The stress-induced martensitic transformation in tensioned nickel-titanium shape-memory alloys proceeds by propagation of macroscopic fronts of localized deformation. We used three-dimensional synchrotron x-ray diffraction to image at micrometer-scale resolution the grain-resolved elastic strains and stresses in austenite around one such front in a prestrained nickel-titanium wire. We found that the local stresses in austenite grains are modified ahead of the nose cone-shaped buried interface where the martensitic transformation begins. Elevated shear stresses at the cone interface explain why the martensitic transformation proceeds in a localized manner. We established the crossover from stresses in individual grains to a continuum macroscopic internal stress field in the wire and rationalized the experimentally observed internal stress field and the topology of the macroscopic front by means of finite element simulations of the localized deformation.
Abstract. This article reports on an ESF S3T EUROCORES sponsored networking activity called Roundrobin SMA modeling organized with the aim to compare capabilities of various thermomechanical models of shape memory alloys capable to simulate their functional responses for applications in smart engineering structures. Five sets of experimental data were measured in thermomechanical tests on thin NiTi filament in tension, torsion and combined tension/torsion. The data were provided to six teams developing advanced SMA models to perform appropriate simulations. Simulation results obtained by individual teams were compared with experimental results and presented on a dedicated Roundrobin SMA modeling website. The evaluation of the activity in terms of the assessment of the capability of individual models to deal with specific features of the experimentally measured SMA thermomechanical responses is provided in this article.
We present a three-dimensional constitutive model for NiTi polycrystalline shape memory alloys exhibiting transformations between three solid phases (austenite, R-phase, martensite). The ‘full modelling sequence’ comprised of formulation of modelling assumptions, construction of the model, mathematical analysis and numerical implementation and validation is presented. Namely, by formulating micromechanics-inspired modelling assumptions we concentrate on describing the dissipation mechanism: a refined form of this description makes our model especially useful for complex loading paths. We then embed the model into the so-called energetic framework (extended to our case) while taking advantage of describing the dissipation mechanism through the so-called dissipation distance. We prove the existence of energetic solutions to our model by a backward Euler scheme. This is then implemented into finite element software, and numerical simulations compared with experiments are also presented.
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