Modeling Of Microstructure Evolution Research Articles

From coherent to semicoherent—Evolution of precipitation crystallography in an fcc/bcc system

How are crystallographic features developed in phase transformation systems with anisotropic misfits (e.g., bcc/fcc systems)? Comprehensive knowledge about this question is still very limited, which impedes the thorough understanding and the quantitative modeling of microstructure evolution. In this work, we simulated the early stage growth of a Cr precipitate (bcc) in a Cu matrix (fcc) by combining Monte Carlo and molecular dynamics. The simulation results reveal fine details about the evolution of crystallographic features, including the orientation relationship (OR) between the two phases, the precipitate morphology, and the interfacial dislocation structures. The governing event during the evolution process is the generation of a dominant set of dislocations. The selection of the dominant dislocations is rationalized based on minimization of the interfacial energy in the major facet, which contains a single set of dislocations. The initial OR between the coherent precipitate and the matrix is close to the Nishiyama–Wassermann OR. In response to the generation of the dominant dislocations, the OR jumps towards the ideal OR corresponding to the O-line condition, which is close to the Kurdjumov–Sachs OR. This tendency reflects the experimental observations in a Cu-Cr system and provides helpful insight into the actual evolution of crystallographic features.

Mechanically Coupled Phase-Field Modeling of Microstructure Evolution in Sodium Ion Batteries Particles of NaxFePO4

The microstructure evolution of the cathode material NaxFePO4 of sodium-ion batteries is investigated during insertion, using a mechanically coupled phase-field model. A direct comparison between NaxFePO4 and LixFePO4 is made in terms of the microstructure evolution and the stress evolution. The dynamics of single wave propagation in spherical particles of NaxFePO4 is obtained, and the interface morphology between phases that goes across the particle dynamically changes to minimize its proportion. When mechanics is accounted for, the interface gets more widened for NaxFePO4, and its miscibility gap is significantly reduced. In contrast to the constant stresses in each phase occurring in shrinking-core dynamics, both, tensile and compressive stresses coexist in each phase, and the related gradient of hydrostatic stress induces NaxFePO4 a steeper concentration inhomogeneity in each phase. It is expected that the particle surface of the species-rich phase is more prone to cracking. Compared with LixFePO4, the stress magnitudes at the interface are smaller in NaxFePO4. Although the miscibility gap of NaxFePO4 is smaller, the stress magnitudes at the particle surface are larger in this material, which makes it less mechanically reliable.

Modeling microstructure evolution during thermomechanical processing and heat treatment of steels and predicting their mechanical properties

Modeling microstructure evolution during thermomechanical processing and heat treatment of steels and predicting their mechanical properties

Mean field and full field modelling of microstructure evolution and phase transformations during hot forming and cooling of low carbon steels

Mean field and full field modelling of microstructure evolution and phase transformations during hot forming and cooling of low carbon steels

Phase-Field Modeling of Microstructure Evolution in the Presence of Bubble During Solidification

Simulation of the solid–liquid–gas interaction during solidification is challenging due to the presence of complex phase interfaces, bubble deformation, and high liquid/gas density ratio. In this work, a hybrid phase-field lattice-Boltzmann (PFLB) approach, together with a parallel and adaptive-mesh-refinement (Para-AMR) algorithm, is developed to model interactions between the gas bubble and solid growth front during solidification. The solid growth and bubble evolution are solved by the phase-field method. Both melt flow and bubble movement are determined by a kinetic-based lattice-Boltzmann model. Bubble dynamics during alloy solidification is modeled and compared with experiments, and a good agreement is achieved for various solid/liquid interfaces including planar, cellular, and dendritic interfaces. Results show that the effect of the bubble on solid array is dependent on the solid/liquid interface morphology, bubble size, and relative position between the bubble center and dendritic tip. Two interaction mechanisms, including engulfment and entrapment, are compared, and the difference is caused mainly by the redistribution of solute. The interaction mechanism between the rising multibubbles with large deformation and the dendritic array is also discussed.

Multi-scale modelling of solidification and microstructure evolution in laser-deposition of T15 high speed steel

Laser powder deposition (LPD) process is used in additive manufacturing for powder deposition of metal alloys, it involves parts building and re-manufacturing. However, this process is subjected to high cooling rates and rapid solidification hence the prediction of solidifying microstructure becomes challenging. In order to model the solidification process of the LPD of single track T15 steel, a phase field model (PFM) was proposed coupled with a nucleation, phase transition and heat transfer models. This model was employed to simulate the different microstructure phases and solute distribution. Further, a level set volume of fluid (LS-VOF) model was used to calculate the cooling rate and thermal gradient of the melt pool where these variables are subsequently used as a comparison with the PFM. PF results showed two main phases of microstructure identified as cellular and equiaxed which evolved as solidification took place. The results were compared to thermal analysis and experimental results. Experimental analysis showed cellular microstructure dominated at the substrate-track interface and equiaxed microstructure in the remainder of the track. The grains size distribution obtained from PFM at different location in the track was compared to Scanning electron microscopy (SEM) imaging. The paper showed that the proposed PFM is a promising tool for microstructure prediction in LPD process.

Review on modeling and simulation of microstructure evolution during dynamic recrystallization using cellular automaton method

The macro-mechanical properties of metal and alloy are largely depended on their chemical composition and microstructures resulting from the complicated processing and heat treatment history in industrial production. During these thermoplastic processes, dynamic recovery, dynamic recrystallization, static recovery and static recrystallization are the key microstructural evolution mechanisms. Accurate prediction and precise control of the microstructural evolution are of great importance for designers to achieve excellent mechanical properties for metals and alloys through hot working. Up to date, dynamic recrystallization has been recognized as a powerful mechanism for grain refinement. In-depth understanding of the microstructural evolution of dynamic recrystallization and furthermore to accurately predict and control the microstructure evolution during dynamic recrystallization process has become a research focus in the field of plastic processing. Cellular automaton (CA) method has been commonly employed to simulate the microstructure evolution of dynamic recrystallization due to its unique advantages, for example, it is easier to represent topological features and more realistically reflect the grain boundary migration process. In this paper, the basic ideas and characteristics of the CA method are briefly introduced. The physical mechanisms of dynamic recrystallization are summarized. Meanwhile, the state-of-the-art overview of the CA method of simulating the DRX process is introduced. Furthermore, this paper points out several problems that need to be solved urgently and prospects the development trend of the CA method for simulating the microstructure evolution in dynamic recrystallization.

Uncertainty propagation in a multiscale CALPHAD-reinforced elastochemical phase-field model

ICME approaches provide decision support for materials design by establishing quantitative process-structure-property relations. Confidence in the decision support, however, must be achieved by establishing uncertainty bounds in ICME model chains. The quantification and propagation of uncertainty in computational materials science, however, remains a rather unexplored aspect of computational materials science approaches. Moreover, traditional uncertainty propagation frameworks tend to be limited in cases with computationally expensive simulations. A rather common and important model chain is that of CALPHAD-based thermodynamic models of phase stability coupled to phase-field models for microstructure evolution. Propagation of uncertainty in these cases is challenging not only due to the sheer computational cost of the simulations but also because of the high dimensionality of the input space. In this work, we present a framework for the quantification and propagation of uncertainty in a CALPHAD-based elastochemical phase-field model. We motivate our work by investigating the microstructure evolution in Mg2SixSn1−x thermoelectric materials. We first carry out a Markov Chain Monte Carlo-based inference of the CALPHAD model parameters for this pseudobinary system and then use advanced sampling schemes to propagate uncertainties across a high-dimensional simulation input space. Through high-throughput phase-field simulations we generate 200,000 time series of synthetic microstructures and use machine learning approaches to understand the effects of propagated uncertainties on the microstructure landscape of the system under study. The microstructure dataset has been curated in the Open Phase-field Microstructure Database (OPMD), available at http://microstructures.net.

Modeling of thermal behavior and microstructure evolution during laser cladding of AlSi10Mg alloys

An improved three-dimensional finite element model has been proposed for studying the thermal behavior and microstructure evolution during laser cladding of AlSi10Mg alloys. Different material properties between AlSi10Mg powders and AlSi10Mg alloys are distinguished from the experiment and theoretical calculation to provide more reliable material parameters for simulation. In order to investigate the melting and solidification process during the formation of cladding layers, a temperature selection judgment mechanism is established to simulate the evolution of AlSi10Mg powders from the powder state to melting state and alloy state. In addition, to simulate the complex thermal behavior associated with powder particles and the voids between particles, a simplified exponential attenuation model is used for correcting the heat source. A complex asymmetric heat source considering about the different material properties and laser absorptivity on both sides of the remelting zone is used for multi-track cladding process.By simulating the temperature distribution of molten pool, the improved FEM could be used to predict the geometric shape of cladding layers (ignoring the effect of melting flow) and the temperature history. The simulation results show that the heat tends to diffuse to the unmelted powder owing to the asymmetric heat source during multi-track cladding, which leads to the asymmetry of cladding layers along the width direction. Based on the results of the temperature field simulations and the solidification characteristics of AlSi10Mg powders, the temperature gradient (G), solidification growth rate (R), cooling rate (G*R) and G/R are investigated to predict the morphology and size of the solidification microstructure under different laser scanning parameters. The scanning speed mainly determines the cooling rate during the laser cladding process, which results in different microstructures. Higher scanning speed leads to higher cooling rate, corresponding to a finer microstructure. Coarse dendrites are generated at the bottom of the molten pool, while finer dendrites are formed at the top.

On the phase field model for microstructure evolution during selective laser melting of powder bed including diffusion-induced stresses

In this paper, we develop a phase field model for microstructure evolution in laser powder-bed additive manufacturing processes, which allows for the effect of elastic stresses due to diffusion of atomic defects (vacancy and interstitial atom) generated at the moving liquid-solid interface. The governing equations of the model including a time-dependent Ginsburg-Landau equation for the phase field with additional stress term, a diffusion-drift Cahn–Hilliard like equation describing atomic defect dynamics, an energy balance equation for the temperature change, and finally the mechanical equilibrium equation for the elastic displacement fields are derived within a thermodynamic framework based on entropy generation guaranteeing thermodynamic consistency. The most simple 1D and isothermal equilibrium situation is considered to study phenomenon of diffusion-flexural instability with the atomic defect clustering and periodic distributions of defects. The effect of this instability on the exfoliation of deposited thin layers on a substrate is also discussed.

Evolution of Microstructure and Creep Behavior in an Fe-Ni-Cr-Nb-C Alloy during Service in Hydrocarbon Cracker Tubes

Heat resistant, cast austenitic Fe-Ni-Cr-Nb-C alloy tubes are used by the petrochemical industry to transport hydrocarbons at temperatures between 850 and 1050 °C. Exposure to carbon from the process stream and nitrogen from the air causes severe carburization and nitridation in the tube walls, which influences creep resistance and degrades their ductility. A better understanding of these processes would enable their service life to be extended. To this end, we report the results of an experimental and computational study of the changes in microstructure and creep behavior in a representative alloy during service. The microstructure of the fresh material is compared to that of 8- and 10-year-old tubes. The results confirm the presence of M23C6, M7C3, and M2(CN) phases reported in prior studies, and also reveal the nucleation and growth of the carbo-nitride phase M6(CN). We show that the spatial variations of carbide and nitride particle volume fractions in aged tubes can be predicted by a simple reaction–diffusion equation. In addition, the uniaxial compressive creep response of the fresh and aged tubes was obtained as functions of temperature and strain rate. The materials deform by power-law creep, with strain rate versus stress relation as $$\dot{\varepsilon } = A\sigma^{n}$$. Aging reduces the stress exponent from n = 8 in fresh tubes to n = 5 in aged tubes, and also reduces the pre-exponential coefficient A. Tests on model alloys with composition identical to that of the matrix combined with finite element simulations of creep in model microstructures reveal that Cr depletion is responsible for the change in stress exponent, while the change in A is caused by the increase in particle volume fraction. By combining the microstructure-scale simulations of creep with the predictions of the reaction–diffusion model of microstructure evolution, the creep behavior of tubes left in service beyond 10 years is estimated.

Mesoscale modeling of jet initiation behavior and microstructural evolution during cold spray single particle impact

Quasi-coarse-grained dynamics (QCGD) simulations are carried out to investigate the mesoscale deformation behavior during the impact of a 20 µm pure aluminum particle onto a substrate of pure aluminum at time and length scales relevant to cold spray deposition. A rigorous analysis of the evolution of pressure, temperature, strain, flow stress and microstructure is carried out to investigate the jetting mechanisms over a range of process parameters (impact velocity and particle temperature). The QCGD simulations identify a critical role of the pressure wave propagation in the initiation of a jet, i.e. outward flow of material at the particle/substrate interface periphery (edge). Jetting is observed to initiate when the shock wave interacts with the edge and results in localized softening of the metal in this region. This localized softening enables outward flow of the material and is accompanied by a release of the pressures in the particle and the substrate at the interface. Observations of final splat microstructures of systems that showed jetting revealed several new “small” grains in the range of 2–4 µm. These grains are mainly found at the interface, suggesting that recrystallization is favored in cold sprayed impacts of aluminum.

Integrated modelling of hot forging of low-alloyed steels for an ICME workflow

One of the key aspects of integrated computational materials engineering approach is the integrated modelling of process chains that capture the essential microstructure physics and predict the final properties. In the current work, such an integrated modelling approach is attempted for analyzing the hot forging process for low-alloyed steels. Traditionally, hot forging process is designed with primary focus on the deformation step, with less attention paid to the incorporation of microstructure information flow between its sub-steps of heating, deformation and cooling. Such a siloed approach restricts its integration with other manufacturing processes, and also with design and material selection stages. To address the issue, in this work, a FEM based thermo-mechanical modelling framework, integrating composition dependent microstructure evolution models for heating, deformation and cooling sub-steps, is implemented for hot forging of low-alloyed steels. The evolution of key microstructural features at each sub-step is tracked and fed to the following step. The integrated modelling framework is then used to study the effect of process parameters and macrosegregation in the billet on the distribution of final microstructure and properties obtained for a sample steel upsetting process. Key observations made in the studies are discussed. Ways of representation of the distribution of microstructure and properties across the forged part, that can enable better decision making in the larger perspective of downstream processing and final use, are highlighted. Consequently, the utility of the integrated modelling approach to aid the development of improved process and product design capabilities for hot forged products is established.

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The microstructure changes taking place in W under irradiation are governed by many factors, amongst which C impurities and their interactions with self-interstitial atoms (SIA). In this work, we specifically study this effect by conducting a dedicated 2-MeV self-ions irradiation experiment, at room temperature. Samples were irradiated up to 0.02, 0.15 and 1.2 dpa. Transmission electron microscopy (TEM) expectedly revealed a large density of SIA loops at all these doses. Surprisingly, however, the loop number density increased in a non-monotonous manner with the received dose. Performing chemical analysis with secondary ion spectroscopy measurements (SIMS), we find that our samples were likely contaminated by C injection during the irradiation. Employing an object kinetic Monte Carlo (OKMC) model for microstructure evolution, we demonstrate that the C injection is the likely factor explaining the evolution of loops number density. Our findings highlight the importance of the well-known issue of C injection during ion irradiation experiments, and demonstrate how OKMC models can help to rationalize this effect.

Multiscale Modeling of Microstructural Evolution in Fused-Coating Additive Manufacturing

A quantitative phase field model with adaptive-computational-domain-expansion (ACDE) method was developed to simulate the microstructural evolution in fused-coating additive manufacturing process. A heat transfer and fluid flow model was established to investigate the solidification behavior of the molten pool in a single deposited layer. The solidification parameters such as temperature gradient and solidification rate were calculated from the macroscopic model and then fed into the phase field model to get the microstructure at different positions within a single deposited layer. Columnar dendrites were formed at the bottom of the deposited layer, and equiaxed dendrites appeared in the upper part of the layer. The ACDE method is used to improve the simulation efficiency. The metallographic experiments and energy-dispersive spectrometer analysis for composition were conducted on the fused-coating specimen, and the results were in good accordance with the simulations.

Deformation behavior and microstructure evolution of titanium alloys with lamellar microstructure in hot working process: A review

Titanium alloys have been widely used in many industrial clusters such as automotive, aerospace and biomedical industries due to their excellent comprehensive properties. In order to obtain fine microstructures and favorable properties, a well-designed multi-step thermomechanical processing (TMP) is critically needed in manufacturing of titanium components. In making of titanium components, subtransus processing is a critical step to breakdown lamellar microstructure to fine-structure in hot working process and thus plays a key role in tailoring the final microstructure and properties. To realize this goal, huge efforts have been made to investigate the mechanisms of microstructure evolution and flow behavior during the subtransus processing. This paper reviews the recent experimental and modelling progresses, which aim to provide some guidelines for the process design and microstructure tailoring for titanium alloy research community. The characteristics of the initial lamellar microstructure are presented, followed by the discussion on microstructure evolution during subtransus processing. The globularization of lamellar α is analyzed in detail from three aspects, i.e., globularization mechanism, heterogeneity and kinetics. The typical features of flow behaviors and the explanations of significant flow softening are then summarized. The recent advances in modelling of microstructure evolution and flow behaviors in the subtransus processing are also articulated. The current tantalized issues and challenges in understanding of the microstructure evolution and flow behaviors of the titanium alloys with lamellar microstructure are presented and specified in future exploration of them.

A new micromechanics based full field numerical framework to simulate the effects of dynamic recrystallization on the formability of HCP metals

This paper presents a new full-field, efficient and mesh-free numerical framework to model microstructure evolution, dynamic recrystallization (DRX) and formability in hexagonal closed-packed (HCP) metals such as magnesium alloys at warm temperatures. A rate tangent-fast Fourier transform-based elasto-viscoplastic crystal plasticity constitutive model for HCP metals (RTCP-FFT-HCP) is coupled with a probabilistic cellular automata (CA) approach to model DRX (CA-DRX). Furthermore, this new model is coupled with the Marciniak-Kuczynski (M-K) approach to model formability of magnesium alloys at elevated temperatures. The RTCP-FFT-HCP model computes macro stress-strain, twinning volume fraction, micromechanical fields, texture evolution and local dislocation density. Nucleation of new grains and their subsequent growth is modeled using the cellular automata approach with probabilistic state switching rule. First, the proposed RTCP-FFT-HCP model is validated by comparing the predicted stress-strain responses and texture evolution under uniaxial tension and compression with experimental measurements for AZ31 sheet alloy at room temperature. The coupled CA-RTCPFFT-HCP model is further validated by comparing the predicted stress-strain responses and texture evolution in uniaxial compression with experimental measurements at 100 °C, 200 °C and 300 °C for the AZ31 sheet alloy. Next, the forming limit diagrams (FLDs) with and without including the effects of DRX are simulated at 100 °C, 200 °C and 300 °C for AZ31 sheet alloy. The predicted FLDs with DRX show very good agreement with the experimental measurements and clearly demonstrate the need for an accurate DRX model. The study reveals that the DRX strongly affects the deformed grain structure, grain size and texture evolution and also highlights the importance accounting for DRX during FLD simulations at high temperatures.

Integrated computational materials engineering simulation studies of nuclear alloys based on crystal plasticity modeling

For nuclear reactor, alloys with excellent corrosion resistance and mechanical properties are widely used in the nuclear fuel cladding, internal component, and steam generator. The processing technology affect the microstructure directly, and hence the mechanical and corrosive properties. It is an important step to study on the performance of nuclear alloys outside reactor to alloy evaluation and improvement. Hence it is significant to predict the “processing-microstructure-mechanical property” of nuclear alloys. Conventional methods just rely on experimental “try-and-error” cycle, which costs lots of money and takes long time. Integrated Computational Materials Engineering based on through process simulation try to combine the models of processing, microstructure evolution and property, can remarkably reduce the R&D period and expense. To promote the application of this methodology in the processing optimization and development of nuclear alloys, the present study employed microstructure-sensitive crystal plasticity models and decoupled finite element simulation technique, to study quantitatively the “processing-microstructure-mechanical property” interrelationship of Zr, Ti, and FeCrAl alloys. The results indicated that the present model was able to predict accurately the hot processing texture and the corresponding tensile/compressive plastic behavior of three typical nuclear alloys. The present simulation method based on crystal plasticity can provide computational tool and reference to processing optimization and mechanical property evaluation of nuclear alloys.

The influence of carbon impurities on the formation of loops in tungsten irradiated with self-ions

The microstructure changes taking place in W under irradiation are governed by many factors, amongst which C impurities and their interactions with self-interstitial atoms (SIA). In this work, we specifically study this effect by conducting a dedicated 2-MeV self-ions irradiation experiment, at room temperature. Samples were irradiated up to 0.02, 0.15 and 1.2 dpa. Transmission electron microscopy (TEM) expectedly revealed a large density of SIA loops at all these doses. Surprisingly, however, the loop number density increased in a non-monotonous manner with the received dose. Performing chemical analysis with secondary ion spectroscopy measurements (SIMS), we find that our samples were likely contaminated by C injection during the irradiation. Employing an object kinetic Monte Carlo (OKMC) model for microstructure evolution, we demonstrate that the C injection is the likely factor explaining the evolution of loops number density. Our findings highlight the importance of the well-known issue of C injection during ion irradiation experiments, and demonstrate how OKMC models can help to rationalize this effect.

From Coherent to Semi-Coherent — Evolution of Precipitation Crystallography in an fcc/bcc System

A comprehensive knowledge about how crystallographic features are developed at the early stage of a phase transformation in an anisotropic misfit system (e.g., bcc/fcc) is limited, which impedes the deep understanding and quantitative modeling of microstructure evolution. In this work, we simulated coherency loss process during the early growth of a Cr precipitate (bcc) in a Cu matrix (fcc) by the combination of Monte Carlo and molecular dynamics. The simulation results reveal the fine details in the evolution of the crystallographic features, including the orientation relationship (OR) between two phases, the precipitate morphology, and interfacial dislocation structure at the early stage of the precipitate growth. Generation of a dominant set of dislocations is the governing event during the evolution process. The selection of the dominant dislocations was rationalized based on the minimization of interfacial energy in the major facet containing a single set of these dislocations. The initial OR developed between the coherent precipitate and the matrix is near the Nishiyama-Wassermann OR, and it changes discretely in response to the early generation of the dominant dislocations, towards the ideal OR corresponding to the O-line condition, near the Kurdjumov-Sachs OR. This tendency reflects the experimental observations in a Cu-Cr system, and provides helpful insight into the evolution of crystallographic features in physical reality.