6-plastic-mechanics-弹塑性力学讲义-英文版-教学课件.ppt

Uni-axialtensiletestcurveElementary Plastic Mechanicsq ReviewingandThinkingWhatwillhappenwhenthestressorreinforcedstrainincrease?elasticdeformationyieldinghomo-plasticdeformationneckingfractureAtwhatconditionswillplasticyieldingtakeplace?Foruni-axialstressstateandcomplexstressstate？yieldconditions:MisesandTrescacriterionWhatmayhappenafteryielding？plasticconstitutiveequations:twotheories,severalsimplifiedmodelsElementary Plastic MechanicsWhy？physicalmechanism：dislocationtheory（Youhavestudiedin“Fundamental Theory of Materials Science”.）Howtosolvetheplasticmechanicalproblems？analyticmethodsforplasticmechanicalproblems：1)engineeringmethod(principalstressmethod,slabmethod):2)sliplinemethod3)upperboundarymethod4)FEMFiniteElementMethodThesewillbestudiedinpost-graduatedcourses:“Modern Mechanics for Materials Working”and“FEM used in Plastic Working”.Elementary Plastic Mechanics7.1 yieldcriteriaItisalsobesaidasplasticconditionsoryieldconditions，describingthestressconditionswhentheelastic-deformedmaterialstartsandcontinuesitsplasticdeformation.Generally the yield conditions can be expressed with yield functions asfollowing：Elementary Plastic MechanicsTrescacriterion（Maximumshearstresscriterion）Misescriterion(Distortionenergycriterion)Reviewing：Elementary Plastic MechanicsRelationshipbetweenthecriteria：（1）Ingeometricalexpression：MisescylindercircumscribeTrescahexagonal prism；There are six overlapped points atplane；（2）ByusingLodesparameter andmediumprincipalstressinfluentindex，thetwocriterioncanbeexpressedinthesameformas：Elementary Plastic MechanicsDiscussion：Whenthematerialisforcedwithanuni-axialstress,=1，thereisnodifferencebetweenthetwoyieldconditions；When the material is loaded with pure shear stress,thedifference between the two yield conditions reaches themaximum.AccordingtoTrescacriterion：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)