Coupled Phase Transformation Research Articles

Magnetocaloric effects in Ni-Mn-Ga-Fe alloys using Monte Carlo simulations

Heusler alloys based on the Ni2MnGa system have been shown to exhibit strong magneto-thermo-structural couplings that make them very attractive multi-functional materials. In this work, first principles calculations combined with Monte Carlo simulations have been used to study the magnetocaloric effect (MCE) in Fe-doped Ni-Mn-Ga alloys. The first principles calculations have been used to determine the magnetic properties of the alloys—specifically, magnetic exchange couplings—and to construct a lattice-based Hamiltonian (q-state Pott's model) for the description of the magnetic transformations. The magnetic Hamiltonian is then coupled to a lattice description of the structural (martensitic) transformation, leading to the development of phenomenological models for the magneto-thermo-structural phase transformation. This model Hamiltonian is then investigated through a Monte Carlo framework to describe the coupled phase transformations as well as the magnetocaloric effect. The field-induced entropy change during the transformation is then calculated and used to estimate the adiabatic temperature change associated to switching of magnetic fields. These calculations are in good agreement with the experimental results with a near linear increase in inverse and conventional MCE as structural and magnetic transformation takes place.

Coupled plastic flow and phase transformation under compression of materials in a diamond anvil cell: Effects of transformation kinetics and yield strength

The large-strain problem on phase transformations (PTs) under compression in a diamond anvil cell is studied in detail using the finite-element method. The combined effect of transformation kinetics and ratios of the yield strengths of low- and high-pressure phases is examined. Some experimental phenomena (e.g., plateaus in pressure distribution and plastic flow to the center of a sample) are reproduced. Results are applied to interpretation of experimental data and characterization of strain-induced PTs.

Coupled phase transformations and plasticity as a field theory of deformation incompatibility

The duality between terminating discontinuities of fields and the incompatibilities of their gradients is used to define a coupled dynamics of the discontinuities of the elastic displacement field and its gradient. The theory goes beyond standard translational and rotational Volterra defects (dislocations and disclinations) by introducing and physically grounding the concept of generalized disclinations in solids without a fundamental rotational kinematic degree of freedom (e.g. directors). All considered incompatibilities have the geometric meaning of a density of lines carrying appropriate topological charge, and a conservation argument provides for natural physical laws for their dynamics. Thermodynamic guidance provides the driving forces conjugate to the kinematic objects characterizing the defect motions, as well as admissible constitutive relations for stress and couple stress. We show that even though higher-order kinematic objects are involved in the specific free energy, couple stresses may not be required in the mechanical description in particular cases. The resulting models are capable of addressing the evolution of defect microstructures under stress with the intent of understanding dislocation plasticity in the presence of phase transformation and grain boundary dynamics.

Electrical cross effects in porous media with ice inclusions. Part II: Double electrical layer mechanism

The paper continues theoretical studying the heat and mass transfer in the biporous material with the coupled phase transformations. The fine-pored part of the medium is saturated by electrolytic solution and has osmotic and electroosmotic properties. Ice is contained in coarse pores. At the low solution concentration the electric polarization of the medium induced by the temperature gradient may be up to 1 V/K.

Phase field simulations of coupled phase transformations in ferroelastic-ferroelastic nanocomposites

We use phase field simulations to study composites made of two different ferroelastics (e.g., two types of martensite). The deformation of one material due to a phase transformation can elastically affect the other constituent and induce it to transform as well. We show that the phase transformation can then occur above its normal critical temperature and even higher above this temperature in nanocomposites than in bulk composites. Microstructures depend on temperature, on the thickness of the layers, and on the crystal structure of the two constituents---certain nanocomposites exhibit a great diversity of microstructures not found in bulk composites. Also, the periodicity of the martensite twins may vary over 1 order of magnitude based on geometry.

Numerical simulation of welding induced damage and residual stress of martensitic steel 15-5PH

This paper is about the modeling of damage and residual stresses induced by a complex history of thermo-elasto-plastic multiphase in welding heat affected zone (HAZ). A two-scale model for elasto-plastic damaged multiphase is developed. The constitutive equations of the model are coupling ductile damage, elasto-plastic strains, phase transformation and transformation plasticity. In this study, an equation of damage evolution is proposed based on the continuum damage mechanics. In order to validate the proposed damage evolution, a set of flat notched bars with various notches are to simulated and then compared to experimental results. An example of laser heated disk is simulated to elaborate the two-scale model and the simulated results of the two-scale model in CAST3M ® is compared the results calculated by a homogenized macroscopic model in SYSWELD ®. The study shows the two-scale model provides valuable freedom to choose the material or mechanical law for each phase. The proposed damage equation extends the application of existing ductile damage models. In the calculation of residual stresses, damage decreases the residual stresses in HAZ by a small amount.

Coupled fluid flow, heat transfer, phase transformation, stress and deformation numerical model for gas quenching

Owing to the growing interest in high-pressure gas quenching, a complete mathematical modelling of this process has been launched with the aim of predicting the microstructural and mechanical state of steel bodies from the quenching operating conditions. The comprehensive numerical modelling combines the calculation of fluid flow and heat transport for the gaseous phase (using Fluent software) and calculation of heat conduction, solid-state phase transformations and residual stresses and distortions in the solid body (using Sysweld software). Our numerical results are compared to the experimental data obtained from a laboratory gas-quenching device set up at the Ecole des Mines d'Albi. Helium- and nitrogen-quenching trials were performed for nickel and 27MnCr5 steel cylinders. The measured gas flow velocities are compared to gas velocities calculated with the Fluent-Sysweld coupling, as well as the temperature evolutions at different locations in the cylinders. On the other hand, the ability of the model for predicting microstructure, residual stresses and deformations is illustrated with the gas quenching of a 60NiCrMo11 steel cylinder.

Coupled phase transformation, chemical decomposition, and deformation in plastic-bonded explosive: Models

A continuum thermomechanochemical model of the behavior of a plastic-bonded explosive (PBX) 9501 formulation consisting of the energetic crystal octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) embedded in a polymeric binder is developed. Our main focus is on the study of the β↔δ phase transformations (PTs) in crystalline HMX under a complex pressure-temperature path. To reproduce the pressure-temperature path, in particular during heating of PBX inside of a rigid cylinder, the β↔δ PTs in HMX are coupled to chemical decomposition of the HMX and binder leading to gas formation, gas leaking from the cylinder, elastic, thermal, and transformational straining as well as straining due to mass loss. A fully physically based thermodynamic and kinetic model of the β↔δ PT in HMX crystal is developed. It is based on a suggested nucleation mechanism via melt mediated nanocluster transformation and the recently revealed growth mechanism via internal stress-induced virtual melting. During the nucleation, nanosize clusters of the β phase dissolve in a molten binder and transform diffusionally into δ phase clusters. During the interface propagation, internal stresses induced by transformation strain cause the melting of the stressed δ phase much below (120 K) the melting temperature and its immediate resolidification into the unstressed δ phase. These mechanisms explain numerous puzzles of HMX polymorphism and result in overall transformation kinetics that is in good agreement with experiments. Simple phenomenological equations for kinetics of chemical decomposition of the HMX and the binder are in good correspondence with experiments as well. A continuum deformation model is developed in two steps. The geometrically linear (small strain) theory is used to prove that the internal stresses and macroscopic shear stresses are negligible. Then a large strain theory is developed under hydrostatic loading. The developed continuum thermomechanochemical model is applied in the accompanying paper [V. I. Levitas, B. F. Henson, L. B. Smilowitz, D. K. Zerkle, and B. W. Asay, J. Appl. Phys. (submitted)] to modeling the heating of PBX inside of a rigid cylinder.

Coupled phase transformation, chemical decomposition, and deformation in plastic-bonded explosive: Simulations

Numerical simulations of the heating with constant rate of a PBX (plastic-bonded explosive) 9501 formulation consisting of the energetic crystal HMX embedded in a polymeric binder inside of a rigid cylinder is performed. The continuum thermo-mechanochemical model of the behavior of a PBX 9501 developed in the preceding paper [V. I. Levitas, B. F. Henson, L. B. Smilowitz, D. K. Zerkle, and B. W. Asay, J. Appl. Phys. 102, 113502 (2007)] is applied. The model describes the β↔δ phase transformations in crystalline HMX, chemical decomposition of the HMX and binder leading to gas formation, gas leaking from the cylinder, elastic, thermal, and transformational straining, as well as straining due to mass loss. We study the kinetics of the β↔δ phase transformations and pressure buildup, as well as how they are affected by the heating rate, initial porosity and prestrain, HMX and binder decomposition, and gas leaking rule.

Heat and mass transfer in saturated porous media with ice inclusions

This paper continues the theoretical exploration of the heat and mass transfer in a biporous medium with the coupled phase transformations. A more complicated system is considered, such as porous medium-ice-aqueous solution. General statements been formulated for a simple medium [4], remain in force for the given system: the heat and mass fluxes each depend linearly on all thermodynamical forces, the transport coefficients satisfy the Onsager reciprocal relations; the coupled phase transformations intensify significantly the cross effects. The presence of contaminants in water imparts the osmotic properties to the biporous medium and decreases the rate of the heat and mass transfer in the system. The dissolved matter takes effect beginning with the concentration of ∼0.001 mol l −1. At the high concentration of the aqueous solution (>0.1 mol l −1) the cross effects become negligible small and the medium loses its unique capacities.

Effect of phase transformations on laser forming of Ti–6Al–4V alloy

In laser forming, phase transformations in the heat-affected zone take place under steep thermal cycles, and have a significant effect on the flow behavior of Ti–6Al–4V alloy and the laser-forming process. The flow-stress data of a material are generally provided as only dependent on strain, strain rate, and temperature, while phase transformations are determined by both temperature and temperature history. Therefore, effect of phase transformations on the flow behavior of materials in thermomechanical processing is not given necessary considerations. In the present work, both the α→β transformation during heating and the decomposition of β phase, producing martensite α′ or lamellae α dependent on cooling rate, are numerically investigated. The spatial distribution of volume fractions of phases is obtained by coupling thermal and phase transformation kinetic modeling. Consequently, the flow stress of Ti–6Al–4V alloy is calculated by the rule of mixtures based on the phase ratio and the flow stress of each single phase, which is also a function of temperature, strain, and strain rate. According to the obtained flow-stress data, the laser-forming process of Ti–6Al–4V alloy is modeled by finite element method, and the deformation is predicted. A series of carefully controlled experiments are conducted to validate the theoretically predicted results.

溶接材料の相変態挙動を利用した溶接継手の残留応力低減効果に関する検討―溶接時における温度・ミクロ組織・熱応力履歴の数値シミュレーションとその応用に関する研究 （第２報）―

Residual stress in welded joints by using a new weld metal with the property of low-temperature phase transformation is numerically analyzed. 10 % Nickel and 10 % Chromium are involved in the developed welding material for producing the property of martensitic phase transformation at a low temperature and for generating compressive residual stress. A fillet-welded joint between plate and stiffener is used for the numerical simulation of the thermal elastic-plastic finite-element analysis with coupling phase transformation effect. Moving heat source is considered by using the gradual deposition of the finite-element during welding process. Distribution of the computed residual stress mostly agrees with the measuring values by strain gauge. Compressive residual stress distributes in the weld metal for both longitudinal and transverse directions with weld line. The effects of the material of weld metal and welding pass sequence on residual stress are then investigated. Residual stresses on the weld toe and root are improved lower by using the low-temperature transformation weld wire than the conventional one, regardless of the sequence of welding deposition. It is found that the weld metal with property of low-temperature phase transformation is effective to reduce residual stress near weld metal.

Generalized enthalpy method for multicomponent phase change

Phase change problems with coupled transport of heat and species occur in solidification and other fields of materials processing. This article describes a new formulation for numerical modeling of coupled phase transformation. The technique is an extension of the conventional heat diffusion enthalpy method and uses the control volume approach. Numerical time-steps are separated into a transport section which updates extensive molar quantities from flux expressions and balance equations, and a thermodynamic section which computes intensive quantities from state functions through local entropy maximization. Heat and species transport are handled in a symmetrical manner with flux expressions from irreversible thermodynamics. The scheme is general enough to cover an unrestricted number of species and phases in various systems and is appropriate for three-dimensional modeling. Applications of the algorithm are illustrated by computations on isomorphous, eutectic, and peritectic binary systems; a simplified dendritic growth problem with coupled heat and species transport is also presented.

Theory of Coupled First-Order Phase Transformations: Application to Bainitic Transformations.

We develop a Ginzburg-Landau theory containing two coupled first-order phase transformations with an application to bainitic transformations familiar to metallurgists and materials engineers. It provides a paradigm for those transitions taking place at intermediate temperatures where both the reconstructive and displacive transformational mechanisms, represented, respectively, by a conserved and a nonconserved order parameter, interplay to manifest a series of phenomena such as diffusion-induced nucleation and incomplete-reaction phenomenon, which are characteristics of the bainitic transformations. The theory can be generalized to the coupling of more phase transitions of various characters.

Composite electroceramics

Abstract Some of the concepts employed in composite electroceramics are reviewed in this paper: connectivity, sum and product properties, coupled phase transformations, polychromatic percolation, mechanical stress and electric field concentration, and symmetry rules. Electronic applications are described for most of the ideas.

Mathematical model coupling phase transformation and temperature evolution during quenching of steels

Mathematical model coupling phase transformation and temperature evolution during quenching of steels

Mathematical model coupling phase transformation and temperature evolution during quenching of steels

AbstractTo calculate the internal stresses in steels during quenching it is necessary to be able to predict accurately the evolution of phase transformations during the cooling process. After a review of published papers, a mathematical model coupling phase transformations with temperature field predictions at each instant during the cooling process is proposed. Incubation and growth periods are treated separately, using Scheil's method and the Johnson–Mehl–Avrami formulation, respectively. Martensitic growth is considered separately using the Koistinen and Marburger law. The temperature field calculation is carried out by the resolution of the heat equation using an implicit finite–difference method. An internal heat source term has been included in the heat equation to take into account the heat generated by the phase transformation. The results of the theoretical calculations are compared with those obtained by experiment, and the validity of the model and the effect of internal stresses on the theoret...

Ferroelectric Composites

Some of the underlying ideas governing composite ferroelectrics and their applications are reviewed: sum and product properties, combination properties and the figure of merit, three-dimensional connectivity patterns leading to field and stress rearrangement, boundary conditions in composites, the symmetry of composite materials and its influence on physical properties, the importance of periodicity and scale in ferroelectric composites, the effect of ferroelectric phase transitions on inter facial phenomena, thermistor effects arising from coupled phase transformations, polyohromatic percolation and the poling of composites through the use of coupled flux paths, electrostriction and other non-linear phenomena, and the important role that porosity and inner surfaces play in many composites.