Modeling Of Microstructure Evolution Research Articles

Computationally Efficient Algorithm for Modeling Grain Growth Using Hillert’s Mean-Field Approach

To investigate the interconnected effects of manufacturing processes on microstructure evolution during hot-rolling, a through process model is required. A novel numerical implementation of the mean-field approach was introduced to efficiently describe the grain growth of larger systems and extended durations. In this approach, each grain is embedded within an average medium and interacts with the average medium, thus avoiding the complexities of individual grain interactions. The proposed upsampling approach dynamically adjusts the simulation grain ensemble, ensuring efficiency and accuracy regardless of the initial number of grains present. This adaptation prevents undersampling artifacts during grain growth. The accuracy of the model is verified against analytical solutions and experimental data, demonstrating high agreement. Moreover, the effects of different initial conditions are successfully investigated, demonstrating the model’s versatility. Due to its simplicity and efficiency, the model can be seamlessly integrated into other microstructure evolution models.

Simulation of Solidification Structure in the Vacuum Arc Remelting Process of Titanium Alloy TC4 Based on 3D CAFE Method

Vacuum arc remelting is the main production method of titanium alloy ingots at present. In order to obtain good quality ingots, it is of great significance to study the formation of the solidification structure of ingots via vacuum arc remelting. In order to select and optimize the nucleation parameters for the solidification microstructure simulation of an ingot, a 3D CAFE model for microstructure evolution during vacuum arc remelting was established, taking into account heat transfer, flow, and solute diffusion. The Gaussian distribution continuous nucleation model and extended KGT model were used to describe the grain nucleation and dendrite tip growth rates, respectively. The multi-point mass source and moving boundary method were used to simulate the ingot growth. The results show that there are three typical crystal regions in the solidification structure of vacuum arc remelting titanium alloy ingots, namely the surface fine crystal region, columnar crystal region, and central equiaxed crystal region. The proportion of the columnar crystal region in the solidification structure of an ingot increases gradually with the increase in the undercooling of the maximum bulk nucleation. With an increase in the maximum bulk nucleation density, the equiaxed grain zone gradually increases, and the grain size gradually decreases. The proportion of the columnar crystal region in the solidification structure of an ingot increases gradually with an increase in the undercooling of the maximum bulk nucleation. The maximum volume nucleation variance has no obvious effect on the change in the solidification structure. When the maximum volume nucleation undercooling is 5.5 K, the maximum volume nucleation standard deviation is 4 K, and the maximum volume nucleation density is 5 × 108. The solidification structure simulation results are in good agreement with the experimental results.

A Mechanics-Based Phase-Field Model and Finite Element Simulations for Microstructure Evolution during Solidification of Ti-6Al-4V

A Mechanics-Based Phase-Field Model and Finite Element Simulations for Microstructure Evolution during Solidification of Ti-6Al-4V

Multiscale microstructural evolution of Fe–Ni–Al–Ti alloy with high magnetization

The Fe–15Ni–3Al–1Ti ribbons are produced by melt-spinning the annealed ingots at 10–40 m/s. The annealed ingots consist of Fe3Ni grains and α-Fe-type grain boundary phase, forming a columnar grain microstructure in the vertical direction and getting the maximum saturation magnetic polarization (Js) of 1.88 ± 0.03 T in the cross-section. Before and after the annealing, the ribbons form a cellular structure composed of the Fe3Ni intragranular phase and γ-(Fe, M), Fe7Ni3, or α-(Fe, M) cell boundary phases. Formation of enhanced <100> orientation is the primary mechanism for obtaining a high Js of 2.35 ± 0.07 T in the ribbons. The grain and grain boundary size of the ribbons is reduced by the phase transformation induced by annealing at 600 °C. The phase transformation processes of the ribbons before and after annealing are as follows: L→γ→melt−spunFe3Ni+γ1→annealedFe3Ni+Fe7Ni3 when melt-spinning at a speed of 10–25 m/s, and L→γ→melt−spunFe3Ni+Fe7Ni3→annealedFe3Ni+α−(Fe,Ni) at 40 m/s. Finally, the multiscale microstructure evolution models are used to summarize the phase transformation process of the alloys.

Innovative microstructures in SmCo5-based ribbons regulated by Fe-Ni-Al-Ti alloy

We proposed a new measure to optimize the comprehensive magnetic properties of SmCo5 alloy. By compounding Fe-15Ni-3Al-1Ti (FNAT) alloy with high saturation magnetization and Sm(Co, Cu)5 matrix alloy in the liquid state, an innovative two-phase separation microstructure or cellular microstructure is formed after melt-spinning using the phase separation effect of the two alloys. At the same time, the element concentration, relative phase content, and microstructure are adjusted by adding different contents of FNAT alloy. The results show that FNAT addition promotes the as-spun ribbons phase separation (or spinodal decomposition) into Co-rich SmCo5- and Sm-Ni-rich CeCo5- or Sm2Co7-type phases. Adding 3 wt.% FNAT increases the coercivity, saturation magnetization, and remanence of the ribbons by 320.6%, 39.8%, and 82.8%, respectively. Adding 5 wt.% FNAT promotes forming the Sm2(Co, M)7 cell-wall phase and increases the coercivity and remanence by 272.7% and 48.1%, respectively. Finally, the corresponding microstructure evolution models, magnetization, and demagnetization mechanisms are proposed.

Microstructure Evolution and Numerical Modeling of TC4 Titanium Alloy during Ultrasonic Shot Peening Process

Ultrasonic shot peening (USP) is a surface treatment technology used in the mechanical properties strengthening of the engineering material and components during manufacturing. TC4 titanium alloy is a commonly used engineering material in the aerospace industry. In this study, a gradient nanostructured surface layer was successfully fabricated on the TC4 titanium alloy via USP technology at room temperature. The microstructure evolution of TC4 titanium alloy during USP was investigated. The surface microhardness was elevated from 330 HV to 438 HV with a penetrating depth of around 900 μm after USP with the duration of 8 min. EBSD characterization results confirmed the presence of high-density grain boundaries within the gradient structure in the region of 0–200 μm, accompanied by proliferation of dislocation density. TEM characterization indicated a substantial amount of nanograin with an average size of 74.58 nm. Furthermore, the USP process was also investigated by the finite element method to evaluate the surface-strengthening effect. The calculated maximum residual stress reached 973 MPa after multi-ball impact. The impact behavior of the shots during the USP process was studied. The effect of the parameters on the USP strengthening intensity was explored based on the validated model. This work provided a clearer understanding of the USP strengthening process of TC4 titanium alloy through an effective method of evaluating the process parameters.

Microstructural evolution and multi-mechanism strengthening model of nanocrystalline Al-Mg alloys

To unravel the determinants contributing to the remarkable strength observed in nanocrystalline binary alloys, we employed a high-pressure torsion method to fabricate Al-Mg alloys with varying Mg concentrations. Mechanical property analysis indicates that, with the increasing Mg content, both the hardness and yield strength exhibit an ascending trend. Notably, the nanocrystalline Al-8Mg alloy boasted an impressive hardness and yield strength of 295 HV and 889 MPa, respectively. Comprehensive characterizations of solute distribution and microstructural evolution were conducted using X-ray diffraction, electron back-scatter diffraction, transmission electron microscopy, and atom probe tomography. We clarified the distribution mechanism of Mg atoms at grain boundaries, developed a method for the precise assessment of inhomogeneous solute distribution, and proposed a multi-mechanism strengthening model, incorporating the inhomogeneous solute distribution strengthening mechanism. The calculated results aligned well with the experimental data.

Modeling of irradiation-induced microstructure evolution in Fe: Impact of Frenkel pair distribution

This study investigated the irradiation-induced microstructure evolution in Fe, employing the Creation-Relaxation Algorithm and different interatomic potentials. The influence of self-interstitial atoms (SIAs), which were either locally or uniformly being distributed during the creation of the Frenkel pairs, was investigated on the evolving microstructure. The spatially localized distribution of SIAs, mimicking the low-energy transfer irradiation conditions, moderated the microstructure development, compared to uniform distribution of SIAs, delaying the nucleation of dislocation for higher irradiation doses. Introducing multiple Frenkel pairs facilitated a cumulative irradiation dose of 5 dpa in large supercells. In small supercells, the accumulation of SIAs led to the formation of an artificially stabilized self-interacting planar interstitial cluster, suggesting a minimum cell dimension of 10 nm for an accurate modeling of microstructure evolution when the development of the dislocation network is of interest. The formation and evolution of the C15 Laves phase structure were explored. The evolving C15 structure developed larger clusters with uniformly distributed SIAs, and their sizes depended on the interatomic potential employed. Finally, a comparison with experimental measurements demonstrated that the density and the average size of interstitial dislocation loops aligned well with those observed in experimentally irradiated ultra-high purity Fe at low and room temperatures.

Application of grazing incidence wide-angle X-ray scattering to characterise mechanically plated coatings

Post-mechanical plating heat treatment on zinc and zinc–tin coatings resulted in the formation of an iron–zinc-rich intermetallic layer between the substrate and the coatings, while the outer coating layer became tin-rich in the case of heat-treated zinc–tin coatings. The novel use of grazing incidence wide-angle X-ray scattering detected not only ζ-FeZn13, δ1p-Fe13Zn126 and δ1k-FeZn6.67 phases but also Γ1-Fe11Zn40 and Γ-Fe4Zn9 phases due to the higher resolution and signal-to-noise ratio of synchrotron X-ray diffraction (XRD) compared to traditional XRD. Microstructure evolution models during the heat treatment of mechanically plated zinc and zinc–tin coatings are proposed. The formation of iron–zinc intermetallic phases was in the sequence of ζ-FeZn13, δ1p-FeZn10, δ1k-FeZn7, Γ-Fe3Zn10 and Γ1-Fe5Zn21 phases when the heat treatment duration increased.

Simulation and Experimental Study on the Effect of Superheat on Solidification Microstructure Evolution of Billet in Continuous Casting.

The control of the solidification structure of a casting billet is directly correlated with the quality of steel. Variations in superheat can influence the transition from columnar crystals to equiaxed crystals during the solidification process, subsequently impacting the final solidification structure of the billet. In this study, a model of microstructure evolution during billet solidification was established by combining simulation and experiment, and the dendrite growth microstructure evolution during billet solidification under different superheat was studied. The results show that when the superheat is 60 K, the complete solidification time of the casting billet from the end of the 50 mm section is 252 s, when the superheat is 40 K, the complete solidification time of the casting billet is 250 s, and when the superheat is 20 K, the complete solidification time of the casting billet is 245 s. When the superheat is 20 K, the proportion of the equiaxed crystal region is higher-the highest value is 53.35%-and the average grain radius is 0.84556 mm. The proportion of the equiaxed crystal region decreases with the increase of superheat. When the superheat is 60 K, the proportion of the equiaxed crystal region is the lowest-the lowest value is 46.27%-and the average grain radius is 1.07653 mm. Proper reduction of superheat can obviously reduce the size of equiaxed crystal, expand the area of equiaxed crystal and improve the quality of casting billet.

3D Model of Carbon Diffusion during Diffusional Phase Transformations.

The microstructure plays a crucial role in determining the properties of metallic materials, in terms of both their strength and functionality in various conditions. In the context of the formation of microstructure, phase transformations that occur in materials are highly significant. These are processes during which the structure of a material undergoes changes, most commonly as a result of variations in temperature, pressure, or chemical composition. The study of phase transformations is a broad and rapidly evolving research area that encompasses both experimental investigations and modeling studies. A foundational understanding of carbon diffusion and phase transformations in materials science is essential for comprehending the behavior of materials under different conditions. This understanding forms the basis for the development and optimization of materials with desired properties. The aim of this paper is to create a three-dimensional model for carbon diffusion in the context of modeling diffusional phase transformations occurring in carbon steels. The proposed model relies on the utilization of the LBM (Lattice Boltzmann Method) and CUDA architecture. The resultant carbon diffusion model is intricately linked with a microstructure evolution model grounded in FCA (Frontal Cellular Automata). This manuscript provides a concise overview of the LBM and the FCA method. It outlines the structure of the developed three-dimensional model for carbon diffusion, details its correlation with the microstructure evolution model, and presents the developed algorithm for simulating carbon diffusion. Demonstrative examples of simulation results, illustrating the growth of the emerging phase and affected by various model parameters within particular planes of the 3D calculation domain, are also presented.

A Comprehensive Material Model for the Super-Duplex Stainless Steel SAF2507 in a Welding Environment

The aim of this work is to describe a reliable methodology for determining parameters of a material model suitable for implementation in a welding simulation using the finite element method (FEM). The adopted methodology employs a multi-scale approach integrating a microstructure evolution model, a representative volume element (RVE) calibrated through experimental methods, including a thermal–mechanical simulator, and electron backscatter diffraction (EBSD) experiments. The result is a complete material model, which covers thermal, mechanical and metallurgical material models for SAF2507 (EN 1.4410), that shows promising results and was successfully implemented in finite element (FE) code. A direct comparison of experimental and calculated results shows a deviation of up to 12% for the phase fraction of austenite and 25% for the mean grain diameter of ferrite.

Grain boundary network plasticity: Reduced-order modeling of deformation-driven shear-coupled microstructure evolution

Microstructural evolution in structural materials is known to occur in response to mechanical loading and can often accommodate substantial plastic deformation through the coupled motion of grain boundaries (GBs). This can produce desirable behavior, such as increased ductility, or undesirable behavior such as mechanically-induced coarsening. In this work a novel, multiscale model is developed for capturing the combined effect of plasticity mediated by multiple GBs simultaneously. This model is referred to as “grain boundary network plasticity”. The mathematical framework of graph theory is used to describe the microstructure connectedness, and the evolution of microstructure is represented as volume flow along the graph. By using the principle of minimum dissipation potential, which has previously been applied to grain boundary migration, a set of evolution equations are developed that transfer volume and eigendeformation along the graph edges in a physically consistent way. It is shown that higher-order geometric effects, such as the pinning effect of triple points, may be accounted for through the incorporation of a geometric hardening that causes geometry-induced GB stagnation. The result is a computationally efficient reduced order model that can be used to simulate the initial motion of grain boundaries in a polycrystal with parameters informed by atomistic simulations. The effectiveness of the model is demonstrated through comparison to multiple bicrystal atomistic simulations, as well as a select number of GB engineered and non-GB engineered data obtained from the literature. The effect of the network of shear-coupling grain boundaries is demonstrated through mechanical response tests and by examining the yield surfaces.

Microstructure evolution, mechanical response and strengthening models for TA15 titanium alloy during thermal processes: A brief review

TA15 titanium alloy is widely used in aerospace industry in terms of its high specific strength, good thermal stability, and excellent corrosion resistance. To further improve its mechanical properties, thermal deformation combined with heat treatment is always used, during which the microstructure evolution and mechanical response are absolutely complex leading to the difficulty in control of final mechanical properties. Therefore, in-depth research on the relationship between microstructure and mechanical response of TA15 titanium alloy during these processes is of great significance. At present, less relevant review has been reported. In this article, the effects of process parameters such as heating temperature, strain rate, deformation amount, deformation mode, deformation path, cooling method and soaking time on the microstructure and mechanical properties of TA15 alloy, namely tensile performance and damage tolerance properties have been discussed. In addition, some strengthening models suitable for TA15 titanium alloy have been analyzed. In conclusion, different microstructure morphologies formed in various processing processes will display diverse mechanical performances in which the direct relationship between the yield strength and microstructure morphology can be established through distinct calculation models but with some limitations. So, in future works, microstructure and mechanical properties should be optimized further through adjusting processing parameters. Moreover, strengthening models remains to be modified by adopting more accurate statistical methods and considering more factors. Finally, establishing the relationship between damage tolerance properties such as fracture toughness, creep performance and LCF property and microstructure features should be considered more for TA15 alloy.

1H NMR monitoring of dynamic microstructure evolution of HACP during adsorption of different fluids

In order to develop functional concrete suitable for sponge city construction, a high adsorbent cement paste (HACP) was prepared. The capillary water absorption performance of the HACP reached 70 kg/m2, and the compressive strength reached more than 30 MPa. Taking advantage of the relatively large proportion of capillary pores in HACP and combining the test results of MIP and BET, a non-linear calibration method for low-field NMR was proposed. The conversion of calibration results of different fluids such as diesel oil (DO), soybean oil (SO), and engine oil (EO) were realized. Through 1H NMR real-time monitoring of the adsorption process of water, DO, SO and EO in cement slurry, it was found that HACP is mainly capillary adsorption, and the adsorption rate of the fluid is negatively correlated with the viscosity. In addition, it was also found that fluid transmission is not always from small pores to large pores, but also from gel pores to interlayer pores. Finally, a dynamic microstructure evolution model of HACP was proposed.

Characterization and modelling of microstructure evolution during partitioning in Q&P steels

Development of a simulation methodology and model which combines the analytical estimation of the microstructure at different points of the Q&P route with the numerical modelling of the main physical phenomena during partitioning was done. Detailed characterization of microstructure was performed at different stages of the Q&P process: at the quenching temperature (QT), at different interrupted conditions of partitioning and after final cooling down to room temperature. In addition, some investigations during the heating step from quenching to partitioning temperature was done by measuring the RA fraction. Then, the evolution of carbon free bainite and retained austenite phase fraction during the partitioning and different processing conditions was analyzed. The austenite grain size distribution produced by the first quenching was experimentally characterized and implemented in the model. Modelling approach to describe the main phenomena taking place during the partitioning step, i.e. carbon diffusion and bainite formation, was proposed. The built one-dimensional model predicts the microstructure evolution during partitioning step in the Q&P processing: starting from quenching temperature and going to the final cooling to room temperature. Finally, model performance was evaluated using two experimental datasets: one for testing and another for the validation.

Finite element modelling of transient behaviours and microstructural evolution during dissimilar rotary friction welding of 316 austenitic stainless steel to A516 ferritic steel

Inertia friction welding (IFW) is a near-net-shape joining process that produces high-integrity welds. The transient nature of this joining process necessitates the availability of reliable computational models to predict the evolution of temperature and deformation throughout welding. In this study, a thermo-mechanical finite element (FE) model, based on an adaptive remeshing technique, is proposed to simulate dissimilar joining of A516 ferritic steel and 316L austenitic stainless steel (SS). The results of FE model were evaluated and verified via comparing the shape/size of the flash, upsetting load and angular velocity profile of a physical weld produced by IFW trials. A good agreement was achieved between the appearance of the weld/flash and those predicted by the FE model, thus verifying the predicted temperature and strain distributions. The microstructural features across different weld regimes were also examined to correlate the concomitant changes with the simulated temperature profile.

A first-principles and CALPHAD-assisted phase-field model for microstructure evolution: Application to Mo-V binary alloy systems

A multiscale computational framework combining the first-principles calculations and the CALPHAD approach with the phase-field method is presented to simulate the microstructure evolution in multicomponent steel alloys. We demonstrate the potential of the framework by predicting the microstructural evolution in elastically periodic arrays of the Mo-V binary sub-system. The framework utilizes the first-principles calculations using special quasi-random structures. Hitherto unavailable thermodynamic and material properties of the alloy are obtained by employing the first-principles calculations and the CALPHAD approach and fed into the phase-field model to predict the microstructure evolution at different temperatures within the miscibility gap region. In addition to the temperature and cooling rates, the model incorporates the role of mechanical fields in decomposition kinetics in the Mo-V binary alloy system. Regimes for temperatures and cooling rates at which spinodal decomposition occurs are identified. Applying external loading leads to directional phase separation in the Mo-V binary system. The elastic inhomogeneity in terms of material properties between the two phases initiates the directional alignment while eigenstrains and applied external loading control the degree of alignment. The framework developed is general and extendable to higher multicomponent sub-systems in steel alloys.

Stress states and point defect capture radii of dislocation a-loops and c-loops in alpha-zirconium

Improving the predictive capability of microstructure evolution in irradiated α-zirconium requires a thorough understanding of the interaction rates between mobile defects and the existing, and evolving, microstructure. One of the parameters necessary to calculate these rates is the defect capture radii of dislocation loops. In order to better quantify this parameter, atomistic binding energy maps of point defects to interstitial a-loops, vacancy a-loops, and vacancy c-loops have been constructed using large-scale molecular statics simulations. Point defect capture radii have been correlated to the decay of binding energies with increasing distance using two criteria: spontaneous and thermal drift capture. Considering the spontaneous capture criteria, SIAs exhibit biased capture to all dislocation loops. However, when thermal drift capture is considered, the local stress state of dislocation loops imparts an inherent bias for the capture of same-type defects (i.e. vacancies to vacancy loops and vice versa). This phenomenon may drive the co-existence of vacancy and interstitial a-loops in irradiated α-Zr microstructure, an aspect that is poorly captured by most current models. The capture radii reported here will directly improve the predictive capability of microstructure evolution modeling in neutron-irradiated α-Zr.

Validation and application of cellular automaton model for microstructure evolution in IN718 during directed energy deposition

In Directed Energy Deposition (DED), the complex and nonuniform thermal history during the laser heating and cooling cycles determines the as-built microstructures and defects and thus affects the ultimate mechanical properties of fabricated parts. In this study, a highly parallel solidification microstructure model based on the Cellular-Automaton method is developed to predict the grain structure evolution in solid-solution strengthened Ni superalloys, IN718. Through coupling with the DED process model via Simufact, the grain structures in single tracks and a multiple-track multiple-layer block are predicted and compared with experiments. Parametric studies are performed to investigate the impact of key parameters in the stochastic nucleation model and calibrate the nucleation parameters, including nucleation density, nucleation undercooling, and its standard derivation. The predictions capture the general grain growth behavior, including remelting, epitaxial growth, and columnar-to-equiaxed transition, with a quantitative agreement with experimental results in terms of grain size and misorientation. This study demonstrates that the 3D grain structural model coupled with a process model has established the capability to model grain evolution for additive manufacturing processes, illustrating a powerful tool to assist the materials design and process development in additive manufacturing.