<title>Thermomechanical representation of the multiaxial behavior of shape memory alloys</title>

Abstract

ThermomechanicalRepresentationoftheMultiaxialBehaviorofShap eMemoryAlloysDirk Helm and PeterHauptInstituteof Mechanics,Departmenthanical Engineering, Universityof Kassel,Moncheb ergstr.7,34109 Kassel,GermanyABSTRACTA thermomechanically consistent material mo del representing the multiaxial b ehavior of shap e memory alloysis prop osed in this article.The constitutive equations describ e the one{way and two{wy shap e memory e ectas well as pseudo elasticity, pseudoplasticity and the transition range b etween pseudo elasticity and pseudoplas-ticity.The material mo del is based on a free energy function as well as evolution equations for internal variables.Indetail,thefreeenergy functionis intro ducedinorder todescrib eenergy storage during thermo elasticpro cesses, the energy di erence b etween the regarded phases (austenite and martensite) as well as the energystorage due to the evolution of the residual stresses.In contrast to this, the evolution equations for the internalvariablesrepresenttheobservedinelasticb ehaviorofshap ememoryalloysaswellrelatedthermome-chanical coupling e ects.Due to the description of the energy storage and release during the martensitic phasetransitionsbymeansofamixturetheory,oneinternalvariableisthefractionmartensite.Othersare theinelastic strain tensor and internal variables describing residual stresses.The viscous material b ehavior of NiTishap e memory alloys, whichis exp erimentally observed, is represented by an inelastic multiplierof Perzyna{typ e.Numerical solutions of the develop ed constitutive equations for isothermal and non{isothermal strain andstress pro cesses demonstrate that the material mo del represents the main e ects of shap e memory alloys.Addi-tionally, the material mo del is able to depict the multiaxial material b ehavior as observed.Numerical solutionsare compared with uniaxial and in particular biaxial exp erimental observations on NiTi shap e memory alloys.Keywords:Shap e memory alloys, thermomechanical mo del, thermoviscoplasticity, phase transitons1. INTRODUCTIONAs a consequence of the exceptional features of shap e memory alloys, more and more applications are based onthis typ e of smart materials.1, 2However, there is still a lack of constitutive equations in order to describ e thebehavior of these materials.3In contrast to the uniaxial material b ehavior,1, 3{7the multiaxial material b ehavior is not suciently inves-tigated:Merely,a small numb er of articles8{10investigate the multiaxial material b ehavior of shap e memoryalloys.As a consequence of the lackofmultiaxial exp erimental data, the results of the published material mo d-els are often compared with uniaxial exp erimental data.11{14In the following we suggest a thermo dynamicallyconsistent material mo del, based on a free energy function and evolution equations for internal variables.Besidethe explanation of the structure of the constitutive equations, the initial{value problem for a thin{walled tub eis numerically solved.The consideration of di erent thermomechanical loading paths is appropriate to comparethe results of the material mo del with the results of exp erimental obsevations, recently published in Ref.10, 15.Further author information:(Send corresp ondence to D. Helm)D. Helm.:helm@ifm.maschinenbau.uni-kassel.de or http://www.ifm.mascassel.de/~helmP. Haupt:haupt@ifm.maschinenbau.uni-kassel.de or http://www.ifm.mascassel.de/~haupt