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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. 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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3. Phase field theory for fracture at large strains including surface stresses

   Jafarzadeh, Hossein; Farrahi, Gholam Hossein; Levitas, Valery I.; Javanbakht, Mahdi (November 2020, ArXivorg)

   null (Ed.)

   Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas in the deformed and undeformed configurations and with the gradient energy in terms of the gradient of the order parameter in the reference configuration. This results in an expression for the surface stresses which is consistent with the sharp surface approach. Namely, the structural part of the Cauchy surface stress represents an isotropic biaxial tension, with the magnitude of a force per unit length equal to the surface energy. The surface stresses are a result of the geometric nonlinearities, even when strains are infinitesimal. They make multiple contributions to the Ginzburg-Landau equation for damage evolution, both in the deformed and undeformed configurations. Important connections between material parameters are obtained using an analytical solution for two separating surfaces, as well as an analysis of the stress-strain curves for homogeneous tension for different degradation and interpolation functions. A complete system of equations is presented in the undeformed and deformed configurations. All the phase field parameters are obtained utilizing the existing first principle simulations for the uniaxial tension of Si crystal in the [100] and [111] directions. 

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4. Accommodation and formation of {-1012} twins in Mg-Y alloys

   https://doi.org/https://doi.org/10.1016/j.actamat.2020.116514  

   Yaddanapudi, Krishna; Leu, Brandon; M, Arul Kumar; Wang, Xin; Schoenung, Julie M; Lavernia, Enrique J; Rupert, Timothy J; Beyerlein, Irene J; Mahajan, Subhash (February 2021, Acta materialia)

   Schuh, Christopher A (Ed.)

   The {-1012} tensile twins terminating inside the grains of a deformed Mg-Y alloy were investigated by transmission electron microscopy. The crystallographic features of terminating twins and associated slip structures were quantified and correlated. The local stresses developed at a terminating {-1012} twin were computed using crystal plasticity simulations in order to interpret the observed slip patterns. Results indicate that both basal and matrix glide were involved in accommodating the plastic stresses developed in the vicinity of terminating twins. Along the twin boundary, the defect contrast consistent with that of lattice dislocations and twinning partials was observed. Based on these observations, a dislocation reaction is proposed that establishes an interrelationship between the observed matrix glide and {-1012} twinning in Mg-Y alloys. 

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5. Review on phase transformations, fracture, chemical reactions, and other structural changes in inelastic materials

   Levitas, Valery I. (August 2021, ArXivorg)

   Review of selected fundamental topics on the interaction between phase transformations, fracture, and other structural changes in inelastic materials is presented. It mostly focuses on the concepts developed in the author's group over last three decades and numerous papers that affected us. It includes a general thermodynamic and kinetic theories with sharp interfaces and within phase field approach. Numerous analytical (even at large strains) and numerical solutions illustrate the main features of the developed theories and their application to the real phenomena. Coherent, semicoherent, and noncoherent interfaces, as well as interfaces with decohesion and with intermediate liquid (disordered) phase are discussed. Importance of the surface- and scale-induced phenomena on interaction between phase transformation with fracture and dislocations as well as inheritance of dislocations and plastic strains is demonstrated. Some nontrivial phenomena, like solid-solid phase transformations via intermediate (virtual) melt, virtual melting as a new mechanism of plastic deformation and stress relaxation under high strain rate loading, and phase transformations and chemical reactions induced by plastic shear under high pressure are discussed and modeled. 

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