Phase Transformation Model Research Articles

Inverse Problem in the Stochastic Approach to Modeling of Phase Transformations in Steels during Cooling after Hot Forming

The motivation for this research was the need for a reliable prediction of the distribution of microstructural parameters in steels during thermomechanical processing. The stochastic model describing the evolution of dislocation populations and grain size, which considers the random phenomena occurring during the hot forming of metallic alloys, was extended by including phase transformations during cooling. Accounting for a stochastic character of the nucleation of the new phase is the main feature of the model. Steel was selected as an example of the metallic alloy and equations describing the nucleation probability were proposed for ferrite, pearlite and bainite. The accuracy and reliability of the model depends on the correctness of the determination of the coefficients corresponding to the specific material. In the present paper these coefficients were identified using the inverse analysis for the experimental data. Experiments composed constant cooling rate tests for cooling rates in the range 0.1-20 °C/s. The inverse approach to a nonlinear model is ill-conditioned and must be transferred into an optimization problem, which requires formulating the appropriate objective function. Since the model is stochastic, it was a crucial, yet demanding task. The objective function based on a metric of the distance between measured and calculated histograms was proposed to achieve this goal. The original stochastic approach to identifying the phase transformation model for steels was tested, and an appropriate optimization strategy was proposed.

Thermodynamically consistent phase-field model for pressure-induced multiphase phase transformation of metals under intensive dynamic loading

Understanding the pressured-induced multiphase phase transformation (MPT) of metals at high strain rate is of great technical and scientific interest. Despite of several decades of studies, the pressured-induced MPT of metals at high strain rate is far from well understood because the deformation at high strain rate is so complex that present in situ diagnostic techniques or atomistic simulations cannot provide the details of the MPT at high strain rate. In the current work, a multiphase phase-field (MPF) model for the dynamic phase transformation (PT) of metals is developed, in which the volume fraction of each phase is chosen as the order parameter. The driving force of the MPT consists of the Gibbs free energy, the gradient energy and the penalizing energy. In particular, a smooth and normalized interpolation function is introduced to establish the Gibbs free energy at the multiphase junction. With the aid of this interpolation function, the explicit forms of the kinetics equation and constitutive relations of the MPT at the multiphase junction are also derived. It is demonstrated that the model satisfies all seven criteria of a consistent MPF model. Compared to previous models, the thermodynamic stability of this model is improved significantly. When applied to address the MPT of bismuth subjected to ramp-wave loading (RWL), the model can quantify the connection between the microstructural evolution of multiple phases and the experimentally measured multiwave structures.Moreover, new insights concerning the MPT-related thermodynamic paths of bismuth at elevated temperatures and the metastable phase during dynamic MPT are gained.

Modeling the effects of initial grain size, martensitic transformation induced dynamic grain refinement, phases, and texture on strength of a high entropy alloy using crystal plasticity

Microstructurally flexible high entropy alloys (HEAs) can be tailored for strength via dual-phase strengthening mechanisms, which originate from the strain-induced phase transformation microstructural phenomena. One such alloy is a recently synthesized Fe42Mn28Co10Cr15Si5 (at%) HEA consisting of metastable gamma austenite (γ), stable epsilon martensite (ε), and stable sigma (σ) phases. In this work, a crystal plasticity homogenization incorporating a physically based phase transformation and hardening models is used to interpret and better understand the effects of strain induced phase transformation phenomena on the overall hardening response of the alloy. The transformation model is conceived based on the grain-scale stress sensitive motion of partial dislocations forming shear bands, while the hardening model is an extended Kocks-Mecking-type dislocation density-based formulation sensitive to grain size and shape. The deformation of constituent grains per phase in the alloy is modeled as a combination of anisotropic elasticity, crystallographic glide, and γ→ε phase transformation. Parameters of the hardening and transformation models within the homogenization are calibrated and validated on a suite of data including flow stress curves and phase fractions measured under compression, while the corresponding texture evolution data is used solely for verification. Good predictions of the model elucidate that the transformation induced dynamic Hall-Petch-type barrier effect is the primary origin of strain hardening along with the increase in the ε-phase fraction and dislocation density, while the individual strength of the phases gives rise to the overall strength. The modeling framework described in the present work is expected to be applicable to other HEA systems.

Modeling Microstructure Development upon Continuous Cooling of 42CrMo4 Steel Grade for Large-Size Components

42CrMo4-type steel grades are widely used in a great variety of components that require ad hoc mechanical properties. However, due to the dimensions of large components and the previous thermomechanical treatments, the presence of heterogeneities in the chemical compositions are expected to impact those mechanical properties. In the present work, a detailed analysis of phase transformation behavior upon cooling was carried out through a dilatometry test on samples of 42CrMo4 belonging to a component that has a non-homogeneous chemical distribution. The analysis of the dilatation signals and the quantitative metallography shows a rather complex behavior depending on the cooling rate as well as on the region of observation. Two different phase transformation models based on Li’s approach were applied to the present composition to determine the CCT curve as well as the fraction of the microconstituents. An extensive discussion was carried out on some aspects about Kirkaldy-based approaches that need to be improved so as to attain more reliable quantitative results when modeling phase transformations in heterogenous systems.

Uncovering the combining V with Ni micro-addition alloying on the mechanical properties and multiphase transformation during solidification and homogenization of Al–Zn–Mg–Cu–Sc alloy

The ultimate tensile strength of the T6-aged Al–Zn–Mg–Cu–Sc alloy is improved by 24 MPa reached 667 MPa with the addition of 0.10 % V, 0.20 %Ni and decrease 0.1 %Sc. The thermodynamic and microalloying mechanisms of phase transformation during solidification and homogenization of Al–Zn–Mg–Cu–Sc–V–Ni alloy were clarified. The phase transformation model of Al3Sc (V, Ni) structure induced by V and Ni addition during homogenization was established. The calculation radius showed that coherent L12-ordered Al3Sc(V, Ni) nanoparticles were formed in the Al–Zn–Mg–Cu–Sc–V–Ni alloy, which had a small critical nucleation radius (22.0 nm). The large thermodynamic driving force and the high kinetic energy migration energy barrier of γ-Al7Cu4Ni and Al3Sc (V, Ni) phases led to the finer microstructure of grain. V element not only promoted the formation of Al21V2 phase containing Sc but also hindered the mutual diffusion of Al and (Sc, Ni) elements in the eutectic system via segregation at the α-Al/Al3Sc (V, Ni) interface, which improved the stability of the whole alloy. The edge nucleation of γ-Al7Cu4Ni phase upon its diffusion into a Sc-containing Al21V2 phase induced the formation of Al3Sc (V, Ni) structure, whereas the segregation of V and Ni further strengthened the alloy matrix.

Investigation of phase transformation model, densification mechanism, and mechanical properties of TiH2 powder metallurgy materials

TiH2 has gradually gained attention in powder metallurgy because of its unique properties. This study systematically investigated the porosity, density, mechanical tensile properties, and fracture toughness of sintered samples of TiH2 as a powder metallurgy starting material. The results showed that, compared with hydrogenation-dehydrogenation titanium (HDH Ti), the density, elongation, and fracture toughness of the sintered TiH2 samples significantly improved. In addition, the contributions of grain size, porosity, and oxygen content to the yield strength of the samples are discussed, and the results revealed that a lower oxygen content and porosity are the main reasons for the differences in the mechanical properties between HDH Ti and TiH2. Finally, the experimental results are combined with first-principles calculations and simulations to construct a TiH2 phase transition model. The contribution of H atoms to the TiH2 phase transition energy barrier and activation sintering densification was investigated and elucidated, revealing the TiH2 sintering densification mechanism from the perspective of phase transition. The derived results contribute to a deeper understanding of the intrinsic mechanism of TiH2 activation sintering densification, which is highly important for the development of advanced titanium materials.

Numerical Modelling of Phase Transformations of Water Droplets for Efficient Heat Recovery from Biofuel Flue Gas

The phase transformations of water droplets in the humid air flow for water injection into the flue gas in biofuel combustion technology under typical boundary conditions have been simulated. The numerical study was performed in two stages. The first one defines the influence of radiation on the thermal state of the water droplets and on the cycle of phase transformation modes. It is shown that the influence of radiation in a flue gas flow of 150℃→200℃ temperature on the thermal state of quantitatively injected water droplets is not significant, but it induces qualitative changes in the temperature field and influences phase transformations cycle of the droplets. In the second step, the cycling of the droplet phase transformation modes for water injection into the exhaust flue gas prior to a condensing economiser under typical boundary conditions was numerically investigated. It was justified that for efficient cooling and humidification of the flue gas before the condensing economiser it is necessary to inject water heated above the dew-point temperature by dispersing it into fine droplets.

Modelling of phase transformations occurring in the process of austempered ductile iron manufacturing

The paper presents mathematical models and their implementation in C # language describing the phase transformations occurring in the process of austempered ductile iron (ADI) manufacture. The research includes two main stages: austenitization and isothermal holding at the bainitic range. The influence of free energy of austenite and ferrite on transformations was taken into account. Parameters of models were identified based on inverse analysis and experimental research. As part of the research, verification and validation of the developed models was carried out based on the results of experimental research. The tool developed and implemented enables the analysis of phase transformations occurring during heat treatment with isothermal holding of ductile iron with Ni addition.

Modeling of localized phase transformation in pseudoelastic shape memory alloys accounting for martensite reorientation

A reliable prediction of the pseudoelastic behavior necessitates the involvement of martensite reorientation in the model. This is important not only under non-proportional loading but in general when the phase transformation proceeds in a localized manner, which results in complex local deformation paths. In this work, an advanced model of pseudoelasticity is developed within the incremental energy minimization framework. A novel enhancement of the model over its original version lies in the formulation of a suitable rate-independent dissipation potential that incorporates the dissipation due to martensitic phase transformation and also due to martensite reorientation, thus yielding an accurate description of the inelastic transformation strain. The finite-element implementation of the model relies on the augmented Lagrangian treatment of the non-smooth incremental energy problem. Thanks to the micromorphic regularization, the related complexities are efficiently handled at the local level, leading to a robust finite-element model. Numerical studies highlight the predictive capabilities of the model. The characteristic mechanical behavior of NiTi tube under non-proportional tension–torsion and the intricate transformation evolution under pure bending are effectively captured by the model. Additionally, a detailed analysis is carried out to elucidate the important role of martensite reorientation in promoting the striations of the phase transformation front.

Modeling of martensitic phase transformation accounting for inertia effects

As a diffusionless phase transformation, martensite evolves at the speed close to sound, with its kinetics and morphology dominated by the mechanical energy. However, the mechanism of martensitic phase transformation with the consideration of inertia is rarely investigated. This paper presents a multiphase-field model, where the transformation strain in martensite performs as the mechanical wave source, and in return the kinetic energy contributes to the driving force for phase transformation. As a result, the mechanical fields, i.e., the stress and the velocity, are derived according to the increment of the transformation strain. The propagation direction of the mechanical wave is corrected by considering the growth of the martensitic nucleus. With the 1D and 2D analysis, as well as the comparison against 2D static case, the mechanism of martensitic phase transformation is investigated, and the advantage of mechanical model accounting for inertia effects is illustrated.

High-fidelity level-set modeling of diffusive solid-state phase transformations for polycrystalline materials

The formation of microstructures in metallic alloys during hot metal forming involves simultaneous metallurgical complex phenomena. Traditional high-fidelity numerical frameworks used on the polycrystalline scale tend to focus on single-phase microstructures or isolate phase transformations from grain boundary migration mechanisms. The level-set method is highlighted as effective in proposing a global framework for modeling multiphase polycrystalline materials and diffusive solid-state phase transformations. This framework includes novel techniques for efficient large-scale microstructural representation, strong coupling with ThermoCalc software for real-time thermodynamic data, application for ternary alloys and beyond by taking solute drag aspects, and the use of advanced nucleation models. Numerous applications are then illustrated.

Determination of phase transformation kinetics under magnetic fields: Modeling based on magnetization and application in a Fe-1 wt.%Cu alloy

A phase transformation model based on magnetization is proposed in this paper, which accurately tracks the change in the phase transformation volume fraction with time/temperature f-T/t by analyzing phase transformation magnetization curves under a magnetic field. This allows for the determination of kinetic parameters related to the nucleation and growth processes such as the phase transformation rate df/dt-T/t and Avrami exponent n, enabling quantitative analysis of phase transformation kinetics under magnetic field effects. Additionally, the phase transformation magnetization under a magnetic field can be accurately fitted by combining the volume fraction calculation model with the Johnson–Mehl–Avrami equation, thus also obtaining the kinetics parameters. The aforementioned two models are applied to study the isothermal and isokinetic transformations of austenite (γ) to ferrite (α) in Fe-1 wt. %Cu alloys, demonstrating the effects of external conditions through variations in kinetic parameters.

Modeling of Grain Size Change and Phase Transformation of Stainless Wire during Drawing with Cryogenic Cooling

Modeling of Grain Size Change and Phase Transformation of Stainless Wire during Drawing with Cryogenic Cooling

Localized plastic strain accumulation in shape memory ceramics under cyclic loading

The premature failure of shape memory ceramics (SMC)s under cyclic loading is a critical issue limiting their applications as actuators and thermal protection layers. Martensitic phase transformation (MPT), essential for superelasticity and shape memory functionalities in SMCs, induces localized plastic deformations due to phase expansion. In polycrystalline materials, the accumulation of localized plastic strain serves as the primary mechanism for fatigue crack initiation under cyclic loading. In this research, a phase-field (PF) phase transformation model coupled with a viscoplasticity model is presented to study the effects of microstructural features, engineered pores, and sample size on plastic strain accumulation (PSA) during cyclic loading of SMCs. Our findings highlight that the grain boundaries (GB)s are critical regions with high PSA, with noticeable reductions observed by decreasing the grain boundary density (GBD). Additionally, we found that engineered pores effectively reduced cyclic PSA, however, we identified a threshold on the volume fraction of pores. Also, textured microstructures with certain characteristics demonstrate significant influence on PSA. A cross-correlation data analysis approach is employed to study the relationship between the studied microstructural features and PSA to facilitate the identification of the most important factors controlling the irreversible PSA during compressive cyclic loading. By mitigating the rate of PSA, significant enhancements in cyclic life before fatigue crack initiation can be achieved, enabling superior performance in practical applications.

Hard-sphere model of the B2 → B19’ phase transformation, and its application to predict the B19’ structure in NiTi alloys and the B19 structures in other binary alloys

The pseudoelastic and pseudoplastic properties of NiTi alloys result from the closeness of the structures between the B2 cubic austenite and the B19’ monoclinic martensite, and from the facility to transform one into each other. The paths followed by the atoms during the B2 → B19’ transformation are usually imagined as combinations of simple shears and shuffles. Here, we propose a simplified hard-sphere atomistic model of phase transformation decomposed into three distinct types of rotational movements. The inputs are the Ti and Ni atomic diameters and the monoclinic angle β. The outputs are the lattice parameters and atomic positions of the B19’ phase. The results are remarkably close to those reported in the literature. The model permits a better understanding of the B19’ structure and the way it is inherited from its parent B2. The value of the monoclinic angle corresponds to the highest molar volume; which suggests that it could be a consequence of a maximization of the vibrational entropy. The hard-sphere model also successfully predicts the B19 structures reported in the binary alloys AuTi, PdTi, and AuCd. The agreement is less satisfying for the B19 structure observed in the ternary NiTiCu alloys. It is concluded that the B19’ phase in NiTi alloys, and the B19 phase in AuTi, PdTi, and AuCd alloys can be considered as “simple” hard-sphere structures.

Thermo-metallo-mechanical based phase transformation modeling for high-speed milling of Ti–6Al–4V through stress-strain and temperature effects

The optimization of machining parameters, tool longevity, and surface quality in High-Speed Milling (HSM) of Ti–6Al–4V relies immensely on understanding the local phase transformation. This study endeavors to build a Finite Element (FE) model capable of forecasting phase alterations during the rapid thermal fluctuations intrinsic to Ti–6Al–4V machining. Dynamic phase transformation models were initially introduced to capture rapid heating and cooling phenomena. Using a user-defined subroutine, the phase transitions predictive models were integrated into the HSM simulation within Abaqus/Explicit. Simulation outcomes unveiled phase transitions primarily occurring within the serrated chip and at the tool-workpiece interface. Notably, during rapid heating, when the cutting speed increased to 350 m/min, the β-phase volume fraction surged from 7.5 to 96.38%. A similar trend was observed with feed rate adjustments (i.e., 0.15–0.25 mm/tooth), where β-phase increased from 7.5 to 67.84%. Rapid cooling facilitated the reversion of the transformed β-phase back into the α'-phase. Finally, some advanced characterization techniques were employed to validate the developed thermo-metallo-mechanical coupled FE model for phase transformation. The simulation results verified by the experimental data promotes a better understanding of phase alteration mechanisms and microstructural evolution in HSM of Ti–6Al–4V. The current research is also beneficial for crucial insights into optimizing the machining conditions and their impact on tool-material interactions and surface integrity.

Effect of Cooling Process on Microstructure and Properties of Low Carbon Bainite Steel

This article used Mn-Mo-Cr-B low-carbon bainitic steel as the experimental material. The continuous cooling transformation curve of the steel during continuous cooling was determined using a Gleeble-1500D thermal simulation test machine, and a corresponding phase transformation model for bainitic steel during continuous cooling was established. The influence of different cooling rates and final cooling temperatures on the microstructure and mechanical properties of the steel was investigated. Employing metallography, SEM, and EBSD techniques, the microstructure, crystallographic orientation, and grain boundary angle distribution of the low-carbon bainitic steel were explored, and their relationship with the steel's strength and toughness was studied. The research findings reveal that varying cooling rates and final cooling temperatures impact the phase transformation process and microstructure of the steel, consequently affecting its mechanical properties indirectly. With increasing cooling rate, the diffusion and fineness of martensite increase, and the quantity of lath bainite grows while the laths become finer. Elevated final cooling temperatures lead to larger martensitic-austenitic (MA) islands and reduced lath bainite quantity, causing the laths to become wider. Through analysis of the substructure of bainitic steel, it was determined that the bainite organization in the tested steel comprises primary austenite grains, lath packet, and lath block in succession. Lath packets are composed of lath blocks with different orientations, where lath size predominantly controls strength. Finer lath size corresponds to higher strength, and the influence of substructure on toughness is comparatively minor.

Research on Wellbore Stability in Deepwater Hydrate-Bearing Formations during Drilling

Marine gas hydrate formations are characterized by considerable water depth, shallow subsea burial, loose strata, and low formation temperatures. Drilling in such formations is highly susceptible to hydrate dissociation, leading to gas invasion, wellbore instability, reservoir subsidence, and sand production, posing significant safety challenges. While previous studies have extensively explored multiphase flow dynamics between the formation and the wellbore during conventional oil and gas drilling, a clear understanding of wellbore stability under the unique conditions of gas hydrate formation drilling remains elusive. Considering the effect of gas hydrate decomposition on formation and reservoir frame deformation, a multi-field coupled mathematical model of seepage, heat transfer, phase transformation, and deformation of near-wellbore gas hydrate formation during drilling is established in this paper. Based on the well logging data of gas hydrate formation at SH2 station in the Shenhu Sea area, the finite element method is used to simulate the drilling conditions of 0.1 MPa differential pressure underbalance drilling with a borehole opening for 36 h. The study results demonstrate a significant tendency for wellbore instability during the drilling process in natural gas hydrate formations, largely due to the decomposition of hydrates. Failure along the minimum principal stress direction in the wellbore wall begins to manifest at around 24.55 h. This is accompanied by an increased displacement velocity of the wellbore wall towards the well axis in the maximum principal stress direction. By 28.07 h, plastic failure is observed around the entire circumference of the well, leading to wellbore collapse at 34.57 h. Throughout this process, the hydrate decomposition extends approximately 0.55 m, predominantly driven by temperature propagation. When hydrate decomposition is taken into account, the maximum equivalent plastic strain in the wellbore wall is found to increase by a factor of 2.1 compared to scenarios where it is not considered. These findings provide crucial insights for enhancing the safety of drilling operations in hydrate-bearing formations.

Microstructure Estimation by Combining Deep Learning and Phase Transformation Model

Microstructure Estimation by Combining Deep Learning and Phase Transformation Model

PHYSICAL-CHEMICAL MODELING AND INVESTIGATION OF THE “HIGH-ENTROPY METAL MATRIX / TiC” SYSTEM COMPONENTS INTERACTION

The research carried out is aimed at developing the scientific basis for obtaining new composite materials based on high-entropy alloys, as well as developing the basic principles of processing and operation of such materials. It was necessary to conduct a theoretical and experimental study of the physical-chemical processes occurring during the interaction of high-entropy alloys with reinforcing TiC particles, as well as to study the effect of temperature and composition of interacting phases on the interaction process and its results. Thermodynamic and kinetic modeling of the interaction processes of the matrix components of high-entropy alloys based on the Cantor alloy (FeCoCrNiMn), including titanium and carbon with the formation of titanium carbide was carried out. Modern modeling approaches were used, which makes it possible to implement modern software. In particular, thermodynamic modeling using methods developed within the framework of the Calphad approach was carried out. Thermo-Calc software (includingTC-PRISMA kinetic modeling software) and FactSage software were used in the research process. An experimental study of the composition and structure of samples of TiC-reinforced metal matrix materials (using electron microscopy, X-ray spectral microanalysis and XRD) was also carried out. The distribution of various elements in the microstructure of materials and their phase composition were investigated. Comparison of the simulation results with experimental data allowed to make conclusions about the qualitative adequacy of thermodynamic and kinetic models of phase equilibria and phase transformations occurring during the formation, possible heat treatment and operation of TiC-reinforced metal matrix materials at high temperatures to the observed experimental data.