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1、Uni-axialtensiletestcurveElementary Plastic Mechanicsq ReviewingandThinkingWhatwillhappenwhenthestressorreinforcedstrainincrease?elasticdeformationyieldinghomo-plasticdeformationneckingfractureAtwhatconditionswillplasticyieldingtakeplace?Foruni-axialstressstateandcomplexstressstate？yieldconditions:M
2、isesandTrescacriterionWhatmayhappenafteryielding？plasticconstitutiveequations:twotheories,severalsimplifiedmodelsElementary Plastic MechanicsWhy？physicalmechanism：dislocationtheory（Youhavestudiedin“Fundamental Theory of Materials Science”.）Howtosolvetheplasticmechanicalproblems？analyticmethodsforpla
3、sticmechanicalproblems：1)engineeringmethod(principalstressmethod,slabmethod):2)sliplinemethod3)upperboundarymethod4)FEMFiniteElementMethodThesewillbestudiedinpost-graduatedcourses:“Modern Mechanics for Materials Working”and“FEM used in Plastic Working”.Elementary Plastic Mechanics7.1 yieldcriteriaIt
4、isalsobesaidasplasticconditionsoryieldconditions，describingthestressconditionswhentheelastic-deformedmaterialstartsandcontinuesitsplasticdeformation.Generally the yield conditions can be expressed with yield functions asfollowing：Elementary Plastic MechanicsTrescacriterion（Maximumshearstresscriterio
5、n）Misescriterion(Distortionenergycriterion)Reviewing：Elementary Plastic MechanicsRelationshipbetweenthecriteria：（1）Ingeometricalexpression：MisescylindercircumscribeTrescahexagonal prism；There are six overlapped points atplane；（2）ByusingLodesparameter andmediumprincipalstressinfluentindex，thetwocrite
6、rioncanbeexpressedinthesameformas：Elementary Plastic MechanicsDiscussion：Whenthematerialisforcedwithanuni-axialstress,=1，thereisnodifferencebetweenthetwoyieldconditions；When the material is loaded with pure shear stress,thedifference between the two yield conditions reaches themaximum.AccordingtoTre
7、scacriterion：AccordingtoMisescriterion：Generally,=11.154(Other yielding theories such as Hills criterion and double shear stress criterion,willbestudiedinpost-graduatedcourse)（ExamplesareshowedinP81）Elementary Plastic Mechanics7.2Constitutiveequationofplasticdeformationsimplifiedmodelsforplasticstress-straincurvesElementary Plastic MechanicsClassexercises：Examplesoftotalstraintheory:makeoutthestressandstrainstates(allintheyieldingconditions)ExamplesofIncrementaltheory(p102)