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Shape memory alloys (SMAs), such as Nitinol (i.e., NiTi), are of great importance in biomedical and engineering applications due to their unique superelasticity and shape memory properties. In recent years, additive manufacturing (AM) processes have been used to produce complex NiTi components, which provide the ability to tailor microstructure and thus the critical properties of the alloys, such as the superelastic behavior and transformation temperatures (TTs), by selection of processing parameters. In biomedical applications, superelasticity in implants play a critical role since it gives the implants bone-like behavior. In this study, a methodology of improving superelasticity in Ni-rich NiTi components without the need for any kind of post-process heat treatments will be revealed. It will be shown that superelasticity with 5.62% strain recovery and 98% recovery ratio can be observed in Ni-rich NiTi after the sample is processed with 250 W laser power, 1250 mm/s scanning speed, and 80 µm hatch spacing without, any post-process heat treatments. This superelasticity in as-fabricated Ni-rich SLM NiTi was not previously possible in the absence of post-process heat treatments. The findings of this study promise the fast, reliable and inexpensive fabrication of complex shaped superelastic NiTi components for many envisioned applications such as patient-specific biomedical implants.

In additive manufacturing processes, solidification velocities are extremely high in comparison to ordinary directional solidification. Therefore, the dependencies of the primary dendrite arm spacing (PDAS) on the process parameters deviate from the dependencies predicted by standard analytical methods. In this work, we investigate the microstructure evolution and element distribution in Fe-18.9Mn and Fe-18.5Mn-Al-C alloys solidified during the selective laser melting process. A quantitative multicomponent phase-field model verified by Green-function calculations (Karma, Rappel: Phys. Rev. E, 1998, 57, 4323) and the convergence analysis is used. The resulting non-standard dependencies of the PDAS on the process parameters in a wide range of solidification velocities are compared with analytical calculations. It is shown that the numerical values of the PDAS are similar to the values predicted by the Kurz–Fisher method for the low and intermediate solidification velocities and are smaller for the solidification velocities higher than 0.03 m/s. The PDAS and the Mn distribution in a Fe-18.5Mn-Al-C alloy are compared to the experimental results and a very good agreement is found.

The present research explores theoretical and computational aspects of the morphological instability of Kirkendall voids induced by a directed flux of vacancies. A quantitative phase-field model is coupled with a multi-component diffusion model and CALPHAD-type thermodynamic and kinetic databases to obtain a meso-scale description of Kirkendall void morphologies under isothermal annealing. The material under investigation is a diffusion couple consisting of a multi-phase multi-component single-crystal Ni-based superalloy on one side and pure Ni on the other side. The flux of the fastest diffuser in the superalloy, Al, towards the pure Ni causes a strong flux of vacancies in the opposite direction. This directed flux of vacancies leads to morphologically instable growth of voids. Phase-field simulations are performed in two (2D) and three dimensions (3D) to understand these instabilities, and the results are compared with experimental observations obtained by synchrotron X-ray tomography. Finally, the simulation results are analyzed with respect to the Mullins–Sekerka linear stability criterion.

A phase-field simulation is performed to study the substructure evolution of lenticular martensite in TRIP steels. The evolution of martensitic phase variants and dislocations is calculated by a coupled phase-field micro-elasticity model. The simulations at isothermal conditions show that during the phase transformation, the accommodation dislocations evolving in the austenite are inherited by the martensitic phase and cause the further evolution of a single martensitic variant in the direction of the dislocation slip. As a result of the interaction, a change of the growth mode from twining to slip can be observed in accordance to the substructure formation of lenticular martensite. This interaction between the dislocations and martensitic phase depends on dislocation slip systems and the orientation of the martensitic variants as well as on the energy barriers for the phase transformation and for the dislocation motion.

This paper published in MATEC Web of Conferences has been withdrawn. It should not be cited or referred to in the future. See the correct version of this article: MATEC Web of Conferences 33, 02009 (2015), DOI: 10.1051/matecconf/20153302009 Request approved by the Editors and the Publisher on December 21, 2015.

Kinetics of the γ / γ ′ phase transformation and the interdiffusion phenomena in single-crystal Ni-based superalloys, under isothermal annealing and composition gradient, is investigated through the phase-field and continuum diffusion models. The employed models in the present work exploit CALPHAD-based thermodynamics and kinetics databases, in order to perform realistic simulations. We specifically predict the interdiffusion of elements for a hypothetical alloy AlCoCrTaNi/Ni diffusion couple, equivalent to the CMSX-10/Ni diffusion couple, at 1323 K. Accordingly, the phase fraction and morphology of γ ′ precipitations in the γ matrix is simulated as well. The implemented multi-component diffusion model takes into account vacancies and pore formation, reflecting Kirkendall effect. Furthermore, the time evolution of morphology parameters of the precipitate-depleted zone in the diffusive region (i.e., the position and the size) are estimated.

An extended non-steady-state model for the interaction between a solid particle and an advancing solid/liquid interface based on the dynamic model of Catalina et al . (Metall Mater Trans A 31:2559–2568, 2000 ) is used to calculate the critical velocities for the pushing/engulfment transition in Si-SiC system under microgravity and under normal gravity conditions. The aim of this study was to explain the abnormal behavior of the critical velocity in experiments. The simulations were carried out for two cases of the drag force formulation. The effects of the non-spherical form of the particles as well as the cluster formation were also taken into account. It is found that in the presence of the gravity force, the particles will be engulfed when the particle size exceeds a certain limit which does not depend on the choice of the drag force formulation.

The structure formation in peritectic Al-4.5at.%Cu-11at.%Ni ternary alloy with four-phase peritectic reaction was investigated using the quantitative phase-field model of eutectic growth. This model, extended to an arbitrary number of phases, guarantees the stability requirements on individual interfaces. The thermal noise terms disturb the stability and produce the heterogeneous nucleation of secondary phases in accordance to the energetic and concentration conditions. In our recent work it was shown that in differential thermal analysis (DTA) experiments specific microstructure parts in Al-4.5at.%Cu-11at.%Ni alloy with a four-phase peritectic reaction were observed, which cannot be explained by Scheil calculation or simple phase-field modeling. In this work, it was found by numerical experiments that, due to the formation of anisotropic quasi-primary Al 3 Ni 2 crystals and the suppression of the nucleation of (Al) phase, the eutectic-like coupled growth of Al 3 Ni 2 and Al 3 Ni phases can be observed. In addition, at further cooling the anisotropic shape of quasi-secondary Al 3 Ni crystals promotes the nucleation of the (Al) phase. The simulated final structure is comparable to the experimental one which is characterized by large Al 3 Ni 2 crystals enveloped by the Al 3 Ni phase.

A thermodynamically consistent method for the investigation of the coarsening behavior and in particular for the prediction of the secondary dendrite arm spacing (SDAS) in multi-component alloys is proposed which is based on the numerical simulation by means of a phase-field model. Existing variants of the phase-field model equations for multi-component systems were considered and their advantages and disadvantages were discussed. For the investigation of the coarsening behavior the variant described by the mixture composition and the entropy change was chosen. The method is applied to a high-alloy tool steel where it was found that elements such as C, Si, Mn decrease the SDAS whereas Cr increases. The resulting dependencies of the SDAS on alloy composition were compared to the analytical prediction of the coarsening model. For this aim the analytical model of the coarsening behavior in multi-component alloys [Rappaz and Boettinger, Acta Mater. 47 (1990)] was extended by taking into account the cross dependencies between the components in multi-component diffusion and the case of slow diffusion in the solid phase. The equilibrium parameters used in the phase-field model and in the analytical model were obtained from Thermo-Calc through global equilibrium calculations using the database TCFE7. The difference between both methods was found to be smaller than 2 pct in the investigated composition region.

We study different forms of linear and non-linear field equations, so-called `phase-field' equations, in relation to the de~Broglie-Bohm double solution program. This defines a framework in which elementary particles are described by localized non-linear wave solutions moving by the guidance of a pilot wave, defined by the solution of a Schr\"odinger type equation. First, we consider the phase-field order parameter as the phase for the linear pilot wave, second as the pilot wave itself and third as a moving soliton interpreted as a massive particle. In the last case, we introduce the equation for a superwave, the amplitude of which can be considered as a particle moving in accordance to the de~Broglie-Bohm theory. Lax pairs for the coupled problems are constructed in order to discover possible non-linear equations which can describe the moving particle and to propose a framework for investigating coupled solutions. Finally, doublons in 1+1 dimensions are constructed as self similar solutions of a non-linear phase-field equation forming a finite space-object. Vacuum quantum oscillations within the doublon determine the evolution of the coupled system. Applying a conservation constraint and using general symmetry considerations, the doublons are arranged as a network in 1+1+2 dimensions where nodes are interpreted as elementary particles. A canonical procedure is proposed to treat charge and electromagnetic exchange.