| Based on the assumption of laminated microstructure from experimental observation of stress induced NiTi shape memory alloys martensite transformation, micromechanical constitutive model of NiTi single crystal and NiTi polycrystal are presented. Differences of elastic properties between austenite phase and martensite phase are considered. According to phenomenological crystallography theory of martensitic transformation, microstructure parameters about martensitic transformation are obtained. Perfect interfacial relations are considered. Using interfacial relations and average relation of two phases, local stress and strain of two phases can be transited to overall stress and strain of respective volume element with laminated microstructure. Free energy function including elastic strain energy and chemistry energy is derived, then phase transformation driving force is obtained. Critical value of phase transformation driving force is used as a material constant which controls martensite phase transformation, combining with expression of phase transformation driving force, equations controlling martensite phase transformation and reverse transformation are derived. Polycrystal constitutive relation is based on constitutive relation of single crystal with laminated microstructure, average is achieved according to Taylor assumption, then constitutive relation is transited from single crystal scale to polycrystal scale.Simulations are implemented for uniaxial loading of NiTi single crystal and NiTi polycrystal with the presented constitutive models. The presented model can well describe superelasticity of NiTi shape memory alloy. Simulation results show asymmetry of tension and compression, softening behavior, influence of temperature, and evolution of microstructure with martensite volume fraction, these results are corresponding to the experimental observation, which indicate the work will offer help to prediction for superelasticity of NiTi shape memory alloy. |
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