Modeling Of Microstructure Evolution Research Articles

Constitutive modeling of creep behavior considering microstructure evolution for directionally solidified nickel-based superalloys

During creep at elevated temperatures, the performance of directionally solidified nickel-based superalloys experiences progressive degradation, accompanied by significant microstructure evolution. In this study, creep tests of varying durations were conducted on smooth specimens, revealing typical microstructure evolution, including dissolution, coarsening, and rafting of the γ′ phase. The process of microstructure evolution during creep was precisely quantified utilizing an advanced image processing technique. Subsequently, a phenomenological model was formulated to predict the evolution of the γ/γ′ microstructure. Furthermore, with the introduction of the microstructure evolution model, a multiscale creep constitutive model was established within the framework of crystal plasticity. This model encompasses various dislocation strengthening mechanisms, including dislocation bypassing, dislocation pairs shearing, and dislocation hardening. The constitutive model can accurately describe both the microstructure evolution and creep deformation of the DZ406 superalloy at various temperatures, with maximum errors of 18.13% and 24.31%, respectively. Finally, the model under multiaxial stress conditions was validated through creep tests on specimens with a film-cooling hole. The maximum prediction errors for microstructure evolution and creep life were 30.46% and 28.00%, respectively.

A Simulation Study on the Effect of Supersonic Ultrasonic Acoustic Streaming on Solidification Dendrite Growth Behavior During Laser Cladding Based on Boundary Coupling

Laser cladding has unique technical advantages, such as precise heat input control, excellent coating properties, and local selective cladding for complex shape parts, which is a vital branch of surface engineering. During the laser cladding process, the parts are subjected to extreme thermal gradients, leading to the formation of micro-defects such as cracks, pores, and segregation. These defects compromise the serviceability of the components. Ultrasonic vibration can produce thermal, mechanical, cavitation, and acoustic flow effects in the melt pool, which can comprehensively affect the formation and evolution for the microstructure of the melt pool and reduce the microscopic defects of the cladding layer. In this paper, the coupling model of temperature and flow field for the laser cladding of 45 steel 316L was established. The transient evolution laws of temperature and flow field under ultrasonic vibration were revealed from a macroscopic point of view. Based on the phase field method, a numerical model of dendrite growth during laser cladding solidification under ultrasonic vibration was established. The mechanism of the effect of ultrasonic vibration on the solidification dendrite growth during laser cladding was revealed on a mesoscopic scale. Based on the microstructure evolution model of the paste region in the scanning direction of the cladding pool, the effects of a static flow field and acoustic flow on dendrite growth were investigated. The results show that the melt flow changes the heat and mass transfer behaviors at the solidification interface, concurrently changing the dendrites’ growth morphology. The acoustic streaming effect increases the flow velocity of the melt pool, which increases the tilt angle of the dendrites to the flow-on side and promotes the growth of secondary dendrite arms on the flow-on side. It improves the solute distribution in the melt pool and reduces elemental segregation.

Modified crystal plasticity constitutive model considering tensorial properties of microstructural evolution and creep life prediction model for Ni-based single crystal superalloy with film cooling hole

Accurate assessment of the creep life of film cooling hole structures is critical for long-life design and safe operation of aero engines and gas turbines. Firstly, through the high temperature creep experiment of nickel-based single crystal superalloy with film cooling hole, the microstructure evolution process under multiaxial stress state around film hole is characterized. Then, considering the directional effect of rafting structure and the influence of multiaxial stress, a fourth-order tensor is used to describe the evolution of γ phase width, and the microstructure evolution model accounting for multi-axial stress states is established. The microstructure evolution is coupled into the crystal plasticity constitutive model by Orowan stress. Meanwhile, based on continuous damage mechanics, a new multiaxial damage evolution law is established by introducing a multiaxial ductility factor into the constitutive model. The improved crystal plasticity constitutive model can effectively predict the microstructural evolution under multiaxial stress conditions. Furthermore, the combination of the modified crystal plasticity constitutive model and the critical distance method considering stress gradients is used for life prediction of film cooling hole structures. The prediction results show the effectiveness and necessity of considering the microstructure evolution in the life prediction.

Deep operator network surrogate for phase-field modeling of metal grain growth during solidification

A deep operator network (DeepONet) has been constructed that generates accurate representations of phase-field model simulations for evolving two dimensional metal grain morphology growing from melt. These representations serve as lower resolution, computationally efficient stand-ins for quick parameter space exploration of solutions to the Allen–Cahn equations that dictate the phase-field model simulations. The experimental target for the phase-field model is a uranium casting system cooling a 434 g uranium charge from a maximum temperature of 1400 °C at an average rate of 30 °Cmin, traversing the crystallographic phases of the pure metal. Experimental parameters inform the phase-field model, whose higher resolution computational model solutions are used to train the DeepONet in a given parameter space with the aim of developing a faster, more efficient method for predicting the solidifying metal’s microstructure at different potential experimental values. The final DeepONet generates high accuracy, lower resolution predictions with cumulative relative approximation error over all timesteps of less than 0.5%, while ensuring solutions remain within physically feasible ranges. These relative error values are comparable with other state-of-the-art DeepONet models for microstructure evolution, while significantly reducing the amount of training data required. Training a convolutional neural network simultaneously with the DeepONet, enforcing realistic values at the complex metal grain boundaries, and mathematically encoding boundary conditions into the structure of the DeepONet improved prediction accuracy and computational efficiency over a standard DeepONet model.

Flat silk cocoons: A candidate material for fabricating lightweight and impact-resistant composites

The utilization of silk cocoons in the production of lightweight and tough composites has been gaining increasing attention. However, the limited applications of normal silk cocoons (NSC) are attributed to their small size and irregular shape. To overcome this deficiency, flat silk cocoons (FSC) with a similar structure and controllable size were prepared. Next, we systematically characterized and compared the microstructures, morphologies, compositions, thermal properties, and mechanical properties of FSC with NSC. Subsequently, FSC was successfully utilized to fabricate a novel silk fibroin fiber reinforced sericin matrix composite (HPFSC) using a hot pressing method, followed by the analysis of its microstructure evolution, mechanical properties, failure modes, and theoretical modeling. This composite has outstanding mechanical properties including hardness, modulus, and strength. HPFSC has a relatively low density of ~1.3 g/cm3, whose absorbed impact energy can reach a maximum value of 11.1 J/mm, exceeding that of most engineering materials, such as aluminum alloy, ceramics, glass, and carbon fiber composites. The exceptional performance of HPFSC can be attributed to the reduced porosity, enhanced bonding between silk fibroin fibers facilitated by sericin, and their structural transformation. This study offers valuable guidance for the fabrication of lightweight and impact-resistant composites using flat silk cocoons.

A general model of microstructure evolution including phase transformation in elasto‐plastic materials

A general model of microstructure evolution including phase transformation in elasto‐plastic materials

Evaluation Methods and Coupled Optimization at Macro- and Micro-Scales for Profiled Ring Rolling of Inconel718 Alloy.

The forming quality of profiled ring rolling not only encompasses macroscopic accuracy but also emphasizes the microstructure. Due to the multiple process parameters and complex metal flow during profiled ring rolling, the various forming defects are difficult to control and difficult to study theoretically. The objective of this study is to establish a comprehensive method for evaluating the forming quality of profiled rings, which considers both the macroscopic forming accuracy and the microstructure. Firstly, the synthetic size factor was defined, and the evolutionary relation between the section forming rate and the diameter growth rate of E-section ring rolling was analyzed in detail. The synthetic size factor can be used to describe the dimensional evolution and evaluate the forming accuracy of the profiled ring rolling process. Taking into full consideration the features of intermittent deformation in local areas, a microstructure evolution model of the Inconel718 alloy during E-section ring rolling, which can accurately predict the recrystallization volume fraction and average grain size of the final ring, was established. Then, combined with finite element simulation, the influence of the rotation speed of the driving roll on the macro-size evolution and microstructure was systematically analyzed. The results indicate that there is often a discrepancy between dimensional accuracy and microstructure uniformity in the optimization trend. For instance, the higher the rotation speed of the driving roll is, the more uniform the microstructure is, but the more difficult it is for the section profile to form. Finally, combined with response surface methodology (RSM), multi-parameter optimization was carried out with section forming accuracy and grain uniformity as the optimization objectives. By using the optimal parameters, an E-section ring with a complete profile and a uniform microstructure was obtained, with a maximum prediction error of the recrystallization volume fraction lower than 5%. The results show that the macroscopic and microscopic quality evaluation methods proposed in this study, as well as the optimization method combining RSM, can be effectively applied to the process optimization of profiled ring rolling.

Microstructure evolution and constitutive modeling of Cu-bearing high-strength low-alloy steel during hot deformation

The microstructural evolution of austenite during hot deformation determines the mechanical properties of steel products. Consequently, industrial applications necessitate a thorough comprehension and modeling of this process. Under varied hot deformation conditions, the flow stress, microstructure evolution, and constitutive modeling of a Cu-bearing steel were examined. At various temperatures and strain rates, compression experiments are conducted, and the resulting microstructures were studied by electron backscatter diffraction (EBSD). Our results indicate that fine prior austenite grains with an average diameter of 22.1 m and a high-angle grain boundary density of 0.25 m1 were produced at a deformation temperature of 950 °C and a strain rate of 1 s−1. The dominating rotating cube components ({001}<110>) in the sample deformed at 1150 °C were gradually replaced by the γ-fiber texture component as the deformation temperature decreased. To accurately predict the flow behavior of this steel, we proposed an improved Arrhenius constitutive model that accounts for strain rate and adiabatic temperature rise. With a correlation coefficient (Rc) of 0.9936, a root mean square error (RMSE) of 4.92%, and a relative error (δ) of 6.05 MPa, our results demonstrate that this model predicts the flow stress of the experimental steel with good precision. This research contributes to the development of high-performance steel products by shedding light on the microstructural evolution and flow behavior of Cu-containing steels under hot deformation conditions.

Precipitate Structure, Microstructure Evolution Modeling and Characterization in an Aluminum Alloy 7050 Friction Stir Weld

Precipitate Structure, Microstructure Evolution Modeling and Characterization in an Aluminum Alloy 7050 Friction Stir Weld

A crystal plasticity-based micromechanical model for precipitate shearing: Application to cyclic softening of polycrystalline Ni-based superalloys

Cyclic deformation of polycrystalline Ni-based superalloys leads to cyclic hardening followed by softening, in terms of the mechanical response. A micromechanical constitutive model is proposed and implemented in a dislocation density-based, crystal plasticity framework to simulate the shearing of γ′ precipitates, which leads to the observed cyclic softening. The framework accounts for physically based deformation mechanisms. A slip-system level backstress model has been implemented to account for the kinematic hardening. Further, a micromechanical model for microstructure evolution due to precipitate shearing is developed that accounts for the dislocation-precipitate interactions and the resultant change in precipitate strengthening. The model is used to simulate cyclic deformation in two polycrystalline Ni-based superalloys, with different microstructures (in terms of the shape, size and volume fraction of precipitates), referred as Alloy 1 and Alloy 2. Room temperature cyclic deformation tests, followed by microstructure characterization were performed at different strain amplitudes for Alloy 1 to validate our predictions. For Alloy 2, the experimental stress–strain response was used from the literature to fit and validate our predictions. It is shown that the model can predict cyclic softening due to precipitate shearing for different initial microstructures and a range of loading conditions in polycrystalline Ni-based superalloys.

A Visualized Microstructure Evolution Model Integrating an Analytical Cutting Model with a Cellular Automaton Method during NiTi Smart Alloy Machining

In this study, a visualized microstructure evolution model for the primary shear zone during NiTi smart alloy machining was established by integrating an analytical cutting model with a cellular automaton method. Experimental verification was conducted using an invented electromagnet rotation-type quick-stop device. The flow stress curve during the dynamic recrystallization of the NiTi smart alloy, the influence of relevant parameters on the dynamic recrystallization process, and the distribution of dynamic recrystallization in the primary shear zone were studied via the model. The simulation results showed that strain rate and deformation temperature significantly affect the relevant parameters during the dynamic recrystallization process. Three typical shear planes were selected for a comparison between simulation results and experimental results, with a minimum error of 3.76% and a maximum error of 11.26%, demonstrating that the model accurately simulates the microstructure evolution of the NiTi smart alloy during the cutting process. These results contribute theoretical and experimental insights into understanding the cutting mechanism of the NiTi smart alloy.

Integrated Framework to Model Microstructure Evolution and Decipher the Microstructure-Property Relationship in Polymeric Porous Materials.

Unraveling the microstructure-property relationship is crucial for improving material performance and advancing the design of next-generation structural and functional materials. However, this is inherently challenging because it requires both the comprehensive quantification of microstructural features and the accurate assessment of corresponding properties. To meet these requirements, we developed an efficient and comprehensive integrated modeling framework, using polymeric porous materials as a representative model system. Our framework generates microstructures using a physics-based phase-field model, characterizes them using various average and localized microstructural features, and evaluates microstructure-aware properties, such as effective diffusivity, using an efficient Fourier-based perturbation numerical scheme. Additionally, the framework incorporates machine learning methods to decipher the intricate microstructure-property relationships. Our findings indicate that the connectivity of phase channels is the most critical microstructural descriptor for determining effective diffusivity, followed by the domain shape represented by curvature distribution, while the domain size has a minor impact. This comprehensive approach offers a novel framework for assessing microstructure-property relationships in polymer-based porous materials, paving the way for the development of advanced materials for diverse applications.

Multiscale modelling of microstructure evolution, and local solidification behaviours of the AlSi10Mg build component in laser powder bed fusion process

Laser powder bed fusion (L-PBF) process is an additive manufacturing process, in which rapid heating and cooling takes place. The microstructure and the solidification behaviour of L-PBF components have significant impacts on their mechanical properties. The solidification takes place in a very short duration which is difficult to capture experimentally, therefore the finite-element (FE) simulation is the best feasible solution. In this paper, to study the evolution of the AlSi10Mg alloy’s microstructure during the L-PBF process, a model composed of macroscopic finite element (FE) model and microscopic phase field (PF) model was built. This model is suitable to predict a more realistic thermal behaviour involving the possible physical phenomena and the thermal behaviour for various heat inputs was calculated. The PF model was then updated with these results in order to simulate the chemical compositions’ concentration field and solidified microstructure. According to the simulation’s results, the primary dendrite arm spacing (PDAS) is significantly influenced by the laser line energy. To validate the FE model along with the Phase field (PF) model, the results were compared with the analytical and experimental findings; and the FE model and PF results exhibited good agreement with the experimental results. Additionally, the solute distribution analysis demonstrated that during the solidification process, micro-segregation developed and the process parameters affected the micro-segregation. Finally, the specimens were subjected to metallographic and element distribution analyses using an energy-dispersive spectrometer (EDS) to compare the results with those from the PF simulation and establish the relationship between the process parameters.

Exploring large language models for microstructure evolution in materials

There is a significant potential for coding skills to transition fully to natural language in the future. In this context, large language models (LLMs) have shown impressive natural language processing abilities to generate sophisticated computer code for research tasks in various domains. We report the first study on the applicability of LLMs to perform computer experiments on microstructure pattern formation in model materials. In particular, we exploit LLM’s ability to generate code for solving various types of phase-field-based partial differential equations (PDEs) that integrate additional physics to model material microstructures. The results indicate that LLMs have a remarkable capacity to generate multi-physics code and can effectively deal with materials microstructure problems up to a certain complexity. However, for complex multi-physics coupled PDEs for which a detailed understanding of the problem is required, LLMs fail to perform the task efficiently, since much more detailed instructions with many iterations of the same query are required to generate the desired output. Nonetheless, at their current stage of development and potential future advancements, LLMs offer a promising outlook for accelerating materials education and research by supporting beginners and experts in their physics-based methodology. We hope this paper will spur further interest to leverage LLMs as a supporting tool in the integrated computational materials engineering (ICME) approach to materials modeling and design.

Numerical simulation and experimental validation of microstructure evolution during the upsetting process of a large size martensitic stainless steel forging

The microstructure evolution, plastic deformation, and damage severity during the open die hot forging of a martensitic stainless steel were investigated using finite element (FE) simulation. A microstructure evolution model was developed and combined with a visco-elastoplastic model to predict the strain, the strain rate, and the temperature distribution, as well as the volume fraction and the size of dynamically recrystallized grains over the entire volume of an industrial size forging. The propensity to damage during hot forging was also evaluated using the Cockcroft & Latham model. The three models were implemented in the FE code and the results analyzed in terms of microstructure inhomogeneity and stress levels in different regions of the forging. A good agreement was obtained between the predicted and the experimental results, demonstrating that the simulation provided a realistic representation of the forging process at the industrial scale.

Microstructure Prediction of 80MnSi8-6 Steel After Hot Deformation Based on Dynamic Recrystallization Kinetics and FEM Simulation

The microstructure evolution during hot deformation of 80MnSi8-6 nanobainitic steel was investigated through hot compression tests at deformation temperatures of 900–1250°C and strain rates of 0.1–20 s−1. The flow curves revealed strain-hardening behavior at the beginning of deformation followed by softening effects caused by microstructure evolution. A Johnson–Mehl–Avrami–Kolmogorov (JMAK) model for grain growth and dynamic recrystallization was developed, and the kinetics were determined. Critical and peak strains were identified, and coefficients for the microstructure evolution models were determined using linear regression. The analysis of S-curves revealed that decreasing the temperature delays the onset of recrystallization and that the strain rate significantly effects the recrystallization rate at lower temperatures. Constitutive modeling and determination of the Zener–Hollomon parameter allowed the determination of the influence of hot processing conditions on material behavior during deformation. Microstructure analysis showed that, at higher deformation temperatures, grain growth occurs simultaneously with grain refinement. Coefficients for the JMAK model were implemented in QForm software. Simulation results were compared with experimental measurements exhibited good arrangement, which confirms the accuracy of the JMAK model in predicting the microstructure evolution. This study demonstrated how microstructure evolution modeling and FEM simulations combined can be used to predict the grain size of 80MnSi8-6 steel after hot deformation.

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.

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.

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