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1、Ramberg-OsgoodrelationshipFromWikipedia,thefreeencyclopediaJumpto:navigation,searchTheRamberg-Osgoodequationwascreatedtodescribethenonlinearrelationshipbetweenstressandstrain—thatis,thestress-straincurve—inmaterialsneartheiryieldpoints.Itisespeciallyusef
2、ulformetalsthathardenwithplasticdeformation(seestrainhardening),showingasmoothelastic-plastictransition.Initsoriginalform,itsaysthat,[1]whereεisstrain,σisstress,EisYoung'smodulus,andKandnareconstantsthatdependonthematerialbeingconsidered.Thefirsttermonth
3、erightside,,isequaltotheelasticpartofthestrain,whilethesecondterm,,accountsfortheplasticpart,theparametersKandndescribingthehardeningbehaviorofthematerial.Introducingtheyieldstrengthofthematerial,σ0,anddefininganewparameter,α,relatedtoKas,itisconvenientt
4、orewritethetermontheextremerightsideasfollows:Replacinginthefirstexpression,theRamberg-Osgoodequationcanbewrittenas[edit]HardeningbehaviorandYieldoffsetInthelastformoftheRamberg-Osgoodmodel,thehardeningbehaviorofthematerialdependsonthematerialconstantsan
5、d.Duetothepower-lawrelationshipbetweenstressandplasticstrain,theRamberg-Osgoodmodelimpliesthatplasticstrainispresentevenforverylowlevelsofstress.Nevertheless,forlowappliedstressesandforthecommonlyusedvaluesofthematerialconstantsαandn,theplasticstrainrema
6、insnegligiblecomparedtotheelasticstrain.Ontheotherhand,forstresslevelshigherthanσ0,plasticstrainbecomesprogressivelylargerthanelasticstrain.Thevaluecanbeseenasayieldoffset,asshowninfigure1.Thiscomesfromthefactthat,when.Accordingly(seeFigure1):elasticstra
7、inatyield=plasticstrainatyield==yieldoffsetCommonlyusedvaluesforare~5orgreater,althoughmoreprecisevaluesareusuallyobtainedbyfittingoftensile(orcompressive)experimentaldata.Valuesforcanalsobefoundbymeansoffittingtoexperimentaldata,althoughforsomematerials
8、,itcanbefixedinordertohavetheyieldoffsetequaltotheacceptedvalueofstrainof0.2%,whichmeans:Figure1:GenericrepresentationoftheStress-StraincurvebymeansoftheRamberg-Osgoodequation.Straincorrespondingtotheyieldpointisthesumofth
