A macroscale phase-field model for shape memory alloys with non-isothermal effects

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1、Availableonlineatwww.sciencedirect.comActaMaterialia60(2012)179–191www.elsevier.com/locate/actamatAmacroscalephase-fieldmodelforshapememoryalloyswithnon-isothermaleffects:Influenceofstrainrateandenvironmentalconditionsonthemechanicalresponseab,⇑cD.Grandi,

2、M.Maraldi,L.MolariaDepartmentofMathematics,UniversityofBologna,PiazzadiPortaS.Donato5,I-40126Bologna,ItalybDIEM,UniversityofBolognaVialeRisorgimento2,I-40136Bologna,ItalycDICAM,UniversityofBolognaVialeRisorgimento2,I-40136Bologna,ItalyReceived17March20

3、11;receivedinrevisedform17September2011;accepted23September2011Availableonline28October2011AbstractAGinzburg–Landaumodelforthemacroscopicbehaviourofashapememoryalloyisproposed.Themodelisessentiallyone-dimen-sional,inthatweconsidertheeffectofthemartensit

4、icphasetransitionintermsofauniaxialdeformationalongafixeddirectionandweuseascalarorderparameterwhoseequilibriumvaluesdescribetheausteniticphaseandthetwomartensiticvariants.ThemodelreliesonaGinzburg–Landaufreeenergydefinedasafunctionofmacroscopicallymeasu

5、rablequantities,andaccountsforthermaleffects;cou-plingsbetweenthevariousrelevantphysicalaspectsareestablishedbasedonthermodynamicprinciples.Thetheoreticalmodelhasbeenimplementedwithinafinite-elementframeworkandanumberofnumericaltestsarepresentedwhichinve

6、stigatethemechanicalbehav-iourofthemodelunderdifferentconditions;theresultsobtainedareanalyzedinrelationtoexperimentalevidenceavailableinthelit-erature.Inparticular,theinfluenceofthestrainrateandoftheambientconditionsontheresponseofthemodelishighlighted.

7、Ó2011ActaMaterialiaInc.PublishedbyElsevierLtd.Allrightsreserved.Keywords:Phasefieldmodel;Shapememoryalloys;Strain-ratesensitivity;Thermo-mechanicalcoupling1.Introductiontransferandofheatdissipationtowardstheambientareofprimaryrelevanceinthestudyofthesem

8、aterials[2,5]Shapememoryalloys(SMAs)havemanyapplicationsandplayaroleintherate-dependentbehaviourofSMAsandareattractingmuchinterestduetotheiruniqueprop-[3,6].ertiesofshapememoryandpseudoelasticity,whichstemInmodellingthemechanicalbehavio