Phase Transformation Model Research Articles

Modelling of cyclic plasticity and phase transformations during repeated local heating events in rail and wheel steels

Short term local friction heating events in railway operations might lead to phase transformations in pearlitic rail and wheel steels. A modelling framework for phase transformations combined with cyclic plasticity for the individual phases is presented. The phase transformation kinetics include e.g. austenitization due to heating, martensite formation due to rapid cooling and martensite tempering. The modelling framework has been calibrated against cyclic dilatometry test data and cyclic mechanical experiments. Simulations of a double heating event followed by rolling contact loadings show phase transformations and how cyclic residual stresses develop in the different phases.

Phase transformation testing and modeling for hot stamping of boron steel considering the effect of the prior austenite deformation

Hot stamping of boron steels is a thermal-mechanical and phase transformation coupled process. The phase transformation of boron steels during continuous cooling is a complex process since the phase transformation is tightly coupled with plastic deformation during the hot stamping process. In the present work, the effects of hot deformation amount, deformation temperature, and strain rate on phase transformation are investigated by using a comprehensive set of methods including in-situ isothermal tensile tests combined with dilatometry and ex-situ microstructure characterization. The dilatation curves, phase fraction evolution curves, continuous cooling transformation (CCT), and deformed continuous cooling transformation (DCCT) diagrams are constructed. Finally, based on the testing results, a new non-isothermal kinetic model of phase transformation are proposed to introduce the effect of the austenite deformation on transformation during the continuous cooling. The proposed model is validated by testing Vickers hardness of DCCT specimens and hot stamping W-channel parts. The results demonstrate that the deformation accelerates the diffusive phase transformation, causing the CCT curves to move in the direction of shorter incubation time. But the acceleration of diffusion transformation is rapidly saturated as the plastic strain increases. Lower deformation temperature and higher strain rate are more favorable to the diffusion phase transformation, and the higher the critical cooling rate of the martensite transformation is needed. The proposed kinetic model not only accurately predicts the final phase fraction and hardness of the DCCT specimen, but also the distribution of mechanical properties of the hot stamping W-channel parts.

CFD-based modelling of phase transformation in laser welded low-carbon steel

This paper presents a numerical model of the laser welding of steel, taking into account the heat and mass flows, as well as thermal effects associated with phase transformations. It was assumed that the heat source is a laser with a symmetrical power distribution of the TEM10 beam in two welding condition variants: a stationary heat source and a source moving at a constant speed along the sample. After reaching the melting temperature, the movement of the liquid phase was forced by the Marangoni effect acting on the surface of the welding pool. For the laser power applied, the surface of the welding pool was assumed to be flat. It was proposed an algorithm for the forecasting of the phase changes during heating and cooling. Diffusive phase transformations during cooling were modelled using Johnson-Mehl-Avrami-Kolmogorov (JMAK) equations. Diffusionless transformations occurring when cooling rates exceed the critical ones were modelled using Koistinen-Marburger (KM) equations. Calculations were made for a rectangular sample welded in air and cooled spontaneously in the atmosphere. The boundary conditions were simulated assuming a constant coefficient of heat exchange and radiation to the environment. The start and end time of the changes occurring in the cooling phase were calculated based on the average cooling rate in the temperature range 800–500°C (v8/5). The model was tested for the test material: S355J2 steel.

Atomic scale modeling of structural phase transformations in AlCrFeMnMo high-entropy alloys during thermal treatments

The objective of this work is to provide an overview of the evolution of phase transformations in AlCrFeMnMo high-entropy alloys (HEAs), a recently proposed family showing great promises in metallurgical industry for coating applications. We perform Monte-Carlo simulations based on ab initio energy parameters, to analyze the order/disorder transition and the phase separation process from the high-temperature A2 single phase. The reliability of the atomic-scale approach, already known to work on AlCoCrFeNi, is first confirmed on AlCrFeMnNi, the presence of A2-(Cr,Fe,Mn) and B2-(Al,Ni) being in good agreement with previous experimental studies. However, simulations of equimolar AlCrFeMnMo show that the A2 solid solution should transform into two B2 phases at ambient temperature, instead of a couple of A2 phases observed experimentally. The reasons for this discrepancy are discussed. Increasing iron and decreasing molybdenum contents in AlCrFeMnMo favors ordering for chromium and phase change for aluminum, without changing the conclusion on A2 / B2 competition previously drawn from the equimolar case.

A phase-transformation based method coupled with entropy to predict fatigue crack initiation of metallic materials

Fatigue crack initiation can be regarded as a generalized phase transformation from the view of breaking energy barrier. A new phase transformation model is proposed to predict fatigue crack initiation based on the second law of thermodynamics. Evolution of dynamic energy during crack initiation and the damage under fatigue loading is considered combining with the entropy theory. The system becomes unstable when the Helmholtz free energy reaches the extremum value, which is adopted to represent fatigue crack initiation. The effects of grain size on the crack initiation and the asymptote of S-shaped S-N curve are discussed. The theoretical predictions are compared with the experimental data and show reasonable accuracy for different metallic materials.

Kinetic model for phase transformation of noncrystalline solids: Application to permanent densification of SiO2 glass

The phase transformation of noncrystalline solids is quite different from that of crystalline solids. To gain a better understanding, a kinetic model for pressure-induced phase transformation of noncrystalline solids is constructed by formulating activation- and free-energy distributions. The model is applied to permanent densification of $\mathrm{Si}{\mathrm{O}}_{2}$ glass, which occurs as a result of a transformation in the network structure. The model is found to be effective in reproducing interesting behavior, including the existence of an infinite number of intermediate states, each of which has a distinct compression curve like a phase, and a halt in the transformation before completion even at sufficiently high temperatures.

Forecasting the Microstructure of a Microalloyed Steel Plate Strip

A description of the experience in the development and implementation of a model for forecasting the microstructure of rolled tubular products steel during thermomechanical processing of a semi-finished product and the relative IT-solution for the plate mill 5000 of PJSC MMK is presented. This solution is based on modeling the kinetics of structure formation in the mill technological line. The article describes briefly the result of analysis of a number of existing kinetics models of phase and structural transformations from the point of view of their application under the conditions of interest to us. An empirical study of the thermal effects of phase transformations and the influence of the heat removal mode on the kinetics of structure formation is described. The process of development of an empirical kinetics model and implementation of IT-solution, that implements this model, is also described.

The Study of the Melting of Waelz Oxide with an Increase in the Temperature of the Calcination Process

Waelz-oxide is a raw material for the production of metallic zinc. Waelz-oxide contains impurities of zinc and lead chlorides and fluorides. Halides have a negative effect on the process of zinc electrolysis. Halides have a relatively low boiling point; therefore, they are removed into the gas phase by calcining Waelz-oxide at 800–850 °С. To intensify the process, calcination is sometimes carried out at elevated temperatures of 1100–1250 °С. However, an increase in temperature leads to partial melting and granulation of the calcined product. In the present work, the chemical and phase composition of the initial and calcined Waelz-oxide was studied. Thermodynamic modeling of phase and chemical transformations of Waelz-oxide components during heating has been performed. Experiments on calcination of Waelz-oxide in laboratory conditions at temperatures of 600–1250 °C were carried out. It was found that partial melting and granulation of Waelz-oxide is the result of the formation of fusible eutectics containing lead oxide. Lead oxide is formed as a result of decomposition of lead sulfate when heated above 1100 °C. A similar effect is not observed at a standard calcination temperature of 850 °C.

PHYSICO-CHEMICAL MODELING OF PHASE SEPARATION IN FE-21.4 CR STEEL WITH 1.14 MO TAKING INTO ACCOUNT CROSS FACTORS

Physicochemical modeling of diffusion phase transformation and determination of the long-term microstructural stability of the Fe-21.4 Cr alloy with 1.16 Mo taking into account cross factors has been carried out. A conventional Fe-21.4 Cr alloy is used as a reference material. The article proposes an integral approach to modeling phase separation in chromium alloys, combining the determination of diffusion coefficients and fluxes of elements, taking into account their dependences on the concentration and an assessment of the mutual diffusion of elements. The calculated values of diffusion fluxes are used to calculate the current concentrations of carbon and chromium in the alloy and the size of chromium formations. They show that the thermal stability of the Fe - 21.4% Cr alloy with 1.16% Mo is much higher than without molybdenum. In alloy Fe – 21,4 % Cr – 1,16 % Mo at a temperature of 973 ° K, the chromium concentration during the same operation time decreases three times slower with the formation of inclusions of the σ-phase about 6 microns in size.

Development and identification of the cellular automata phase transformation model

The development and identification of the complex microscale austenite to ferrite transformation model during continuous cooling based on the Cellular Automata method and DigiCore library is the main goal of the work. The model is designed to predict phase transformation from a fully austenitic range and involves nucleation of ferrite grains with their further growth. The major driving force for the CA grain growth is based on the carbon concentration differences across the microstructure. The model parameters are identified with the inverse analysis method with the goal function defined on the basis of the dilatometric investigation. The basic assumption of the developed model, experimental procedure, as well as subsequent identification stages, are presented within the work.

Development of a novel high temperature open tribometer with laser-based heating system

Contacts operating under severe conditions such as high temperatures, contact pressures and/or sliding velocities, can occur in many applications and especially in metalworking processes. The extreme thermomechanical loadings withstood by the tooling during such interaction directly govern their lifetime but also the functional properties of the component surface. Understanding the friction and wear mechanisms behind is still an issue and can only be addressed with a relevant experimental set-up. This work presents the development of a new laser-based heating system fitted on an open tribometer with the aim of investigating such severe contact conditions for a AISI1045 carbon steel during sliding against uncoated cemented carbide. A 3D numerical approach is adopted to design the system and predict the temperature distribution, as well as the heating rates, below the laser beam and at the expected contact zone. A phase transformation model based on the simulated thermal kinetics is applied to identify the conditions leading to the potential formation of austenite and to show that a proper combination of laser power and sliding velocity has to be selected to ensure the desired contact conditions. It is shown for example that even at high sliding velocities, a maximum temperature of 600∘C can be reached in the contact zone without exceeding the melting temperature ahead while only a thin layer can be affected by the laser. The experimental set-up is described with the integration of a laser head into the test bench. An experimental campaign is carried out to show the influence of the temperature and sliding conditions on the tribological behavior especially in terms of friction, wear mechanisms and microstructural evolution beneath the contact track.

Solid state phase transformation kinetics in Zr-base alloys

We present a kinetic model for solid state phase transformation (alpha rightleftharpoons beta) of common zirconium alloys used as fuel cladding material in light water reactors. The model computes the relative amounts of beta or alpha phase fraction as a function of time or temperature in the alloys. The model accounts for the influence of excess oxygen (due to oxidation) and hydrogen concentration (due to hydrogen pickup) on phase transformation kinetics. Two variants of the model denoted by A and B are presented. Model A is suitable for simulation of laboratory experiments in which the heating/cooling rate is constant and is prescribed. Model B is more generic. We compare the results of our model computations, for both A and B variants, with accessible experimental data reported in the literature covering heating/cooling rates of up to 100 K/s. The results of our comparison are satisfactory, especially for model A. Our model B is intended for implementation in fuel rod behavior computer programs, applicable to a reactor accident situation, in which the Zr-based fuel cladding may go through alpha rightleftharpoons beta phase transformation.

Microstructure-Based FEM Modeling of Phase Transformation During Quenching of Large-Size Steel Forgings

The current investigation encompasses the development of a microstructure-based 3D finite element model (FEM) of water quenching process of large-size, high-strength steel forgings with accurate predictions of the volume fraction of phases. The approach is based on modified TTT/CCT curves that consider a lower martensite start temperature value. An experimental procedure consisting in the validation of the FEM simulations was conducted using high-resolution dilatometry, optical and scanning electron microscopy, and instrumentation of a large-size steel block with several thermocouples at different locations. Results showed a very good agreement between the temperature predictions of the 3D FEM model and those obtained from direct measurement of instrumented forged block with an average error of about 1 pct in the quarter region. The volume fraction of phases and hardness distribution across the block were also predicted by the proposed 3D FEM model. The numerical results revealed bainitic volume fractions of about 74 pct at the center of the block and about 91 pct in the quarter region. These predictions were also confirmed by dilatometry test and metallographic examination of the microstructure. Micro hardness measurements were conducted on dilatometry samples that simulate the heat treatment cycle of different thicknesses of the forged block were compared with those predicted by the FEM, and very good agreements were obtained, further confirming the validity of the simulations. The proposed procedure in this research improves the quality of predictions by increasing the reliability of material parameters such as TTT optimization and accurate determination of thermo-physical parameters.

Constitutive modeling of TA15 alloy sheet coupling phase transformation in non-isothermal hot stamping process

The simultaneous occurrence of phase transformation and deformation for titanium alloy sheets is an important feature in hot stamping process where components are formed in room-temperature tools by hot blanks. This work takes a research on the constitutive modeling of TA15 alloy by coupling the effect of phase transformation under hot stamping conditions. Based on Gleeble testing system, the continuous cooling tests and interrupted tensile tests are conducted to study the effects of cooling rate and deformation on phase transformation. Subsequently, a diffusion controlled phase transformation model is extended to describe the phase transformation kinetics. The flow behaviors of TA15 alloy are found to be not only sensitive to temperature and strain rate, but also cooling rate dependent, which can be ascribed to the phase transformation. Hence, a physically based model coupling the effect of phase transformation is proposed. Compared with experimental stress–strain values, the average relative error of predicted results by the proposed model is 2.29%. Finally, hot stamping simulations and experiments of a U-shape part are performed. The simulation results of the proposed model show a better agreement with the experiments.

A finite strain thermomechanically-coupled constitutive model for phase transformation and (transformation-induced) plastic deformation in NiTi single crystals

A 3D finite-strain constitutive model for the deformation response of NiTi at the single crystal level is proposed. The model accounts for reversible phase transformation from austenite to martensite habit plane variants, plastic deformation in the austenite phase, and rate effects induced from latent heat. It is developed within the formalism of irreversible thermodynamics with internal state variables based on the Eulerian logarithmic strain and its corrotational objective rate. The inelastic deformation is defined as an average over a representative volume element as classical in the micromechanics-based modeling approach. Transformation-induced plastic deformation is viewed as a mechanism for accommodation of the local deformation incompatibility at the austenite–martensite interface. It is accounted for by introducing an interaction term in the free energy, which is described through the Eshelby tensor by regarding the habit plane variants as ellipsoidal inclusions embedded in the austenite matrix, in order to accurately reflect the internal stress states that contribute to dislocation slipping. The numerical implementation of the model in an efficient scheme and its calibration are described in detail. The proposed model is validated by comparing simulations with available experimental data in single NiTi crystals. Numerical simulations of polycrystals are performed to obtain an insight into the interaction between phase transformation and plastic deformation induced by intergrannular constraints. The efficiency of the numerical implementation of the model is verified by simulations of indentation tests.

Solutions to a phase‐field model for martensitic phase transformations driven by configurational forces

AbstractWe study the existence of weak solutions to an initial‐boundary value problem for a new phase‐field model, which consists of a degenerate parabolic equation coupled to linear elasticity equations. This model is used to describe the evolution of interfaces in elastically deformable solid materials which moves by configurational forces, such as martensitic phase transformations in shape memory alloys. The existence proof is valid only for one‐dimensional case.

Correction to: Thermodynamic Modeling of Chemical and Phase Transformations in a Waelz Process-Slag – Carbon System

To the article “Thermodynamic Modeling of Chemical and Phase Transformations in a Waelz Process-Slag – Carbon System,” by A. S. Kolesnikov, G. S. Kenzhibaeva, N. E. Botabaev, A. N. Kutzhanova, G. M. Iztleuov, A. Zh. Suigenbaeva, Kh. A. Ashirbekov, and O. G. Kolesnikova, Vol. 61, No. 3, pp. 289-292, September, 2020.

Mean field model of phase transformations in steels during cooling, which predicts evolution of carbon concentration in the austenite

The objectives of the paper were twofold. The first was exploring possibility of fast and reliable modelling of phase transformations during cooling of steels, accounting for the evolution of the carbon concentration in the austenite. Existing discrete models require long computing times and their application to optimization of industrial processes is limited. Therefore, a model based on the modified JMAK equation was proposed. Control of the carbon concentration in the austenite during ferritic and bainitic transformations allowed to predict incomplete austenite transformation and occurrence of the retained austenite. Moreover, prediction of the onset of pearlitic transformation after the bainitic was possible. The model was validated by comparison the predictions with the results of physical simulations. Numerical simulations for various industrial processes were performed. Problem of the difference in the incubation time between isothermal and constant cooling rate tests was raised.

Physico-chemical Modeling of Phase Separation in Fe-21.4 Cr Steel with 1.14 Mo Using the Provisions of Non-equilibrium Thermodynamics

The use of ferritic-martensitic steels, for example, Fe-Cr and Fe-Cr-Al alloys as structural material for fast neutron reactors has been advocated due to their relatively low rate of swelling at elevated temperatures. Because of the high Cr-content, the Fe-Cr alloys are not suitable for use at temperatures around 500°С due to the miscibility gap in the Fe-Cr system. Phase separation in such alloys can also be prevented by doping with elements that impede the segregation of chromium. In solid state physics for calculating phase separation in similar metal systems are used physicochemical and phase-field modeling. The aim of the work is the physicochemical modeling of diffusion phase transformation and determination of the long-term microstructural stability of the Fe-21.4 Cr-1.16 Mo. A conventional Fe-21.4 Cr alloy is used as a reference material. The article proposes an integral approach to modeling phase separation in chromium alloys, combining the determination of diffusion coefficients and fluxes of elements, taking into account their dependences on the concentration and an assessment of the mutual diffusion of elements, using the provisions of nonequilibrium thermodynamics. The calculated values of diffusion fluxes are used to calculate the current concentrations of carbon and chromium in the alloy and the size of chromium formations. They show that the thermal stability of the Fe - 21.4% Cr alloy with 1.16% Mo is much higher than without molybdenum. In alloy Fe – 21,4% Cr – 1,16% Mo at a temperature of 973°K, the chromium concentration during the same operation time decreases three times slower with the formation of inclusions of the σ-phase about 6 microns in size.

Strength mismatch effect on residual stress of high strength steel butt-welded joints

This study was mainly concerned with the residual stresses of 10CrNi3MoV high strength steel multipass butt welded joints by experimental measurement and numerical calculation considering the weld metal strength mismatch effect. Firstly, the Solid-State Phase Transformation (SSPT) processing of weldment was described by the thermo-metallurgical-mechanical simulation model. The residual stress distribution on the basis of the established procedure. Phase transformation modeling of diffusionless transformation kinetics based on the Koistinen-Marburger formula was performed by a user subroutine implemented in ABAQUS. Additionally, strain transformation calculation due to volumetric and heating change during the SSPT was completed by the user-defined subroutine. The results show that more accurate predictions of welding residual stress are obtained when the SSPT effect is incorporated in the simulation procedure. For evenmatched welded joints, the compressive residual stresses were distributed in the top and back weld layer due to the involving of SSPT behavior. The proposed finite element model can predict residual stress of high strength steel multipass welded joints and provide a theoretical basis to conduct the structural integrity assessment.