Phase-Field Reaction-Pathway Kinetics of Martensitic Transformations in a ModelFe3NiAlloy

We have investigated athermal and isothermal martensitic transformations (typical displacive transformations) in Fe–Ni, Fe–Ni–Cr, and Ni-Co-Mn-In alloys under magnetic fields and hydrostatic pressures in order to understand the time-dependent nature of martensitic transformation, that is, the kinetics of martensitic transformation. We have confirmed that the two transformation processes are closely related to each other, that is, the athermal process changes to the isothermal process and the isothermal process changes to the athermal one under a hydrostatic pressure or a magnetic field. These findings can be explained by the phenomenological theory, which gives a unified explanation for the two transformation processes previously proposed by our group.

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

Mathematics and Mechanics of Solids ◽

10.1177/1081286520905352 ◽

2020 ◽

Vol 25 (6) ◽

pp. 1219-1246 ◽

Cited By ~ 1

Author(s):

Anup Basak ◽

Valery I Levitas

Keyword(s):

Phase Field ◽

Kinematic Model ◽

Martensitic Transformations ◽

Order Parameters ◽

Field Approach ◽

Natural Logarithm ◽

Stretch Tensor ◽

Second Derivatives ◽

Derivatives Of ◽

Martensitic Variants

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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Explicit nonlinear finite element approach to the Lagrangian-based coupled phase field and elasticity equations for nanoscale thermal- and stress-induced martensitic transformations

Continuum Mechanics and Thermodynamics ◽

10.1007/s00161-020-00912-1 ◽

2020 ◽

Author(s):

Mahdi Javanbakht ◽

Hossein Rahbar ◽

Milad Ashourian

Keyword(s):

Finite Element ◽

Phase Field ◽

Martensitic Transformations ◽

Nonlinear Finite Element ◽

Finite Element Approach ◽

Elasticity Equations ◽

Element Approach

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Hydrothermal Carbonization Kinetics of Lignocellulosic Agro-Wastes: Experimental Data and Modeling

Energies ◽

10.3390/en12030516 ◽

2019 ◽

Vol 12 (3) ◽

pp. 516 ◽

Cited By ~ 23

Author(s):

Michela Lucian ◽

Maurizio Volpe ◽

Luca Fiori

Keyword(s):

Experimental Data ◽

Reaction Kinetics ◽

Reaction Pathway ◽

Hydrothermal Carbonization ◽

Kinetics Model ◽

Transient Phase ◽

Lumped Model ◽

Gaseous Products ◽

Best Fitting ◽

Kinetics Of

Olive trimmings (OT) were used as feedstock for an in-depth experimental study on the reaction kinetics controlling hydrothermal carbonization (HTC). OT were hydrothermally carbonized for a residence time τ of up to 8 h at temperatures between 180 and 250 °C to systematically investigate the chemical and energy properties changes of hydrochars during HTC. Additional experiments at 120 and 150 °C at τ = 0 h were carried out to analyze the heat-up transient phase required to reach the HTC set-point temperature. Furthermore, an original HTC reaction kinetics model was developed. The HTC reaction pathway was described through a lumped model, in which biomass is converted into solid (distinguished between primary and secondary char), liquid, and gaseous products. The kinetics model, written in MATLABTM, was used in best fitting routines with HTC experimental data obtained using OT and two other agro-wastes previously tested: grape marc and Opuntia Ficus Indica. The HTC kinetics model effectively predicts carbon distribution among HTC products versus time with the thermal transient phase included; it represents an effective tool for R&D in the HTC field. Importantly, both modeling and experimental data suggest that already during the heat-up phase, biomass greatly carbonizes, in particular at the highest temperature tested of 250 °C.

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