機械工程導論(雙語)課件五

mechanicalengineeringAnintroductionto1Lecturer:LiuJu-rongCHAPTER5MaterialsandStressOVERVIEW1TENSIONANDCOMPRESSION23RESPONSEOFENGINEERINGMATERIALS

2SHEAR4FACTOROFSAFETY5Vocabulary3shearstress剪應力stress-strain應力-應變aluminum鋁elasticmodulus彈性模數plasticbehaviorn.塑性roundrod圓鋼shrink收縮Poissoncontraction(泊松收縮gauge測量rubberband橡皮筋springbackvi.彈回hypothetical假想的chassis底盤low-carbonsteel低碳鋼stiffness剛度ductility延展性;塑性brittlematerials脆性材料castiron鑄鐵;生鐵concrete混凝土Vocabulary4ceramics陶器glass玻璃low-strain小應變permanentset永久變形;殘余變形proportionallimit比例極限pipefittings管接頭bushings襯套annealed退火tempered回火heattreatmentn.熱處理quenchingn.淬火artificialagingn.人工時效;人工老化hingepinn.鉸銷1OVERVIEW5Aspartoftheirresponsibilities,mechanicalengineersmustdesignhardwaresothatitdoesn'tbreak.Knowingthoseforcesalone,however,isnotsufficientforanengineertopredictwhetheracertainmechanicalcomponentwillbestrongenoughandnotfailinthetaskathand.By"fail"or"failure"wemeanthatthehardwarewillnotbreak,stretch,orbendsomuchastobecomenonusable.Inshort,engineersareabletocombinetheirknowledgeofforces,materials,shapes,anddimensionsinordertolearnfrompastfailuresandtobetterdesignnewhardware.1OVERVIEW6Inthischapter,wewilldiscussthepropertiesofengineeringmaterialsandexaminethevarioustypesofstressesthatcandevelopwithinthem.Tension,compression,andshearstressarequantifiesthatengineerscalculatewhentheyrelatethedimensionsofamechanicalcomponenttotheforcesactingonit.Thosestressesarethencomparedwiththematerial'sphysicalpropertiesinordertodeterminewhetherornotfailureisexpectedtooccur.Engineersgenerallyconductthistypeofforce,stress,andfailanalysisearlyinaproduct'sdesigncycleaschoicesaremadefordimensions,materials,andoperatingconditions.1OVERVIEW7FINGURE5.1Abrokencrankshaftfromasingle-cylinderinternalcombustionengine.1OVERVIEW---Theabilitytobeavailableinthischapter8Afterstudy,whatshouldyoubeabletohave?Identifycircumstanceswhereamachinecomponentisloadedintension,compression,orshear,andcalculatethestressthatispresent.Drawstress-straincurvesforandsteel,anddeterminetheelasticmodulusandyieldstrengthfromsuchUnderstandthedifferencesbetweenelasticandplasticbehaviorApplyafactorofsafetytocomponentsthataresubjectedtotensionorshearstress.2TENSIONANDCOMPRESSION

ElasticbehaviorPlasticbehavior9theroddoesnottakeonapermanentsetafterFhasbeenapplied,thestretchingissaidtooccurelastically.theforcecouldhavebeenlargeenoughthattherodwouldhavebeenplasticallydeformed,meaningthatwhentheforcewasapplied,andthenremoved,therodwouldendupbeinglongerthanitwasinitially.ThediameteroftherodshrinksbyasmallamountduetotheeffectknownasPoissoncontraction.2TENSIONANDCOMPRESSION10FINGURE5.3descriptionoftensilestressinarod.(a)Thestretchedrodwithendload,(b)asectionslicedfromtherodexposingtheinternalforceF,(c)thestressdistributedoverthecrosssection,and(d)tensilestressesactingontheendsofanyelementslicedfromtherod.2TENSIONANDCOMPRESSION

internalforceTesion11imagineslicingthroughthebaratsomepointinwardoftheright-handend.Whenthestresstendstolengthentherod,itiscalledtension,andσ>0.CompressionwhentherodwouldbeCompressionshortened,thestressiscalledcompression,andσ<0.σ=F/A2TENSIONANDCOMPRESSION

Elongation12Thestretchorelongation△LisonewaytodescribehowtherodlengthenswhenFisapplied,butitisnottheonlyway,norisitnecessarilythebestway.Strainisdefinedastheamountofstretchingthatoccursperunitoflength.Strainε(thelowercaseGreekcharacterepsilon)isscaledtotherod'soriginallengthandcalculatedfromtheexpressionε=△L/LStrain3RESPONSEOFENGINEERINGMATERIALS13Figure5.7showsanidealizedstress-straincurveforamaterialsuchasductile(韌性;可塑)low-carbonsteel(低碳鋼).SpringconstantforceFandelongation△LareproportionalaccordingtoF=k△L.Theparameterkiscalledthestiffnessorspringconstant.ThisobservationistheHooke'slawbasisoftheconceptcalledHooke'slaw,whichstatesthatforceanddeflectionareproportional.

springconstantHooke’slawStress-straincurve3RESPONSEOFENGINEERINGMATERIALS14FINGURE5.76Eachrodhassimilarstress-strainbehavior.3RESPONSEOFENGINEERINGMATERIALS15FINGURE5.7Idealizedstress-straincurveforaductilelow-carbonsteel.3RESPONSEOFENGINEERINGMATERIALS16Thestress-straindiagramforaductilematerialisbrokendownintotworegions:thelow-strainelasticregion(wherenopermanentsetremainsregionsafteraloadhasbeenappliedandremoved)andthehigher-strainplasticregion(wheretheloadislargeenoughthat,uponremoval,thematerialispermanentlyelongated).Structuralsteelsductilematerialandsomealuminumalloysareexamplesofductilemetals,andtheyareoftenusedinmachinecomponentsbecausewhentheybecomeoverloaded,theytendtonoticeablystretchorbendbeforetheybreak.Brittlematerialssuchascastiron,concrete,ceramics,andglassbreaksuddenlyandwithoutmuchpriorwarningwhentheyareoverloaded.DuctilematerialBrittlematerialElasticandplasticregions3RESPONSEOFENGINEERINGMATERIALS17ThematerialpropertythatquantifieschangesinthecrosssectioniscalledthePoissonratio,v(thelowercaseGreekcharacternu).v=εdiameter/εlength=-(△d/d)/(△L/L)△d=-vd△L/LForstrainsbelowtheproportionallimitAinFigure5.7,stressandstrainarelinearlyrelatedaccordingtoσ=EεTheelasticmodulusisamaterialproperty,anditismeasuredsimplyastheslopeofthestress-straincurveinitsstraight-lineregion.△L=εL=(σ/E)L=((F/A)/E)L==FL/EAF=k△Lwherek=EA/LEsteel≈210GPa≈30MpsiEaluminum≈70GPa≈10MpsiProportionallimitElasticmodulusPoissonratio3RESPONSEOFENGINEERINGMATERIALS18Forthatreason,theonset

ofyieldingisoftentakenbyengineersasanindicationoffailure.ThevalueofstressinregionB-Cdefinesaquantitycalledtheyieldstrength,Sy.Returningtoourdiscussionofthestress-strainbehaviorinFigure5.7,pointBiscalledtheelasticlimit.YieldingoccursintheregionbetweenBandC;forsmallchangesinstress,therodexperiencesalargechangeinstrain.elasticlimityieldingYieldstrengthAstheloadisincreasedevenfurtherbeyondUltimatestrengthpointC,σgrowstotheultimatetensilestrengthSuatpointD.Ultimatestrength19AstheforceFisapplied,thematerialtendstobesliced,sheared,orcutalongthetwoedgesmarkedasshearplanesThetwoforcesVarecalledshearforces,andtheyareorientedparalleltotheshearplanes.Theshearforcesare,infact,distributedwithinthematerialovertheentirecrosssectionsothatVistheresultantoftheshearstressShearplaneShearforce4SHEARτ=V/A204SHEARFINGURE5.11ShearforceVandsheatstressesτactonanelasticblockthatisbeingpressedbetweentworigidsupports.214SHEARSingleshearDoubleshearFINGURE5.12Adhesivelybondedconnectionsthatareplacedin(a)singleshearwithV=Fand(b)doubleshearwithV=F/2.Theadhesivelayersareindicatedbytheheavilyweightedlines.5FACTOROFSAFETY22Failureduetoductileyieldingispredictedifσ>Sy.Engineersdefinethetensilefactorofsafetyas

ntension=sy/σIfn>1,thisviewpointpredictsthatthecomponentwillnotyield,andifn<1,failisexpectedtooccur.Asdevelopedinmoreadvancedtreatmentsofstressanalysis,onetheoryformaterialfailurerelatestheyieldstrengthinsheartothevalueintensionaccordingtoSsy=Sy/2Toevaluatethepossibilityofaductilematerialyieldinginshear,wecomparestressandstrengthaccordingtotheshearfactorofsafety

nshear

=Ssy/τSUMMARY23Inthischapter,wehavediscussedtheloadingconditionsknownastension,compression,andshear,andafailuremechanismcalledductileyielding.Stressistheintensityofaforcedistributedoveranareaofmaterial.Dependingonthedirectioninwhichthestressacts,itcanbetensionorshear.Strainisdefinedasthechangeinlengthperunitoforiginallength.Becauseofitsdefinitionasaratiooftwolengths,strainisadimensionlessquantity,anditisoftenexpressedas