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1. A multiphase phase-field study of three-dimensional martensitic twinned microstructures at large strains

   https://doi.org/10.1007/s00161-022-01177-6  

   Basak, Anup; Levitas, Valery I. (January 2023, Continuum Mechanics and Thermodynamics)

   The nanoscale multiphase phase-field model for stress and temperature-induced multivariant martensitic transformation under large strains developed by the authors in Basak and Levitas (J Mech Phys Solids 113:162–196, 2018) is revisited, the issues related to the gradient energy and coupled kinetic equations for the order parameters are resolved, and a thermodynamically consistent non-contradictory model for the same purpose is developed in this paper. The model considers N+1 order parameters to describe austenite and N martensitic variants. One of the order parameters describes austenite↔martensite transformations, and the remaining N order parameters, whose summation is constrained to the unity, describe the transformations between the variants. A non-contradictory gradient energy is used within the free energy of the system to account for the energies of the interfaces. In addition, a kinetic relationship for the rate of the order parameters versus thermodynamic driving forces is suggested, which leads to a system of consistent coupled Ginzburg–Landau equations for the order parameters. An approximate general crystallographic solution for twins within twins is presented, and the explicit solution for the cubic to tetragonal transformations is derived. A large strain-based finite element method is developed for solving the coupled Ginzburg–Landau and elasticity equations, and it is used to simulate a 3D complex twins within twins microstructure. A comparative study between the crystallographic solution and the simulation results is presented. 

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2. A multiphase phase-field study of three-dimensional martensitic twinned microstructures at large strains

   Basak, Anup; Levitas, Valery I. (June 2022, ArXivorg)

   A thermodynamically consistent multiphase phase-field approach for stress and temperature-induced martensitic phase transformation at the nanoscale and under large strains is developed. A total of N independent order parameters are considered for materials with N variants, where one of the order parameters describes A ↔ M transformations and the remaining N − 1 independent order parameters describe the transformations between the variants. A non-contradictory gradient energy is used within the free energy of the system to account for the energies of the interfaces. In addition, a non-contradictory kinetic relationships for the rate of the order parameters versus thermodynamic driving forces is suggested. As a result, a system of consistent coupled Ginzburg-Landau equations for the order parameters are derived. The crystallographic solution for twins within twins is presented for the cubic to tetragonal transformations. A 3D complex twins within twins microstructure is simulated using the developed phase-field approach and a large-strain-based nonlinear finite element method. A comparative study between the crystallographic solution and the simulation result is presented. 

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3. An exact formulation for exponential-logarithmic transformation stretches in a multiphase phase field approach to martensitic transformations

   https://doi.org/10.1177/1081286520905352  

   Basak, Anup; Levitas, Valery_I (February 2020, Mathematics and Mechanics of Solids)

   A general theoretical and computational procedure for dealing with an exponential-logarithmic kinematic model for transformation stretch tensor in a multiphase phase field approach to stress- and temperature-induced martensitic transformations with N martensitic variants is developed for transformations between all possible crystal lattices. This kinematic model, where the natural logarithm of transformation stretch tensor is a linear combination of natural logarithm of the Bain tensors, yields isochoric variant–variant transformations for the entire transformation path. Such a condition is plausible and cannot be satisfied by the widely used kinematic model where the transformation stretch tensor is linear in Bain tensors. Earlier general multiphase phase field studies can handle commutative Bain tensors only. In the present treatment, the exact expressions for the first and second derivatives of the transformation stretch tensor with respect to the order parameters are obtained. Using these relations, the transformation work for austenite ↔ martensite and variant ↔ variant transformations is analyzed and the thermodynamic instability criteria for all homogeneous phases are expressed explicitly. The finite element procedure with an emphasis on the derivation of the tangent matrix for the phase field equations, which involves second derivatives of the transformation deformation gradients with respect to the order parameters, is developed. Change in anisotropic elastic properties during austenite–martensitic variants and variant–variant transformations is taken into account. The numerical results exhibiting twinned microstructures for cubic to orthorhombic and cubic to monoclinic-I transformations are presented. 

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4. Nontrivial nanostructure, stress relaxation mechanisms, and crystallography for pressure-induced Si-I → Si-II phase transformation

   https://doi.org/10.1038/s41467-022-28604-1  

   Chen, Hao; Levitas, Valery I.; Popov, Dmitry; Velisavljevic, Nenad (February 2022, Nature Communications)

   Abstract Crystallographic theory based on energy minimization suggests austenite-twinned martensite interfaces with specific orientation, which are confirmed experimentally for various materials. Pressure-induced phase transformation (PT) from semiconducting Si-I to metallic Si-II, due to very large and anisotropic transformation strain, may challenge this theory. Here, unexpected nanostructure evolution during Si-I → Si-II PT is revealed by combining molecular dynamics (MD), crystallographic theory, generalized for strained crystals, and in situ real-time Laue X-ray diffraction (XRD). Twinned Si-II, consisting of two martensitic variants, and unexpected nanobands, consisting of alternating strongly deformed and rotated residual Si-I and third variant of Si-II, form$$\{111\}$$ $\left\{111\right\}$interface with Si-I and produce almost self-accommodated nanostructure despite the large transformation volumetric strain of$$-0.237$$ $-0.237$. The interfacial bands arrest the$$\{111\}$$ $\left\{111\right\}$interfaces, leading to repeating nucleation-growth-arrest process and to growth by propagating$$\{110\}$$ $\left\{110\right\}$interface, which (as well as$$\{111\}$$ $\left\{111\right\}$interface) do not appear in traditional crystallographic theory. 

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5. Characterizing Changes in Grain Growth, Mechanical Properties, and Transformation Properties in Differently Sintered and Annealed Binder-Jet 3D Printed 14M Ni–Mn–Ga Magnetic Shape Memory Alloys

   https://doi.org/10.3390/met12050724  

   Acierno, Aaron; Mostafaei, Amir; Toman, Jakub; Kimes, Katerina; Boin, Mirko; Wimpory, Robert C.; Laitinen, Ville; Saren, Andrey; Ullakko, Kari; Chmielus, Markus (May 2022, Metals)

   Ni–Mn–Ga Heusler alloys are multifunctional materials that demonstrate macroscopic strain under an externally applied magnetic field through the motion of martensite twin boundaries within the microstructure. This study sought to comprehensively characterize the microstructural, mechanical, thermal, and magnetic properties near the solidus in binder-jet 3D printed 14M Ni50Mn30Ga20. Neutron diffraction data were analyzed to identify the martensite modulation and observe the grain size evolution in samples sintered at temperatures of 1080 °C and 1090 °C. Large clusters of high neutron-count pixels in samples sintered at 1090 °C were identified, suggesting Bragg diffraction of large grains (near doubling in size) compared to 1080 °C sintered samples. The grain size was confirmed through quantitative stereology of polished surfaces for differently sintered and heat-treated samples. Nanoindentation testing revealed a greater resistance to plasticity and a larger elastic modulus in 1090 °C sintered samples (relative density ~95%) compared to the samples sintered at 1080 °C (relative density ~80%). Martensitic transformation temperatures were lower for samples sintered at 1090 °C than 1080 °C, though a further heat treatment step could be added to tailor the transformation temperature. Microstructurally, twin variants ≤10 μm in width were observed and the presence of magnetic anisotropy was confirmed through magnetic force microscopy. This study indicates that a 10 °C sintering temperature difference can largely affect the microstructure and mechanical properties (including elastic modulus and hardness) while still allowing for the presence of magnetic twin variants in the resulting modulated martensite. 

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