工程力學之材料的力學特性

Chapter3MechanicalPropertiesofMaterials13.1TheTensionandCompressionTests

*Specimenissubjectedtoaxialload.*Specimen–uniformcross-section*Useelectrical-resistancestraingauge*Measure:loadP,cross-sectionareaA0originallengthL0,changeinlength

233.2TheStress-StrainDiagram4ConventionalStress-StrainDiagram*Linearelasticbehavior

pl–proportionallimit,

y–yieldstress,

pl

yIftheloadiswithdrawn,nodeformationisleft.*YieldingWhile

increasing,

remainsthesame.

yisimportant,usedfordesignusually.*StrainhardeningMaterialbecomesharderuntil

reaches

u.*NeckingThecross-sectionbeginstoshrinkinalocalizedregion,thestressdecreases,andthethespecimenbreaksat

f.5TrueStress-StrainDiagram*InsteadofA0andL0,true(changing)AandLareused.*Beforeyielding,AandLchangelittle,twodiagramsareveryclose.Afteryielding,twocurvesdivergent.*Materialsareusuallyusedinelasticreginbeforeyielding,it’soktouseeitherone.63.3Stress-StrainBehaviorofDuctileandBrittleMaterialsDuctileMaterials*Ductilematerial–largestrain(deformation)beforeruptures.*Twowaytospecifytheductility:L0–originallength,Lf–lengthatfractureFormildsteel,

f=0.380A0–originalarea,Af–areaatfractureFormildsteel,60%

7*Someductilematerialshaveaconstant

y.steels,zinc,brass,etc.*Formostmetals(e.g.aluminum),constantyieldingdoesnotoccur.Use0.2%offsetmethodtodetermine

y.8*Someductilematerialsexhibitsnonlinearelasticbehavior.91011Stress-straincurveof304SSsample-1underquasi-statictensileloading.NameValueUnitsDiameter1.560mmPeakLoad"P"1.489kNStrainAtBreak"F"(Elongation)63.149%Young'sModulus(BetweenBandM)129.214kN/mm^2PeakStress"P"(UltimateTensileStress)778.8MPaBreakStress719.31MPaStressAtOffsetYield(0.2%Strain)297.17MPa11BrittleMaterials*Brittlematerials–littleornoyieldingbeforefailurecastiron,concrete,ceramic12*Lowstrengthintension,highstrengthincompression.1314*Ingeneral,amaterialhavebothductileandbrittlebehaviors.Steelwithhighcarboncontentismorebrittle.(ii)Atlowtemperature,materialsaremorebrittle.1516Gradient-nanostructuredmetals3.4Hooke’sLawHooke’sLaw*Inthelinearelasticstage:E–modulusofelasticity,orYoung’smodulus*E=

/

,slopeof-line*UnitofE–sameas

(stress),force/area*Eisamaterialproperty.

E–indicationofmaterialstiffnessstiffmaterial(steel)-largeEspongematerial(rubber)-smallE17*Young’smodulusremainsthesameforsteelswithdifferentcarboncontents.E=29

106psior200GPa18StrainHardeningO

A

A

OMaterialbecomesharder*Higher

pland

y*Largerelasticregion*SameE*Lessductility(morebrittle)1920Materialbecomesharder*Higher

pland

y*Largerelasticregion*SameE*Lessductility(morebrittle)3.5StrainEnergyStrainEnergy*Similartoaspring,abodywithelasticdeformationstorespotentialenergy,calledstrainenergy.*Strain-energydensityu-strainenergyperunitvolume21ModulusofResilienceur*ur–strain-energydensitywhenstress

reachestheproportionallimit

pl.

*ur–areaunder-curveinthelinearelasticrange.*urindicatestheabilitytoabsorbenergywithoutanypermanentdamagetothematerial.22ModulusofToughnessut*ut–strain-energydensitywhenmaterialisbroken.stress*ut–totalareaunder-curve.*utindicatestheabilitytoabsorbenergybeforefailure.23Alloyschangethepropertiesbychangingtheingredientcontent.2425Nanotwinnedpolycrystallinemetals2627282930313.6Poisson’sRatioWhencompressed,thebarisshortenedlongitudinally,butexpandsinlateraldirection.32Undertensionforce,thebarincreasesitslengthby

,andtheradiusreducesby

.Thestrainsinlongitudinalandlateraldirectionsare33S.D.Poissonfound(1880s)that,withintheelasticrangeandforahomogeneousandisotropicmaterial,*Since

longand

lathaveoppositesigns,

ispositive.*

isanon-dimensionalquantity.*Formostnonporoussolids,

isintherangeof1/4~1/3.*Itwasprovedtheoretically

max=1/2.Thus01/23435363.7TheShe