Mechanical properties of materials: Stress and strain - Linear ...

The most common way to analyze the relationship between stress and strain for a particular material is with a stress-strain diagram. SkiptoprimarynavigationSkiptomaincontentSkiptoprimarysidebarSkiptofooter Everycomponentinalinearmotionsystemexperiencessomeformofloadingduetoappliedforcesormotion.Thecomponent’sreactionstotheseloadsaredescribedbyitsmechanicalproperties. Forcomponentssubjectedtotensionorcompression—suchasload-carryingballsandrollers,shaftsmountedvertically,orfasteningandjoininghardware—themechanicalpropertiesofstressandstrainplayanimportantroleindeterminingwhetherthecomponentcanwithstandtheapplication’sloadingconditions. Therearefivefundamentaltypesofloading:compression,tension,shear,torsion,andbending. Stressistheforceappliedtoamaterial,dividedbythematerial’scross-sectionalarea.  σ=stress(N/m2,Pa) F=force(N) A0=originalcross-sectionalarea(m2) Strainisthedeformationordisplacementofmaterialthatresultsfromanappliedstress. ε=strain L=lengthafterloadisapplied(mm) L0=originallength(mm) Note:Amaterial’schangeinlength(L–L0) issometimesrepresentedasδ. Themostcommonwaytoanalyzetherelationshipbetweenstressandstrainforaparticularmaterialiswithastress-straindiagram. Thestress-straindiagramprovidesvaluableinformationabouthowmuchforceamaterialcanwithstandbeforepermanentdeformationorfailureoccurs. Manymaterialsexhibitaproportionalrelationshipbetweenstressandstrainuptocertainpoint,referredtoastheproportionallimit,shownhereaspoint“A.”Thisstress-strainrelationshipisknownasHooke’sLaw,andinthisregion,theslopeofthestress-straincurveisreferredtoasthemodulusofelasticity(akaYoung’smodulus),denotedE. Themodulusofelasticityisessentiallyameasureofstiffnessandisoneofthefactorsusedtocalculateamaterial’sdeflection underload. Justbeyondtheproportionallimit istheelasticlimit,atwhichpointthematerialtransitionsfromelasticbehavior,whereanydeformationduetoappliedstressisreversedwhentheforceisremoved, toplasticbehavior,wheredeformationscausedbystressremainevenafterthestressisremoved.Formanymaterials,theproportionallimitandtheelasticlimitarethesameornearlyequal.(Inthestress-straincurveshownhere,theproportionallimitandtheelasticlimitareassumedtobethesame.) Aslongastheappliedstressesarebelowtheproportionallimit,stress-strainrelationshipsarethesamewhetherthematerialisundertensionorcompression. Theyieldpoint,shownhereaspoint“C,”isthepointwherestrainincreasesfasterthanstress(referredtoas“strainhardening”),andthematerialexperiencessomeamountofpermanentdeformation. Formaterialsthatdonothaveawell-definedyieldpoint,orwhoseyieldpointisdifficulttodetermine,anoffsetyieldstrength—shownhereaspoint“B”— isused.Offsetyieldstrengthisthestressthatwillcauseaspecifiedamountofpermanentstrain(typically0.2percent).ItisfoundbydrawingalinethatcrossestheX(strain)axisat0.002andrunsparalleltothestress-strainline(slope=E).Thepointwherethislineintersectsthestress-straincurveistheoffsetyieldpoint. Finally,atpoint“D,”wherethecurvebeginstofall,thematerial’sultimatetensilestrengthhasbeenreached.Thispointdenotesthemaximumstressthatcanbeappliedtoamaterialintensionbeforefailureoccurs. Theterm“strength”canbeusedwithvariousmaterialproperties(tensilestrength,yield strength,shearstrength,etc.).But regardless ofthepropertybeingdescribed,“strength”typicallyreferstoamaterial’sresistancetofailure,eitherthroughfractureorexcessivedeformation. Notethatinthediscussionabove,theoriginalcross-sectionalareaandlength(beforeanydeformationhadtakenplace)wereusedtocalculatestressandstrain,respectively.Thus,thediagramisreferredtoasan“engineeringstress-straindiagram.”Butasamaterialdeforms,itscross-sectionalareaandlengthchange.Astress-straindiagramthattakestheinstantaneousvaluesofcross-sectionalareaandlengthtodeterminestressandstrainisreferredtoasa“truestress-straindiagram.” Formostapplications,theengineeringstress-straindiagramissufficient,sincethedifferencesbetweentheengineeringandtrueversionsareverysmallbelowthematerial’syieldpoint. Youmayalsolike: Tribologybasicsforlinearbearings What’sthedifferencebetweendynamicloadcapacityandstaticload… Whathappenswhenabearingreachestheendofits… WhatisL10lifeandwhydoesitmatter? Whenisstaticloadcapacityimportant? ReaderInteractions LeaveaReplyYoumustbeloggedintopostacomment. 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