg.

（ii）TheVickershardnesstest

Thistestutilisesasquarebasedpyramidaldiamondindenterinwhichtheanglebetweentheoppositefacesis136o.Theforcemaybevariedfrom49Nto1176Nbyvaryingthemassfrom5to120kg.VaryingthemasshasnoeffectonhardnessvaluesintheVickerstestbecauseVickershardnessisindependentof

ratio.

Asquarepyramidaldiamondindenter,withanincludedangle

=136o,betweenoppositefacesisforcedintothesurfaceofametalunderaconstantloadfor15s.

Hardnessnumber,HV=

WhereF=indentingforceinNewtonsandd=meanlengthofimpressiondiagonals（mm）

Vickershardnesstestresultsarealwaysreportedas:

XHVy/z,（e.g.250HV30）

where,x=hardnessnumber,y=massusedinkg

Example11.1–p212

Indentationhardnesstestsaremadeonasampleofmetalandthefollowingresultsrecorded:

（1）usingVickersdiamondtestwith30kgloadthemeanlengthsofdiagonalswere:

1stimpression–0.527mm,2ndimpression–0.481mm,3rdimpression–0.497mm;

HD=1.854F/d2.Forthefirstimpression,HD=（1.854×30）/0.5272=200.ForthesecondimpressionHD=240,forthethirdHD=225.TheaverageofthreeimpressionsgivesHD=221.7.

（2）usingBrinelltestwith10mmballand3000kgloadthediameterofimpressionwas4.01mm.

CalculatethediamondandBrinellhardnessnumbersforthematerialandexplainanyvariationsintheresults.

HB=（2×3000）÷{10π（10-

）}=228

ThesmallsizeoftheindenterusedintheVickerstestmeansthatinanalloyanimpressionmaybeonanon-representativehardorsoftspot.Anumberofdeterminationsmayhavetobemadetoobtainatrueaveragevalue.Usinga10mmdiameterballindentertheBrinelltestgivesaresultmorerepresentativeofthemeanhardnessofthematerial.

Example11.1

TheindentingloadsnormallyusedinconnectionwithVickersdiamondtestsare:

1kg,2.5kg,5kg,10kg,20kg,30kgand50kg.Ifdeterminationsaremostaccuratewhenimpressiondiagonalsareapproximately0.5mm,whatindentingloadsshouldbeselectedforthetestingof:

（i）aluminiumsampleswithhardnessoftheorderofHD=20,

（ii）brasssampleswithhardnessoftheorderofHD=60,and

（iii）SteelsampleswithhardnessoftheorderofHD=200?

Example11.3

Samplesofpurecopperinboththeannealedandcold-workedconditionsweresubjectedtoBrinellhardnesstests,usinga1mmdiameterballindenter,withvariousloads.Thetestdataaregivenbelow.

（1）CalculatetheBrinellhardnessofthecoppersamples.

（2）CompleteaMeyeranalysisanddeterminetheMeyerconstants.

Material

Indentingload（kg）

Indentationdiameter（mm）

Annealedcopper

5

10

15

0.386

0.540

0.636

Coldworkedcopper

10

20

30

0.375

0.527

0.632

（iii）TheRockwellhardnesstest

Th

Example11.1

（iii）Meyerhardnessanalysis

TheMeyerrelationshipfortheBrinelltestisF=adnwhereFistheload（kgf）,disthediameteroftheindentationandaandnareconstantsofthematerialanditscondition.Theaisrelatedtotheresistancetoindenterpenetrationandnistheworkhardeningindex.Therelationshipcanbewritten:

logF=loga+nlogd

Usingaballindenteroffixeddiameterandaseriesofloads,thedatarecordedcanbeplottedaslogFagainstlogd.Astraightlineshouldbeobtainedandthevaluesofaandndetermined.

Thereareothertypesofhardnesstests:

▪Scratchhardnesstestswhichutilisematerialsofknownhardnessto‘scratch’unknowntestpiecesorspecimens.

▪Wearhardnesswhichisameasurementofresistancetowearunderspecificconditions.

▪Reboundhardnesswhichismeasureasenergyabsorbedunderimpactloads.

Toughness

Toughnessisameasureoftheamountofenergyrequiredtocausefailure（fracture）ofaspecimen.Onemeasureoftoughnessistheareacontainedbeneaththestress/straincurveforthematerial.Toughnessismeasuredinjoules（J）where

1J=1N.m=103N.mm

Theproductofstressandstrainis

N.mm-2mm.mm-1=N.mm.mm-3,i.etoughnessperunitvolume.

Themorecommonmethodsformeasuringthetoughnessofamaterialarethedifferenttypesofnotchedbarimpacttest,suchastheIzodtestandCharpytestusedformetalandfortheimpacttestingofpolymers.

Mostmaterialsbecomemoresensitivetonotchesasthetemperatureisreduced.Inparticularferrousmetalsundergoarelativelysuddenreductionintoughnessatatemperaturereferredtoasitstransitiontemperature-thetransitiontemperaturecanvaryfromalmost+100oCto-100oCdependinguponthechemicalcompositionandthemetallurgicalstructureofthesteel.

Elasticity

Elasticityreferstotheabilityofamaterialtodeformwithoutundergoingapermanentsetorpermanent