Phase Transformation Model Research Articles

A unified model for isothermal and non-isothermal phase transformation in hot stamping of 22MnB5 steel

The hot stamping of tailored properties is widely established in the automotive industry. However, unlike conventional press hardening, this technique is designed to generate varying mechanical properties by controlling the cooling rate locally. Current material models cannot accurately represent the locally very different thermomechanical paths. This research aims to address this problem by developing a new phase transformation model capable of handling complicated thermal histories and the effects of deformation. A ’unified JMAK‘ model is proposed to capture various thermal-mechanical loading conditions. These conditions include the deformation effect and cooling paths where isothermal conditions range from 450° to 725°C and non-isothermal conditions range from 5° to 40°C/s. Furthermore, for the extension to linear and non-linear cooling paths, correction factors for the phase transformations are introduced into the model. Finally, the model's performance is compared to well-known transformation models, such as the non-isothermal JMAK and the K-V (Kirkaldy and Venugopalan), by comparing the results obtained from isothermal and non-isothermal dilatometer tests and a scaled-down b-pillar experiment. The results from the comparison are classified into 3 cases, isothermal, continuous cooling and non-linear cooling (b-pillar). Case 1 shows that the non-isothermal and K-V models provide low accuracy, while the proposed model yields an error below 2 %. For Case 2, the proposed models and non-iso JMAK are agreeable with the experiment, and the K-V model shows a maximum error of 15 %. Finally, in the b-pillar case study mean absolute errors of hardness predictions are 33.06 HV (mean relative error is 9 %), 43.92 HV (13 %), and 67.70 HV (20 %) for the unified JMAK, non-iso JMAK, and K-V model, respectively.

Accounting for the random character of nucleation in the modelling of phase transformations in steels

Accounting for the random character of nucleation in the modelling of phase transformations in steels

Математический подход к изучению процесса синтеза муллита

Today the introduction of «smart» automated systems is the basis in system engineering and operations management in various industries, but not yet widespread in the field of mineral processing. 
 The object of the study is the process of interphase changes of kaolinite (Vezhayu-Vorykvinsky deposit, Knyazhpogost district, Komi Republic) during thermal treatment at a temperature range of 25—1200 °C. XRD examinations (Rietveld method and Profex programs) were carried out for quantitative estimation of the phase transformations. XRD patterns were processed by algorithms for determining the positions and heights of peaks implemented in the Python programming language. 
 We obtained a novel simplified mathematical model of kaolinite phase transformations during mullite synthesis based on XRD. The main parameters, influencing the kinetics of mullite synthesis process, have been specified.

Effects of martensitic phase transformation on fatigue indicator parameters determined by a crystal plasticity model

Fatigue indicator parameters are a powerful tool for materials design. These parameters represent the potency of various microstructures to incubate fatigue cracks in metal alloys and are useful in ranking deleterious microstructural features on which to focus process improvements. These fatigue indicator parameters are generally a function of irreversible plastic strain; however, for alloys with solid-state phase transformations (such as Nitinol), reversible transformation strains occur along with plastic strain. This article addresses the question of whether modeling a reversible transformation will affect the predicted value of a fatigue indicator parameter. For Nitinol, the effects of a reversible phase transformation on the fatigue indicator parameter and fatigue life are studied for a polygranular microstructure with and without an inclusion. The crystal mechanics of both plasticity and phase transformations are modeled using the finite element method. It is shown that the usage of a crystal-mechanics-based phase transformation model affects the values of fatigue indicator parameters, the shape of predicted strain–life curves, the distribution of fatigue indicator parameter values in the microstructure, and also the rank ordering of deleterious microstructural features.

A micromechanically motivated multiscale approach for residual distortion in laser powder bed fusion processes

For the broader industrial usage of metal additive manufactured parts, especially made by laser powder bed fusion, a better prediction and understanding of the warpage and of eigenstresses within the final part are necessary. Due to the diverse and sophisticated metallurgical and thermal processes during production, physically motivated simulations are rather complex and time consuming. Therefore, various simplifications concerning the process and material models are frequently made, which leads to practicable simulation times at the expense of physical accuracy. This motivates the procedure in this contribution: A multiscale approach combining various modelling levels, in particular regarding the heat source and material model. The model is based on three finite element simulations on different levels and with different specific aims, i.e. the laser scan model, the layer hatch model and the part model. For the smallest scale considered, a sophisticated thermomechanically fully coupled model based on a phase transformation model explicitly considering the powder, molten, and re-solidified material is incorporated. The goal of this detailed simulation is to extract an effective heat source for the next level of simulation, i.e. the layer hatch model. The layer hatch model is used to extract the inherent strains for the part model. With these strains, the remaining deformation and eigenstresses of arbitrary large parts with the same material and laser parameters can be efficiently and directly computed. The capabilities of the present framework are investigated by simulations on the behaviour of a twin cantilever beam, where the effect of different process parameters on the overall material and structural response is carried out.

Effect of Cr on Isothermal Structure Transformation of Iron Oxide Scale

Herein, the effect of different contents of Cr on the isothermal structure transformation of FeO is systematically studied by a thermogravimetric analyzer, and it is found that the temperature range of eutectoid transformation of FeO in Fe–Cr alloy is 300–500 °C. Combined with the experimental data, the kinetic model of isothermal phase transformation of FeO is established based on Johnson–Mehl–Avrami–Kolmogorov equation, and the time–temperature–transformation curve of isothermal transformation of FeO is predicted, which follows the law of C curve, and the C curve shifts backward with the increase of Cr content. Therm‐calc thermodynamic software calculates the Fe–O phase diagrams of different Cr contents. Combined with the experimental results, the effect mechanism of Cr content on FeO eutectoid transformation is clarified. With the increase of Cr content, the stability of FeO decreases, and under the same isothermal temperature and time, high Cr content has greater undercooling, a higher driving force of phase transition, and the starting time of eutectoid transformation is earlier than that of lower Cr content.

Stress evolution mechanisms under different SSPT-related effects during laser welding

In this study, a thermal-metallurgical-mechanical (TMM) model was developed for finite element (FE) analysis in laser welding of ultra-high-strength steel (UHSS). The solid-state phase transformation (SSPT) model of austenization was improved by introducing a heating rate-dependent coefficient. Seven cases considering different SSPT-related effects (Case 1–5) and different austenization models (Case 5–7) were considered for the simulation of welding stress to study the stress evolution mechanism during welding. The effects include changes in the yield strength, coefficient of thermal expansion, volume strain, and plastic strain, all of which are induced by the SSPT. By comparing the predicted and measured partial austenitized zone (PAZ), it was found the proposed model had good accuracy for the ultra-high heating rates during laser welding. The predicted transverse/longitudinal welding stresses were also in good agreement with the measurements. The results show that each effect can dramatically change the evolution process and the final magnitude and sign of stress. For example, the SSPT-induced plastic strain always results in a plastic strain having the same sign as the stress, and, in return, gives rise to a decrease in the magnitude of stress. In addition, the SSPT-related effects are weakened when the austenization model underestimates the austenite fraction, leading to a larger error in the predicted stress.

A level-set formulation to simulate diffusive solid/solid phase transformation in polycrystalline metallic materials - Application to austenite decomposition in steels

Numerous full-field numerical methods exist concerning the digital description of polycrystalline materials and the modeling of their evolution during thermomechanical treatments. However, these strategies are globally dedicated to the modeling of recrystallization and grain growth for single-phase materials, or to the modeling of phase transformations without considering recrystallization and related phenomena. A generalized numerical framework capable of making predictions in a multi-phase polycrystalline context while respecting the concomitance of the different microstructural mechanisms is thus of prime interest. A novel finite element level-set based full-field numerical formulation is proposed to principally simulate diffusive solid–solid phase transformation at the mesoscopic scale in the context of two-phase metallic alloys. A global kinetic framework, capable of accounting for other concomitant mechanisms such as recrystallization and grain growth is considered in this numerical model. The proposed numerical framework is shown to be promising through a couple of illustrative 1D and 2D test cases in the context of austenite decomposition in steels and compared with ThermoCalc estimations.

Solid phase transformation effects on stress and strain in the thick plate EH40 welded butt joint

To accurately predict welding-induced residual stress and strain of high strength steel thick plate EH40 butt joint in single-pass full penetration laser welding, a complete solid phase transformation model according to the actual weld microstructure was proposed through material constitutive development. At the same time, the Case 1 considering the traditional thermo-elastoplastic were used as comparative study. The simulation calculation results and experimental results of each phase content were compared and verified. The stress and strain distribution of welded joints and the evolution mechanism of nodes in three zone including fusion zone, heat-affected zone and base metal were deeply studied and compared. The results indicated that the solid phase transformation had an obvious effect on the peak and distribution of longitudinal, transverse, normal and equivalent residual stress, as well as the stress gradient at the junction of heat-affected zone and BM. It increased the peak value of longitudinal residual compressive stress from –103 MPa to –768 MPa, with an increase of 645.6%. The stress gradient at the junction of heat-affected zone and base metal was up to 1299 MPa. The state distribution of longitudinal and transverse stress in the weld and its vicinity were completely opposite to the Case 1. The peak value of transverse plastic compressive strain increased from –0.059 to –0.111, with an increase of 88.1%. The fusion zone and heat-affected zone of the plastic strain in welded joints were more easily observed. It was found that martensitic transformation was the main reason for the obvious difference of stress and strain distribution and the evolution mechanism of stress and strain in the later stage of cooling stage.

Intelligent Iterative Experimental Design to Achieve Maximum Model Quality for Phase Change of 22MnB5

Conducting experiments for material modeling is very costly and time-consuming when many parameters are involved, resulting in a large number of test conditions. Therefore, it is expedient to develop algorithms for the iterative identification of optimal test conditions. This method should allow the model to learn automatically so that only a small number of test conditions are selected at the beginning of the model calibration. In order to decide whether further experiments should be carried out and which test conditions need to be investigated, meta-models are generated, and the expected gain score is calculated. The next sample is selected based on the highest score, and this procedure continues until the material models meet a termination criteria. The result from the study shows that the implemented method uses 12 test conditions to generate a phase transformation model for 22MnB5 steel. The material models fitted with the proposed method provide acceptable predictions when compared with experimental data.

Crystal plasticity modeling of strain-induced martensitic transformations to predict strain rate and temperature sensitive behavior of 304 L steels: Applications to tension, compression, torsion, and impact

This paper advances crystallographically-based Olson-Cohen (direct γ → α’) and deformation mechanism (indirect γ→ε→α’) phase transformation models for predicting strain-induced austenite to martensite transformation. The advanced transformation models enable predictions of not only strain-path sensitive, but also of strain-rate and temperature sensitive deformation of polycrystalline stainless steels (SSs). The deformation of constituent grains in SSs is modeled as a combination of anisotropic elasticity, crystallographic slip, and phase transformation, while the hardening is based on the evolution of dislocation density and explicit shifts in phase fractions. Such grain-scale deformation is implemented within the meso‑scale elasto-plastic self-consistent (EPSC) homogenization model, which is coupled with the implicit finite element (FE) method to provide a constitutive response at each FE integration point for solving boundary value problems at the macro-scale. Parameters pertaining to the hardening and transformation models within FE-EPSC are calibrated and validated on a suite of data including flow curves and phase fractions for monotonic compression, tension, and torsion as a function of strain-rate and temperature for wrought and additively manufactured (AM) SS304L. To illustrate the potential and accuracy of the integrated multi-level FE-EPSC simulation framework, geometry, mechanical response, phase fractions, and texture evolution are simulated during gas-gun impact deformation of a cylinder and quasi-static tension of a notched specimen made of AM SS304L. Details of the simulation framework, comparison between experimental and simulation results, and insights from the results are presented and discussed.

Modelling of Phase Transformations in Solid State and Dilatometric Curves Using Interpolation Methods to Determine CCT Diagrams

Modelling of Phase Transformations in Solid State and Dilatometric Curves Using Interpolation Methods to Determine CCT Diagrams

Logistic Model of Phase Transformation of Hardening Concrete.

The objective of this study was to analyze the effects of the modification of cementitious materials with the admixture of a superplasticizer and mineral additive in the form of microsilica. We analyzed the hardening process of cementitious materials as an autocatalytic transformation from a viscous liquid to a pseudo-solid body. The main achievement of the research involved the identification of changes in the content of the solid phase during the hardening of concrete mix as a model of the logistic curve. The phase transformation process begins with a viscous liquid which consists of water, cement, microsilica, superplasticizer and sand. The laboratory tests comprised research on the development of the kinetics of hardening heat of binder cement pastes and the development of mechanical properties of concrete in the hardening process. Three groups of mixtures with different concentrations of binders, determined by different water–binder indexes, were used. The first group was made up by cement paste consisting of cement and water. The second group contained cement paste from the first group supplemented with a superplasticizer, and the third group comprised the cement paste as in the second group, but additionally modified with microsilica. Using appropriate analyses, we defined a mathematical model of the phase transformation process. The model was then used for computer-aided numerical analyses. This made it possible to compare the relevant parameters of the logistic curve obtained for the seven different concrete mixes analyzed. Active impact of the applied mineral additive (microsilica) and that of chemical admixture in the form of a superplasticizer was demonstrated. All approximations of the measurement results with the use of a logistic curve had a determination level of over 0.98, indicating high agreement.

A Multiphysics Model for Predicting Microstructure Changes and Microhardness of Machined AerMet100 Steel.

The machined-surface integrity plays a critical role in corrosion resistance and fatigue properties of ultra-high-strength steels. This work develops a multiphysics model for predicting the microstructure changes and microhardness of machined AerMet100 steel. The variations of stress, strain and temperature of the machined workpiece are evaluated by constructing a finite-element model of the orthogonal cutting process. Based on the multiphysics fields, the analytical models of phase transformation and dislocation density evolution are built up. The white layer is modeled according to the phase-transformation mechanism and the effects of stress and plastic strain on real phase-transformation temperature are taken into consideration. The microhardness changes are predicted by a model that accounts for both dislocation density and phase-transformation evolution processes. Experimental tests are carried out for model validation. The predicted results of cutting force, white-layer thickness and microhardness are in good agreement with the measured data. Additionally, from the proposed model, the correlation between the machined-surface characteristics and processing parameters is established.

Research on welding-induced inhomogeneous stress in thick plate EH40 butt joint considering phase transformation

In this work, the inhomogeneous residual stress distribution and evolution of thick plate in single-pass full penetration laser welding are systematically investigated using phase transformation model. The material constitutive model considering solid-state phase transformation according to the actual weld microstructure is proposed to predict the inhomogeneous stress distribution of the welded joint. The inhomogeneous stress distributions along the longitudinal, transverse and thickness direction surfaces of the welded joint are systematically analyzed and deeply discussed, respectively. The results show that there is an obvious inhomogeneous distribution of the temperature field between the start-welding, middle section and end-welding position of the weld. It is obviously observed that the top and bottom surfaces of welded joint produce remarkably high stress areas and high stress gradients. The maximum longitudinal and transverse stress gradient values in the top surface are up to 1240.1 MPa and 1175.7 MPa, respectively. It is found that martensitic transformation is the main reason for the inhomogeneous stress distribution including high stress areas and high stress gradients in thick plate welded joint. The current research is beneficial to reduce the detrimental effects of welding-induced inhomogeneous residual stress on thick plate welded joints.

A large deformation constitutive model for plastic strain-induced phase transformation of stainless steels at cryogenic temperatures

In this paper, a new constitutive model for plastic behavior of the metastable austenitic stainless steels at cryogenic temperatures is presented. The constitutive model is a phenomenological hyperelastic-based large deformation model developed in the framework of continuum damage mechanics considering the dissipative phenomena of strain-induced phase transformation and damage growth during plastic deformation. To solve the coupled nonlinear set of equations, incremental equations and the related implicit integration method have been developed. Numerical analysis is performed by implementing the constitutive model in a UMAT subroutine in ABAQUS/STANDARD. In addition, experiments have been conducted to identify the material model parameters for AISI304 steel at the 77K temperature. In addition to calibration, the constitutive model was validated via a tensile test of a notched sample. Also, the model has been compared with the experimental data at 4.2 K available in the literature. The results show that the model is well able to predict the hardening behavior, martensite evolution, and damage growth during the plastic deformation until the fracture with acceptable accuracy.

MODELING OF PHASE TRANSFORMATIONS DURING COOLING OF ALLOY STEELS

Modern studies on the modeling of phase transformations in low-alloy steels to a certain extent allow solving the problem of quantitative determination of phase transformations for a given chemical composition of steel and different cooling rates. However, the capabilities of the available universal software products for the analysis of complexly alloyed steels are currently very limited. To conduct research, steels 25Cr2Mo1V and 38CrNi3MoV and existing analytical models were used, which were adapted to carry out the corresponding calculations. Structural diagrams are plotted for the steels under study depending on the rate of continuous cooling. The amount of residual austenite was taken into account by the developed method for the first time. Steel 25Cr2Mo1V, with continuous cooling at a rate of 1.0 °C/s (conditions close to natural air cooling), consists of 18 % ferrite, 1 % pearlite, 80 % bainite and 1 % residual austenite. Steel 38CrNi3MoV cooled at a rate of 1.0 °C/s consists of 2 % ferrite, 47.5 % bainite, 50 % martensite and 0.5 % retained austenite. It is shown that for the conditions of natural air cooling, the calculated data correlate well with practical results.

Anode reaction mechanisms of Na|NaCl-CaCl2|Zn liquid metal battery

Na|NaCl-CaCl2|Zn liquid metal battery is regarded as a promising energy storage system for power grids. Despite intensive attempts to present a real mechanism of metal electrodes reaction, those for Na||Zn LMBs are not clear yet. Herein, the anode reactions for the multiple discharge potential plateaus were deduced by means of FactSage thermochemical software, which were subsequently validated by X-ray diffraction analysis and the modeling of phase transformation in the cooling process. A pre-treatment process was proposed for the analysis of anode product composition using the atomic absorption spectrometry method, and the anode states at working temperature (560 °C) were obtained by the Na-Ca-Zn ternary phase for the first time. The results indicate the discharge of Na and Ca led to the formation of Ca-Zn intermetallic compounds, whilst the extraction of Ca in Ca-Zn intermetallic compounds was responsible for the multiple discharge plateaus. Moreover, it was found that the charging product was in electrochemical double liquid metal layers, which are composed of Na and Ca with dissolved Zn respectively..

Homogenization based macroscopic model of phase transformations and cyclic plasticity in pearlitic steel

In this contribution macroscopic modeling of phase transformations and mechanical behavior of low alloy steels are developed and investigated. Such modeling is of importance in simulations of transient thermo-mechanical processes which can cause phase transformations, examples from the railway industry include train braking induced frictional heating as well as rail grinding and welding operations. We adopt a modeling approach which includes phase transformation kinetics and individual constitutive models for the phases in combination with different homogenization methods. Algorithmic implementations of the isostrain, isostress and self-consistent homogenization methods are presented and demonstrated in finite element simulations of a laser heating experiment. Stress field results from the different homogenization methods are compared against each other and also against experimental data. The importance of including transformation induced plasticity in the modeling is highlighted, as well as the multi-phase stages of the heating and cooling.

Thermodynamic analysis of casting titanium alloys is the basis of information support in the optimal foundry technology development

The necessity of systematic formation of intellectual connections for integration into a single complex of currently fragmented software products for the technological analysis of the castings geometry, thermodynamic modeling of the titanium alloys properties, calculation of molding mixtures thermophysical characteristics for the purpose of conjugate implementation of a set of modeling procedures and casting processes diagnostics of is proved. Lack of such an integrated software package, computer analysis of modeling results in the existing manufacturing products practice demonstrates (by the example of the shrinkage defects distribution in a responsible casting of TL3 alloy) the need for radical technological design tools’ improvement.One of the key components of the “digital technology” being formed in the future is thermodynamic modeling of equilibrium phase transformations, which allows calculating the physico-chemical parameters, thermodynamic, thermophysical and casting parameters of titanium alloys and their evolution in the temperature range of crystallization. Based on thermodynamic simulation, experimental planning apparatus and the experience of statistical analysis carried out, a method for forming models for estimating equilibrium parameters used in modeling foundry processes has been developed, and it shows the possibility of applying it to various casting titanium alloys. For the standard composition of the TL3 alloy, a multifactor system of equations was obtained, reflecting the degree of influence of the components on the fluctuations of the alloy characteristics complex, which determine the development of a series of casting defects. The possibilities of using the obtained models for TL3 alloy and methods of obtaining them for use in computer modeling systems to increase the adequacy and accuracy of the results obtained are described.